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00-XX - General and overarching topics; collections 00-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general 00-02 - Research exposition (monographs, survey articles) pertaining to mathematics in general 00Axx - General and miscellaneous specific topics 00A05 - Mathematics in general 00A06 - Mathematics for nonmathematicians (engineering, social sciences, etc.) 00A07 - Problem books 00A08 - Recreational mathematics 00A09 - Popularization of mathematics 00A15 - Bibliographies for mathematics in general 00A17 - External book reviews 00A20 - Dictionaries and other general reference works 00A22 - Formularies 00A27 - Lists of open problems 00A30 - Philosophy of mathematics 00A35 - Methodology of mathematics 00A64 - Mathematics and literature 00A65 - Mathematics and music 00A66 - Mathematics and visual arts 00A67 - Mathematics and architecture 00A69 - General applied mathematics 00A71 - General theory of mathematical modeling 00A72 - General theory of simulation 00A79 - Physics 00A99 - General and miscellaneous specific topics 00Bxx - Conference proceedings and collections of articles 00B05 - Collections of abstracts of lectures 00B10 - Collections of articles of general interest 00B15 - Collections of articles of miscellaneous specific interest 00B20 - Proceedings of conferences of general interest 00B25 - Proceedings of conferences of miscellaneous specific interest 00B30 - Festschriften 00B50 - Collections of translated articles of general interest 00B55 - Collections of translated articles of miscellaneous specific interest 00B60 - Collections of reprinted articles 00B99 - Conference proceedings and collections of articles 01-XX - History and biography 01-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography 01-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography 01-02 - Research exposition (monographs, survey articles) pertaining to history and biography 01-06 - Proceedings, conferences, collections, etc. pertaining to history and biography 01-11 - Research data for problems pertaining to history and biography 01Axx - History of mathematics and mathematicians 01A05 - General histories, source books 01A07 - Ethnomathematics (general) 01A10 - History of mathematics in Paleolithic and Neolithic times 01A11 - History of mathematics of the indigenous cultures of Africa, Asia, and Oceania 01A12 - History of mathematics of the indigenous cultures of the Americas 01A15 - History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.) 01A16 - History of Egyptian mathematics 01A17 - History of Babylonian mathematics 01A20 - History of Greek and Roman mathematics 01A25 - History of Chinese mathematics 01A27 - History of Japanese mathematics 01A29 - History of East and Southeast Asian mathematics (non-Chinese, non-Japanese) 01A30 - History of mathematics in the Golden Age of Islam 01A32 - History of Indian mathematics 01A35 - History of mathematics in Late Antiquity and medieval Europe 01A40 - History of mathematics in the 15th and 16th centuries, Renaissance 01A45 - History of mathematics in the 17th century 01A50 - History of mathematics in the 18th century 01A55 - History of mathematics in the 19th century 01A60 - History of mathematics in the 20th century 01A61 - History of mathematics in the 21st century 01A65 - Development of contemporary mathematics 01A67 - Future perspectives in mathematics 01A70 - Biographies, obituaries, personalia, bibliographies 01A72 - Schools of mathematics 01A73 - History of mathematics at specific universities 01A74 - History of mathematics at institutions and academies (non-university) 01A75 - Collected or selected works; reprintings or translations of classics 01A80 - Sociology (and profession) of mathematics 01A85 - Historiography 01A90 - Bibliographic studies 01A99 - History of mathematics and mathematicians 03-XX - Mathematical logic and foundations 03-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations 03-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations 03-02 - Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations 03-03 - History of mathematical logic and foundations 03-04 - Software, source code, etc. for problems pertaining to mathematical logic and foundations 03-06 - Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations 03-08 - Computational methods for problems pertaining to mathematical logic and foundations 03-11 - Research data for problems pertaining to mathematical logic and foundations 03Axx - Philosophical aspects of logic and foundations 03A05 - Philosophical and critical aspects of logic and foundations 03A10 - Logic in the philosophy of science 03A99 - Philosophical aspects of logic and foundations 03Bxx - General logic 03B05 - Classical propositional logic 03B10 - Classical first-order logic 03B16 - Higher-order logic 03B20 - Subsystems of classical logic (including intuitionistic logic) 03B22 - Abstract deductive systems 03B25 - Decidability of theories and sets of sentences 03B30 - Foundations of classical theories (including reverse mathematics) 03B35 - Mechanization of proofs and logical operations 03B38 - Type theory 03B40 - Combinatory logic and lambda calculus 03B42 - Logics of knowledge and belief (including belief change) 03B44 - Temporal logic 03B45 - Modal logic (including the logic of norms) 03B47 - Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) 03B48 - Probability and inductive logic 03B50 - Many-valued logic 03B52 - Fuzzy logic; logic of vagueness 03B53 - Paraconsistent logics 03B55 - Intermediate logics 03B60 - Other nonclassical logic 03B62 - Combined logics 03B65 - Logic of natural languages 03B70 - Logic in computer science 03B80 - Other applications of logic 03B99 - General logic 03Cxx - Model theory 03C05 - Equational classes, universal algebra in model theory 03C07 - Basic properties of first-order languages and structures 03C10 - Quantifier elimination, model completeness, and related topics 03C13 - Model theory of finite structures 03C15 - Model theory of denumerable and separable structures 03C20 - Ultraproducts and related constructions 03C25 - Model-theoretic forcing 03C30 - Other model constructions 03C35 - Categoricity and completeness of theories 03C40 - Interpolation, preservation, definability 03C45 - Classification theory, stability, and related concepts in model theory 03C48 - Abstract elementary classes and related topics 03C50 - Models with special properties (saturated, rigid, etc.) 03C52 - Properties of classes of models 03C55 - Set-theoretic model theory 03C57 - Computable structure theory, computable model theory 03C60 - Model-theoretic algebra 03C62 - Models of arithmetic and set theory 03C64 - Model theory of ordered structures; o-minimality 03C65 - Models of other mathematical theories 03C66 - Continuous model theory, model theory of metric structures 03C68 - Other classical first-order model theory 03C70 - Logic on admissible sets 03C75 - Other infinitary logic 03C80 - Logic with extra quantifiers and operators 03C85 - Second- and higher-order model theory 03C90 - Nonclassical models (Boolean-valued, sheaf, etc.) 03C95 - Abstract model theory 03C98 - Applications of model theory 03C99 - Model theory 03Dxx - Computability and recursion theory 03D03 - Thue and Post systems, etc. 03D05 - Automata and formal grammars in connection with logical questions 03D10 - Turing machines and related notions 03D15 - Complexity of computation (including implicit computational complexity) 03D20 - Recursive functions and relations, subrecursive hierarchies 03D25 - Recursively (computably) enumerable sets and degrees 03D28 - Other Turing degree structures 03D30 - Other degrees and reducibilities in computability and recursion theory 03D32 - Algorithmic randomness and dimension 03D35 - Undecidability and degrees of sets of sentences 03D40 - Word problems, etc. in computability and recursion theory 03D45 - Theory of numerations, effectively presented structures 03D50 - Recursive equivalence types of sets and structures, isols 03D55 - Hierarchies of computability and definability 03D60 - Computability and recursion theory on ordinals, admissible sets, etc. 03D65 - Higher-type and set recursion theory 03D70 - Inductive definability 03D75 - Abstract and axiomatic computability and recursion theory 03D78 - Computation over the reals, computable analysis 03D80 - Applications of computability and recursion theory 03D99 - Computability and recursion theory 03Exx - Set theory 03E02 - Partition relations 03E04 - Ordered sets and their cofinalities; pcf theory 03E05 - Other combinatorial set theory 03E10 - Ordinal and cardinal numbers 03E15 - Descriptive set theory 03E17 - Cardinal characteristics of the continuum 03E20 - Other classical set theory (including functions, relations, and set algebra) 03E25 - Axiom of choice and related propositions 03E30 - Axiomatics of classical set theory and its fragments 03E35 - Consistency and independence results 03E40 - Other aspects of forcing and Boolean-valued models 03E45 - Inner models, including constructibility, ordinal definability, and core models 03E47 - Other notions of set-theoretic definability 03E50 - Continuum hypothesis and Martin's axiom 03E55 - Large cardinals 03E57 - Generic absoluteness and forcing axioms 03E60 - Determinacy principles 03E65 - Other set-theoretic hypotheses and axioms 03E70 - Nonclassical and second-order set theories 03E72 - Theory of fuzzy sets, etc. 03E75 - Applications of set theory 03E99 - Set theory 03Fxx - Proof theory and constructive mathematics 03F03 - Proof theory in general (including proof-theoretic semantics) 03F05 - Cut-elimination and normal-form theorems 03F07 - Structure of proofs 03F10 - Functionals in proof theory 03F15 - Recursive ordinals and ordinal notations 03F20 - Complexity of proofs 03F25 - Relative consistency and interpretations 03F30 - First-order arithmetic and fragments 03F35 - Second- and higher-order arithmetic and fragments 03F40 - G�del numberings and issues of incompleteness 03F45 - Provability logics and related algebras (e.g., diagonalizable algebras) 03F50 - Metamathematics of constructive systems 03F52 - Proof-theoretic aspects of linear logic and other substructural logics 03F55 - Intuitionistic mathematics 03F60 - Constructive and recursive analysis 03F65 - Other constructive mathematics 03F99 - Proof theory and constructive mathematics 03Gxx - Algebraic logic 03G05 - Logical aspects of Boolean algebras 03G10 - Logical aspects of lattices and related structures 03G12 - Quantum logic 03G15 - Cylindric and polyadic algebras; relation algebras 03G20 - Logical aspects of ?ukasiewicz and Post algebras 03G25 - Other algebras related to logic 03G27 - Abstract algebraic logic 03G30 - Categorical logic, topoi 03G99 - Algebraic logic 03Hxx - Nonstandard models 03H05 - Nonstandard models in mathematics 03H10 - Other applications of nonstandard models (economics, physics, etc.) 03H15 - Nonstandard models of arithmetic 03H99 - Nonstandard models 05-XX - Combinatorics 05-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics 05-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics 05-02 - Research exposition (monographs, survey articles) pertaining to combinatorics 05-03 - History of combinatorics 05-04 - Software, source code, etc. for problems pertaining to combinatorics 05-06 - Proceedings, conferences, collections, etc. pertaining to combinatorics 05-08 - Computational methods for problems pertaining to combinatorics 05-11 - Research data for problems pertaining to combinatorics 05Axx - Enumerative combinatorics 05A05 - Permutations, words, matrices 05A10 - Factorials, binomial coefficients, combinatorial functions 05A15 - Exact enumeration problems, generating functions 05A16 - Asymptotic enumeration 05A17 - Combinatorial aspects of partitions of integers 05A18 - Partitions of sets 05A19 - Combinatorial identities, bijective combinatorics 05A20 - Combinatorial inequalities 05A30 - (q)-calculus and related topics 05A40 - Umbral calculus 05A99 - Enumerative combinatorics 05Bxx - Designs and configurations 05B05 - Combinatorial aspects of block designs 05B07 - Triple systems 05B10 - Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) 05B15 - Orthogonal arrays, Latin squares, Room squares 05B20 - Combinatorial aspects of matrices (incidence, Hadamard, etc.) 05B25 - Combinatorial aspects of finite geometries 05B30 - Other designs, configurations 05B35 - Combinatorial aspects of matroids and geometric lattices 05B40 - Combinatorial aspects of packing and covering 05B45 - Combinatorial aspects of tessellation and tiling problems 05B50 - Polyominoes 05B99 - Designs and configurations 05Cxx - Graph theory 05C05 - Trees 05C07 - Vertex degrees 05C09 - Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) 05C10 - Planar graphs; geometric and topological aspects of graph theory 05C12 - Distance in graphs 05C15 - Coloring of graphs and hypergraphs 05C17 - Perfect graphs 05C20 - Directed graphs (digraphs), tournaments 05C21 - Flows in graphs 05C22 - Signed and weighted graphs 05C25 - Graphs and abstract algebra (groups, rings, fields, etc.) 05C30 - Enumeration in graph theory 05C31 - Graph polynomials 05C35 - Extremal problems in graph theory 05C38 - Paths and cycles 05C40 - Connectivity 05C42 - Density (toughness, etc.) 05C45 - Eulerian and Hamiltonian graphs 05C48 - Expander graphs 05C50 - Graphs and linear algebra (matrices, eigenvalues, etc.) 05C51 - Graph designs and isomorphic decomposition 05C55 - Generalized Ramsey theory 05C57 - Games on graphs (graph-theoretic aspects) 05C60 - Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C62 - Graph representations (geometric and intersection representations, etc.) 05C63 - Infinite graphs 05C65 - Hypergraphs 05C69 - Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C70 - Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C72 - Fractional graph theory, fuzzy graph theory 05C75 - Structural characterization of families of graphs 05C76 - Graph operations (line graphs, products, etc.) 05C78 - Graph labelling (graceful graphs, bandwidth, etc.) 05C80 - Random graphs (graph-theoretic aspects) 05C81 - Random walks on graphs 05C82 - Small world graphs, complex networks (graph-theoretic aspects) 05C83 - Graph minors 05C85 - Graph algorithms (graph-theoretic aspects) 05C90 - Applications of graph theory 05C92 - Chemical graph theory 05C99 - Graph theory 05Dxx - Extremal combinatorics 05D05 - Extremal set theory 05D10 - Ramsey theory 05D15 - Transversal (matching) theory 05D40 - Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) 05D99 - Extremal combinatorics 05Exx - Algebraic combinatorics 05E05 - Symmetric functions and generalizations 05E10 - Combinatorial aspects of representation theory 05E14 - Combinatorial aspects of algebraic geometry 05E16 - Combinatorial aspects of groups and algebras 05E18 - Group actions on combinatorial structures 05E30 - Association schemes, strongly regular graphs 05E40 - Combinatorial aspects of commutative algebra 05E45 - Combinatorial aspects of simplicial complexes 05E99 - Algebraic combinatorics 06-XX - Order, lattices, ordered algebraic structures 06-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered structures 06-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures 06-02 - Research exposition (monographs, survey articles) pertaining to ordered structures 06-03 - History of ordered structures 06-04 - Software, source code, etc. for problems pertaining to ordered structures 06-06 - Proceedings, conferences, collections, etc. pertaining to ordered structures 06-08 - Computational methods for problems pertaining to ordered structures 06-11 - Research data for problems pertaining to ordered structures 06Axx - Ordered sets 06A05 - Total orders 06A06 - Partial orders, general 06A07 - Combinatorics of partially ordered sets 06A11 - Algebraic aspects of posets 06A12 - Semilattices 06A15 - Galois correspondences, closure operators (in relation to ordered sets) 06A75 - Generalizations of ordered sets 06A99 - Ordered sets 06Bxx - Lattices 06B05 - Structure theory of lattices 06B10 - Lattice ideals, congruence relations 06B15 - Representation theory of lattices 06B20 - Varieties of lattices 06B23 - Complete lattices, completions 06B25 - Free lattices, projective lattices, word problems 06B30 - Topological lattices 06B35 - Continuous lattices and posets, applications 06B75 - Generalizations of lattices 06B99 - Lattices 06Cxx - Modular lattices, complemented lattices 06C05 - Modular lattices, Desarguesian lattices 06C10 - Semimodular lattices, geometric lattices 06C15 - Complemented lattices, orthocomplemented lattices and posets 06C20 - Complemented modular lattices, continuous geometries 06C99 - Modular lattices, complemented lattices 06Dxx - Distributive lattices 06D05 - Structure and representation theory of distributive lattices 06D10 - Complete distributivity 06D15 - Pseudocomplemented lattices 06D20 - Heyting algebras (lattice-theoretic aspects) 06D22 - Frames, locales 06D25 - Post algebras (lattice-theoretic aspects) 06D30 - De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) 06D35 - MV-algebras 06D50 - Lattices and duality 06D72 - Fuzzy lattices (soft algebras) and related topics 06D75 - Other generalizations of distributive lattices 06D99 - Distributive lattices 06Exx - Boolean algebras (Boolean rings) 06E05 - Structure theory of Boolean algebras 06E10 - Chain conditions, complete algebras 06E15 - Stone spaces (Boolean spaces) and related structures 06E20 - Ring-theoretic properties of Boolean algebras 06E25 - Boolean algebras with additional operations (diagonalizable algebras, etc.) 06E30 - Boolean functions 06E75 - Generalizations of Boolean algebras 06E99 - Boolean algebras (Boolean rings) 06Fxx - Ordered structures 06F05 - Ordered semigroups and monoids 06F07 - Quantales 06F10 - Noether lattices 06F15 - Ordered groups 06F20 - Ordered abelian groups, Riesz groups, ordered linear spaces 06F25 - Ordered rings, algebras, modules 06F30 - Ordered topological structures 06F35 - BCK-algebras, BCI-algebras 06F99 - Ordered structures 08-XX - General algebraic systems 08-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general algebraic systems 08-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems 08-02 - Research exposition (monographs, survey articles) pertaining to general algebraic systems 08-03 - History of general algebraic systems 08-04 - Software, source code, etc. for problems pertaining to general algebraic systems 08-06 - Proceedings, conferences, collections, etc. pertaining to general algebraic systems 08-08 - Computational methods for problems pertaining to general algebraic systems 08-11 - Research data for problems pertaining to general algebraic systems 08Axx - Algebraic structures 08A02 - Relational systems, laws of composition 08A05 - Structure theory of algebraic structures 08A30 - Subalgebras, congruence relations 08A35 - Automorphisms and endomorphisms of algebraic structures 08A40 - Operations and polynomials in algebraic structures, primal algebras 08A45 - Equational compactness 08A50 - Word problems (aspects of algebraic structures) 08A55 - Partial algebras 08A60 - Unary algebras 08A62 - Finitary algebras 08A65 - Infinitary algebras 08A68 - Heterogeneous algebras 08A70 - Applications of universal algebra in computer science 08A72 - Fuzzy algebraic structures 08A99 - Algebraic structures 08Bxx - Varieties 08B05 - Equational logic, Mal'tsev conditions 08B10 - Congruence modularity, congruence distributivity 08B15 - Lattices of varieties 08B20 - Free algebras 08B25 - Products, amalgamated products, and other kinds of limits and colimits 08B26 - Subdirect products and subdirect irreducibility 08B30 - Injectives, projectives 08B99 - Varieties 08Cxx - Other classes of algebras 08C05 - Categories of algebras 08C10 - Axiomatic model classes 08C15 - Quasivarieties 08C20 - Natural dualities for classes of algebras 08C99 - Other classes of algebras 11-XX - Number theory 11-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory 11-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 11-02 - Research exposition (monographs, survey articles) pertaining to number theory 11-03 - History of number theory 11-04 - Software, source code, etc. for problems pertaining to number theory 11-06 - Proceedings, conferences, collections, etc. pertaining to number theory 11-11 - Research data for problems pertaining to number theory 11Axx - Elementary number theory 11A05 - Multiplicative structure; Euclidean algorithm; greatest common divisors 11A07 - Congruences; primitive roots; residue systems 11A15 - Power residues, reciprocity 11A25 - Arithmetic functions; related numbers; inversion formulas 11A41 - Primes 11A51 - Factorization; primality 11A55 - Continued fractions 11A63 - Radix representation; digital problems 11A67 - Other number representations 11A99 - Elementary number theory 11Bxx - Sequences and sets 11B05 - Density, gaps, topology 11B13 - Additive bases, including sumsets 11B25 - Arithmetic progressions 11B30 - Arithmetic combinatorics; higher degree uniformity 11B34 - Representation functions 11B37 - Recurrences 11B39 - Fibonacci and Lucas numbers and polynomials and generalizations 11B50 - Sequences (mod (m)) 11B57 - Farey sequences; the sequences (1^k, 2^k, dots) 11B65 - Binomial coefficients; factorials; (q)-identities 11B68 - Bernoulli and Euler numbers and polynomials 11B73 - Bell and Stirling numbers 11B75 - Other combinatorial number theory 11B83 - Special sequences and polynomials 11B85 - Automata sequences 11B99 - Sequences and sets 11Cxx - Polynomials and matrices 11C08 - Polynomials in number theory 11C20 - Matrices, determinants in number theory 11C99 - Polynomials and matrices 11Dxx - Diophantine equations 11D04 - Linear Diophantine equations 11D07 - The Frobenius problem 11D09 - Quadratic and bilinear Diophantine equations 11D25 - Cubic and quartic Diophantine equations 11D41 - Higher degree equations; Fermat's equation 11D45 - Counting solutions of Diophantine equations 11D57 - Multiplicative and norm form equations 11D59 - Thue-Mahler equations 11D61 - Exponential Diophantine equations 11D68 - Rational numbers as sums of fractions 11D72 - Diophantine equations in many variables 11D75 - Diophantine inequalities 11D79 - Congruences in many variables 11D85 - Representation problems 11D88 - (p)-adic and power series fields 11D99 - Diophantine equations 11Exx - Forms and linear algebraic groups 11E04 - Quadratic forms over general fields 11E08 - Quadratic forms over local rings and fields 11E10 - Forms over real fields 11E12 - Quadratic forms over global rings and fields 11E16 - General binary quadratic forms 11E20 - General ternary and quaternary quadratic forms; forms of more than two variables 11E25 - Sums of squares and representations by other particular quadratic forms 11E39 - Bilinear and Hermitian forms 11E41 - Class numbers of quadratic and Hermitian forms 11E45 - Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) 11E57 - Classical groups 11E70 - (K)-theory of quadratic and Hermitian forms 11E72 - Galois cohomology of linear algebraic groups 11E76 - Forms of degree higher than two 11E81 - Algebraic theory of quadratic forms; Witt groups and rings 11E88 - Quadratic spaces; Clifford algebras 11E95 - (p)-adic theory 11E99 - Forms and linear algebraic groups 11Fxx - Discontinuous groups and automorphic forms 11F03 - Modular and automorphic functions 11F06 - Structure of modular groups and generalizations; arithmetic groups 11F11 - Holomorphic modular forms of integral weight 11F12 - Automorphic forms, one variable 11F20 - Dedekind eta function, Dedekind sums 11F22 - Relationship to Lie algebras and finite simple groups 11F23 - Relations with algebraic geometry and topology 11F25 - Hecke-Petersson operators, differential operators (one variable) 11F27 - Theta series; Weil representation; theta correspondences 11F30 - Fourier coefficients of automorphic forms 11F32 - Modular correspondences, etc. 11F33 - Congruences for modular and (p)-adic modular forms 11F37 - Forms of half-integer weight; nonholomorphic modular forms 11F41 - Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F46 - Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11F50 - Jacobi forms 11F52 - Modular forms associated to Drinfel'd modules 11F55 - Other groups and their modular and automorphic forms (several variables) 11F60 - Hecke-Petersson operators, differential operators (several variables) 11F66 - Langlands (L)-functions; one variable Dirichlet series and functional equations 11F67 - Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols 11F68 - Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 11F70 - Representation-theoretic methods; automorphic representations over local and global fields 11F72 - Spectral theory; trace formulas (e.g., that of Selberg) 11F75 - Cohomology of arithmetic groups 11F77 - Automorphic forms and their relations with perfectoid spaces 11F80 - Galois representations 11F85 - (p)-adic theory, local fields 11F99 - Discontinuous groups and automorphic forms 11Gxx - Arithmetic algebraic geometry (Diophantine geometry) 11G05 - Elliptic curves over global fields 11G07 - Elliptic curves over local fields 11G09 - Drinfel'd modules; higher-dimensional motives, etc. 11G10 - Abelian varieties of dimension (> 1) 11G15 - Complex multiplication and moduli of abelian varieties 11G16 - Elliptic and modular units 11G18 - Arithmetic aspects of modular and Shimura varieties 11G20 - Curves over finite and local fields 11G25 - Varieties over finite and local fields 11G30 - Curves of arbitrary genus or genus (e 1) over global fields 11G32 - Arithmetic aspects of dessins d'enfants, Bely? theory 11G35 - Varieties over global fields 11G40 - (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11G42 - Arithmetic mirror symmetry 11G45 - Geometric class field theory 11G50 - Heights 11G55 - Polylogarithms and relations with (K)-theory 11G99 - Arithmetic algebraic geometry (Diophantine geometry) 11Hxx - Geometry of numbers 11H06 - Lattices and convex bodies (number-theoretic aspects) 11H16 - Nonconvex bodies 11H31 - Lattice packing and covering (number-theoretic aspects) 11H46 - Products of linear forms 11H50 - Minima of forms 11H55 - Quadratic forms (reduction theory, extreme forms, etc.) 11H56 - Automorphism groups of lattices 11H60 - Mean value and transfer theorems 11H71 - Relations with coding theory 11H99 - Geometry of numbers 11Jxx - Diophantine approximation, transcendental number theory 11J04 - Homogeneous approximation to one number 11J06 - Markov and Lagrange spectra and generalizations 11J13 - Simultaneous homogeneous approximation, linear forms 11J17 - Approximation by numbers from a fixed field 11J20 - Inhomogeneous linear forms 11J25 - Diophantine inequalities 11J54 - Small fractional parts of polynomials and generalizations 11J61 - Approximation in non-Archimedean valuations 11J68 - Approximation to algebraic numbers 11J70 - Continued fractions and generalizations 11J71 - Distribution modulo one 11J72 - Irrationality; linear independence over a field 11J81 - Transcendence (general theory) 11J82 - Measures of irrationality and of transcendence 11J83 - Metric theory 11J85 - Algebraic independence; Gel'fond's method 11J86 - Linear forms in logarithms; Baker's method 11J87 - Schmidt Subspace Theorem and applications 11J89 - Transcendence theory of elliptic and abelian functions 11J91 - Transcendence theory of other special functions 11J93 - Transcendence theory of Drinfel'd and (t)-modules 11J95 - Results involving abelian varieties 11J97 - Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) 11J99 - Diophantine approximation, transcendental number theory 11Kxx - Probabilistic theory: distribution modulo (1); metric theory of algorithms 11K06 - General theory of distribution modulo (1) 11K16 - Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 11K31 - Special sequences 11K36 - Well-distributed sequences and other variations 11K38 - Irregularities of distribution, discrepancy 11K41 - Continuous, (p)-adic and abstract analogues 11K45 - Pseudo-random numbers; Monte Carlo methods 11K50 - Metric theory of continued fractions 11K55 - Metric theory of other algorithms and expansions; measure and Hausdorff dimension 11K60 - Diophantine approximation in probabilistic number theory 11K65 - Arithmetic functions in probabilistic number theory 11K70 - Harmonic analysis and almost periodicity in probabilistic number theory 11K99 - Probabilistic theory: distribution modulo (1); metric theory of algorithms 11Lxx - Exponential sums and character sums 11L03 - Trigonometric and exponential sums (general theory) 11L05 - Gauss and Kloosterman sums; generalizations 11L07 - Estimates on exponential sums 11L10 - Jacobsthal and Brewer sums; other complete character sums 11L15 - Weyl sums 11L20 - Sums over primes 11L26 - Sums over arbitrary intervals 11L40 - Estimates on character sums 11L99 - Exponential sums and character sums 11Mxx - Zeta and (L)-functions: analytic theory 11M06 - (zeta (s)) and (L(s, chi)) 11M20 - Real zeros of (L(s, chi)); results on (L(1, chi)) 11M26 - Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses 11M32 - Multiple Dirichlet series and zeta functions and multizeta values 11M35 - Hurwitz and Lerch zeta functions 11M36 - Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) 11M38 - Zeta and (L)-functions in characteristic (p) 11M41 - Other Dirichlet series and zeta functions 11M45 - Tauberian theorems 11M50 - Relations with random matrices 11M55 - Relations with noncommutative geometry 11M99 - Zeta and (L)-functions: analytic theory 11Nxx - Multiplicative number theory 11N05 - Distribution of primes 11N13 - Primes in congruence classes 11N25 - Distribution of integers with specified multiplicative constraints 11N30 - Tur�n theory 11N32 - Primes represented by polynomials; other multiplicative structures of polynomial values 11N35 - Sieves 11N36 - Applications of sieve methods 11N37 - Asymptotic results on arithmetic functions 11N45 - Asymptotic results on counting functions for algebraic and topological structures 11N56 - Rate of growth of arithmetic functions 11N60 - Distribution functions associated with additive and positive multiplicative functions 11N64 - Other results on the distribution of values or the characterization of arithmetic functions 11N69 - Distribution of integers in special residue classes 11N75 - Applications of automorphic functions and forms to multiplicative problems 11N80 - Generalized primes and integers 11N99 - Multiplicative number theory 11Pxx - Additive number theory; partitions 11P05 - Waring's problem and variants 11P21 - Lattice points in specified regions 11P32 - Goldbach-type theorems; other additive questions involving primes 11P55 - Applications of the Hardy-Littlewood method 11P70 - Inverse problems of additive number theory, including sumsets 11P81 - Elementary theory of partitions 11P82 - Analytic theory of partitions 11P83 - Partitions; congruences and congruential restrictions 11P84 - Partition identities; identities of Rogers-Ramanujan type 11P99 - Additive number theory; partitions 11Rxx - Algebraic number theory: global fields 11R04 - Algebraic numbers; rings of algebraic integers 11R06 - PV-numbers and generalizations; other special algebraic numbers; Mahler measure 11R09 - Polynomials (irreducibility, etc.) 11R11 - Quadratic extensions 11R16 - Cubic and quartic extensions 11R18 - Cyclotomic extensions 11R20 - Other abelian and metabelian extensions 11R21 - Other number fields 11R23 - Iwasawa theory 11R27 - Units and factorization 11R29 - Class numbers, class groups, discriminants 11R32 - Galois theory 11R33 - Integral representations related to algebraic numbers; Galois module structure of rings of integers 11R34 - Galois cohomology 11R37 - Class field theory 11R39 - Langlands-Weil conjectures, nonabelian class field theory 11R42 - Zeta functions and (L)-functions of number fields 11R44 - Distribution of prime ideals 11R45 - Density theorems 11R47 - Other analytic theory 11R52 - Quaternion and other division algebras: arithmetic, zeta functions 11R54 - Other algebras and orders, and their zeta and (L)-functions 11R56 - Ad�le rings and groups 11R58 - Arithmetic theory of algebraic function fields 11R59 - Zeta functions and (L)-functions of function fields 11R60 - Cyclotomic function fields (class groups, Bernoulli objects, etc.) 11R65 - Class groups and Picard groups of orders 11R70 - (K)-theory of global fields 11R80 - Totally real fields 11R99 - Algebraic number theory: global fields 11Sxx - Algebraic number theory: local fields 11S05 - Polynomials 11S15 - Ramification and extension theory 11S20 - Galois theory 11S23 - Integral representations 11S25 - Galois cohomology 11S31 - Class field theory; (p)-adic formal groups 11S37 - Langlands-Weil conjectures, nonabelian class field theory 11S40 - Zeta functions and (L)-functions 11S45 - Algebras and orders, and their zeta functions 11S70 - (K)-theory of local fields 11S80 - Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) 11S82 - Non-Archimedean dynamical systems 11S85 - Other nonanalytic theory 11S90 - Prehomogeneous vector spaces 11S99 - Algebraic number theory: local fields 11Txx - Finite fields and commutative rings (number-theoretic aspects) 11T06 - Polynomials over finite fields 11T22 - Cyclotomy 11T23 - Exponential sums 11T24 - Other character sums and Gauss sums 11T30 - Structure theory for finite fields and commutative rings (number-theoretic aspects) 11T55 - Arithmetic theory of polynomial rings over finite fields 11T60 - Finite upper half-planes 11T71 - Algebraic coding theory; cryptography (number-theoretic aspects) 11T99 - Finite fields and commutative rings (number-theoretic aspects) 11Uxx - Connections of number theory and logic 11U05 - Decidability (number-theoretic aspects) 11U07 - Ultraproducts (number-theoretic aspects) 11U09 - Model theory (number-theoretic aspects) 11U10 - Nonstandard arithmetic (number-theoretic aspects) 11U99 - Connections of number theory and logic 11Yxx - Computational number theory 11Y05 - Factorization 11Y11 - Primality 11Y16 - Number-theoretic algorithms; complexity 11Y35 - Analytic computations 11Y40 - Algebraic number theory computations 11Y50 - Computer solution of Diophantine equations 11Y55 - Calculation of integer sequences 11Y60 - Evaluation of number-theoretic constants 11Y65 - Continued fraction calculations (number-theoretic aspects) 11Y70 - Values of arithmetic functions; tables 11Y99 - Computational number theory 11Zxx - Miscellaneous applications of number theory 11Z05 - Miscellaneous applications of number theory 11Z99 - Miscellaneous applications of number theory 12-XX - Field theory and polynomials 12-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory 12-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory 12-02 - Research exposition (monographs, survey articles) pertaining to field theory 12-03 - History of field theory 12-04 - Software, source code, etc. for problems pertaining to field theory 12-06 - Proceedings, conferences, collections, etc. pertaining to field theory 12-08 - Computational methods for problems pertaining to field theory 12-11 - Research data for problems pertaining to field theory 12Dxx - Real and complex fields 12D05 - Polynomials in real and complex fields: factorization 12D10 - Polynomials in real and complex fields: location of zeros (algebraic theorems) 12D15 - Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 12D99 - Real and complex fields 12Exx - General field theory 12E05 - Polynomials in general fields (irreducibility, etc.) 12E10 - Special polynomials in general fields 12E12 - Equations in general fields 12E15 - Skew fields, division rings 12E20 - Finite fields (field-theoretic aspects) 12E25 - Hilbertian fields; Hilbert's irreducibility theorem 12E30 - Field arithmetic 12E99 - General field theory 12Fxx - Field extensions 12F05 - Algebraic field extensions 12F10 - Separable extensions, Galois theory 12F12 - Inverse Galois theory 12F15 - Inseparable field extensions 12F20 - Transcendental field extensions 12F99 - Field extensions 12Gxx - Homological methods (field theory) 12G05 - Galois cohomology 12G10 - Cohomological dimension of fields 12G99 - Homological methods (field theory) 12Hxx - Differential and difference algebra 12H05 - Differential algebra 12H10 - Difference algebra 12H20 - Abstract differential equations 12H25 - (p)-adic differential equations 12H99 - Differential and difference algebra 12Jxx - Topological fields 12J05 - Normed fields 12J10 - Valued fields 12J12 - Formally (p)-adic fields 12J15 - Ordered fields 12J17 - Topological semifields 12J20 - General valuation theory for fields 12J25 - Non-Archimedean valued fields 12J27 - Krasner-Tate algebras 12J99 - Topological fields 12Kxx - Generalizations of fields 12K05 - Near-fields 12K10 - Semifields 12K99 - Generalizations of fields 12Lxx - Connections between field theory and logic 12L05 - Decidability and field theory 12L10 - Ultraproducts and field theory 12L12 - Model theory of fields 12L15 - Nonstandard arithmetic and field theory 12L99 - Connections between field theory and logic 13-XX - Commutative algebra 13-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra 13-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra 13-02 - Research exposition (monographs, survey articles) pertaining to commutative algebra 13-03 - History of commutative algebra 13-04 - Software, source code, etc. for problems pertaining to commutative algebra 13-06 - Proceedings, conferences, collections, etc. pertaining to commutative algebra 13-11 - Research data for problems pertaining to commutative algebra 13Axx - General commutative ring theory 13A02 - Graded rings 13A05 - Divisibility and factorizations in commutative rings 13A15 - Ideals and multiplicative ideal theory in commutative rings 13A18 - Valuations and their generalizations for commutative rings 13A30 - Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13A35 - Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure 13A50 - Actions of groups on commutative rings; invariant theory 13A70 - General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) 13A99 - General commutative ring theory 13Bxx - Commutative ring extensions and related topics 13B02 - Extension theory of commutative rings 13B05 - Galois theory and commutative ring extensions 13B10 - Morphisms of commutative rings 13B21 - Integral dependence in commutative rings; going up, going down 13B22 - Integral closure of commutative rings and ideals 13B25 - Polynomials over commutative rings 13B30 - Rings of fractions and localization for commutative rings 13B35 - Completion of commutative rings 13B40 - �tale and flat extensions; Henselization; Artin approximation 13B99 - Commutative ring extensions and related topics 13Cxx - Theory of modules and ideals in commutative rings 13C05 - Structure, classification theorems for modules and ideals in commutative rings 13C10 - Projective and free modules and ideals in commutative rings 13C11 - Injective and flat modules and ideals in commutative rings 13C12 - Torsion modules and ideals in commutative rings 13C13 - Other special types of modules and ideals in commutative rings 13C14 - Cohen-Macaulay modules 13C15 - Dimension theory, depth, related commutative rings (catenary, etc.) 13C20 - Class groups 13C40 - Linkage, complete intersections and determinantal ideals 13C60 - Module categories and commutative rings 13C70 - Theory of modules and ideals in commutative rings described by combinatorial properties 13C99 - Theory of modules and ideals in commutative rings 13Dxx - Homological methods in commutative ring theory 13D02 - Syzygies, resolutions, complexes and commutative rings 13D03 - (Co)homology of commutative rings and algebras (e.g., Hochschild, Andr�-Quillen, cyclic, dihedral, etc.) 13D05 - Homological dimension and commutative rings 13D07 - Homological functors on modules of commutative rings (Tor, Ext, etc.) 13D09 - Derived categories and commutative rings 13D10 - Deformations and infinitesimal methods in commutative ring theory 13D15 - Grothendieck groups, (K)-theory and commutative rings 13D22 - Homological conjectures (intersection theorems) in commutative ring theory 13D30 - Torsion theory for commutative rings 13D40 - Hilbert-Samuel and Hilbert-Kunz functions; Poincar� series 13D45 - Local cohomology and commutative rings 13D99 - Homological methods in commutative ring theory 13Exx - Chain conditions, finiteness conditions in commutative ring theory 13E05 - Commutative Noetherian rings and modules 13E10 - Commutative Artinian rings and modules, finite-dimensional algebras 13E15 - Commutative rings and modules of finite generation or presentation; number of generators 13E99 - Chain conditions, finiteness conditions in commutative ring theory 13Fxx - Arithmetic rings and other special commutative rings 13F05 - Dedekind, Pr�fer, Krull and Mori rings and their generalizations 13F07 - Euclidean rings and generalizations 13F10 - Principal ideal rings 13F15 - Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) 13F20 - Polynomial rings and ideals; rings of integer-valued polynomials 13F25 - Formal power series rings 13F30 - Valuation rings 13F35 - Witt vectors and related rings 13F40 - Excellent rings 13F45 - Seminormal rings 13F50 - Rings with straightening laws, Hodge algebras 13F55 - Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes 13F60 - Cluster algebras 13F65 - Commutative rings defined by binomial ideals, toric rings, etc. 13F70 - Other commutative rings defined by combinatorial properties 13F99 - Arithmetic rings and other special commutative rings 13Gxx - Integral domains 13G05 - Integral domains 13G99 - Integral domains 13Hxx - Local rings and semilocal rings 13H05 - Regular local rings 13H10 - Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 13H15 - Multiplicity theory and related topics 13H99 - Local rings and semilocal rings 13Jxx - Topological rings and modules 13J05 - Power series rings 13J07 - Analytical algebras and rings 13J10 - Complete rings, completion 13J15 - Henselian rings 13J20 - Global topological rings 13J25 - Ordered rings 13J30 - Real algebra 13J99 - Topological rings and modules 13Lxx - Applications of logic to commutative algebra 13L05 - Applications of logic to commutative algebra 13L99 - Applications of logic to commutative algebra 13Mxx - Finite commutative rings 13M05 - Structure of finite commutative rings 13M10 - Polynomials and finite commutative rings 13M99 - Finite commutative rings 13Nxx - Differential algebra 13N05 - Modules of differentials 13N10 - Commutative rings of differential operators and their modules 13N15 - Derivations and commutative rings 13N99 - Differential algebra 13Pxx - Computational aspects and applications of commutative rings 13P05 - Polynomials, factorization in commutative rings 13P10 - Gr�bner bases; other bases for ideals and modules (e.g., Janet and border bases) 13P15 - Solving polynomial systems; resultants 13P20 - Computational homological algebra 13P25 - Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 13P99 - Computational aspects and applications of commutative rings 14-XX - Algebraic geometry 14-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry 14-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry 14-02 - Research exposition (monographs, survey articles) pertaining to algebraic geometry 14-03 - History of algebraic geometry 14-04 - Software, source code, etc. for problems pertaining to algebraic geometry 14-06 - Proceedings, conferences, collections, etc. pertaining to algebraic geometry 14-11 - Research data for problems pertaining to algebraic geometry 14Axx - Foundations of algebraic geometry 14A05 - Relevant commutative algebra 14A10 - Varieties and morphisms 14A15 - Schemes and morphisms 14A20 - Generalizations (algebraic spaces, stacks) 14A21 - Logarithmic algebraic geometry, log schemes 14A22 - Noncommutative algebraic geometry 14A23 - Geometry over the field with one element 14A25 - Elementary questions in algebraic geometry 14A30 - Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) 14A99 - Foundations of algebraic geometry 14Bxx - Local theory in algebraic geometry 14B05 - Singularities in algebraic geometry 14B07 - Deformations of singularities 14B10 - Infinitesimal methods in algebraic geometry 14B12 - Local deformation theory, Artin approximation, etc. 14B15 - Local cohomology and algebraic geometry 14B20 - Formal neighborhoods in algebraic geometry 14B25 - Local structure of morphisms in algebraic geometry: �tale, flat, etc. 14B99 - Local theory in algebraic geometry 14Cxx - Cycles and subschemes 14C05 - Parametrization (Chow and Hilbert schemes) 14C15 - (Equivariant) Chow groups and rings; motives 14C17 - Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14C20 - Divisors, linear systems, invertible sheaves 14C21 - Pencils, nets, webs in algebraic geometry 14C22 - Picard groups 14C25 - Algebraic cycles 14C30 - Transcendental methods, Hodge theory (algebro-geometric aspects) 14C34 - Torelli problem 14C35 - Applications of methods of algebraic (K)-theory in algebraic geometry 14C40 - Riemann-Roch theorems 14C99 - Cycles and subschemes 14Dxx - Families, fibrations in algebraic geometry 14D05 - Structure of families (Picard-Lefschetz, monodromy, etc.) 14D06 - Fibrations, degenerations in algebraic geometry 14D07 - Variation of Hodge structures (algebro-geometric aspects) 14D10 - Arithmetic ground fields (finite, local, global) and families or fibrations 14D15 - Formal methods and deformations in algebraic geometry 14D20 - Algebraic moduli problems, moduli of vector bundles 14D21 - Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 14D22 - Fine and coarse moduli spaces 14D23 - Stacks and moduli problems 14D24 - Geometric Langlands program (algebro-geometric aspects) 14D99 - Families, fibrations in algebraic geometry 14Exx - Birational geometry 14E05 - Rational and birational maps 14E07 - Birational automorphisms, Cremona group and generalizations 14E08 - Rationality questions in algebraic geometry 14E15 - Global theory and resolution of singularities (algebro-geometric aspects) 14E16 - McKay correspondence 14E18 - Arcs and motivic integration 14E20 - Coverings in algebraic geometry 14E22 - Ramification problems in algebraic geometry 14E25 - Embeddings in algebraic geometry 14E30 - Minimal model program (Mori theory, extremal rays) 14E99 - Birational geometry 14Fxx - (Co)homology theory in algebraic geometry 14F06 - Sheaves in algebraic geometry 14F08 - Derived categories of sheaves, dg categories, and related constructions in algebraic geometry 14F10 - Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14F17 - Vanishing theorems in algebraic geometry 14F18 - Multiplier ideals 14F20 - �tale and other Grothendieck topologies and (co)homologies 14F22 - Brauer groups of schemes 14F25 - Classical real and complex (co)homology in algebraic geometry 14F30 - (p)-adic cohomology, crystalline cohomology 14F35 - Homotopy theory and fundamental groups in algebraic geometry 14F40 - de Rham cohomology and algebraic geometry 14F42 - Motivic cohomology; motivic homotopy theory 14F43 - Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14F45 - Topological properties in algebraic geometry 14F99 - (Co)homology theory in algebraic geometry 14Gxx - Arithmetic problems in algebraic geometry; Diophantine geometry 14G05 - Rational points 14G10 - Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 14G12 - Hasse principle, weak and strong approximation, Brauer-Manin obstruction 14G15 - Finite ground fields in algebraic geometry 14G17 - Positive characteristic ground fields in algebraic geometry 14G20 - Local ground fields in algebraic geometry 14G22 - Rigid analytic geometry 14G25 - Global ground fields in algebraic geometry 14G27 - Other nonalgebraically closed ground fields in algebraic geometry 14G32 - Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) 14G35 - Modular and Shimura varieties 14G40 - Arithmetic varieties and schemes; Arakelov theory; heights 14G45 - Perfectoid spaces and mixed characteristic 14G50 - Applications to coding theory and cryptography of arithmetic geometry 14G99 - Arithmetic problems in algebraic geometry; Diophantine geometry 14Hxx - Curves in algebraic geometry 14H05 - Algebraic functions and function fields in algebraic geometry 14H10 - Families, moduli of curves (algebraic) 14H15 - Families, moduli of curves (analytic) 14H20 - Singularities of curves, local rings 14H25 - Arithmetic ground fields for curves 14H30 - Coverings of curves, fundamental group 14H37 - Automorphisms of curves 14H40 - Jacobians, Prym varieties 14H42 - Theta functions and curves; Schottky problem 14H45 - Special algebraic curves and curves of low genus 14H50 - Plane and space curves 14H51 - Special divisors on curves (gonality, Brill-Noether theory) 14H52 - Elliptic curves 14H55 - Riemann surfaces; Weierstrass points; gap sequences 14H57 - Dessins d'enfants theory 14H60 - Vector bundles on curves and their moduli 14H70 - Relationships between algebraic curves and integrable systems 14H81 - Relationships between algebraic curves and physics 14H99 - Curves in algebraic geometry 14Jxx - Surfaces and higher-dimensional varieties 14J10 - Families, moduli, classification: algebraic theory 14J15 - Moduli, classification: analytic theory; relations with modular forms 14J17 - Singularities of surfaces or higher-dimensional varieties 14J20 - Arithmetic ground fields for surfaces or higher-dimensional varieties 14J25 - Special surfaces 14J26 - Rational and ruled surfaces 14J27 - Elliptic surfaces, elliptic or Calabi-Yau fibrations 14J28 - (K3) surfaces and Enriques surfaces 14J29 - Surfaces of general type 14J30 - (3)-folds 14J32 - Calabi-Yau manifolds (algebro-geometric aspects) 14J33 - Mirror symmetry (algebro-geometric aspects) 14J35 - (4)-folds 14J40 - (n)-folds ((n>4)) 14J42 - Holomorphic symplectic varieties, hyper-K�hler varieties 14J45 - Fano varieties 14J50 - Automorphisms of surfaces and higher-dimensional varieties 14J60 - Vector bundles on surfaces and higher-dimensional varieties, and their moduli 14J70 - Hypersurfaces and algebraic geometry 14J80 - Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) 14J81 - Relationships between surfaces, higher-dimensional varieties, and physics 14J99 - Surfaces and higher-dimensional varieties 14Kxx - Abelian varieties and schemes 14K02 - Isogeny 14K05 - Algebraic theory of abelian varieties 14K10 - Algebraic moduli of abelian varieties, classification 14K12 - Subvarieties of abelian varieties 14K15 - Arithmetic ground fields for abelian varieties 14K20 - Analytic theory of abelian varieties; abelian integrals and differentials 14K22 - Complex multiplication and abelian varieties 14K25 - Theta functions and abelian varieties 14K30 - Picard schemes, higher Jacobians 14K99 - Abelian varieties and schemes 14Lxx - Algebraic groups 14L05 - Formal groups, (p)-divisible groups 14L10 - Group varieties 14L15 - Group schemes 14L17 - Affine algebraic groups, hyperalgebra constructions 14L24 - Geometric invariant theory 14L30 - Group actions on varieties or schemes (quotients) 14L35 - Classical groups (algebro-geometric aspects) 14L40 - Other algebraic groups (geometric aspects) 14L99 - Algebraic groups 14Mxx - Special varieties 14M05 - Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14M06 - Linkage 14M07 - Low codimension problems in algebraic geometry 14M10 - Complete intersections 14M12 - Determinantal varieties 14M15 - Grassmannians, Schubert varieties, flag manifolds 14M17 - Homogeneous spaces and generalizations 14M20 - Rational and unirational varieties 14M22 - Rationally connected varieties 14M25 - Toric varieties, Newton polyhedra, Okounkov bodies 14M27 - Compactifications; symmetric and spherical varieties 14M30 - Supervarieties 14M35 - Character varieties 14M99 - Special varieties 14Nxx - Projective and enumerative algebraic geometry 14N05 - Projective techniques in algebraic geometry 14N07 - Secant varieties, tensor rank, varieties of sums of powers 14N10 - Enumerative problems (combinatorial problems) in algebraic geometry 14N15 - Classical problems, Schubert calculus 14N20 - Configurations and arrangements of linear subspaces 14N25 - Varieties of low degree 14N30 - Adjunction problems 14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 14N99 - Projective and enumerative algebraic geometry 14Pxx - Real algebraic and real-analytic geometry 14P05 - Real algebraic sets 14P10 - Semialgebraic sets and related spaces 14P15 - Real-analytic and semi-analytic sets 14P20 - Nash functions and manifolds 14P25 - Topology of real algebraic varieties 14P99 - Real algebraic and real-analytic geometry 14Qxx - Computational aspects in algebraic geometry 14Q05 - Computational aspects of algebraic curves 14Q10 - Computational aspects of algebraic surfaces 14Q15 - Computational aspects of higher-dimensional varieties 14Q20 - Effectivity, complexity and computational aspects of algebraic geometry 14Q25 - Computational algebraic geometry over arithmetic ground fields 14Q30 - Computational real algebraic geometry 14Q65 - Geometric aspects of numerical algebraic geometry 14Q99 - Computational aspects in algebraic geometry 14Rxx - Affine geometry 14R05 - Classification of affine varieties 14R10 - Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 14R15 - Jacobian problem 14R20 - Group actions on affine varieties 14R25 - Affine fibrations 14R99 - Affine geometry 14Txx - Tropical geometry 14T10 - Foundations of tropical geometry and relations with algebra 14T15 - Combinatorial aspects of tropical varieties 14T20 - Geometric aspects of tropical varieties 14T25 - Arithmetic aspects of tropical varieties 14T90 - Applications of tropical geometry 14T99 - Tropical geometry 15-XX - Linear and multilinear algebra; matrix theory 15-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to linear algebra 15-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra 15-02 - Research exposition (monographs, survey articles) pertaining to linear algebra 15-03 - History of linear algebra 15-04 - Software, source code, etc. for problems pertaining to linear algebra 15-06 - Proceedings, conferences, collections, etc. pertaining to linear algebra 15-11 - Research data for problems pertaining to linear algebra 15Axx - Basic linear algebra 15A03 - Vector spaces, linear dependence, rank, lineability 15A04 - Linear transformations, semilinear transformations 15A06 - Linear equations (linear algebraic aspects) 15A09 - Theory of matrix inversion and generalized inverses 15A10 - Applications of generalized inverses 15A12 - Conditioning of matrices 15A15 - Determinants, permanents, traces, other special matrix functions 15A16 - Matrix exponential and similar functions of matrices 15A18 - Eigenvalues, singular values, and eigenvectors 15A20 - Diagonalization, Jordan forms 15A21 - Canonical forms, reductions, classification 15A22 - Matrix pencils 15A23 - Factorization of matrices 15A24 - Matrix equations and identities 15A27 - Commutativity of matrices 15A29 - Inverse problems in linear algebra 15A30 - Algebraic systems of matrices 15A39 - Linear inequalities of matrices 15A42 - Inequalities involving eigenvalues and eigenvectors 15A45 - Miscellaneous inequalities involving matrices 15A54 - Matrices over function rings in one or more variables 15A60 - Norms of matrices, numerical range, applications of functional analysis to matrix theory 15A63 - Quadratic and bilinear forms, inner products 15A66 - Clifford algebras, spinors 15A67 - Applications of Clifford algebras to physics, etc. 15A69 - Multilinear algebra, tensor calculus 15A72 - Vector and tensor algebra, theory of invariants 15A75 - Exterior algebra, Grassmann algebras 15A78 - Other algebras built from modules 15A80 - Max-plus and related algebras 15A83 - Matrix completion problems 15A86 - Linear preserver problems 15A99 - Basic linear algebra 15Bxx - Special matrices 15B05 - Toeplitz, Cauchy, and related matrices 15B10 - Orthogonal matrices 15B15 - Fuzzy matrices 15B30 - Matrix Lie algebras 15B33 - Matrices over special rings (quaternions, finite fields, etc.) 15B34 - Boolean and Hadamard matrices 15B35 - Sign pattern matrices 15B36 - Matrices of integers 15B48 - Positive matrices and their generalizations; cones of matrices 15B51 - Stochastic matrices 15B52 - Random matrices (algebraic aspects) 15B57 - Hermitian, skew-Hermitian, and related matrices 15B99 - Special matrices 16-XX - Associative rings and algebras 16-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras 16-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras 16-02 - Research exposition (monographs, survey articles) pertaining to associative rings and algebras 16-03 - History of associative rings and algebras 16-04 - Software, source code, etc. for problems pertaining to associative rings and algebras 16-06 - Proceedings, conferences, collections, etc. pertaining to associative rings and algebras 16-11 - Research data for problems pertaining to associative rings and algebras 16Bxx - General and miscellaneous 16B50 - Category-theoretic methods and results in associative algebras (except as in 16D90) 16B70 - Applications of logic in associative algebras 16B99 - General and miscellaneous 16Dxx - Modules, bimodules and ideals in associative algebras 16D10 - General module theory in associative algebras 16D20 - Bimodules in associative algebras 16D25 - Ideals in associative algebras 16D30 - Infinite-dimensional simple rings (except as in 16Kxx) 16D40 - Free, projective, and flat modules and ideals in associative algebras 16D50 - Injective modules, self-injective associative rings 16D60 - Simple and semisimple modules, primitive rings and ideals in associative algebras 16D70 - Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) 16D80 - Other classes of modules and ideals in associative algebras 16D90 - Module categories in associative algebras 16D99 - Modules, bimodules and ideals in associative algebras 16Exx - Homological methods in associative algebras 16E05 - Syzygies, resolutions, complexes in associative algebras 16E10 - Homological dimension in associative algebras 16E20 - Grothendieck groups, (K)-theory, etc. 16E30 - Homological functors on modules (Tor, Ext, etc.) in associative algebras 16E35 - Derived categories and associative algebras 16E40 - (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) 16E45 - Differential graded algebras and applications (associative algebraic aspects) 16E50 - von Neumann regular rings and generalizations (associative algebraic aspects) 16E60 - Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. 16E65 - Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 16E99 - Homological methods in associative algebras 16Gxx - Representation theory of associative rings and algebras 16G10 - Representations of associative Artinian rings 16G20 - Representations of quivers and partially ordered sets 16G30 - Representations of orders, lattices, algebras over commutative rings 16G50 - Cohen-Macaulay modules in associative algebras 16G60 - Representation type (finite, tame, wild, etc.) of associative algebras 16G70 - Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 16G99 - Representation theory of associative rings and algebras 16Hxx - Associative algebras and orders 16H05 - Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16H10 - Orders in separable algebras 16H15 - Commutative orders 16H20 - Lattices over orders 16H99 - Associative algebras and orders 16Kxx - Division rings and semisimple Artin rings 16K20 - Finite-dimensional division rings 16K40 - Infinite-dimensional and general division rings 16K50 - Brauer groups (algebraic aspects) 16K99 - Division rings and semisimple Artin rings 16Lxx - Local rings and generalizations 16L30 - Noncommutative local and semilocal rings, perfect rings 16L60 - Quasi-Frobenius rings 16L99 - Local rings and generalizations 16Nxx - Radicals and radical properties of associative rings 16N20 - Jacobson radical, quasimultiplication 16N40 - Nil and nilpotent radicals, sets, ideals, associative rings 16N60 - Prime and semiprime associative rings 16N80 - General radicals and associative rings 16N99 - Radicals and radical properties of associative rings 16Pxx - Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras 16P10 - Finite rings and finite-dimensional associative algebras 16P20 - Artinian rings and modules (associative rings and algebras) 16P40 - Noetherian rings and modules (associative rings and algebras) 16P50 - Localization and associative Noetherian rings 16P60 - Chain conditions on annihilators and summands: Goldie-type conditions 16P70 - Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) 16P90 - Growth rate, Gelfand-Kirillov dimension 16P99 - Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras 16Rxx - Rings with polynomial identity 16R10 - (T)-ideals, identities, varieties of associative rings and algebras 16R20 - Semiprime p.i. rings, rings embeddable in matrices over commutative rings 16R30 - Trace rings and invariant theory (associative rings and algebras) 16R40 - Identities other than those of matrices over commutative rings 16R50 - Other kinds of identities (generalized polynomial, rational, involution) 16R60 - Functional identities (associative rings and algebras) 16R99 - Rings with polynomial identity 16Sxx - Associative rings and algebras arising under various constructions 16S10 - Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 16S15 - Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) 16S20 - Centralizing and normalizing extensions 16S30 - Universal enveloping algebras of Lie algebras 16S32 - Rings of differential operators (associative algebraic aspects) 16S34 - Group rings 16S35 - Twisted and skew group rings, crossed products 16S36 - Ordinary and skew polynomial rings and semigroup rings 16S37 - Quadratic and Koszul algebras 16S38 - Rings arising from noncommutative algebraic geometry 16S40 - Smash products of general Hopf actions 16S50 - Endomorphism rings; matrix rings 16S60 - Associative rings of functions, subdirect products, sheaves of rings 16S70 - Extensions of associative rings by ideals 16S80 - Deformations of associative rings 16S85 - Associative rings of fractions and localizations 16S88 - Leavitt path algebras 16S90 - Torsion theories; radicals on module categories (associative algebraic aspects) 16S99 - Associative rings and algebras arising under various constructions 16Txx - Hopf algebras, quantum groups and related topics 16T05 - Hopf algebras and their applications 16T10 - Bialgebras 16T15 - Coalgebras and comodules; corings 16T20 - Ring-theoretic aspects of quantum groups 16T25 - Yang-Baxter equations 16T30 - Connections of Hopf algebras with combinatorics 16T99 - Hopf algebras, quantum groups and related topics 16Uxx - Conditions on elements 16U10 - Integral domains (associative rings and algebras) 16U20 - Ore rings, multiplicative sets, Ore localization 16U30 - Divisibility, noncommutative UFDs 16U40 - Idempotent elements (associative rings and algebras) 16U60 - Units, groups of units (associative rings and algebras) 16U70 - Center, normalizer (invariant elements) (associative rings and algebras) 16U80 - Generalizations of commutativity (associative rings and algebras) 16U90 - Generalized inverses (associative rings and algebras) 16U99 - Conditions on elements 16Wxx - Associative rings and algebras with additional structure 16W10 - Rings with involution; Lie, Jordan and other nonassociative structures 16W20 - Automorphisms and endomorphisms 16W22 - Actions of groups and semigroups; invariant theory (associative rings and algebras) 16W25 - Derivations, actions of Lie algebras 16W50 - Graded rings and modules (associative rings and algebras) 16W55 - ``Super'' (or ``skew'') structure 16W60 - Valuations, completions, formal power series and related constructions (associative rings and algebras) 16W70 - Filtered associative rings; filtrational and graded techniques 16W80 - Topological and ordered rings and modules 16W99 - Associative rings and algebras with additional structure 16Yxx - Generalizations 16Y20 - Hyperrings 16Y30 - Near-rings 16Y60 - Semirings 16Y80 - (Gamma) and fuzzy structures 16Y99 - Generalizations 16Zxx - Computational aspects of associative rings 16Z05 - Computational aspects of associative rings (general theory) 16Z10 - Gr�bner-Shirshov bases 16Z99 - Computational aspects of associative rings 17-XX - Nonassociative rings and algebras 17-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to nonassociative rings and algebras 17-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras 17-02 - Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras 17-03 - History of nonassociative rings and algebras 17-04 - Software, source code, etc. for problems pertaining to nonassociative rings and algebras 17-06 - Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras 17-08 - Computational methods for problems pertaining to nonassociative rings and algebras 17-11 - Research data for problems pertaining to nonassociative rings and algebras 17Axx - General nonassociative rings 17A01 - General theory of nonassociative rings and algebras 17A05 - Power-associative rings 17A15 - Noncommutative Jordan algebras 17A20 - Flexible algebras 17A30 - Nonassociative algebras satisfying other identities 17A32 - Leibniz algebras 17A35 - Nonassociative division algebras 17A36 - Automorphisms, derivations, other operators (nonassociative rings and algebras) 17A40 - Ternary compositions 17A42 - Other (n)-ary compositions ((n ge 3)) 17A45 - Quadratic algebras (but not quadratic Jordan algebras) 17A50 - Free nonassociative algebras 17A60 - Structure theory for nonassociative algebras 17A61 - Gr�bner-Shirshov bases in nonassociative algebras 17A65 - Radical theory (nonassociative rings and algebras) 17A70 - Superalgebras 17A75 - Composition algebras 17A80 - Valued algebras 17A99 - General nonassociative rings 17Bxx - Lie algebras and Lie superalgebras 17B01 - Identities, free Lie (super)algebras 17B05 - Structure theory for Lie algebras and superalgebras 17B08 - Coadjoint orbits; nilpotent varieties 17B10 - Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B15 - Representations of Lie algebras and Lie superalgebras, analytic theory 17B20 - Simple, semisimple, reductive (super)algebras 17B22 - Root systems 17B25 - Exceptional (super)algebras 17B30 - Solvable, nilpotent (super)algebras 17B35 - Universal enveloping (super)algebras 17B37 - Quantum groups (quantized enveloping algebras) and related deformations 17B38 - Yang-Baxter equations and Rota-Baxter operators 17B40 - Automorphisms, derivations, other operators for Lie algebras and super algebras 17B45 - Lie algebras of linear algebraic groups 17B50 - Modular Lie (super)algebras 17B55 - Homological methods in Lie (super)algebras 17B56 - Cohomology of Lie (super)algebras 17B60 - Lie (super)algebras associated with other structures (associative, Jordan, etc.) 17B61 - Hom-Lie and related algebras 17B62 - Lie bialgebras; Lie coalgebras 17B63 - Poisson algebras 17B65 - Infinite-dimensional Lie (super)algebras 17B66 - Lie algebras of vector fields and related (super) algebras 17B67 - Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B68 - Virasoro and related algebras 17B69 - Vertex operators; vertex operator algebras and related structures 17B70 - Graded Lie (super)algebras 17B75 - Color Lie (super)algebras 17B80 - Applications of Lie algebras and superalgebras to integrable systems 17B81 - Applications of Lie (super)algebras to physics, etc. 17B99 - Lie algebras and Lie superalgebras 17Cxx - Jordan algebras (algebras, triples and pairs) 17C05 - Identities and free Jordan structures 17C10 - Structure theory for Jordan algebras 17C17 - Radicals in Jordan algebras 17C20 - Simple, semisimple Jordan algebras 17C27 - Idempotents, Peirce decompositions 17C30 - Associated groups, automorphisms of Jordan algebras 17C36 - Associated manifolds of Jordan algebras 17C37 - Associated geometries of Jordan algebras 17C40 - Exceptional Jordan structures 17C50 - Jordan structures associated with other structures 17C55 - Finite-dimensional structures of Jordan algebras 17C60 - Division algebras and Jordan algebras 17C65 - Jordan structures on Banach spaces and algebras 17C70 - Super structures 17C90 - Applications of Jordan algebras to physics, etc. 17C99 - Jordan algebras (algebras, triples and pairs) 17Dxx - Other nonassociative rings and algebras 17D05 - Alternative rings 17D10 - Mal'tsev rings and algebras 17D15 - Right alternative rings 17D20 - ((gamma, delta))-rings, including ((1,-1))-rings 17D25 - Lie-admissible algebras 17D30 - (non-Lie) Hom algebras and topics 17D92 - Genetic algebras 17D99 - Other nonassociative rings and algebras 18-XX - Category theory; homological algebra 18-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory 18-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory 18-02 - Research exposition (monographs, survey articles) pertaining to category theory 18-03 - History of category theory 18-04 - Software, source code, etc. for problems pertaining to category theory 18-06 - Proceedings, conferences, collections, etc. pertaining to category theory 18-08 - Computational methods for problems pertaining to category theory 18-11 - Research data for problems pertaining to category theory 18Axx - General theory of categories and functors 18A05 - Definitions and generalizations in theory of categories 18A10 - Graphs, diagram schemes, precategories 18A15 - Foundations, relations to logic and deductive systems 18A20 - Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18A22 - Special properties of functors (faithful, full, etc.) 18A23 - Natural morphisms, dinatural morphisms 18A25 - Functor categories, comma categories 18A30 - Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 18A32 - Factorization systems, substructures, quotient structures, congruences, amalgams 18A35 - Categories admitting limits (complete categories), functors preserving limits, completions 18A40 - Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18A50 - Graded categories (general) 18A99 - General theory of categories and functors 18Bxx - Special categories 18B05 - Categories of sets, characterizations 18B10 - Categories of spans/cospans, relations, or partial maps 18B15 - Embedding theorems, universal categories 18B20 - Categories of machines, automata 18B25 - Topoi 18B35 - Preorders, orders, domains and lattices (viewed as categories) 18B40 - Groupoids, semigroupoids, semigroups, groups (viewed as categories) 18B50 - Extensive, distributive, and adhesive categories 18B99 - Special categories 18Cxx - Categories and theories 18C05 - Equational categories 18C10 - Theories (e.g., algebraic theories), structure, and semantics 18C15 - Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads 18C20 - Eilenberg-Moore and Kleisli constructions for monads 18C30 - Sketches and generalizations 18C35 - Accessible and locally presentable categories 18C40 - Structured objects in a category (group objects, etc.) 18C50 - Categorical semantics of formal languages 18C99 - Categories and theories 18Dxx - Categorical structures 18D15 - Closed categories (closed monoidal and Cartesian closed categories, etc.) 18D20 - Enriched categories (over closed or monoidal categories) 18D25 - Actions of a monoidal category, tensorial strength 18D30 - Fibered categories 18D40 - Internal categories and groupoids 18D60 - Profunctors (= correspondences, distributors, modules) 18D65 - Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads) 18D70 - Formal category theory 18D99 - Categorical structures 18Exx - Categorical algebra 18E05 - Preadditive, additive categories 18E08 - Regular categories, Barr-exact categories 18E10 - Abelian categories, Grothendieck categories 18E13 - Protomodular categories, semi-abelian categories, Mal'tsev categories 18E20 - Categorical embedding theorems 18E35 - Localization of categories, calculus of fractions 18E40 - Torsion theories, radicals 18E45 - Definable subcategories and connections with model theory 18E50 - Categorical Galois theory 18E99 - Categorical algebra 18Fxx - Categories in geometry and topology 18F05 - Local categories and functors 18F10 - Grothendieck topologies and Grothendieck topoi 18F15 - Abstract manifolds and fiber bundles (category-theoretic aspects) 18F20 - Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) 18F25 - Algebraic (K)-theory and (L)-theory (category-theoretic aspects) 18F30 - Grothendieck groups (category-theoretic aspects) 18F40 - Synthetic differential geometry, tangent categories, differential categories 18F50 - Goodwillie calculus and functor calculus 18F60 - Categories of topological spaces and continuous mappings 18F70 - Frames and locales, pointfree topology, Stone duality 18F75 - Quantales 18F99 - Categories in geometry and topology 18Gxx - Homological algebra in category theory, derived categories and functors 18G05 - Projectives and injectives (category-theoretic aspects) 18G10 - Resolutions; derived functors (category-theoretic aspects) 18G15 - Ext and Tor, generalizations, K�nneth formula (category-theoretic aspects) 18G20 - Homological dimension (category-theoretic aspects) 18G25 - Relative homological algebra, projective classes (category-theoretic aspects) 18G31 - Simplicial modules and Dold-Kan correspondence 18G35 - Chain complexes (category-theoretic aspects), dg categories 18G40 - Spectral sequences, hypercohomology 18G45 - 2-groups, crossed modules, crossed complexes 18G50 - Nonabelian homological algebra (category-theoretic aspects) 18G65 - Stable module categories 18G70 - (A_{infty})-categories, relations with homological mirror symmetry 18G80 - Derived categories, triangulated categories 18G85 - Graph complexes and graph homology 18G90 - Other (co)homology theories (category-theoretic aspects) 18G99 - Homological algebra in category theory, derived categories and functors 18Mxx - Monoidal categories and operads 18M05 - Monoidal categories, symmetric monoidal categories 18M10 - Traced monoidal categories, compact closed categories, star-autonomous categories 18M15 - Braided monoidal categories and ribbon categories 18M20 - Fusion categories, modular tensor categories, modular functors 18M25 - Tannakian categories 18M30 - String diagrams and graphical calculi 18M35 - Categories of networks and processes, compositionality 18M40 - Dagger categories, categorical quantum mechanics 18M45 - Categorical aspects of linear logic 18M50 - Bimonoidal, skew-monoidal, duoidal categories 18M60 - Operads (general) 18M65 - Non-symmetric operads, multicategories, generalized multicategories 18M70 - Algebraic operads, cooperads, and Koszul duality 18M75 - Topological and simplicial operads 18M80 - Species, Hopf monoids, operads in combinatorics 18M85 - Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads 18M90 - Globular operads 18M99 - Monoidal categories and operads 18Nxx - Higher categories and homotopical algebra 18N10 - 2-categories, bicategories, double categories 18N15 - 2-dimensional monad theory 18N20 - Tricategories, weak (n)-categories, coherence, semi-strictification 18N25 - Categorification 18N30 - Strict omega-categories, computads, polygraphs 18N40 - Homotopical algebra, Quillen model categories, derivators 18N45 - Categories of fibrations, relations to (K)-theory, relations to type theory 18N50 - Simplicial sets, simplicial objects 18N55 - Localizations (e.g., simplicial localization, Bousfield localization) 18N60 - ((infty,1))-categories (quasi-categories, Segal spaces, etc.); (infty)-topoi, stable (infty)-categories 18N65 - ((infty, n))-categories and ((infty,infty))-categories 18N70 - (infty)-operads and higher algebra 18N99 - Higher categories and homotopical algebra 19-XX - (K)-theory 19-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to (K)-theory 19-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to (K)-theory 19-02 - Research exposition (monographs, survey articles) pertaining to (K)-theory 19-03 - History of (K)-theory 19-04 - Software, source code, etc. for problems pertaining to (K)-theory 19-06 - Proceedings, conferences, collections, etc. pertaining to (K)-theory 19-08 - Computational methods for problems pertaining to (K)-theory 19-11 - Research data for problems pertaining to (K)-theory 19Axx - Grothendieck groups and (K_0) 19A13 - Stability for projective modules 19A15 - Efficient generation of modules 19A22 - Frobenius induction, Burnside and representation rings 19A31 - (K_0) of group rings and orders 19A49 - (K_0) of other rings 19A99 - Grothendieck groups and (K_0) 19Bxx - Whitehead groups and (K_1) 19B10 - Stable range conditions 19B14 - Stability for linear groups 19B28 - (K_1) of group rings and orders 19B37 - Congruence subgroup problems 19B99 - Whitehead groups and (K_1) 19Cxx - Steinberg groups and (K_2) 19C09 - Central extensions and Schur multipliers 19C20 - Symbols, presentations and stability of (K_2) 19C30 - (K_2) and the Brauer group 19C40 - Excision for (K_2) 19C99 - Steinberg groups and (K_2) 19Dxx - Higher algebraic (K)-theory 19D06 - (Q)- and plus-constructions 19D10 - Algebraic (K)-theory of spaces 19D23 - Symmetric monoidal categories 19D25 - Karoubi-Villamayor-Gersten (K)-theory 19D35 - Negative (K)-theory, NK and Nil 19D45 - Higher symbols, Milnor (K)-theory 19D50 - Computations of higher (K)-theory of rings 19D55 - (K)-theory and homology; cyclic homology and cohomology 19D99 - Higher algebraic (K)-theory 19Exx - (K)-theory in geometry 19E08 - (K)-theory of schemes 19E15 - Algebraic cycles and motivic cohomology ((K)-theoretic aspects) 19E20 - Relations of (K)-theory with cohomology theories 19E99 - (K)-theory in geometry 19Fxx - (K)-theory in number theory 19F05 - Generalized class field theory ((K)-theoretic aspects) 19F15 - Symbols and arithmetic ((K)-theoretic aspects) 19F27 - �tale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) 19F99 - (K)-theory in number theory 19Gxx - (K)-theory of forms 19G05 - Stability for quadratic modules 19G12 - Witt groups of rings 19G24 - (L)-theory of group rings 19G38 - Hermitian (K)-theory, relations with (K)-theory of rings 19G99 - (K)-theory of forms 19Jxx - Obstructions from topology 19J05 - Finiteness and other obstructions in (K_0) 19J10 - Whitehead (and related) torsion 19J25 - Surgery obstructions ((K)-theoretic aspects) 19J35 - Obstructions to group actions ((K)-theoretic aspects) 19J99 - Obstructions from topology 19Kxx - (K)-theory and operator algebras 19K14 - (K_0) as an ordered group, traces 19K33 - Ext and (K)-homology 19K35 - Kasparov theory ((KK)-theory) 19K56 - Index theory 19K99 - (K)-theory and operator algebras 19Lxx - Topological (K)-theory 19L10 - Riemann-Roch theorems, Chern characters 19L20 - (J)-homomorphism, Adams operations 19L41 - Connective (K)-theory, cobordism 19L47 - Equivariant (K)-theory 19L50 - Twisted (K)-theory; differential (K)-theory 19L64 - Geometric applications of topological (K)-theory 19L99 - Topological (K)-theory 19Mxx - Miscellaneous applications of (K)-theory 19M05 - Miscellaneous applications of (K)-theory 19M99 - Miscellaneous applications of (K)-theory 20-XX - Group theory and generalizations 20-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to group theory 20-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory 20-02 - Research exposition (monographs, survey articles) pertaining to group theory 20-03 - History of group theory 20-04 - Software, source code, etc. for problems pertaining to group theory 20-06 - Proceedings, conferences, collections, etc. pertaining to group theory 20-08 - Computational methods for problems pertaining to group theory 20-11 - Research data for problems pertaining to group theory 20Axx - Foundations 20A05 - Axiomatics and elementary properties of groups 20A10 - Metamathematical considerations in group theory 20A15 - Applications of logic to group theory 20A99 - Foundations 20Bxx - Permutation groups 20B05 - General theory for finite permutation groups 20B07 - General theory for infinite permutation groups 20B10 - Characterization theorems for permutation groups 20B15 - Primitive groups 20B20 - Multiply transitive finite groups 20B22 - Multiply transitive infinite groups 20B25 - Finite automorphism groups of algebraic, geometric, or combinatorial structures 20B27 - Infinite automorphism groups 20B30 - Symmetric groups 20B35 - Subgroups of symmetric groups 20B99 - Permutation groups 20Cxx - Representation theory of groups 20C05 - Group rings of finite groups and their modules (group-theoretic aspects) 20C07 - Group rings of infinite groups and their modules (group-theoretic aspects) 20C08 - Hecke algebras and their representations 20C10 - Integral representations of finite groups 20C11 - (p)-adic representations of finite groups 20C12 - Integral representations of infinite groups 20C15 - Ordinary representations and characters 20C20 - Modular representations and characters 20C25 - Projective representations and multipliers 20C30 - Representations of finite symmetric groups 20C32 - Representations of infinite symmetric groups 20C33 - Representations of finite groups of Lie type 20C34 - Representations of sporadic groups 20C35 - Applications of group representations to physics and other areas of science 20C99 - Representation theory of groups 20Dxx - Abstract finite groups 20D05 - Finite simple groups and their classification 20D06 - Simple groups: alternating groups and groups of Lie type 20D08 - Simple groups: sporadic groups 20D10 - Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks 20D15 - Finite nilpotent groups, (p)-groups 20D20 - Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure 20D25 - Special subgroups (Frattini, Fitting, etc.) 20D30 - Series and lattices of subgroups 20D35 - Subnormal subgroups of abstract finite groups 20D40 - Products of subgroups of abstract finite groups 20D45 - Automorphisms of abstract finite groups 20D60 - Arithmetic and combinatorial problems involving abstract finite groups 20D99 - Abstract finite groups 20Exx - Structure and classification of infinite or finite groups 20E05 - Free nonabelian groups 20E06 - Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20E07 - Subgroup theorems; subgroup growth 20E08 - Groups acting on trees 20E10 - Quasivarieties and varieties of groups 20E15 - Chains and lattices of subgroups, subnormal subgroups 20E18 - Limits, profinite groups 20E22 - Extensions, wreath products, and other compositions of groups 20E25 - Local properties of groups 20E26 - Residual properties and generalizations; residually finite groups 20E28 - Maximal subgroups 20E32 - Simple groups 20E34 - General structure theorems for groups 20E36 - Automorphisms of infinite groups 20E42 - Groups with a (BN)-pair; buildings 20E45 - Conjugacy classes for groups 20E99 - Structure and classification of infinite or finite groups 20Fxx - Special aspects of infinite or finite groups 20F05 - Generators, relations, and presentations of groups 20F06 - Cancellation theory of groups; application of van Kampen diagrams 20F10 - Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 20F11 - Groups of finite Morley rank 20F12 - Commutator calculus 20F14 - Derived series, central series, and generalizations for groups 20F16 - Solvable groups, supersolvable groups 20F17 - Formations of groups, Fitting classes 20F18 - Nilpotent groups 20F19 - Generalizations of solvable and nilpotent groups 20F22 - Other classes of groups defined by subgroup chains 20F24 - FC-groups and their generalizations 20F28 - Automorphism groups of groups 20F29 - Representations of groups as automorphism groups of algebraic systems 20F34 - Fundamental groups and their automorphisms (group-theoretic aspects) 20F36 - Braid groups; Artin groups 20F38 - Other groups related to topology or analysis 20F40 - Associated Lie structures for groups 20F45 - Engel conditions 20F50 - Periodic groups; locally finite groups 20F55 - Reflection and Coxeter groups (group-theoretic aspects) 20F60 - Ordered groups (group-theoretic aspects) 20F65 - Geometric group theory 20F67 - Hyperbolic groups and nonpositively curved groups 20F69 - Asymptotic properties of groups 20F70 - Algebraic geometry over groups; equations over groups 20F99 - Special aspects of infinite or finite groups 20Gxx - Linear algebraic groups and related topics 20G05 - Representation theory for linear algebraic groups 20G07 - Structure theory for linear algebraic groups 20G10 - Cohomology theory for linear algebraic groups 20G15 - Linear algebraic groups over arbitrary fields 20G20 - Linear algebraic groups over the reals, the complexes, the quaternions 20G25 - Linear algebraic groups over local fields and their integers 20G30 - Linear algebraic groups over global fields and their integers 20G35 - Linear algebraic groups over ad�les and other rings and schemes 20G40 - Linear algebraic groups over finite fields 20G41 - Exceptional groups 20G42 - Quantum groups (quantized function algebras) and their representations 20G43 - Schur and (q)-Schur algebras 20G44 - Kac-Moody groups 20G45 - Applications of linear algebraic groups to the sciences 20G99 - Linear algebraic groups and related topics 20Hxx - Other groups of matrices 20H05 - Unimodular groups, congruence subgroups (group-theoretic aspects) 20H10 - Fuchsian groups and their generalizations (group-theoretic aspects) 20H15 - Other geometric groups, including crystallographic groups 20H20 - Other matrix groups over fields 20H25 - Other matrix groups over rings 20H30 - Other matrix groups over finite fields 20H99 - Other groups of matrices 20Jxx - Connections of group theory with homological algebra and category theory 20J05 - Homological methods in group theory 20J06 - Cohomology of groups 20J15 - Category of groups 20J99 - Connections of group theory with homological algebra and category theory 20Kxx - Abelian groups 20K01 - Finite abelian groups 20K10 - Torsion groups, primary groups and generalized primary groups 20K15 - Torsion-free groups, finite rank 20K20 - Torsion-free groups, infinite rank 20K21 - Mixed groups 20K25 - Direct sums, direct products, etc. for abelian groups 20K27 - Subgroups of abelian groups 20K30 - Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups 20K35 - Extensions of abelian groups 20K40 - Homological and categorical methods for abelian groups 20K45 - Topological methods for abelian groups 20K99 - Abelian groups 20Lxx - Groupoids (i.e. small categories in which all morphisms are isomorphisms) 20L05 - Groupoids (i.e. small categories in which all morphisms are isomorphisms) 20L99 - Groupoids (i.e. small categories in which all morphisms are isomorphisms) 20Mxx - Semigroups 20M05 - Free semigroups, generators and relations, word problems 20M07 - Varieties and pseudovarieties of semigroups 20M10 - General structure theory for semigroups 20M11 - Radical theory for semigroups 20M12 - Ideal theory for semigroups 20M13 - Arithmetic theory of semigroups 20M14 - Commutative semigroups 20M15 - Mappings of semigroups 20M17 - Regular semigroups 20M18 - Inverse semigroups 20M19 - Orthodox semigroups 20M20 - Semigroups of transformations, relations, partitions, etc. 20M25 - Semigroup rings, multiplicative semigroups of rings 20M30 - Representation of semigroups; actions of semigroups on sets 20M32 - Algebraic monoids 20M35 - Semigroups in automata theory, linguistics, etc. 20M50 - Connections of semigroups with homological algebra and category theory 20M75 - Generalizations of semigroups 20M99 - Semigroups 20Nxx - Other generalizations of groups 20N02 - Sets with a single binary operation (groupoids) 20N05 - Loops, quasigroups 20N10 - Ternary systems (heaps, semiheaps, heapoids, etc.) 20N15 - (n)-ary systems ((nge 3)) 20N20 - Hypergroups 20N25 - Fuzzy groups 20N99 - Other generalizations of groups 20Pxx - Probabilistic methods in group theory 20P05 - Probabilistic methods in group theory 20P99 - Probabilistic methods in group theory 22-XX - Topological groups, Lie groups 22-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to topological groups 22-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups 22-02 - Research exposition (monographs, survey articles) pertaining to topological groups 22-03 - History of topological groups 22-04 - Software, source code, etc. for problems pertaining to topological groups 22-06 - Proceedings, conferences, collections, etc. pertaining to topological groups 22-08 - Computational methods for problems pertaining to topological groups 22-11 - Research data for problems pertaining to topological groups 22Axx - Topological and differentiable algebraic systems 22A05 - Structure of general topological groups 22A10 - Analysis on general topological groups 22A15 - Structure of topological semigroups 22A20 - Analysis on topological semigroups 22A22 - Topological groupoids (including differentiable and Lie groupoids) 22A25 - Representations of general topological groups and semigroups 22A26 - Topological semilattices, lattices and applications 22A30 - Other topological algebraic systems and their representations 22A99 - Topological and differentiable algebraic systems 22Bxx - Locally compact abelian groups (LCA groups) 22B05 - General properties and structure of LCA groups 22B10 - Structure of group algebras of LCA groups 22B99 - Locally compact abelian groups (LCA groups) 22Cxx - Compact groups 22C05 - Compact groups 22C99 - Compact groups 22Dxx - Locally compact groups and their algebras 22D05 - General properties and structure of locally compact groups 22D10 - Unitary representations of locally compact groups 22D12 - Other representations of locally compact groups 22D15 - Group algebras of locally compact groups 22D20 - Representations of group algebras 22D25 - (C^*)-algebras and (W^*)-algebras in relation to group representations 22D30 - Induced representations for locally compact groups 22D35 - Duality theorems for locally compact groups 22D40 - Ergodic theory on groups 22D45 - Automorphism groups of locally compact groups 22D50 - Rigidity in locally compact groups 22D55 - Kazhdan's property (T), the Haagerup property, and generalizations 22D99 - Locally compact groups and their algebras 22Exx - Lie groups 22E05 - Local Lie groups 22E10 - General properties and structure of complex Lie groups 22E15 - General properties and structure of real Lie groups 22E20 - General properties and structure of other Lie groups 22E25 - Nilpotent and solvable Lie groups 22E27 - Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) 22E30 - Analysis on real and complex Lie groups 22E35 - Analysis on (p)-adic Lie groups 22E40 - Discrete subgroups of Lie groups 22E41 - Continuous cohomology of Lie groups 22E43 - Structure and representation of the Lorentz group 22E45 - Representations of Lie and linear algebraic groups over real fields: analytic methods 22E46 - Semisimple Lie groups and their representations 22E47 - Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) 22E50 - Representations of Lie and linear algebraic groups over local fields 22E55 - Representations of Lie and linear algebraic groups over global fields and ad�le rings 22E57 - Geometric Langlands program: representation-theoretic aspects 22E60 - Lie algebras of Lie groups 22E65 - Infinite-dimensional Lie groups and their Lie algebras: general properties 22E66 - Analysis on and representations of infinite-dimensional Lie groups 22E67 - Loop groups and related constructions, group-theoretic treatment 22E70 - Applications of Lie groups to the sciences; explicit representations 22E99 - Lie groups 22Fxx - Noncompact transformation groups 22F05 - General theory of group and pseudogroup actions 22F10 - Measurable group actions 22F30 - Homogeneous spaces 22F50 - Groups as automorphisms of other structures 22F99 - Noncompact transformation groups 26-XX - Real functions 26-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions 26-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions 26-02 - Research exposition (monographs, survey articles) pertaining to real functions 26-03 - History of real functions 26-04 - Software, source code, etc. for problems pertaining to real functions 26-06 - Proceedings, conferences, collections, etc. pertaining to real functions 26-08 - Computational methods for problems pertaining to real functions 26-11 - Research data for problems pertaining to real functions 26Axx - Functions of one variable 26A03 - Foundations: limits and generalizations, elementary topology of the line 26A06 - One-variable calculus 26A09 - Elementary functions 26A12 - Rate of growth of functions, orders of infinity, slowly varying functions 26A15 - Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 26A16 - Lipschitz (H�lder) classes 26A18 - Iteration of real functions in one variable 26A21 - Classification of real functions; Baire classification of sets and functions 26A24 - Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems 26A27 - Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives 26A30 - Singular functions, Cantor functions, functions with other special properties 26A33 - Fractional derivatives and integrals 26A36 - Antidifferentiation 26A39 - Denjoy and Perron integrals, other special integrals 26A42 - Integrals of Riemann, Stieltjes and Lebesgue type 26A45 - Functions of bounded variation, generalizations 26A46 - Absolutely continuous real functions in one variable 26A48 - Monotonic functions, generalizations 26A51 - Convexity of real functions in one variable, generalizations 26A99 - Functions of one variable 26Bxx - Functions of several variables 26B05 - Continuity and differentiation questions 26B10 - Implicit function theorems, Jacobians, transformations with several variables 26B12 - Calculus of vector functions 26B15 - Integration of real functions of several variables: length, area, volume 26B20 - Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) 26B25 - Convexity of real functions of several variables, generalizations 26B30 - Absolutely continuous real functions of several variables, functions of bounded variation 26B35 - Special properties of functions of several variables, H�lder conditions, etc. 26B40 - Representation and superposition of functions 26B99 - Functions of several variables 26Cxx - Polynomials, rational functions in real analysis 26C05 - Real polynomials: analytic properties, etc. 26C10 - Real polynomials: location of zeros 26C15 - Real rational functions 26C99 - Polynomials, rational functions in real analysis 26Dxx - Inequalities in real analysis 26D05 - Inequalities for trigonometric functions and polynomials 26D07 - Inequalities involving other types of functions 26D10 - Inequalities involving derivatives and differential and integral operators 26D15 - Inequalities for sums, series and integrals 26D20 - Other analytical inequalities 26D99 - Inequalities in real analysis 26Exx - Miscellaneous topics in real functions 26E05 - Real-analytic functions 26E10 - (C^infty)-functions, quasi-analytic functions 26E15 - Calculus of functions on infinite-dimensional spaces 26E20 - Calculus of functions taking values in infinite-dimensional spaces 26E25 - Set-valued functions 26E30 - Non-Archimedean analysis 26E35 - Nonstandard analysis 26E40 - Constructive real analysis 26E50 - Fuzzy real analysis 26E60 - Means 26E70 - Real analysis on time scales or measure chains 26E99 - Miscellaneous topics in real functions 28-XX - Measure and integration 28-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration 28-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration 28-02 - Research exposition (monographs, survey articles) pertaining to measure and integration 28-03 - History of measure and integration 28-04 - Software, source code, etc. for problems pertaining to measure and integration 28-06 - Proceedings, conferences, collections, etc. pertaining to measure and integration 28-08 - Computational methods for problems pertaining to measure and integration 28-11 - Research data for problems pertaining to measure and integration 28Axx - Classical measure theory 28A05 - Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets 28A10 - Real- or complex-valued set functions 28A12 - Contents, measures, outer measures, capacities 28A15 - Abstract differentiation theory, differentiation of set functions 28A20 - Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 28A25 - Integration with respect to measures and other set functions 28A33 - Spaces of measures, convergence of measures 28A35 - Measures and integrals in product spaces 28A50 - Integration and disintegration of measures 28A51 - Lifting theory 28A60 - Measures on Boolean rings, measure algebras 28A75 - Length, area, volume, other geometric measure theory 28A78 - Hausdorff and packing measures 28A80 - Fractals 28A99 - Classical measure theory 28Bxx - Set functions, measures and integrals with values in abstract spaces 28B05 - Vector-valued set functions, measures and integrals 28B10 - Group- or semigroup-valued set functions, measures and integrals 28B15 - Set functions, measures and integrals with values in ordered spaces 28B20 - Set-valued set functions and measures; integration of set-valued functions; measurable selections 28B99 - Set functions, measures and integrals with values in abstract spaces 28Cxx - Set functions and measures on spaces with additional structure 28C05 - Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures 28C10 - Set functions and measures on topological groups or semigroups, Haar measures, invariant measures 28C15 - Set functions and measures on topological spaces (regularity of measures, etc.) 28C20 - Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) 28C99 - Set functions and measures on spaces with additional structure 28Dxx - Measure-theoretic ergodic theory 28D05 - Measure-preserving transformations 28D10 - One-parameter continuous families of measure-preserving transformations 28D15 - General groups of measure-preserving transformations 28D20 - Entropy and other invariants 28D99 - Measure-theoretic ergodic theory 28Exx - Miscellaneous topics in measure theory 28E05 - Nonstandard measure theory 28E10 - Fuzzy measure theory 28E15 - Other connections with logic and set theory 28E99 - Miscellaneous topics in measure theory 30-XX - Functions of a complex variable 30-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable 30-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable 30-02 - Research exposition (monographs, survey articles) pertaining to functions of a complex variable 30-03 - History of functions of a complex variable 30-04 - Software, source code, etc. for problems pertaining to functions of a complex variable 30-06 - Proceedings, conferences, collections, etc. pertaining to functions of a complex variable 30-08 - Computational methods for problems pertaining to functions of a complex variable 30-11 - Research data for problems pertaining to functions of a complex variable 30Axx - General properties of functions of one complex variable 30A05 - Monogenic and polygenic functions of one complex variable 30A10 - Inequalities in the complex plane 30A99 - General properties of functions of one complex variable 30Bxx - Series expansions of functions of one complex variable 30B10 - Power series (including lacunary series) in one complex variable 30B20 - Random power series in one complex variable 30B30 - Boundary behavior of power series in one complex variable; over-convergence 30B40 - Analytic continuation of functions of one complex variable 30B50 - Dirichlet series, exponential series and other series in one complex variable 30B60 - Completeness problems, closure of a system of functions of one complex variable 30B70 - Continued fractions; complex-analytic aspects 30B99 - Series expansions of functions of one complex variable 30Cxx - Geometric function theory 30C10 - Polynomials and rational functions of one complex variable 30C15 - Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) 30C20 - Conformal mappings of special domains 30C25 - Covering theorems in conformal mapping theory 30C30 - Schwarz-Christoffel-type mappings 30C35 - General theory of conformal mappings 30C40 - Kernel functions in one complex variable and applications 30C45 - Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C50 - Coefficient problems for univalent and multivalent functions of one complex variable 30C55 - General theory of univalent and multivalent functions of one complex variable 30C62 - Quasiconformal mappings in the complex plane 30C65 - Quasiconformal mappings in (mathbb{R}^n), other generalizations 30C70 - Extremal problems for conformal and quasiconformal mappings, variational methods 30C75 - Extremal problems for conformal and quasiconformal mappings, other methods 30C80 - Maximum principle, Schwarz's lemma, Lindel�f principle, analogues and generalizations; subordination 30C85 - Capacity and harmonic measure in the complex plane 30C99 - Geometric function theory 30Dxx - Entire and meromorphic functions of one complex variable, and related topics 30D05 - Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 30D10 - Representations of entire functions of one complex variable by series and integrals 30D15 - Special classes of entire functions of one complex variable and growth estimates 30D20 - Entire functions of one complex variable (general theory) 30D30 - Meromorphic functions of one complex variable (general theory) 30D35 - Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D40 - Cluster sets, prime ends, boundary behavior 30D45 - Normal functions of one complex variable, normal families 30D60 - Quasi-analytic and other classes of functions of one complex variable 30D99 - Entire and meromorphic functions of one complex variable, and related topics 30Exx - Miscellaneous topics of analysis in the complex plane 30E05 - Moment problems and interpolation problems in the complex plane 30E10 - Approximation in the complex plane 30E15 - Asymptotic representations in the complex plane 30E20 - Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane 30E25 - Boundary value problems in the complex plane 30E99 - Miscellaneous topics of analysis in the complex plane 30Fxx - Riemann surfaces 30F10 - Compact Riemann surfaces and uniformization 30F15 - Harmonic functions on Riemann surfaces 30F20 - Classification theory of Riemann surfaces 30F25 - Ideal boundary theory for Riemann surfaces 30F30 - Differentials on Riemann surfaces 30F35 - Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) 30F40 - Kleinian groups (aspects of compact Riemann surfaces and uniformization) 30F45 - Conformal metrics (hyperbolic, Poincar�, distance functions) 30F50 - Klein surfaces 30F60 - Teichm�ller theory for Riemann surfaces 30F99 - Riemann surfaces 30Gxx - Generalized function theory 30G06 - Non-Archimedean function theory 30G12 - Finely holomorphic functions and topological function theory 30G20 - Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) 30G25 - Discrete analytic functions 30G30 - Other generalizations of analytic functions (including abstract-valued functions) 30G35 - Functions of hypercomplex variables and generalized variables 30G99 - Generalized function theory 30Hxx - Spaces and algebras of analytic functions of one complex variable 30H05 - Spaces of bounded analytic functions of one complex variable 30H10 - Hardy spaces 30H15 - Nevanlinna spaces and Smirnov spaces 30H20 - Bergman spaces and Fock spaces 30H25 - Besov spaces and (Q_p)-spaces 30H30 - Bloch spaces 30H35 - BMO-spaces 30H40 - Zygmund spaces 30H45 - de Branges-Rovnyak spaces 30H50 - Algebras of analytic functions of one complex variable 30H80 - Corona theorems 30H99 - Spaces and algebras of analytic functions of one complex variable 30Jxx - Function theory on the disc 30J05 - Inner functions of one complex variable 30J10 - Blaschke products 30J15 - Singular inner functions of one complex variable 30J99 - Function theory on the disc 30Kxx - Universal holomorphic functions of one complex variable 30K05 - Universal Taylor series in one complex variable 30K10 - Universal Dirichlet series in one complex variable 30K15 - Universal functions of one complex variable 30K20 - Compositional universality 30K99 - Universal holomorphic functions of one complex variable 30Lxx - Analysis on metric spaces 30L05 - Geometric embeddings of metric spaces 30L10 - Quasiconformal mappings in metric spaces 30L15 - Inequalities in metric spaces 30L99 - Analysis on metric spaces 31-XX - Potential theory 31-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to potential theory 31-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory 31-02 - Research exposition (monographs, survey articles) pertaining to potential theory 31-03 - History of potential theory 31-04 - Software, source code, etc. for problems pertaining to potential theory 31-06 - Proceedings, conferences, collections, etc. pertaining to potential theory 31-08 - Computational methods for problems pertaining to potential theory 31-11 - Research data for problems pertaining to potential theory 31Axx - Two-dimensional potential theory 31A05 - Harmonic, subharmonic, superharmonic functions in two dimensions 31A10 - Integral representations, integral operators, integral equations methods in two dimensions 31A15 - Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions 31A20 - Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions 31A25 - Boundary value and inverse problems for harmonic functions in two dimensions 31A30 - Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions 31A35 - Connections of harmonic functions with differential equations in two dimensions 31A99 - Two-dimensional potential theory 31Bxx - Higher-dimensional potential theory 31B05 - Harmonic, subharmonic, superharmonic functions in higher dimensions 31B10 - Integral representations, integral operators, integral equations methods in higher dimensions 31B15 - Potentials and capacities, extremal length and related notions in higher dimensions 31B20 - Boundary value and inverse problems for harmonic functions in higher dimensions 31B25 - Boundary behavior of harmonic functions in higher dimensions 31B30 - Biharmonic and polyharmonic equations and functions in higher dimensions 31B35 - Connections of harmonic functions with differential equations in higher dimensions 31B99 - Higher-dimensional potential theory 31Cxx - Generalizations of potential theory 31C05 - Harmonic, subharmonic, superharmonic functions on other spaces 31C10 - Pluriharmonic and plurisubharmonic functions 31C12 - Potential theory on Riemannian manifolds and other spaces 31C15 - Potentials and capacities on other spaces 31C20 - Discrete potential theory 31C25 - Dirichlet forms 31C35 - Martin boundary theory 31C40 - Fine potential theory; fine properties of sets and functions 31C45 - Other generalizations (nonlinear potential theory, etc.) 31C99 - Generalizations of potential theory 31Dxx - Axiomatic potential theory 31D05 - Axiomatic potential theory 31D99 - Axiomatic potential theory 31Exx - Potential theory on fractals and metric spaces 31E05 - Potential theory on fractals and metric spaces 31E99 - Potential theory on fractals and metric spaces 32-XX - Several complex variables and analytic spaces 32-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces 32-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces 32-02 - Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces 32-03 - History of several complex variables and analytic spaces 32-04 - Software, source code, etc. for problems pertaining to several complex variables and analytic spaces 32-06 - Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces 32-08 - Computational methods for problems pertaining to several complex variables and analytic spaces 32-11 - Research data for problems pertaining to several complex variables and analytic spaces 32Axx - Holomorphic functions of several complex variables 32A05 - Power series, series of functions of several complex variables 32A08 - Polynomials and rational functions of several complex variables 32A10 - Holomorphic functions of several complex variables 32A12 - Multifunctions of several complex variables 32A15 - Entire functions of several complex variables 32A17 - Special families of functions of several complex variables 32A18 - Bloch functions, normal functions of several complex variables 32A19 - Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.) 32A20 - Meromorphic functions of several complex variables 32A22 - Nevanlinna theory; growth estimates; other inequalities of several complex variables 32A25 - Integral representations; canonical kernels (Szeg?, Bergman, etc.) 32A26 - Integral representations, constructed kernels (e.g., Cauchy, Fantappi�-type kernels) 32A27 - Residues for several complex variables 32A30 - Other generalizations of function theory of one complex variable 32A35 - (H^p)-spaces, Nevanlinna spaces of functions in several complex variables 32A36 - Bergman spaces of functions in several complex variables 32A37 - Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 32A38 - Algebras of holomorphic functions of several complex variables 32A40 - Boundary behavior of holomorphic functions of several complex variables 32A45 - Hyperfunctions 32A50 - Harmonic analysis of several complex variables 32A55 - Singular integrals of functions in several complex variables 32A60 - Zero sets of holomorphic functions of several complex variables 32A65 - Banach algebra techniques applied to functions of several complex variables 32A70 - Functional analysis techniques applied to functions of several complex variables 32A99 - Holomorphic functions of several complex variables 32Bxx - Local analytic geometry 32B05 - Analytic algebras and generalizations, preparation theorems 32B10 - Germs of analytic sets, local parametrization 32B15 - Analytic subsets of affine space 32B20 - Semi-analytic sets, subanalytic sets, and generalizations 32B25 - Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions 32B99 - Local analytic geometry 32Cxx - Analytic spaces 32C05 - Real-analytic manifolds, real-analytic spaces 32C07 - Real-analytic sets, complex Nash functions 32C09 - Embedding of real-analytic manifolds 32C11 - Complex supergeometry 32C15 - Complex spaces 32C18 - Topology of analytic spaces 32C20 - Normal analytic spaces 32C22 - Embedding of analytic spaces 32C25 - Analytic subsets and submanifolds 32C30 - Integration on analytic sets and spaces, currents 32C35 - Analytic sheaves and cohomology groups 32C36 - Local cohomology of analytic spaces 32C37 - Duality theorems for analytic spaces 32C38 - Sheaves of differential operators and their modules, (D)-modules 32C55 - The Levi problem in complex spaces; generalizations 32C81 - Applications of analytic spaces to physics and other areas of science 32C99 - Analytic spaces 32Dxx - Analytic continuation 32D05 - Domains of holomorphy 32D10 - Envelopes of holomorphy 32D15 - Continuation of analytic objects in several complex variables 32D20 - Removable singularities in several complex variables 32D26 - Riemann domains 32D99 - Analytic continuation 32Exx - Holomorphic convexity 32E05 - Holomorphically convex complex spaces, reduction theory 32E10 - Stein spaces 32E20 - Polynomial convexity, rational convexity, meromorphic convexity in several complex variables 32E30 - Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs 32E35 - Global boundary behavior of holomorphic functions of several complex variables 32E40 - The Levi problem 32E99 - Holomorphic convexity 32Fxx - Geometric convexity in several complex variables 32F10 - (q)-convexity, (q)-concavity 32F17 - Other notions of convexity in relation to several complex variables 32F18 - Finite-type conditions for the boundary of a domain 32F27 - Topological consequences of geometric convexity 32F32 - Analytical consequences of geometric convexity (vanishing theorems, etc.) 32F45 - Invariant metrics and pseudodistances in several complex variables 32F99 - Geometric convexity in several complex variables 32Gxx - Deformations of analytic structures 32G05 - Deformations of complex structures 32G07 - Deformations of special (e.g., CR) structures 32G08 - Deformations of fiber bundles 32G10 - Deformations of submanifolds and subspaces 32G13 - Complex-analytic moduli problems 32G15 - Moduli of Riemann surfaces, Teichm�ller theory (complex-analytic aspects in several variables) 32G20 - Period matrices, variation of Hodge structure; degenerations 32G34 - Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) 32G81 - Applications of deformations of analytic structures to the sciences 32G99 - Deformations of analytic structures 32Hxx - Holomorphic mappings and correspondences 32H02 - Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 32H04 - Meromorphic mappings in several complex variables 32H12 - Boundary uniqueness of mappings in several complex variables 32H25 - Picard-type theorems and generalizations for several complex variables 32H30 - Value distribution theory in higher dimensions 32H35 - Proper holomorphic mappings, finiteness theorems 32H40 - Boundary regularity of mappings in several complex variables 32H50 - Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables 32H99 - Holomorphic mappings and correspondences 32Jxx - Compact analytic spaces 32J05 - Compactification of analytic spaces 32J10 - Algebraic dependence theorems 32J15 - Compact complex surfaces 32J17 - Compact complex (3)-folds 32J18 - Compact complex (n)-folds 32J25 - Transcendental methods of algebraic geometry (complex-analytic aspects) 32J27 - Compact K�hler manifolds: generalizations, classification 32J81 - Applications of compact analytic spaces to the sciences 32J99 - Compact analytic spaces 32Kxx - Generalizations of analytic spaces 32K05 - Banach analytic manifolds and spaces 32K07 - Formal and graded complex spaces 32K12 - Holomorphic maps with infinite-dimensional arguments or values 32K15 - Differentiable functions on analytic spaces, differentiable spaces 32K99 - Generalizations of analytic spaces 32Lxx - Holomorphic fiber spaces 32L05 - Holomorphic bundles and generalizations 32L10 - Sheaves and cohomology of sections of holomorphic vector bundles, general results 32L15 - Bundle convexity 32L20 - Vanishing theorems 32L25 - Twistor theory, double fibrations (complex-analytic aspects) 32L81 - Applications of holomorphic fiber spaces to the sciences 32L99 - Holomorphic fiber spaces 32Mxx - Complex spaces with a group of automorphisms 32M05 - Complex Lie groups, group actions on complex spaces 32M10 - Homogeneous complex manifolds 32M12 - Almost homogeneous manifolds and spaces 32M15 - Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) 32M17 - Automorphism groups of (mathbb{C}^n) and affine manifolds 32M18 - Automorphism groups of other complex spaces 32M25 - Complex vector fields, holomorphic foliations, (mathbb{C})-actions 32M99 - Complex spaces with a group of automorphisms 32Nxx - Automorphic functions 32N05 - General theory of automorphic functions of several complex variables 32N10 - Automorphic forms in several complex variables 32N15 - Automorphic functions in symmetric domains 32N99 - Automorphic functions 32Pxx - Non-Archimedean analysis 32P05 - Non-Archimedean analysis 32P99 - Non-Archimedean analysis 32Qxx - Complex manifolds 32Q02 - Special domains (Reinhardt, Hartogs, circular, tube, etc.) in (mathbb{C}^n) and complex manifolds 32Q05 - Negative curvature complex manifolds 32Q10 - Positive curvature complex manifolds 32Q15 - K�hler manifolds 32Q20 - K�hler-Einstein manifolds 32Q25 - Calabi-Yau theory (complex-analytic aspects) 32Q26 - Notions of stability for complex manifolds 32Q28 - Stein manifolds 32Q30 - Uniformization of complex manifolds 32Q35 - Complex manifolds as subdomains of Euclidean space 32Q40 - Embedding theorems for complex manifolds 32Q45 - Hyperbolic and Kobayashi hyperbolic manifolds 32Q55 - Topological aspects of complex manifolds 32Q56 - Oka principle and Oka manifolds 32Q57 - Classification theorems for complex manifolds 32Q60 - Almost complex manifolds 32Q65 - Pseudoholomorphic curves 32Q99 - Complex manifolds 32Sxx - Complex singularities 32S05 - Local complex singularities 32S10 - Invariants of analytic local rings 32S15 - Equisingularity (topological and analytic) 32S20 - Global theory of complex singularities; cohomological properties 32S22 - Relations with arrangements of hyperplanes 32S25 - Complex surface and hypersurface singularities 32S30 - Deformations of complex singularities; vanishing cycles 32S35 - Mixed Hodge theory of singular varieties (complex-analytic aspects) 32S40 - Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) 32S45 - Modifications; resolution of singularities (complex-analytic aspects) 32S50 - Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants 32S55 - Milnor fibration; relations with knot theory 32S60 - Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 32S65 - Singularities of holomorphic vector fields and foliations 32S70 - Other operations on complex singularities 32S99 - Complex singularities 32Txx - Pseudoconvex domains 32T05 - Domains of holomorphy 32T15 - Strongly pseudoconvex domains 32T20 - Worm domains 32T25 - Finite-type domains 32T27 - Geometric and analytic invariants on weakly pseudoconvex boundaries 32T35 - Exhaustion functions 32T40 - Peak functions 32T99 - Pseudoconvex domains 32Uxx - Pluripotential theory 32U05 - Plurisubharmonic functions and generalizations 32U10 - Plurisubharmonic exhaustion functions 32U15 - General pluripotential theory 32U20 - Capacity theory and generalizations 32U25 - Lelong numbers 32U30 - Removable sets in pluripotential theory 32U35 - Plurisubharmonic extremal functions, pluricomplex Green functions 32U40 - Currents 32U99 - Pluripotential theory 32Vxx - CR manifolds 32V05 - CR structures, CR operators, and generalizations 32V10 - CR functions 32V15 - CR manifolds as boundaries of domains 32V20 - Analysis on CR manifolds 32V25 - Extension of functions and other analytic objects from CR manifolds 32V30 - Embeddings of CR manifolds 32V35 - Finite-type conditions on CR manifolds 32V40 - Real submanifolds in complex manifolds 32V99 - CR manifolds 32Wxx - Differential operators in several variables 32W05 - (overlinepartial) and (overlinepartial)-Neumann operators 32W10 - (overlinepartial_b) and (overlinepartial_b)-Neumann operators 32W20 - Complex Monge-Amp�re operators 32W25 - Pseudodifferential operators in several complex variables 32W30 - Heat kernels in several complex variables 32W50 - Other partial differential equations of complex analysis in several variables 32W99 - Differential operators in several variables 33-XX - Special functions 33-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions 33-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions 33-02 - Research exposition (monographs, survey articles) pertaining to special functions 33-03 - History of special functions 33-04 - Software, source code, etc. for problems pertaining to special functions 33-06 - Proceedings, conferences, collections, etc. pertaining to special functions 33-11 - Research data for problems pertaining to special functions 33Bxx - Elementary classical functions 33B10 - Exponential and trigonometric functions 33B15 - Gamma, beta and polygamma functions 33B20 - Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) 33B30 - Higher logarithm functions 33B99 - Elementary classical functions 33Cxx - Hypergeometric functions 33C05 - Classical hypergeometric functions, ({}_2F_1) 33C10 - Bessel and Airy functions, cylinder functions, ({}_0F_1) 33C15 - Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) 33C20 - Generalized hypergeometric series, ({}_pF_q) 33C45 - Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 33C47 - Other special orthogonal polynomials and functions 33C50 - Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable 33C52 - Orthogonal polynomials and functions associated with root systems 33C55 - Spherical harmonics 33C60 - Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) 33C65 - Appell, Horn and Lauricella functions 33C67 - Hypergeometric functions associated with root systems 33C70 - Other hypergeometric functions and integrals in several variables 33C75 - Elliptic integrals as hypergeometric functions 33C80 - Connections of hypergeometric functions with groups and algebras, and related topics 33C90 - Applications of hypergeometric functions 33C99 - Hypergeometric functions 33Dxx - Basic hypergeometric functions 33D05 - (q)-gamma functions, (q)-beta functions and integrals 33D15 - Basic hypergeometric functions in one variable, ({}_rphi_s) 33D45 - Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D50 - Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 33D52 - Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) 33D60 - Basic hypergeometric integrals and functions defined by them 33D65 - Bibasic functions and multiple bases 33D67 - Basic hypergeometric functions associated with root systems 33D70 - Other basic hypergeometric functions and integrals in several variables 33D80 - Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics 33D90 - Applications of basic hypergeometric functions 33D99 - Basic hypergeometric functions 33Exx - Other special functions 33E05 - Elliptic functions and integrals 33E10 - Lam�, Mathieu, and spheroidal wave functions 33E12 - Mittag-Leffler functions and generalizations 33E15 - Other wave functions 33E17 - Painlev�-type functions 33E20 - Other functions defined by series and integrals 33E30 - Other functions coming from differential, difference and integral equations 33E50 - Special functions in characteristic (p) (gamma functions, etc.) 33E99 - Other special functions 33Fxx - Computational aspects of special functions 33F05 - Numerical approximation and evaluation of special functions 33F10 - Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) 33F99 - Computational aspects of special functions 34-XX - Ordinary differential equations 34-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations 34-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations 34-02 - Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34-03 - History of ordinary differential equations 34-04 - Software, source code, etc. for problems pertaining to ordinary differential equations 34-06 - Proceedings, conferences, collections, etc. pertaining to ordinary differential equations 34-11 - Research data for problems pertaining to ordinary differential equations 34Axx - General theory for ordinary differential equations 34A05 - Explicit solutions, first integrals of ordinary differential equations 34A06 - Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) 34A07 - Fuzzy ordinary differential equations 34A08 - Fractional ordinary differential equations 34A09 - Implicit ordinary differential equations, differential-algebraic equations 34A12 - Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A25 - Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A26 - Geometric methods in ordinary differential equations 34A30 - Linear ordinary differential equations and systems 34A33 - Ordinary lattice differential equations 34A34 - Nonlinear ordinary differential equations and systems 34A35 - Ordinary differential equations of infinite order 34A36 - Discontinuous ordinary differential equations 34A37 - Ordinary differential equations with impulses 34A38 - Hybrid systems of ordinary differential equations 34A40 - Differential inequalities involving functions of a single real variable 34A45 - Theoretical approximation of solutions to ordinary differential equations 34A55 - Inverse problems involving ordinary differential equations 34A60 - Ordinary differential inclusions 34A99 - General theory for ordinary differential equations 34Bxx - Boundary value problems for ordinary differential equations 34B05 - Linear boundary value problems for ordinary differential equations 34B07 - Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter 34B08 - Parameter dependent boundary value problems for ordinary differential equations 34B09 - Boundary eigenvalue problems for ordinary differential equations 34B10 - Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 - Nonlinear boundary value problems for ordinary differential equations 34B16 - Singular nonlinear boundary value problems for ordinary differential equations 34B18 - Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B20 - Weyl theory and its generalizations for ordinary differential equations 34B24 - Sturm-Liouville theory 34B27 - Green's functions for ordinary differential equations 34B30 - Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34B37 - Boundary value problems with impulses for ordinary differential equations 34B40 - Boundary value problems on infinite intervals for ordinary differential equations 34B45 - Boundary value problems on graphs and networks for ordinary differential equations 34B60 - Applications of boundary value problems involving ordinary differential equations 34B99 - Boundary value problems for ordinary differential equations 34Cxx - Qualitative theory for ordinary differential equations 34C05 - Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C07 - Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations 34C08 - Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 34C10 - Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C11 - Growth and boundedness of solutions to ordinary differential equations 34C12 - Monotone systems involving ordinary differential equations 34C14 - Symmetries, invariants of ordinary differential equations 34C15 - Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C20 - Transformation and reduction of ordinary differential equations and systems, normal forms 34C23 - Bifurcation theory for ordinary differential equations 34C25 - Periodic solutions to ordinary differential equations 34C26 - Relaxation oscillations for ordinary differential equations 34C27 - Almost and pseudo-almost periodic solutions to ordinary differential equations 34C28 - Complex behavior and chaotic systems of ordinary differential equations 34C29 - Averaging method for ordinary differential equations 34C37 - Homoclinic and heteroclinic solutions to ordinary differential equations 34C40 - Ordinary differential equations and systems on manifolds 34C41 - Equivalence and asymptotic equivalence of ordinary differential equations 34C45 - Invariant manifolds for ordinary differential equations 34C46 - Multifrequency systems of ordinary differential equations 34C55 - Hysteresis for ordinary differential equations 34C60 - Qualitative investigation and simulation of ordinary differential equation models 34C99 - Qualitative theory for ordinary differential equations 34Dxx - Stability theory for ordinary differential equations 34D05 - Asymptotic properties of solutions to ordinary differential equations 34D06 - Synchronization of solutions to ordinary differential equations 34D08 - Characteristic and Lyapunov exponents of ordinary differential equations 34D09 - Dichotomy, trichotomy of solutions to ordinary differential equations 34D10 - Perturbations of ordinary differential equations 34D15 - Singular perturbations of ordinary differential equations 34D20 - Stability of solutions to ordinary differential equations 34D23 - Global stability of solutions to ordinary differential equations 34D30 - Structural stability and analogous concepts of solutions to ordinary differential equations 34D35 - Stability of manifolds of solutions to ordinary differential equations 34D45 - Attractors of solutions to ordinary differential equations 34D99 - Stability theory for ordinary differential equations 34Exx - Asymptotic theory for ordinary differential equations 34E05 - Asymptotic expansions of solutions to ordinary differential equations 34E10 - Perturbations, asymptotics of solutions to ordinary differential equations 34E13 - Multiple scale methods for ordinary differential equations 34E15 - Singular perturbations for ordinary differential equations 34E17 - Canard solutions to ordinary differential equations 34E18 - Methods of nonstandard analysis for ordinary differential equations 34E20 - Singular perturbations, turning point theory, WKB methods for ordinary differential equations 34E99 - Asymptotic theory for ordinary differential equations 34Fxx - Ordinary differential equations and systems with randomness 34F05 - Ordinary differential equations and systems with randomness 34F10 - Bifurcation of solutions to ordinary differential equations involving randomness 34F15 - Resonance phenomena for ordinary differential equations involving randomness 34F99 - Ordinary differential equations and systems with randomness 34Gxx - Differential equations in abstract spaces 34G10 - Linear differential equations in abstract spaces 34G20 - Nonlinear differential equations in abstract spaces 34G25 - Evolution inclusions 34G99 - Differential equations in abstract spaces 34Hxx - Control problems involving ordinary differential equations 34H05 - Control problems involving ordinary differential equations 34H10 - Chaos control for problems involving ordinary differential equations 34H15 - Stabilization of solutions to ordinary differential equations 34H20 - Bifurcation control of ordinary differential equations 34H99 - Control problems involving ordinary differential equations 34Kxx - Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34K04 - Symmetries, invariants of functional-differential equations 34K05 - General theory of functional-differential equations 34K06 - Linear functional-differential equations 34K07 - Theoretical approximation of solutions to functional-differential equations 34K08 - Spectral theory of functional-differential operators 34K09 - Functional-differential inclusions 34K10 - Boundary value problems for functional-differential equations 34K11 - Oscillation theory of functional-differential equations 34K12 - Growth, boundedness, comparison of solutions to functional-differential equations 34K13 - Periodic solutions to functional-differential equations 34K14 - Almost and pseudo-almost periodic solutions to functional-differential equations 34K16 - Heteroclinic and homoclinic orbits of functional-differential equations 34K17 - Transformation and reduction of functional-differential equations and systems, normal forms 34K18 - Bifurcation theory of functional-differential equations 34K19 - Invariant manifolds of functional-differential equations 34K20 - Stability theory of functional-differential equations 34K21 - Stationary solutions of functional-differential equations 34K23 - Complex (chaotic) behavior of solutions to functional-differential equations 34K24 - Synchronization of functional-differential equations 34K25 - Asymptotic theory of functional-differential equations 34K26 - Singular perturbations of functional-differential equations 34K27 - Perturbations of functional-differential equations 34K29 - Inverse problems for functional-differential equations 34K30 - Functional-differential equations in abstract spaces 34K31 - Lattice functional-differential equations 34K32 - Implicit functional-differential equations 34K33 - Averaging for functional-differential equations 34K34 - Hybrid systems of functional-differential equations 34K35 - Control problems for functional-differential equations 34K36 - Fuzzy functional-differential equations 34K37 - Functional-differential equations with fractional derivatives 34K38 - Functional-differential inequalities 34K39 - Discontinuous functional-differential equations 34K40 - Neutral functional-differential equations 34K41 - Functional-differential equations in the complex domain 34K42 - Functional-differential equations on time scales or measure chains 34K43 - Functional-differential equations with state-dependent arguments 34K45 - Functional-differential equations with impulses 34K50 - Stochastic functional-differential equations 34K60 - Qualitative investigation and simulation of models involving functional-differential equations 34K99 - Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34Lxx - Ordinary differential operators 34L05 - General spectral theory of ordinary differential operators 34L10 - Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators 34L15 - Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators 34L16 - Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators 34L20 - Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators 34L25 - Scattering theory, inverse scattering involving ordinary differential operators 34L30 - Nonlinear ordinary differential operators 34L40 - Particular ordinary differential operators (Dirac, one-dimensional Schr�dinger, etc.) 34L99 - Ordinary differential operators 34Mxx - Ordinary differential equations in the complex domain 34M03 - Linear ordinary differential equations and systems in the complex domain 34M04 - Nonlinear ordinary differential equations and systems in the complex domain 34M05 - Entire and meromorphic solutions to ordinary differential equations in the complex domain 34M10 - Oscillation, growth of solutions to ordinary differential equations in the complex domain 34M15 - Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain 34M25 - Formal solutions and transform techniques for ordinary differential equations in the complex domain 34M30 - Asymptotics and summation methods for ordinary differential equations in the complex domain 34M35 - Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms 34M40 - Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain 34M45 - Ordinary differential equations on complex manifolds 34M46 - Spectral theory for ordinary differential operators in the complex domain 34M50 - Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain 34M55 - Painlev� and other special ordinary differential equations in the complex domain; classification, hierarchies 34M56 - Isomonodromic deformations for ordinary differential equations in the complex domain 34M60 - Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) 34M65 - Topological structure of trajectories of ordinary differential equations in the complex domain 34M99 - Ordinary differential equations in the complex domain 34Nxx - Dynamic equations on time scales or measure chains 34N05 - Dynamic equations on time scales or measure chains 34N99 - Dynamic equations on time scales or measure chains 35-XX - Partial differential equations 35-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations 35-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations 35-02 - Research exposition (monographs, survey articles) pertaining to partial differential equations 35-03 - History of partial differential equations 35-04 - Software, source code, etc. for problems pertaining to partial differential equations 35-06 - Proceedings, conferences, collections, etc. pertaining to partial differential equations 35-11 - Research data for problems pertaining to partial differential equations 35Axx - General topics in partial differential equations 35A01 - Existence problems for PDEs: global existence, local existence, non-existence 35A02 - Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35A08 - Fundamental solutions to PDEs 35A09 - Classical solutions to PDEs 35A10 - Cauchy-Kovalevskaya theorems 35A15 - Variational methods applied to PDEs 35A16 - Topological and monotonicity methods applied to PDEs 35A17 - Parametrices in context of PDEs 35A18 - Wave front sets in context of PDEs 35A20 - Analyticity in context of PDEs 35A21 - Singularity in context of PDEs 35A22 - Transform methods (e.g., integral transforms) applied to PDEs 35A23 - Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals 35A24 - Methods of ordinary differential equations applied to PDEs 35A25 - Other special methods applied to PDEs 35A27 - Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs 35A30 - Geometric theory, characteristics, transformations in context of PDEs 35A35 - Theoretical approximation in context of PDEs 35A99 - General topics in partial differential equations 35Bxx - Qualitative properties of solutions to partial differential equations 35B05 - Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B06 - Symmetries, invariants, etc. in context of PDEs 35B07 - Axially symmetric solutions to PDEs 35B08 - Entire solutions to PDEs 35B09 - Positive solutions to PDEs 35B10 - Periodic solutions to PDEs 35B15 - Almost and pseudo-almost periodic solutions to PDEs 35B20 - Perturbations in context of PDEs 35B25 - Singular perturbations in context of PDEs 35B27 - Homogenization in context of PDEs; PDEs in media with periodic structure 35B30 - Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B32 - Bifurcations in context of PDEs 35B33 - Critical exponents in context of PDEs 35B34 - Resonance in context of PDEs 35B35 - Stability in context of PDEs 35B36 - Pattern formations in context of PDEs 35B38 - Critical points of functionals in context of PDEs (e.g., energy functionals) 35B40 - Asymptotic behavior of solutions to PDEs 35B41 - Attractors 35B42 - Inertial manifolds 35B44 - Blow-up in context of PDEs 35B45 - A priori estimates in context of PDEs 35B50 - Maximum principles in context of PDEs 35B51 - Comparison principles in context of PDEs 35B53 - Liouville theorems and Phragm�n-Lindel�f theorems in context of PDEs 35B60 - Continuation and prolongation of solutions to PDEs 35B65 - Smoothness and regularity of solutions to PDEs 35B99 - Qualitative properties of solutions to partial differential equations 35Cxx - Representations of solutions to partial differential equations 35C05 - Solutions to PDEs in closed form 35C06 - Self-similar solutions to PDEs 35C07 - Traveling wave solutions 35C08 - Soliton solutions 35C09 - Trigonometric solutions to PDEs 35C10 - Series solutions to PDEs 35C11 - Polynomial solutions to PDEs 35C15 - Integral representations of solutions to PDEs 35C20 - Asymptotic expansions of solutions to PDEs 35C99 - Representations of solutions to partial differential equations 35Dxx - Generalized solutions to partial differential equations 35D30 - Weak solutions to PDEs 35D35 - Strong solutions to PDEs 35D40 - Viscosity solutions to PDEs 35D99 - Generalized solutions to partial differential equations 35Exx - Partial differential equations and systems of partial differential equations with constant coefficients 35E05 - Fundamental solutions to PDEs and systems of PDEs with constant coefficients 35E10 - Convexity properties of solutions to PDEs with constant coefficients 35E15 - Initial value problems for PDEs and systems of PDEs with constant coefficients 35E20 - General theory of PDEs and systems of PDEs with constant coefficients 35E99 - Partial differential equations and systems of partial differential equations with constant coefficients 35Fxx - General first-order partial differential equations and systems of first-order partial differential equations 35F05 - Linear first-order PDEs 35F10 - Initial value problems for linear first-order PDEs 35F15 - Boundary value problems for linear first-order PDEs 35F16 - Initial-boundary value problems for linear first-order PDEs 35F20 - Nonlinear first-order PDEs 35F21 - Hamilton-Jacobi equations 35F25 - Initial value problems for nonlinear first-order PDEs 35F30 - Boundary value problems for nonlinear first-order PDEs 35F31 - Initial-boundary value problems for nonlinear first-order PDEs 35F35 - Systems of linear first-order PDEs 35F40 - Initial value problems for systems of linear first-order PDEs 35F45 - Boundary value problems for systems of linear first-order PDEs 35F46 - Initial-boundary value problems for systems of linear first-order PDEs 35F50 - Systems of nonlinear first-order PDEs 35F55 - Initial value problems for systems of nonlinear first-order PDEs 35F60 - Boundary value problems for systems of nonlinear first-order PDEs 35F61 - Initial-boundary value problems for systems of nonlinear first-order PDEs 35F99 - General first-order partial differential equations and systems of first-order partial differential equations 35Gxx - General higher-order partial differential equations and systems of higher-order partial differential equations 35G05 - Linear higher-order PDEs 35G10 - Initial value problems for linear higher-order PDEs 35G15 - Boundary value problems for linear higher-order PDEs 35G16 - Initial-boundary value problems for linear higher-order PDEs 35G20 - Nonlinear higher-order PDEs 35G25 - Initial value problems for nonlinear higher-order PDEs 35G30 - Boundary value problems for nonlinear higher-order PDEs 35G31 - Initial-boundary value problems for nonlinear higher-order PDEs 35G35 - Systems of linear higher-order PDEs 35G40 - Initial value problems for systems of linear higher-order PDEs 35G45 - Boundary value problems for systems of linear higher-order PDEs 35G46 - Initial-boundary value problems for systems of linear higher-order PDEs 35G50 - Systems of nonlinear higher-order PDEs 35G55 - Initial value problems for systems of nonlinear higher-order PDEs 35G60 - Boundary value problems for systems of nonlinear higher-order PDEs 35G61 - Initial-boundary value problems for systems of nonlinear higher-order PDEs 35G99 - General higher-order partial differential equations and systems of higher-order partial differential equations 35Hxx - Close-to-elliptic equations 35H10 - Hypoelliptic equations 35H20 - Subelliptic equations 35H30 - Quasielliptic equations 35H99 - Close-to-elliptic equations 35Jxx - Elliptic equations and elliptic systems 35J05 - Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35J08 - Green's functions for elliptic equations 35J10 - Schr�dinger operator, Schr�dinger equation 35J15 - Second-order elliptic equations 35J20 - Variational methods for second-order elliptic equations 35J25 - Boundary value problems for second-order elliptic equations 35J30 - Higher-order elliptic equations 35J35 - Variational methods for higher-order elliptic equations 35J40 - Boundary value problems for higher-order elliptic equations 35J46 - First-order elliptic systems 35J47 - Second-order elliptic systems 35J48 - Higher-order elliptic systems 35J50 - Variational methods for elliptic systems 35J56 - Boundary value problems for first-order elliptic systems 35J57 - Boundary value problems for second-order elliptic systems 35J58 - Boundary value problems for higher-order elliptic systems 35J60 - Nonlinear elliptic equations 35J61 - Semilinear elliptic equations 35J62 - Quasilinear elliptic equations 35J65 - Nonlinear boundary value problems for linear elliptic equations 35J66 - Nonlinear boundary value problems for nonlinear elliptic equations 35J67 - Boundary values of solutions to elliptic equations and elliptic systems 35J70 - Degenerate elliptic equations 35J75 - Singular elliptic equations 35J86 - Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators 35J87 - Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators 35J88 - Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators 35J91 - Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian 35J92 - Quasilinear elliptic equations with (p)-Laplacian 35J93 - Quasilinear elliptic equations with mean curvature operator 35J94 - Elliptic equations with infinity-Laplacian 35J96 - Monge-Amp�re equations 35J99 - Elliptic equations and elliptic systems 35Kxx - Parabolic equations and parabolic systems 35K05 - Heat equation 35K08 - Heat kernel 35K10 - Second-order parabolic equations 35K15 - Initial value problems for second-order parabolic equations 35K20 - Initial-boundary value problems for second-order parabolic equations 35K25 - Higher-order parabolic equations 35K30 - Initial value problems for higher-order parabolic equations 35K35 - Initial-boundary value problems for higher-order parabolic equations 35K40 - Second-order parabolic systems 35K41 - Higher-order parabolic systems 35K45 - Initial value problems for second-order parabolic systems 35K46 - Initial value problems for higher-order parabolic systems 35K51 - Initial-boundary value problems for second-order parabolic systems 35K52 - Initial-boundary value problems for higher-order parabolic systems 35K55 - Nonlinear parabolic equations 35K57 - Reaction-diffusion equations 35K58 - Semilinear parabolic equations 35K59 - Quasilinear parabolic equations 35K60 - Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35K61 - Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 35K65 - Degenerate parabolic equations 35K67 - Singular parabolic equations 35K70 - Ultraparabolic equations, pseudoparabolic equations, etc. 35K85 - Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators 35K86 - Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators 35K87 - Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators 35K90 - Abstract parabolic equations 35K91 - Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian 35K92 - Quasilinear parabolic equations with (p)-Laplacian 35K93 - Quasilinear parabolic equations with mean curvature operator 35K96 - Parabolic Monge-Amp�re equations 35K99 - Parabolic equations and parabolic systems 35Lxx - Hyperbolic equations and hyperbolic systems 35L02 - First-order hyperbolic equations 35L03 - Initial value problems for first-order hyperbolic equations 35L04 - Initial-boundary value problems for first-order hyperbolic equations 35L05 - Wave equation 35L10 - Second-order hyperbolic equations 35L15 - Initial value problems for second-order hyperbolic equations 35L20 - Initial-boundary value problems for second-order hyperbolic equations 35L25 - Higher-order hyperbolic equations 35L30 - Initial value problems for higher-order hyperbolic equations 35L35 - Initial-boundary value problems for higher-order hyperbolic equations 35L40 - First-order hyperbolic systems 35L45 - Initial value problems for first-order hyperbolic systems 35L50 - Initial-boundary value problems for first-order hyperbolic systems 35L51 - Second-order hyperbolic systems 35L52 - Initial value problems for second-order hyperbolic systems 35L53 - Initial-boundary value problems for second-order hyperbolic systems 35L55 - Higher-order hyperbolic systems 35L56 - Initial value problems for higher-order hyperbolic systems 35L57 - Initial-boundary value problems for higher-order hyperbolic systems 35L60 - First-order nonlinear hyperbolic equations 35L65 - Hyperbolic conservation laws 35L67 - Shocks and singularities for hyperbolic equations 35L70 - Second-order nonlinear hyperbolic equations 35L71 - Second-order semilinear hyperbolic equations 35L72 - Second-order quasilinear hyperbolic equations 35L75 - Higher-order nonlinear hyperbolic equations 35L76 - Higher-order semilinear hyperbolic equations 35L77 - Higher-order quasilinear hyperbolic equations 35L80 - Degenerate hyperbolic equations 35L81 - Singular hyperbolic equations 35L82 - Pseudohyperbolic equations 35L85 - Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators 35L86 - Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators 35L87 - Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators 35L90 - Abstract hyperbolic equations 35L99 - Hyperbolic equations and hyperbolic systems 35Mxx - Partial differential equations of mixed type and mixed-type systems of partial differential equations 35M10 - PDEs of mixed type 35M11 - Initial value problems for PDEs of mixed type 35M12 - Boundary value problems for PDEs of mixed type 35M13 - Initial-boundary value problems for PDEs of mixed type 35M30 - Mixed-type systems of PDEs 35M31 - Initial value problems for mixed-type systems of PDEs 35M32 - Boundary value problems for mixed-type systems of PDEs 35M33 - Initial-boundary value problems for mixed-type systems of PDEs 35M85 - Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type 35M86 - Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type 35M87 - Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type 35M99 - Partial differential equations of mixed type and mixed-type systems of partial differential equations 35Nxx - Overdetermined problems for partial differential equations and systems of partial differential equations 35N05 - Overdetermined systems of PDEs with constant coefficients 35N10 - Overdetermined systems of PDEs with variable coefficients 35N15 - (overlinepartial)-Neumann problems and formal complexes in context of PDEs 35N20 - Overdetermined initial value problems for PDEs and systems of PDEs 35N25 - Overdetermined boundary value problems for PDEs and systems of PDEs 35N30 - Overdetermined initial-boundary value problems for PDEs and systems of PDEs 35N99 - Overdetermined problems for partial differential equations and systems of partial differential equations 35Pxx - Spectral theory and eigenvalue problems for partial differential equations 35P05 - General topics in linear spectral theory for PDEs 35P10 - Completeness of eigenfunctions and eigenfunction expansions in context of PDEs 35P15 - Estimates of eigenvalues in context of PDEs 35P20 - Asymptotic distributions of eigenvalues in context of PDEs 35P25 - Scattering theory for PDEs 35P30 - Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35P99 - Spectral theory and eigenvalue problems for partial differential equations 35Qxx - Partial differential equations of mathematical physics and other areas of application 35Q05 - Euler-Poisson-Darboux equations 35Q07 - Fuchsian PDEs 35Q15 - Riemann-Hilbert problems in context of PDEs 35Q20 - Boltzmann equations 35Q30 - Navier-Stokes equations 35Q31 - Euler equations 35Q35 - PDEs in connection with fluid mechanics 35Q40 - PDEs in connection with quantum mechanics 35Q41 - Time-dependent Schr�dinger equations and Dirac equations 35Q49 - Transport equations 35Q51 - Soliton equations 35Q53 - KdV equations (Korteweg-de Vries equations) 35Q55 - NLS equations (nonlinear Schr�dinger equations) 35Q56 - Ginzburg-Landau equations 35Q60 - PDEs in connection with optics and electromagnetic theory 35Q61 - Maxwell equations 35Q62 - PDEs in connection with statistics 35Q68 - PDEs in connection with computer science 35Q70 - PDEs in connection with mechanics of particles and systems of particles 35Q74 - PDEs in connection with mechanics of deformable solids 35Q75 - PDEs in connection with relativity and gravitational theory 35Q76 - Einstein equations 35Q79 - PDEs in connection with classical thermodynamics and heat transfer 35Q81 - PDEs in connection with semiconductor devices 35Q82 - PDEs in connection with statistical mechanics 35Q83 - Vlasov equations 35Q84 - Fokker-Planck equations 35Q85 - PDEs in connection with astronomy and astrophysics 35Q86 - PDEs in connection with geophysics 35Q89 - PDEs in connection with mean field game theory 35Q90 - PDEs in connection with mathematical programming 35Q91 - PDEs in connection with game theory, economics, social and behavioral sciences 35Q92 - PDEs in connection with biology, chemistry and other natural sciences 35Q93 - PDEs in connection with control and optimization 35Q94 - PDEs in connection with information and communication 35Q99 - Partial differential equations of mathematical physics and other areas of application 35Rxx - Miscellaneous topics in partial differential equations 35R01 - PDEs on manifolds 35R02 - PDEs on graphs and networks (ramified or polygonal spaces) 35R03 - PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. 35R05 - PDEs with low regular coefficients and/or low regular data 35R06 - PDEs with measure 35R07 - PDEs on time scales 35R09 - Integro-partial differential equations 35R10 - Partial functional-differential equations 35R11 - Fractional partial differential equations 35R12 - Impulsive partial differential equations 35R13 - Fuzzy partial differential equations 35R15 - PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) 35R20 - Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) 35R25 - Ill-posed problems for PDEs 35R30 - Inverse problems for PDEs 35R35 - Free boundary problems for PDEs 35R37 - Moving boundary problems for PDEs 35R45 - Partial differential inequalities and systems of partial differential inequalities 35R50 - PDEs of infinite order 35R60 - PDEs with randomness, stochastic partial differential equations 35R70 - PDEs with multivalued right-hand sides 35R99 - Miscellaneous topics in partial differential equations 35Sxx - Pseudodifferential operators and other generalizations of partial differential operators 35S05 - Pseudodifferential operators as generalizations of partial differential operators 35S10 - Initial value problems for PDEs with pseudodifferential operators 35S15 - Boundary value problems for PDEs with pseudodifferential operators 35S16 - Initial-boundary value problems for PDEs with pseudodifferential operators 35S30 - Fourier integral operators applied to PDEs 35S35 - Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc. 35S50 - Paradifferential operators as generalizations of partial differential operators in context of PDEs 35S99 - Pseudodifferential operators and other generalizations of partial differential operators 37-XX - Dynamical systems and ergodic theory 37-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to dynamical systems and ergodic theory 37-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory 37-02 - Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory 37-03 - History of dynamical systems and ergodic theory 37-04 - Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory 37-06 - Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory 37-11 - Research data for problems pertaining to dynamical systems and ergodic theory 37Axx - Ergodic theory 37A05 - Dynamical aspects of measure-preserving transformations 37A10 - Dynamical systems involving one-parameter continuous families of measure-preserving transformations 37A15 - General groups of measure-preserving transformations and dynamical systems 37A17 - Homogeneous flows 37A20 - Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations 37A25 - Ergodicity, mixing, rates of mixing 37A30 - Ergodic theorems, spectral theory, Markov operators 37A35 - Entropy and other invariants, isomorphism, classification in ergodic theory 37A40 - Nonsingular (and infinite-measure preserving) transformations 37A44 - Relations between ergodic theory and number theory 37A46 - Relations between ergodic theory and harmonic analysis 37A50 - Dynamical systems and their relations with probability theory and stochastic processes 37A55 - Dynamical systems and the theory of (C^*)-algebras 37A60 - Dynamical aspects of statistical mechanics 37A99 - Ergodic theory 37Bxx - Topological dynamics 37B02 - Dynamics in general topological spaces 37B05 - Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 37B10 - Symbolic dynamics 37B15 - Dynamical aspects of cellular automata 37B20 - Notions of recurrence and recurrent behavior in topological dynamical systems 37B25 - Stability of topological dynamical systems 37B30 - Index theory for dynamical systems, Morse-Conley indices 37B35 - Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems 37B40 - Topological entropy 37B45 - Continua theory in dynamics 37B51 - Multidimensional shifts of finite type 37B52 - Tiling dynamics 37B55 - Topological dynamics of nonautonomous systems 37B65 - Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems 37B99 - Topological dynamics 37Cxx - Smooth dynamical systems: general theory 37C05 - Dynamical systems involving smooth mappings and diffeomorphisms 37C10 - Dynamics induced by flows and semiflows 37C15 - Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 37C20 - Generic properties, structural stability of dynamical systems 37C25 - Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 37C27 - Periodic orbits of vector fields and flows 37C29 - Homoclinic and heteroclinic orbits for dynamical systems 37C30 - Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 37C35 - Orbit growth in dynamical systems 37C40 - Smooth ergodic theory, invariant measures for smooth dynamical systems 37C45 - Dimension theory of smooth dynamical systems 37C50 - Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics 37C55 - Periodic and quasi-periodic flows and diffeomorphisms 37C60 - Nonautonomous smooth dynamical systems 37C65 - Monotone flows as dynamical systems 37C70 - Attractors and repellers of smooth dynamical systems and their topological structure 37C75 - Stability theory for smooth dynamical systems 37C79 - Symmetries and invariants of dynamical systems 37C81 - Equivariant dynamical systems 37C83 - Dynamical systems with singularities (billiards, etc.) 37C85 - Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) 37C86 - Foliations generated by dynamical systems 37C99 - Smooth dynamical systems: general theory 37Dxx - Dynamical systems with hyperbolic behavior 37D05 - Dynamical systems with hyperbolic orbits and sets 37D10 - Invariant manifold theory for dynamical systems 37D15 - Morse-Smale systems 37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37D30 - Partially hyperbolic systems and dominated splittings 37D35 - Thermodynamic formalism, variational principles, equilibrium states for dynamical systems 37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 37D45 - Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37D99 - Dynamical systems with hyperbolic behavior 37Exx - Low-dimensional dynamical systems 37E05 - Dynamical systems involving maps of the interval 37E10 - Dynamical systems involving maps of the circle 37E15 - Combinatorial dynamics (types of periodic orbits) 37E20 - Universality and renormalization of dynamical systems 37E25 - Dynamical systems involving maps of trees and graphs 37E30 - Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37E35 - Flows on surfaces 37E40 - Dynamical aspects of twist maps 37E45 - Rotation numbers and vectors 37E99 - Low-dimensional dynamical systems 37Fxx - Dynamical systems over complex numbers 37F05 - Dynamical systems involving relations and correspondences in one complex variable 37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets 37F12 - Critical orbits for holomorphic dynamical systems 37F15 - Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems 37F20 - Combinatorics and topology in relation with holomorphic dynamical systems 37F25 - Renormalization of holomorphic dynamical systems 37F31 - Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics 37F32 - Fuchsian and Kleinian groups as dynamical systems 37F34 - Teichm�ller theory; moduli spaces of holomorphic dynamical systems 37F35 - Conformal densities and Hausdorff dimension for holomorphic dynamical systems 37F40 - Geometric limits in holomorphic dynamics 37F44 - Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps 37F46 - Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets 37F50 - Small divisors, rotation domains and linearization in holomorphic dynamics 37F75 - Dynamical aspects of holomorphic foliations and vector fields 37F80 - Higher-dimensional holomorphic and meromorphic dynamics 37F99 - Dynamical systems over complex numbers 37Gxx - Local and nonlocal bifurcation theory for dynamical systems 37G05 - Normal forms for dynamical systems 37G10 - Bifurcations of singular points in dynamical systems 37G15 - Bifurcations of limit cycles and periodic orbits in dynamical systems 37G20 - Hyperbolic singular points with homoclinic trajectories in dynamical systems 37G25 - Bifurcations connected with nontransversal intersection in dynamical systems 37G30 - Infinite nonwandering sets arising in bifurcations of dynamical systems 37G35 - Dynamical aspects of attractors and their bifurcations 37G40 - Dynamical aspects of symmetries, equivariant bifurcation theory 37G99 - Local and nonlocal bifurcation theory for dynamical systems 37Hxx - Random dynamical systems 37H05 - General theory of random and stochastic dynamical systems 37H10 - Generation, random and stochastic difference and differential equations 37H12 - Random iteration 37H15 - Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents 37H20 - Bifurcation theory for random and stochastic dynamical systems 37H30 - Stability theory for random and stochastic dynamical systems 37H99 - Random dynamical systems 37Jxx - Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37J06 - General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants 37J11 - Symplectic and canonical mappings 37J12 - Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems 37J20 - Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems 37J25 - Stability problems for finite-dimensional Hamiltonian and Lagrangian systems 37J30 - Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) 37J35 - Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37J37 - Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures 37J38 - Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions 37J39 - Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) 37J40 - Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion 37J46 - Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems 37J51 - Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods 37J55 - Contact systems 37J60 - Nonholonomic dynamical systems 37J65 - Nonautonomous Hamiltonian dynamical systems (Painlev� equations, etc.) 37J70 - Completely integrable discrete dynamical systems 37J99 - Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37Kxx - Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems 37K06 - General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws 37K10 - Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K15 - Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 37K20 - Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions 37K25 - Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry 37K30 - Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures 37K35 - Lie-B�cklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 37K40 - Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 37K45 - Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems 37K50 - Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 37K55 - Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems 37K58 - Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems 37K60 - Lattice dynamics; integrable lattice equations 37K65 - Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics 37K99 - Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems 37Lxx - Infinite-dimensional dissipative dynamical systems 37L05 - General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 37L10 - Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems 37L15 - Stability problems for infinite-dimensional dissipative dynamical systems 37L20 - Symmetries of infinite-dimensional dissipative dynamical systems 37L25 - Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 37L30 - Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 37L40 - Invariant measures for infinite-dimensional dissipative dynamical systems 37L45 - Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems 37L50 - Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems 37L55 - Infinite-dimensional random dynamical systems; stochastic equations 37L60 - Lattice dynamics and infinite-dimensional dissipative dynamical systems 37L65 - Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems 37L99 - Infinite-dimensional dissipative dynamical systems 37Mxx - Approximation methods and numerical treatment of dynamical systems 37M05 - Simulation of dynamical systems 37M10 - Time series analysis of dynamical systems 37M15 - Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems 37M20 - Computational methods for bifurcation problems in dynamical systems 37M21 - Computational methods for invariant manifolds of dynamical systems 37M22 - Computational methods for attractors of dynamical systems 37M25 - Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) 37M99 - Approximation methods and numerical treatment of dynamical systems 37Nxx - Applications of dynamical systems 37N05 - Dynamical systems in classical and celestial mechanics 37N10 - Dynamical systems in fluid mechanics, oceanography and meteorology 37N15 - Dynamical systems in solid mechanics 37N20 - Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 37N25 - Dynamical systems in biology 37N30 - Dynamical systems in numerical analysis 37N35 - Dynamical systems in control 37N40 - Dynamical systems in optimization and economics 37N99 - Applications of dynamical systems 37Pxx - Arithmetic and non-Archimedean dynamical systems 37P05 - Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 37P10 - Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps 37P15 - Dynamical systems over global ground fields 37P20 - Dynamical systems over non-Archimedean local ground fields 37P25 - Dynamical systems over finite ground fields 37P30 - Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems 37P35 - Arithmetic properties of periodic points 37P40 - Non-Archimedean Fatou and Julia sets 37P45 - Families and moduli spaces in arithmetic and non-Archimedean dynamical systems 37P50 - Dynamical systems on Berkovich spaces 37P55 - Arithmetic dynamics on general algebraic varieties 37P99 - Arithmetic and non-Archimedean dynamical systems 39-XX - Difference and functional equations 39-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to difference and functional equations 39-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations 39-02 - Research exposition (monographs, survey articles) pertaining to difference and functional equations 39-03 - History of difference and functional equations 39-04 - Software, source code, etc. for problems pertaining to difference and functional equations 39-06 - Proceedings, conferences, collections, etc. pertaining to difference and functional equations 39-08 - Computational methods for problems pertaining to difference and functional equations 39-11 - Research data for problems pertaining to difference and functional equations 39Axx - Difference equations 39A05 - General theory of difference equations 39A06 - Linear difference equations 39A10 - Additive difference equations 39A12 - Discrete version of topics in analysis 39A13 - Difference equations, scaling ((q)-differences) 39A14 - Partial difference equations 39A20 - Multiplicative and other generalized difference equations 39A21 - Oscillation theory for difference equations 39A22 - Growth, boundedness, comparison of solutions to difference equations 39A23 - Periodic solutions of difference equations 39A24 - Almost periodic solutions of difference equations 39A26 - Fuzzy difference equations 39A27 - Boundary value problems for difference equations 39A28 - Bifurcation theory for difference equations 39A30 - Stability theory for difference equations 39A33 - Chaotic behavior of solutions of difference equations 39A36 - Integrable difference and lattice equations; integrability tests 39A45 - Difference equations in the complex domain 39A50 - Stochastic difference equations 39A60 - Applications of difference equations 39A70 - Difference operators 39A99 - Difference equations 39Bxx - Functional equations and inequalities 39B05 - General theory of functional equations and inequalities 39B12 - Iteration theory, iterative and composite equations 39B22 - Functional equations for real functions 39B32 - Functional equations for complex functions 39B42 - Matrix and operator functional equations 39B52 - Functional equations for functions with more general domains and/or ranges 39B55 - Orthogonal additivity and other conditional functional equations 39B62 - Functional inequalities, including subadditivity, convexity, etc. 39B72 - Systems of functional equations and inequalities 39B82 - Stability, separation, extension, and related topics for functional equations 39B99 - Functional equations and inequalities 40-XX - Sequences, series, summability 40-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability 40-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability 40-02 - Research exposition (monographs, survey articles) pertaining to sequences, series, summability 40-03 - History of sequences, series, summability 40-04 - Software, source code, etc. for problems pertaining to sequences, series, summability 40-06 - Proceedings, conferences, collections, etc. pertaining to sequences, series, summability 40-08 - Computational methods for problems pertaining to sequences, series, summability 40-11 - Research data for problems pertaining to sequences, series, summability 40Axx - Convergence and divergence of infinite limiting processes 40A05 - Convergence and divergence of series and sequences 40A10 - Convergence and divergence of integrals 40A15 - Convergence and divergence of continued fractions 40A20 - Convergence and divergence of infinite products 40A25 - Approximation to limiting values (summation of series, etc.) 40A30 - Convergence and divergence of series and sequences of functions 40A35 - Ideal and statistical convergence 40A99 - Convergence and divergence of infinite limiting processes 40Bxx - Multiple sequences and series 40B05 - Multiple sequences and series 40B99 - Multiple sequences and series 40Cxx - General summability methods 40C05 - Matrix methods for summability 40C10 - Integral methods for summability 40C15 - Function-theoretic methods (including power series methods and semicontinuous methods) for summability 40C99 - General summability methods 40Dxx - Direct theorems on summability 40D05 - General theorems on summability 40D09 - Structure of summability fields 40D10 - Tauberian constants and oscillation limits in summability theory 40D15 - Convergence factors and summability factors 40D20 - Summability and bounded fields of methods 40D25 - Inclusion and equivalence theorems in summability theory 40D99 - Direct theorems on summability 40Exx - Inversion theorems 40E05 - Tauberian theorems 40E10 - Growth estimates 40E15 - Lacunary inversion theorems 40E20 - Tauberian constants 40E99 - Inversion theorems 40Fxx - Absolute and strong summability 40F05 - Absolute and strong summability 40F99 - Absolute and strong summability 40Gxx - Special methods of summability 40G05 - Ces�ro, Euler, N�rlund and Hausdorff methods 40G10 - Abel, Borel and power series methods 40G15 - Summability methods using statistical convergence 40G99 - Special methods of summability 40Hxx - Functional analytic methods in summability 40H05 - Functional analytic methods in summability 40H99 - Functional analytic methods in summability 40Jxx - Summability in abstract structures 40J05 - Summability in abstract structures 40J99 - Summability in abstract structures 41-XX - Approximations and expansions 41-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to approximations and expansions 41-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to approximations and expansions 41-02 - Research exposition (monographs, survey articles) pertaining to approximations and expansions 41-03 - History of approximations and expansions 41-04 - Software, source code, etc. for problems pertaining to approximations and expansions 41-06 - Proceedings, conferences, collections, etc. pertaining to approximations and expansions 41-11 - Research data for problems pertaining to approximations and expansions 41Axx - Approximations and expansions 41A05 - Interpolation in approximation theory 41A10 - Approximation by polynomials 41A15 - Spline approximation 41A17 - Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) 41A20 - Approximation by rational functions 41A21 - Pad� approximation 41A25 - Rate of convergence, degree of approximation 41A27 - Inverse theorems in approximation theory 41A28 - Simultaneous approximation 41A29 - Approximation with constraints 41A30 - Approximation by other special function classes 41A35 - Approximation by operators (in particular, by integral operators) 41A36 - Approximation by positive operators 41A40 - Saturation in approximation theory 41A44 - Best constants in approximation theory 41A45 - Approximation by arbitrary linear expressions 41A46 - Approximation by arbitrary nonlinear expressions; widths and entropy 41A50 - Best approximation, Chebyshev systems 41A52 - Uniqueness of best approximation 41A55 - Approximate quadratures 41A58 - Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) 41A60 - Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 41A63 - Multidimensional problems 41A65 - Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A80 - Remainders in approximation formulas 41A81 - Weighted approximation 41A99 - Approximations and expansions 42-XX - Harmonic analysis on Euclidean spaces 42-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to harmonic analysis on Euclidean spaces 42-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces 42-02 - Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces 42-03 - History of harmonic analysis on Euclidean spaces 42-04 - Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces 42-06 - Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces 42-08 - Computational methods for problems pertaining to harmonic analysis on Euclidean spaces 42-11 - Research data for problems pertaining to harmonic analysis on Euclidean spaces 42Axx - Harmonic analysis in one variable 42A05 - Trigonometric polynomials, inequalities, extremal problems 42A10 - Trigonometric approximation 42A15 - Trigonometric interpolation 42A16 - Fourier coefficients, Fourier series of functions with special properties, special Fourier series 42A20 - Convergence and absolute convergence of Fourier and trigonometric series 42A24 - Summability and absolute summability of Fourier and trigonometric series 42A32 - Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) 42A38 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42A45 - Multipliers in one variable harmonic analysis 42A50 - Conjugate functions, conjugate series, singular integrals 42A55 - Lacunary series of trigonometric and other functions; Riesz products 42A61 - Probabilistic methods for one variable harmonic analysis 42A63 - Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization 42A65 - Completeness of sets of functions in one variable harmonic analysis 42A70 - Trigonometric moment problems in one variable harmonic analysis 42A75 - Classical almost periodic functions, mean periodic functions 42A82 - Positive definite functions in one variable harmonic analysis 42A85 - Convolution, factorization for one variable harmonic analysis 42A99 - Harmonic analysis in one variable 42Bxx - Harmonic analysis in several variables 42B05 - Fourier series and coefficients in several variables 42B08 - Summability in several variables 42B10 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42B15 - Multipliers for harmonic analysis in several variables 42B20 - Singular and oscillatory integrals (Calder�n-Zygmund, etc.) 42B25 - Maximal functions, Littlewood-Paley theory 42B30 - (H^p)-spaces 42B35 - Function spaces arising in harmonic analysis 42B37 - Harmonic analysis and PDEs 42B99 - Harmonic analysis in several variables 42Cxx - Nontrigonometric harmonic analysis 42C05 - Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42C15 - General harmonic expansions, frames 42C20 - Other transformations of harmonic type 42C25 - Uniqueness and localization for orthogonal series 42C30 - Completeness of sets of functions in nontrigonometric harmonic analysis 42C40 - Nontrigonometric harmonic analysis involving wavelets and other special systems 42C99 - Nontrigonometric harmonic analysis 43-XX - Abstract harmonic analysis 43-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to abstract harmonic analysis 43-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to abstract harmonic analysis 43-02 - Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis 43-03 - History of abstract harmonic analysis 43-04 - Software, source code, etc. for problems pertaining to abstract harmonic analysis 43-06 - Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis 43-08 - Computational methods for problems pertaining to abstract harmonic analysis 43-11 - Research data for problems pertaining to abstract harmonic analysis 43Axx - Abstract harmonic analysis 43A05 - Measures on groups and semigroups, etc. 43A07 - Means on groups, semigroups, etc.; amenable groups 43A10 - Measure algebras on groups, semigroups, etc. 43A15 - (L^p)-spaces and other function spaces on groups, semigroups, etc. 43A17 - Analysis on ordered groups, (H^p)-theory 43A20 - (L^1)-algebras on groups, semigroups, etc. 43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A25 - Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 43A30 - Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A32 - Other transforms and operators of Fourier type 43A35 - Positive definite functions on groups, semigroups, etc. 43A40 - Character groups and dual objects 43A45 - Spectral synthesis on groups, semigroups, etc. 43A46 - Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 43A50 - Convergence of Fourier series and of inverse transforms 43A55 - Summability methods on groups, semigroups, etc. 43A60 - Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 43A62 - Harmonic analysis on hypergroups 43A65 - Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) 43A70 - Analysis on specific locally compact and other abelian groups 43A75 - Harmonic analysis on specific compact groups 43A77 - Harmonic analysis on general compact groups 43A80 - Analysis on other specific Lie groups 43A85 - Harmonic analysis on homogeneous spaces 43A90 - Harmonic analysis and spherical functions 43A95 - Categorical methods for abstract harmonic analysis 43A99 - Abstract harmonic analysis 44-XX - Integral transforms, operational calculus 44-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral transforms 44-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms 44-02 - Research exposition (monographs, survey articles) pertaining to integral transforms 44-03 - History of integral transforms 44-04 - Software, source code, etc. for problems pertaining to integral transforms 44-06 - Proceedings, conferences, collections, etc. pertaining to integral transforms 44-11 - Research data for problems pertaining to integral transforms 44Axx - Integral transforms, operational calculus 44A05 - General integral transforms 44A10 - Laplace transform 44A12 - Radon transform 44A15 - Special integral transforms (Legendre, Hilbert, etc.) 44A20 - Integral transforms of special functions 44A30 - Multiple integral transforms 44A35 - Convolution as an integral transform 44A40 - Calculus of Mikusi?ski and other operational calculi 44A45 - Classical operational calculus 44A55 - Discrete operational calculus 44A60 - Moment problems 44A99 - Integral transforms, operational calculus 45-XX - Integral equations 45-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral equations 45-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral equations 45-02 - Research exposition (monographs, survey articles) pertaining to integral equations 45-03 - History of integral equations 45-04 - Software, source code, etc. for problems pertaining to integral equations 45-06 - Proceedings, conferences, collections, etc. pertaining to integral equations 45-11 - Research data for problems pertaining to integral equations 45Axx - Linear integral equations 45A05 - Linear integral equations 45A99 - Linear integral equations 45Bxx - Fredholm integral equations 45B05 - Fredholm integral equations 45B99 - Fredholm integral equations 45Cxx - Eigenvalue problems for integral equations 45C05 - Eigenvalue problems for integral equations 45C99 - Eigenvalue problems for integral equations 45Dxx - Volterra integral equations 45D05 - Volterra integral equations 45D99 - Volterra integral equations 45Exx - Singular integral equations 45E05 - Integral equations with kernels of Cauchy type 45E10 - Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) 45E99 - Singular integral equations 45Fxx - Systems of linear integral equations 45F05 - Systems of nonsingular linear integral equations 45F10 - Dual, triple, etc., integral and series equations 45F15 - Systems of singular linear integral equations 45F99 - Systems of linear integral equations 45Gxx - Nonlinear integral equations 45G05 - Singular nonlinear integral equations 45G10 - Other nonlinear integral equations 45G15 - Systems of nonlinear integral equations 45G99 - Nonlinear integral equations 45Hxx - Integral equations with miscellaneous special kernels 45H05 - Integral equations with miscellaneous special kernels 45H99 - Integral equations with miscellaneous special kernels 45Jxx - Integro-ordinary differential equations 45J05 - Integro-ordinary differential equations 45J99 - Integro-ordinary differential equations 45Kxx - Integro-partial differential equations 45K05 - Integro-partial differential equations 45K99 - Integro-partial differential equations 45Lxx - Theoretical approximation of solutions to integral equations 45L05 - Theoretical approximation of solutions to integral equations 45L99 - Theoretical approximation of solutions to integral equations 45Mxx - Qualitative behavior of solutions to integral equations 45M05 - Asymptotics of solutions to integral equations 45M10 - Stability theory for integral equations 45M15 - Periodic solutions of integral equations 45M20 - Positive solutions of integral equations 45M99 - Qualitative behavior of solutions to integral equations 45Nxx - Abstract integral equations, integral equations in abstract spaces 45N05 - Abstract integral equations, integral equations in abstract spaces 45N99 - Abstract integral equations, integral equations in abstract spaces 45Pxx - Integral operators 45P05 - Integral operators 45P99 - Integral operators 45Qxx - Inverse problems for integral equations 45Q05 - Inverse problems for integral equations 45Q99 - Inverse problems for integral equations 45Rxx - Random integral equations 45R05 - Random integral equations 45R99 - Random integral equations 46-XX - Functional analysis 46-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analysis 46-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis 46-02 - Research exposition (monographs, survey articles) pertaining to functional analysis 46-03 - History of functional analysis 46-04 - Software, source code, etc. for problems pertaining to functional analysis 46-06 - Proceedings, conferences, collections, etc. pertaining to functional analysis 46-08 - Computational methods for problems pertaining to functional analysis 46-11 - Research data for problems pertaining to functional analysis 46Axx - Topological linear spaces and related structures 46A03 - General theory of locally convex spaces 46A04 - Locally convex Fr�chet spaces and (DF)-spaces 46A08 - Barrelled spaces, bornological spaces 46A11 - Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 46A13 - Spaces defined by inductive or projective limits (LB, LF, etc.) 46A16 - Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46A17 - Bornologies and related structures; Mackey convergence, etc. 46A19 - Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) 46A20 - Duality theory for topological vector spaces 46A22 - Theorems of Hahn-Banach type; extension and lifting of functionals and operators 46A25 - Reflexivity and semi-reflexivity 46A30 - Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) 46A32 - Spaces of linear operators; topological tensor products; approximation properties 46A35 - Summability and bases in topological vector spaces 46A40 - Ordered topological linear spaces, vector lattices 46A45 - Sequence spaces (including K�the sequence spaces) 46A50 - Compactness in topological linear spaces; angelic spaces, etc. 46A55 - Convex sets in topological linear spaces; Choquet theory 46A61 - Graded Fr�chet spaces and tame operators 46A63 - Topological invariants ((DN), ((Omega)), etc.) for locally convex spaces 46A70 - Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 46A80 - Modular spaces 46A99 - Topological linear spaces and related structures 46Bxx - Normed linear spaces and Banach spaces; Banach lattices 46B03 - Isomorphic theory (including renorming) of Banach spaces 46B04 - Isometric theory of Banach spaces 46B06 - Asymptotic theory of Banach spaces 46B07 - Local theory of Banach spaces 46B08 - Ultraproduct techniques in Banach space theory 46B09 - Probabilistic methods in Banach space theory 46B10 - Duality and reflexivity in normed linear and Banach spaces 46B15 - Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces 46B20 - Geometry and structure of normed linear spaces 46B22 - Radon-Nikod�m, Kre?n-Milman and related properties 46B25 - Classical Banach spaces in the general theory 46B26 - Nonseparable Banach spaces 46B28 - Spaces of operators; tensor products; approximation properties 46B40 - Ordered normed spaces 46B42 - Banach lattices 46B45 - Banach sequence spaces 46B50 - Compactness in Banach (or normed) spaces 46B70 - Interpolation between normed linear spaces 46B80 - Nonlinear classification of Banach spaces; nonlinear quotients 46B85 - Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science 46B87 - Lineability in functional analysis 46B99 - Normed linear spaces and Banach spaces; Banach lattices 46Cxx - Inner product spaces and their generalizations, Hilbert spaces 46C05 - Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 46C07 - Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) 46C15 - Characterizations of Hilbert spaces 46C20 - Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) 46C50 - Generalizations of inner products (semi-inner products, partial inner products, etc.) 46C99 - Inner product spaces and their generalizations, Hilbert spaces 46Exx - Linear function spaces and their duals 46E05 - Lattices of continuous, differentiable or analytic functions 46E10 - Topological linear spaces of continuous, differentiable or analytic functions 46E15 - Banach spaces of continuous, differentiable or analytic functions 46E20 - Hilbert spaces of continuous, differentiable or analytic functions 46E22 - Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) 46E25 - Rings and algebras of continuous, differentiable or analytic functions 46E27 - Spaces of measures 46E30 - Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, K�the function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35 - Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems 46E36 - Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces 46E39 - Sobolev (and similar kinds of) spaces of functions of discrete variables 46E40 - Spaces of vector- and operator-valued functions 46E50 - Spaces of differentiable or holomorphic functions on infinite-dimensional spaces 46E99 - Linear function spaces and their duals 46Fxx - Distributions, generalized functions, distribution spaces 46F05 - Topological linear spaces of test functions, distributions and ultradistributions 46F10 - Operations with distributions and generalized functions 46F12 - Integral transforms in distribution spaces 46F15 - Hyperfunctions, analytic functionals 46F20 - Distributions and ultradistributions as boundary values of analytic functions 46F25 - Distributions on infinite-dimensional spaces 46F30 - Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 46F99 - Distributions, generalized functions, distribution spaces 46Gxx - Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) 46G05 - Derivatives of functions in infinite-dimensional spaces 46G10 - Vector-valued measures and integration 46G12 - Measures and integration on abstract linear spaces 46G15 - Functional analytic lifting theory 46G20 - Infinite-dimensional holomorphy 46G25 - (Spaces of) multilinear mappings, polynomials 46G99 - Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) 46Hxx - Topological algebras, normed rings and algebras, Banach algebras 46H05 - General theory of topological algebras 46H10 - Ideals and subalgebras 46H15 - Representations of topological algebras 46H20 - Structure, classification of topological algebras 46H25 - Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46H30 - Functional calculus in topological algebras 46H35 - Topological algebras of operators 46H40 - Automatic continuity 46H70 - Nonassociative topological algebras 46H99 - Topological algebras, normed rings and algebras, Banach algebras 46Jxx - Commutative Banach algebras and commutative topological algebras 46J05 - General theory of commutative topological algebras 46J10 - Banach algebras of continuous functions, function algebras 46J15 - Banach algebras of differentiable or analytic functions, (H^p)-spaces 46J20 - Ideals, maximal ideals, boundaries 46J25 - Representations of commutative topological algebras 46J30 - Subalgebras of commutative topological algebras 46J40 - Structure and classification of commutative topological algebras 46J45 - Radical Banach algebras 46J99 - Commutative Banach algebras and commutative topological algebras 46Kxx - Topological (rings and) algebras with an involution 46K05 - General theory of topological algebras with involution 46K10 - Representations of topological algebras with involution 46K15 - Hilbert algebras 46K50 - Nonselfadjoint (sub)algebras in algebras with involution 46K70 - Nonassociative topological algebras with an involution 46K99 - Topological (rings and) algebras with an involution 46Lxx - Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) 46L05 - General theory of (C^*)-algebras 46L06 - Tensor products of (C^*)-algebras 46L07 - Operator spaces and completely bounded maps 46L08 - (C^*)-modules 46L09 - Free products of (C^*)-algebras 46L10 - General theory of von Neumann algebras 46L30 - States of selfadjoint operator algebras 46L35 - Classifications of (C^*)-algebras 46L36 - Classification of factors 46L37 - Subfactors and their classification 46L40 - Automorphisms of selfadjoint operator algebras 46L45 - Decomposition theory for (C^*)-algebras 46L51 - Noncommutative measure and integration 46L52 - Noncommutative function spaces 46L53 - Noncommutative probability and statistics 46L54 - Free probability and free operator algebras 46L55 - Noncommutative dynamical systems 46L57 - Derivations, dissipations and positive semigroups in (C^*)-algebras 46L60 - Applications of selfadjoint operator algebras to physics 46L65 - Quantizations, deformations for selfadjoint operator algebras 46L67 - Quantum groups (operator algebraic aspects) 46L70 - Nonassociative selfadjoint operator algebras 46L80 - (K)-theory and operator algebras (including cyclic theory) 46L85 - Noncommutative topology 46L87 - Noncommutative differential geometry 46L89 - Other ``noncommutative'' mathematics based on (C^*)-algebra theory 46L99 - Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) 46Mxx - Methods of category theory in functional analysis 46M05 - Tensor products in functional analysis 46M07 - Ultraproducts in functional analysis 46M10 - Projective and injective objects in functional analysis 46M15 - Categories, functors in functional analysis 46M18 - Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 46M20 - Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 46M35 - Abstract interpolation of topological vector spaces 46M40 - Inductive and projective limits in functional analysis 46M99 - Methods of category theory in functional analysis 46Nxx - Miscellaneous applications of functional analysis 46N10 - Applications of functional analysis in optimization, convex analysis, mathematical programming, economics 46N20 - Applications of functional analysis to differential and integral equations 46N30 - Applications of functional analysis in probability theory and statistics 46N40 - Applications of functional analysis in numerical analysis 46N50 - Applications of functional analysis in quantum physics 46N55 - Applications of functional analysis in statistical physics 46N60 - Applications of functional analysis in biology and other sciences 46N99 - Miscellaneous applications of functional analysis 46Sxx - Other (nonclassical) types of functional analysis 46S05 - Quaternionic functional analysis 46S10 - Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis 46S20 - Nonstandard functional analysis 46S30 - Constructive functional analysis 46S40 - Fuzzy functional analysis 46S50 - Functional analysis in probabilistic metric linear spaces 46S60 - Functional analysis on superspaces (supermanifolds) or graded spaces 46S99 - Other (nonclassical) types of functional analysis 46Txx - Nonlinear functional analysis 46T05 - Infinite-dimensional manifolds 46T10 - Manifolds of mappings 46T12 - Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds 46T20 - Continuous and differentiable maps in nonlinear functional analysis 46T25 - Holomorphic maps in nonlinear functional analysis 46T30 - Distributions and generalized functions on nonlinear spaces 46T99 - Nonlinear functional analysis 47-XX - Operator theory 47-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operator theory 47-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory 47-02 - Research exposition (monographs, survey articles) pertaining to operator theory 47-03 - History of operator theory 47-04 - Software, source code, etc. for problems pertaining to operator theory 47-06 - Proceedings, conferences, collections, etc. pertaining to operator theory 47-08 - Computational methods for problems pertaining to operator theory 47-11 - Research data for problems pertaining to operator theory 47Axx - General theory of linear operators 47A05 - General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A06 - Linear relations (multivalued linear operators) 47A07 - Forms (bilinear, sesquilinear, multilinear) 47A08 - Operator matrices 47A10 - Spectrum, resolvent 47A11 - Local spectral properties of linear operators 47A12 - Numerical range, numerical radius 47A13 - Several-variable operator theory (spectral, Fredholm, etc.) 47A15 - Invariant subspaces of linear operators 47A16 - Cyclic vectors, hypercyclic and chaotic operators 47A20 - Dilations, extensions, compressions of linear operators 47A25 - Spectral sets of linear operators 47A30 - Norms (inequalities, more than one norm, etc.) of linear operators 47A35 - Ergodic theory of linear operators 47A40 - Scattering theory of linear operators 47A45 - Canonical models for contractions and nonselfadjoint linear operators 47A46 - Chains (nests) of projections or of invariant subspaces, integrals along chains, etc. 47A48 - Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. 47A50 - Equations and inequalities involving linear operators, with vector unknowns 47A52 - Linear operators and ill-posed problems, regularization 47A53 - (Semi-) Fredholm operators; index theories 47A55 - Perturbation theory of linear operators 47A56 - Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 47A57 - Linear operator methods in interpolation, moment and extension problems 47A58 - Linear operator approximation theory 47A60 - Functional calculus for linear operators 47A62 - Equations involving linear operators, with operator unknowns 47A63 - Linear operator inequalities 47A64 - Operator means involving linear operators, shorted linear operators, etc. 47A65 - Structure theory of linear operators 47A66 - Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators 47A67 - Representation theory of linear operators 47A68 - Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators 47A70 - (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces 47A75 - Eigenvalue problems for linear operators 47A80 - Tensor products of linear operators 47A99 - General theory of linear operators 47Bxx - Special classes of linear operators 47B01 - Operators on Banach spaces 47B02 - Operators on Hilbert spaces (general) 47B06 - Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators 47B07 - Linear operators defined by compactness properties 47B10 - Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) 47B12 - Sectorial operators 47B13 - Cowen-Douglas operators 47B15 - Hermitian and normal operators (spectral measures, functional calculus, etc.) 47B20 - Subnormal operators, hyponormal operators, etc. 47B25 - Linear symmetric and selfadjoint operators (unbounded) 47B28 - Nonselfadjoint operators 47B32 - Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) 47B33 - Linear composition operators 47B34 - Kernel operators 47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B36 - Jacobi (tridiagonal) operators (matrices) and generalizations 47B37 - Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B38 - Linear operators on function spaces (general) 47B39 - Linear difference operators 47B40 - Spectral operators, decomposable operators, well-bounded operators, etc. 47B44 - Linear accretive operators, dissipative operators, etc. 47B47 - Commutators, derivations, elementary operators, etc. 47B48 - Linear operators on Banach algebras 47B49 - Transformers, preservers (linear operators on spaces of linear operators) 47B50 - Linear operators on spaces with an indefinite metric 47B60 - Linear operators on ordered spaces 47B65 - Positive linear operators and order-bounded operators 47B80 - Random linear operators 47B90 - Operator theory and harmonic analysis 47B91 - Operators on complex function spaces 47B92 - Operators on real function spaces 47B93 - Operators arising in mathematical physics 47B99 - Special classes of linear operators 47Cxx - Individual linear operators as elements of algebraic systems 47C05 - Linear operators in algebras 47C10 - Linear operators in ({}^*)-algebras 47C15 - Linear operators in (C^*)- or von Neumann algebras 47C99 - Individual linear operators as elements of algebraic systems 47Dxx - Groups and semigroups of linear operators, their generalizations and applications 47D03 - Groups and semigroups of linear operators 47D06 - One-parameter semigroups and linear evolution equations 47D07 - Markov semigroups and applications to diffusion processes 47D08 - Schr�dinger and Feynman-Kac semigroups 47D09 - Operator sine and cosine functions and higher-order Cauchy problems 47D60 - (C)-semigroups, regularized semigroups 47D62 - Integrated semigroups 47D99 - Groups and semigroups of linear operators, their generalizations and applications 47Exx - Ordinary differential operators 47E05 - General theory of ordinary differential operators 47E07 - Functional-differential and differential-difference operators 47E99 - Ordinary differential operators 47Fxx - Partial differential operators 47F05 - General theory of partial differential operators 47F10 - Elliptic operators and their generalizations 47F99 - Partial differential operators 47Gxx - Integral, integro-differential, and pseudodifferential operators 47G10 - Integral operators 47G20 - Integro-differential operators 47G30 - Pseudodifferential operators 47G40 - Potential operators 47G99 - Integral, integro-differential, and pseudodifferential operators 47Hxx - Nonlinear operators and their properties 47H04 - Set-valued operators 47H05 - Monotone operators and generalizations 47H06 - Nonlinear accretive operators, dissipative operators, etc. 47H07 - Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 47H08 - Measures of noncompactness and condensing mappings, (K)-set contractions, etc. 47H09 - Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. 47H10 - Fixed-point theorems 47H11 - Degree theory for nonlinear operators 47H14 - Perturbations of nonlinear operators 47H20 - Semigroups of nonlinear operators 47H25 - Nonlinear ergodic theorems 47H30 - Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) 47H40 - Random nonlinear operators 47H60 - Multilinear and polynomial operators 47H99 - Nonlinear operators and their properties 47Jxx - Equations and inequalities involving nonlinear operators 47J05 - Equations involving nonlinear operators (general) 47J06 - Nonlinear ill-posed problems 47J07 - Abstract inverse mapping and implicit function theorems involving nonlinear operators 47J10 - Nonlinear spectral theory, nonlinear eigenvalue problems 47J15 - Abstract bifurcation theory involving nonlinear operators 47J20 - Variational and other types of inequalities involving nonlinear operators (general) 47J22 - Variational and other types of inclusions 47J25 - Iterative procedures involving nonlinear operators 47J26 - Fixed-point iterations 47J30 - Variational methods involving nonlinear operators 47J35 - Nonlinear evolution equations 47J40 - Equations with nonlinear hysteresis operators 47J99 - Equations and inequalities involving nonlinear operators 47Lxx - Linear spaces and algebras of operators 47L05 - Linear spaces of operators 47L07 - Convex sets and cones of operators 47L10 - Algebras of operators on Banach spaces and other topological linear spaces 47L15 - Operator algebras with symbol structure 47L20 - Operator ideals 47L22 - Ideals of polynomials and of multilinear mappings in operator theory 47L25 - Operator spaces (= matricially normed spaces) 47L30 - Abstract operator algebras on Hilbert spaces 47L35 - Nest algebras, CSL algebras 47L40 - Limit algebras, subalgebras of (C^*)-algebras 47L45 - Dual algebras; weakly closed singly generated operator algebras 47L50 - Dual spaces of operator algebras 47L55 - Representations of (nonselfadjoint) operator algebras 47L60 - Algebras of unbounded operators; partial algebras of operators 47L65 - Crossed product algebras (analytic crossed products) 47L70 - Nonassociative nonselfadjoint operator algebras 47L75 - Other nonselfadjoint operator algebras 47L80 - Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) 47L90 - Applications of operator algebras to the sciences 47L99 - Linear spaces and algebras of operators 47Nxx - Miscellaneous applications of operator theory 47N10 - Applications of operator theory in optimization, convex analysis, mathematical programming, economics 47N20 - Applications of operator theory to differential and integral equations 47N30 - Applications of operator theory in probability theory and statistics 47N40 - Applications of operator theory in numerical analysis 47N50 - Applications of operator theory in the physical sciences 47N60 - Applications of operator theory in chemistry and life sciences 47N70 - Applications of operator theory in systems, signals, circuits, and control theory 47N99 - Miscellaneous applications of operator theory 47Sxx - Other (nonclassical) types of operator theory 47S05 - Quaternionic operator theory 47S10 - Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory 47S20 - Nonstandard operator theory 47S30 - Constructive operator theory 47S40 - Fuzzy operator theory 47S50 - Operator theory in probabilistic metric linear spaces 47S99 - Other (nonclassical) types of operator theory 49-XX - Calculus of variations and optimal control; optimization 49-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to calculus of variations and optimal control 49-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control 49-02 - Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control 49-03 - History of calculus of variations and optimal control 49-04 - Software, source code, etc. for problems pertaining to calculus of variations and optimal control 49-06 - Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control 49-11 - Research data for problems pertaining to calculus of variations and optimal control 49Jxx - Existence theories in calculus of variations and optimal control 49J05 - Existence theories for free problems in one independent variable 49J10 - Existence theories for free problems in two or more independent variables 49J15 - Existence theories for optimal control problems involving ordinary differential equations 49J20 - Existence theories for optimal control problems involving partial differential equations 49J21 - Existence theories for optimal control problems involving relations other than differential equations 49J27 - Existence theories for problems in abstract spaces 49J30 - Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 49J35 - Existence of solutions for minimax problems 49J40 - Variational inequalities 49J45 - Methods involving semicontinuity and convergence; relaxation 49J50 - Fr�chet and Gateaux differentiability in optimization 49J52 - Nonsmooth analysis 49J53 - Set-valued and variational analysis 49J55 - Existence of optimal solutions to problems involving randomness 49J99 - Existence theories in calculus of variations and optimal control 49Kxx - Optimality conditions 49K05 - Optimality conditions for free problems in one independent variable 49K10 - Optimality conditions for free problems in two or more independent variables 49K15 - Optimality conditions for problems involving ordinary differential equations 49K20 - Optimality conditions for problems involving partial differential equations 49K21 - Optimality conditions for problems involving relations other than differential equations 49K27 - Optimality conditions for problems in abstract spaces 49K30 - Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 49K35 - Optimality conditions for minimax problems 49K40 - Sensitivity, stability, well-posedness 49K45 - Optimality conditions for problems involving randomness 49K99 - Optimality conditions 49Lxx - Hamilton-Jacobi theories 49L12 - Hamilton-Jacobi equations in optimal control and differential games 49L20 - Dynamic programming in optimal control and differential games 49L25 - Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 49L99 - Hamilton-Jacobi theories 49Mxx - Numerical methods in optimal control 49M05 - Numerical methods based on necessary conditions 49M15 - Newton-type methods 49M20 - Numerical methods of relaxation type 49M25 - Discrete approximations in optimal control 49M27 - Decomposition methods 49M29 - Numerical methods involving duality 49M37 - Numerical methods based on nonlinear programming 49M41 - PDE constrained optimization (numerical aspects) 49M99 - Numerical methods in optimal control 49Nxx - Miscellaneous topics in calculus of variations and optimal control 49N05 - Linear optimal control problems 49N10 - Linear-quadratic optimal control problems 49N15 - Duality theory (optimization) 49N20 - Periodic optimal control problems 49N25 - Impulsive optimal control problems 49N30 - Problems with incomplete information (optimization) 49N35 - Optimal feedback synthesis 49N45 - Inverse problems in optimal control 49N60 - Regularity of solutions in optimal control 49N70 - Differential games and control 49N75 - Pursuit and evasion games 49N80 - Mean field games and control 49N90 - Applications of optimal control and differential games 49N99 - Miscellaneous topics in calculus of variations and optimal control 49Qxx - Manifolds and measure-geometric topics 49Q05 - Minimal surfaces and optimization 49Q10 - Optimization of shapes other than minimal surfaces 49Q12 - Sensitivity analysis for optimization problems on manifolds 49Q15 - Geometric measure and integration theory, integral and normal currents in optimization 49Q20 - Variational problems in a geometric measure-theoretic setting 49Q22 - Optimal transportation 49Q99 - Manifolds and measure-geometric topics 49Rxx - Variational methods for eigenvalues of operators 49R05 - Variational methods for eigenvalues of operators 49R99 - Variational methods for eigenvalues of operators 49Sxx - Variational principles of physics 49S05 - Variational principles of physics 49S99 - Variational principles of physics 51-XX - Geometry 51-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry 51-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry 51-02 - Research exposition (monographs, survey articles) pertaining to geometry 51-03 - History of geometry 51-04 - Software, source code, etc. for problems pertaining to geometry 51-06 - Proceedings, conferences, collections, etc. pertaining to geometry 51-08 - Computational methods for problems pertaining to geometry 51-11 - Research data for problems pertaining to geometry 51Axx - Linear incidence geometry 51A05 - General theory of linear incidence geometry and projective geometries 51A10 - Homomorphism, automorphism and dualities in linear incidence geometry 51A15 - Linear incidence geometric structures with parallelism 51A20 - Configuration theorems in linear incidence geometry 51A25 - Algebraization in linear incidence geometry 51A30 - Desarguesian and Pappian geometries 51A35 - Non-Desarguesian affine and projective planes 51A40 - Translation planes and spreads in linear incidence geometry 51A45 - Incidence structures embeddable into projective geometries 51A50 - Polar geometry, symplectic spaces, orthogonal spaces 51A99 - Linear incidence geometry 51Bxx - Nonlinear incidence geometry 51B05 - General theory of nonlinear incidence geometry 51B10 - M�bius geometries 51B15 - Laguerre geometries 51B20 - Minkowski geometries in nonlinear incidence geometry 51B25 - Lie geometries in nonlinear incidence geometry 51B99 - Nonlinear incidence geometry 51Cxx - Ring geometry (Hjelmslev, Barbilian, etc.) 51C05 - Ring geometry (Hjelmslev, Barbilian, etc.) 51C99 - Ring geometry (Hjelmslev, Barbilian, etc.) 51Dxx - Geometric closure systems 51D05 - Abstract (Maeda) geometries 51D10 - Abstract geometries with exchange axiom 51D15 - Abstract geometries with parallelism 51D20 - Combinatorial geometries and geometric closure systems 51D25 - Lattices of subspaces and geometric closure systems 51D30 - Continuous geometries, geometric closure systems and related topics 51D99 - Geometric closure systems 51Exx - Finite geometry and special incidence structures 51E05 - General block designs in finite geometry 51E10 - Steiner systems in finite geometry 51E12 - Generalized quadrangles and generalized polygons in finite geometry 51E14 - Finite partial geometries (general), nets, partial spreads 51E15 - Finite affine and projective planes (geometric aspects) 51E20 - Combinatorial structures in finite projective spaces 51E21 - Blocking sets, ovals, (k)-arcs 51E22 - Linear codes and caps in Galois spaces 51E23 - Spreads and packing problems in finite geometry 51E24 - Buildings and the geometry of diagrams 51E25 - Other finite nonlinear geometries 51E26 - Other finite linear geometries 51E30 - Other finite incidence structures (geometric aspects) 51E99 - Finite geometry and special incidence structures 51Fxx - Metric geometry 51F05 - Absolute planes in metric geometry 51F10 - Absolute spaces in metric geometry 51F15 - Reflection groups, reflection geometries 51F20 - Congruence and orthogonality in metric geometry 51F25 - Orthogonal and unitary groups in metric geometry 51F30 - Lipschitz and coarse geometry of metric spaces 51F99 - Metric geometry 51Gxx - Ordered geometries (ordered incidence structures, etc.) 51G05 - Ordered geometries (ordered incidence structures, etc.) 51G99 - Ordered geometries (ordered incidence structures, etc.) 51Hxx - Topological geometry 51H05 - General theory of topological geometry 51H10 - Topological linear incidence structures 51H15 - Topological nonlinear incidence structures 51H20 - Topological geometries on manifolds 51H25 - Geometries with differentiable structure 51H30 - Geometries with algebraic manifold structure 51H99 - Topological geometry 51Jxx - Incidence groups 51J05 - General theory of incidence groups 51J10 - Projective incidence groups 51J15 - Kinematic spaces 51J20 - Representation by near-fields and near-algebras 51J99 - Incidence groups 51Kxx - Distance geometry 51K05 - General theory of distance geometry 51K10 - Synthetic differential geometry 51K99 - Distance geometry 51Lxx - Geometric order structures 51L05 - Geometry of orders of nondifferentiable curves 51L10 - Directly differentiable curves in geometric order structures 51L15 - (n)-vertex theorems via direct methods 51L20 - Geometry of orders of surfaces 51L99 - Geometric order structures 51Mxx - Real and complex geometry 51M04 - Elementary problems in Euclidean geometries 51M05 - Euclidean geometries (general) and generalizations 51M09 - Elementary problems in hyperbolic and elliptic geometries 51M10 - Hyperbolic and elliptic geometries (general) and generalizations 51M15 - Geometric constructions in real or complex geometry 51M16 - Inequalities and extremum problems in real or complex geometry 51M20 - Polyhedra and polytopes; regular figures, division of spaces 51M25 - Length, area and volume in real or complex geometry 51M30 - Line geometries and their generalizations 51M35 - Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) 51M99 - Real and complex geometry 51Nxx - Analytic and descriptive geometry 51N05 - Descriptive geometry 51N10 - Affine analytic geometry 51N15 - Projective analytic geometry 51N20 - Euclidean analytic geometry 51N25 - Analytic geometry with other transformation groups 51N30 - Geometry of classical groups 51N35 - Questions of classical algebraic geometry 51N99 - Analytic and descriptive geometry 51Pxx - Classical or axiomatic geometry and physics 51P05 - Classical or axiomatic geometry and physics 51P99 - Classical or axiomatic geometry and physics 52-XX - Convex and discrete geometry 52-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to convex and discrete geometry 52-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry 52-02 - Research exposition (monographs, survey articles) pertaining to convex and discrete geometry 52-03 - History of convex and discrete geometry 52-04 - Software, source code, etc. for problems pertaining to convex and discrete geometry 52-06 - Proceedings, conferences, collections, etc. pertaining to convex and discrete geometry 52-08 - Computational methods for problems pertaining to convex and discrete geometry 52-11 - Research data for problems pertaining to convex and discrete geometry 52Axx - General convexity 52A01 - Axiomatic and generalized convexity 52A05 - Convex sets without dimension restrictions (aspects of convex geometry) 52A07 - Convex sets in topological vector spaces (aspects of convex geometry) 52A10 - Convex sets in (2) dimensions (including convex curves) 52A15 - Convex sets in (3) dimensions (including convex surfaces) 52A20 - Convex sets in (n) dimensions (including convex hypersurfaces) 52A21 - Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) 52A22 - Random convex sets and integral geometry (aspects of convex geometry) 52A23 - Asymptotic theory of convex bodies 52A27 - Approximation by convex sets 52A30 - Variants of convex sets (star-shaped, ((m, n))-convex, etc.) 52A35 - Helly-type theorems and geometric transversal theory 52A37 - Other problems of combinatorial convexity 52A38 - Length, area, volume and convex sets (aspects of convex geometry) 52A39 - Mixed volumes and related topics in convex geometry 52A40 - Inequalities and extremum problems involving convexity in convex geometry 52A41 - Convex functions and convex programs in convex geometry 52A55 - Spherical and hyperbolic convexity 52A99 - General convexity 52Bxx - Polytopes and polyhedra 52B05 - Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) 52B10 - Three-dimensional polytopes 52B11 - (n)-dimensional polytopes 52B12 - Special polytopes (linear programming, centrally symmetric, etc.) 52B15 - Symmetry properties of polytopes 52B20 - Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 52B22 - Shellability for polytopes and polyhedra 52B35 - Gale and other diagrams 52B40 - Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) 52B45 - Dissections and valuations (Hilbert's third problem, etc.) 52B55 - Computational aspects related to convexity 52B60 - Isoperimetric problems for polytopes 52B70 - Polyhedral manifolds 52B99 - Polytopes and polyhedra 52Cxx - Discrete geometry 52C05 - Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) 52C07 - Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) 52C10 - Erd?s problems and related topics of discrete geometry 52C15 - Packing and covering in (2) dimensions (aspects of discrete geometry) 52C17 - Packing and covering in (n) dimensions (aspects of discrete geometry) 52C20 - Tilings in (2) dimensions (aspects of discrete geometry) 52C22 - Tilings in (n) dimensions (aspects of discrete geometry) 52C23 - Quasicrystals and aperiodic tilings in discrete geometry 52C25 - Rigidity and flexibility of structures (aspects of discrete geometry) 52C26 - Circle packings and discrete conformal geometry 52C30 - Planar arrangements of lines and pseudolines (aspects of discrete geometry) 52C35 - Arrangements of points, flats, hyperplanes (aspects of discrete geometry) 52C40 - Oriented matroids in discrete geometry 52C45 - Combinatorial complexity of geometric structures 52C99 - Discrete geometry 53-XX - Differential geometry 53-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to differential geometry 53-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry 53-02 - Research exposition (monographs, survey articles) pertaining to differential geometry 53-03 - History of differential geometry 53-04 - Software, source code, etc. for problems pertaining to differential geometry 53-06 - Proceedings, conferences, collections, etc. pertaining to differential geometry 53-08 - Computational methods for problems pertaining to differential geometry 53-11 - Research data for problems pertaining to differential geometry 53Axx - Classical differential geometry 53A04 - Curves in Euclidean and related spaces 53A05 - Surfaces in Euclidean and related spaces 53A07 - Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces 53A10 - Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53A15 - Affine differential geometry 53A17 - Differential geometric aspects in kinematics 53A20 - Projective differential geometry 53A25 - Differential line geometry 53A31 - Differential geometry of submanifolds of M�bius space 53A35 - Non-Euclidean differential geometry 53A40 - Other special differential geometries 53A45 - Differential geometric aspects in vector and tensor analysis 53A55 - Differential invariants (local theory), geometric objects 53A60 - Differential geometry of webs 53A70 - Discrete differential geometry 53A99 - Classical differential geometry 53Bxx - Local differential geometry 53B05 - Linear and affine connections 53B10 - Projective connections 53B12 - Differential geometric aspects of statistical manifolds and information geometry 53B15 - Other connections 53B20 - Local Riemannian geometry 53B21 - Methods of local Riemannian geometry 53B25 - Local submanifolds 53B30 - Local differential geometry of Lorentz metrics, indefinite metrics 53B35 - Local differential geometry of Hermitian and K�hlerian structures 53B40 - Local differential geometry of Finsler spaces and generalizations (areal metrics) 53B50 - Applications of local differential geometry to the sciences 53B99 - Local differential geometry 53Cxx - Global differential geometry 53C05 - Connections (general theory) 53C07 - Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) 53C08 - Differential geometric aspects of gerbes and differential characters 53C10 - (G)-structures 53C12 - Foliations (differential geometric aspects) 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C17 - Sub-Riemannian geometry 53C18 - Conformal structures on manifolds 53C20 - Global Riemannian geometry, including pinching 53C21 - Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C22 - Geodesics in global differential geometry 53C23 - Global geometric and topological methods (� la Gromov); differential geometric analysis on metric spaces 53C24 - Rigidity results 53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C26 - Hyper-K�hler and quaternionic K�hler geometry, ``special'' geometry 53C27 - Spin and Spin({}^c) geometry 53C28 - Twistor methods in differential geometry 53C29 - Issues of holonomy in differential geometry 53C30 - Differential geometry of homogeneous manifolds 53C35 - Differential geometry of symmetric spaces 53C38 - Calibrations and calibrated geometries 53C40 - Global submanifolds 53C42 - Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C43 - Differential geometric aspects of harmonic maps 53C45 - Global surface theory (convex surfaces � la A. D. Aleksandrov) 53C50 - Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C55 - Global differential geometry of Hermitian and K�hlerian manifolds 53C56 - Other complex differential geometry 53C60 - Global differential geometry of Finsler spaces and generalizations (areal metrics) 53C65 - Integral geometry 53C70 - Direct methods ((G)-spaces of Busemann, etc.) 53C75 - Geometric orders, order geometry 53C80 - Applications of global differential geometry to the sciences 53C99 - Global differential geometry 53Dxx - Symplectic geometry, contact geometry 53D05 - Symplectic manifolds (general theory) 53D10 - Contact manifolds (general theory) 53D12 - Lagrangian submanifolds; Maslov index 53D15 - Almost contact and almost symplectic manifolds 53D17 - Poisson manifolds; Poisson groupoids and algebroids 53D18 - Generalized geometries (� la Hitchin) 53D20 - Momentum maps; symplectic reduction 53D22 - Canonical transformations in symplectic and contact geometry 53D25 - Geodesic flows in symplectic geometry and contact geometry 53D30 - Symplectic structures of moduli spaces 53D35 - Global theory of symplectic and contact manifolds 53D37 - Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category 53D40 - Symplectic aspects of Floer homology and cohomology 53D42 - Symplectic field theory; contact homology 53D45 - Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 53D50 - Geometric quantization 53D55 - Deformation quantization, star products 53D99 - Symplectic geometry, contact geometry 53Exx - Geometric evolution equations 53E10 - Flows related to mean curvature 53E20 - Ricci flows 53E30 - Flows related to complex manifolds (e.g., K�hler-Ricci flows, Chern-Ricci flows) 53E40 - Higher-order geometric flows 53E50 - Flows related to symplectic and contact structures 53E99 - Geometric evolution equations 53Zxx - Applications of differential geometry to sciences and engineering 53Z05 - Applications of differential geometry to physics 53Z10 - Applications of differential geometry to biology 53Z15 - Applications of differential geometry to chemistry 53Z30 - Applications of differential geometry to engineering 53Z50 - Applications of differential geometry to data and computer science 53Z99 - Applications of differential geometry to sciences and engineering 54-XX - General topology 54-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general topology 54-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology 54-02 - Research exposition (monographs, survey articles) pertaining to general topology 54-03 - History of general topology 54-04 - Software, source code, etc. for problems pertaining to general topology 54-06 - Proceedings, conferences, collections, etc. pertaining to general topology 54-08 - Computational methods for problems pertaining to general topology 54-11 - Research data for problems pertaining to general topology 54Axx - Generalities in topology 54A05 - Topological spaces and generalizations (closure spaces, etc.) 54A10 - Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54A15 - Syntopogeneous structures 54A20 - Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54A25 - Cardinality properties (cardinal functions and inequalities, discrete subsets) 54A35 - Consistency and independence results in general topology 54A40 - Fuzzy topology 54A99 - Generalities in topology 54Bxx - Basic constructions in general topology 54B05 - Subspaces in general topology 54B10 - Product spaces in general topology 54B15 - Quotient spaces, decompositions in general topology 54B17 - Adjunction spaces and similar constructions in general topology 54B20 - Hyperspaces in general topology 54B30 - Categorical methods in general topology 54B35 - Spectra in general topology 54B40 - Presheaves and sheaves in general topology 54B99 - Basic constructions in general topology 54Cxx - Maps and general types of topological spaces defined by maps 54C05 - Continuous maps 54C08 - Weak and generalized continuity 54C10 - Special maps on topological spaces (open, closed, perfect, etc.) 54C15 - Retraction 54C20 - Extension of maps 54C25 - Embedding 54C30 - Real-valued functions in general topology 54C35 - Function spaces in general topology 54C40 - Algebraic properties of function spaces in general topology 54C45 - (C)- and (C^*)-embedding 54C50 - Topology of special sets defined by functions 54C55 - Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 54C56 - Shape theory in general topology 54C60 - Set-valued maps in general topology 54C65 - Selections in general topology 54C70 - Entropy in general topology 54C99 - Maps and general types of topological spaces defined by maps 54Dxx - Fairly general properties of topological spaces 54D05 - Connected and locally connected spaces (general aspects) 54D10 - Lower separation axioms ((T_0)--(T_3), etc.) 54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 - Noncompact covering properties (paracompact, Lindel�f, etc.) 54D25 - ``(P)-minimal'' and ``(P)-closed'' spaces 54D30 - Compactness 54D35 - Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54D40 - Remainders in general topology 54D45 - Local compactness, (sigma)-compactness 54D50 - (k)-spaces 54D55 - Sequential spaces 54D60 - Realcompactness and realcompactification 54D65 - Separability of topological spaces 54D70 - Base properties of topological spaces 54D80 - Special constructions of topological spaces (spaces of ultrafilters, etc.) 54D99 - Fairly general properties of topological spaces 54Exx - Topological spaces with richer structures 54E05 - Proximity structures and generalizations 54E15 - Uniform structures and generalizations 54E17 - Nearness spaces 54E18 - (p)-spaces, (M)-spaces, (sigma)-spaces, etc. 54E20 - Stratifiable spaces, cosmic spaces, etc. 54E25 - Semimetric spaces 54E30 - Moore spaces 54E35 - Metric spaces, metrizability 54E40 - Special maps on metric spaces 54E45 - Compact (locally compact) metric spaces 54E50 - Complete metric spaces 54E52 - Baire category, Baire spaces 54E55 - Bitopologies 54E70 - Probabilistic metric spaces 54E99 - Topological spaces with richer structures 54Fxx - Special properties of topological spaces 54F05 - Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 54F15 - Continua and generalizations 54F16 - Hyperspaces of continua 54F17 - Inverse limits of set-valued functions 54F35 - Higher-dimensional local connectedness 54F45 - Dimension theory in general topology 54F50 - Topological spaces of dimension (leq 1); curves, dendrites 54F55 - Unicoherence, multicoherence 54F65 - Topological characterizations of particular spaces 54F99 - Special properties of topological spaces 54Gxx - Peculiar topological spaces 54G05 - Extremally disconnected spaces, (F)-spaces, etc. 54G10 - (P)-spaces 54G12 - Scattered spaces 54G15 - Pathological topological spaces 54G20 - Counterexamples in general topology 54G99 - Peculiar topological spaces 54Hxx - Connections of general topology with other structures, applications 54H05 - Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 54H10 - Topological representations of algebraic systems 54H11 - Topological groups (topological aspects) 54H12 - Topological lattices, etc. (topological aspects) 54H13 - Topological fields, rings, etc. (topological aspects) 54H15 - Transformation groups and semigroups (topological aspects) 54H25 - Fixed-point and coincidence theorems (topological aspects) 54H30 - Applications of general topology to computer science (e.g., digital topology, image processing) 54H99 - Connections of general topology with other structures, applications 54Jxx - Nonstandard topology 54J05 - Nonstandard topology 54J99 - Nonstandard topology 55-XX - Algebraic topology 55-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic topology 55-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology 55-02 - Research exposition (monographs, survey articles) pertaining to algebraic topology 55-03 - History of algebraic topology 55-04 - Software, source code, etc. for problems pertaining to algebraic topology 55-06 - Proceedings, conferences, collections, etc. pertaining to algebraic topology 55-08 - Computational methods for problems pertaining to algebraic topology 55-11 - Research data for problems pertaining to algebraic topology 55Mxx - Classical topics in algebraic topology 55M05 - Duality in algebraic topology 55M10 - Dimension theory in algebraic topology 55M15 - Absolute neighborhood retracts 55M20 - Fixed points and coincidences in algebraic topology 55M25 - Degree, winding number 55M30 - Lyusternik-Shnirel'man category of a space, topological complexity � la Farber, topological robotics (topological aspects) 55M35 - Finite groups of transformations in algebraic topology (including Smith theory) 55M99 - Classical topics in algebraic topology 55Nxx - Homology and cohomology theories in algebraic topology 55N05 - ?ech types 55N07 - Steenrod-Sitnikov homologies 55N10 - Singular homology and cohomology theory 55N15 - Topological (K)-theory 55N20 - Generalized (extraordinary) homology and cohomology theories in algebraic topology 55N22 - Bordism and cobordism theories and formal group laws in algebraic topology 55N25 - Homology with local coefficients, equivariant cohomology 55N30 - Sheaf cohomology in algebraic topology 55N31 - Persistent homology and applications, topological data analysis 55N32 - Orbifold cohomology 55N33 - Intersection homology and cohomology in algebraic topology 55N34 - Elliptic cohomology 55N35 - Other homology theories in algebraic topology 55N40 - Axioms for homology theory and uniqueness theorems in algebraic topology 55N45 - Products and intersections in homology and cohomology 55N91 - Equivariant homology and cohomology in algebraic topology 55N99 - Homology and cohomology theories in algebraic topology 55Pxx - Homotopy theory 55P05 - Homotopy extension properties, cofibrations in algebraic topology 55P10 - Homotopy equivalences in algebraic topology 55P15 - Classification of homotopy type 55P20 - Eilenberg-Mac Lane spaces 55P25 - Spanier-Whitehead duality 55P30 - Eckmann-Hilton duality 55P35 - Loop spaces 55P40 - Suspensions 55P42 - Stable homotopy theory, spectra 55P43 - Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) 55P45 - (H)-spaces and duals 55P47 - Infinite loop spaces 55P48 - Loop space machines and operads in algebraic topology 55P50 - String topology 55P55 - Shape theory 55P57 - Proper homotopy theory 55P60 - Localization and completion in homotopy theory 55P62 - Rational homotopy theory 55P65 - Homotopy functors in algebraic topology 55P91 - Equivariant homotopy theory in algebraic topology 55P92 - Relations between equivariant and nonequivariant homotopy theory in algebraic topology 55P99 - Homotopy theory 55Qxx - Homotopy groups 55Q05 - Homotopy groups, general; sets of homotopy classes 55Q07 - Shape groups 55Q10 - Stable homotopy groups 55Q15 - Whitehead products and generalizations 55Q20 - Homotopy groups of wedges, joins, and simple spaces 55Q25 - Hopf invariants 55Q35 - Operations in homotopy groups 55Q40 - Homotopy groups of spheres 55Q45 - Stable homotopy of spheres 55Q50 - (J)-morphism 55Q51 - (v_n)-periodicity 55Q52 - Homotopy groups of special spaces 55Q55 - Cohomotopy groups 55Q70 - Homotopy groups of special types 55Q91 - Equivariant homotopy groups 55Q99 - Homotopy groups 55Rxx - Fiber spaces and bundles in algebraic topology 55R05 - Fiber spaces in algebraic topology 55R10 - Fiber bundles in algebraic topology 55R12 - Transfer for fiber spaces and bundles in algebraic topology 55R15 - Classification of fiber spaces or bundles in algebraic topology 55R20 - Spectral sequences and homology of fiber spaces in algebraic topology 55R25 - Sphere bundles and vector bundles in algebraic topology 55R35 - Classifying spaces of groups and (H)-spaces in algebraic topology 55R37 - Maps between classifying spaces in algebraic topology 55R40 - Homology of classifying spaces and characteristic classes in algebraic topology 55R45 - Homology and homotopy of (Bmathrm{O}) and (Bmathrm{U}); Bott periodicity 55R50 - Stable classes of vector space bundles in algebraic topology and relations to (K)-theory 55R55 - Fiberings with singularities in algebraic topology 55R60 - Microbundles and block bundles in algebraic topology 55R65 - Generalizations of fiber spaces and bundles in algebraic topology 55R70 - Fibrewise topology 55R80 - Discriminantal varieties and configuration spaces in algebraic topology 55R91 - Equivariant fiber spaces and bundles in algebraic topology 55R99 - Fiber spaces and bundles in algebraic topology 55Sxx - Operations and obstructions in algebraic topology 55S05 - Primary cohomology operations in algebraic topology 55S10 - Steenrod algebra 55S12 - Dyer-Lashof operations 55S15 - Symmetric products and cyclic products in algebraic topology 55S20 - Secondary and higher cohomology operations in algebraic topology 55S25 - (K)-theory operations and generalized cohomology operations in algebraic topology 55S30 - Massey products 55S35 - Obstruction theory in algebraic topology 55S36 - Extension and compression of mappings in algebraic topology 55S37 - Classification of mappings in algebraic topology 55S40 - Sectioning fiber spaces and bundles in algebraic topology 55S45 - Postnikov systems, (k)-invariants 55S91 - Equivariant operations and obstructions in algebraic topology 55S99 - Operations and obstructions in algebraic topology 55Txx - Spectral sequences in algebraic topology 55T05 - General theory of spectral sequences in algebraic topology 55T10 - Serre spectral sequences 55T15 - Adams spectral sequences 55T20 - Eilenberg-Moore spectral sequences 55T25 - Generalized cohomology and spectral sequences in algebraic topology 55T99 - Spectral sequences in algebraic topology 55Uxx - Applied homological algebra and category theory in algebraic topology 55U05 - Abstract complexes in algebraic topology 55U10 - Simplicial sets and complexes in algebraic topology 55U15 - Chain complexes in algebraic topology 55U20 - Universal coefficient theorems, Bockstein operator 55U25 - Homology of a product, K�nneth formula 55U30 - Duality in applied homological algebra and category theory (aspects of algebraic topology) 55U35 - Abstract and axiomatic homotopy theory in algebraic topology 55U40 - Topological categories, foundations of homotopy theory 55U99 - Applied homological algebra and category theory in algebraic topology 57-XX - Manifolds and cell complexes 57-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes 57-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes 57-02 - Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes 57-03 - History of manifolds and cell complexes 57-04 - Software, source code, etc. for problems pertaining to manifolds and cell complexes 57-06 - Proceedings, conferences, collections, etc. pertaining to manifolds and cell complexes 57-08 - Computational methods for problems pertaining to manifolds and cell complexes 57-11 - Research data for problems pertaining to manifolds and cell complexes 57Kxx - Low-dimensional topology in specific dimensions 57K10 - Knot theory 57K12 - Generalized knots (virtual knots, welded knots, quandles, etc.) 57K14 - Knot polynomials 57K16 - Finite-type and quantum invariants, topological quantum field theories (TQFT) 57K18 - Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) 57K20 - 2-dimensional topology (including mapping class groups of surfaces, Teichm�ller theory, curve complexes, etc.) 57K30 - General topology of 3-manifolds 57K31 - Invariants of 3-manifolds (including skein modules, character varieties) 57K32 - Hyperbolic 3-manifolds 57K33 - Contact structures in 3 dimensions 57K35 - Other geometric structures on 3-manifolds 57K40 - General topology of 4-manifolds 57K41 - Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants) 57K43 - Symplectic structures in 4 dimensions 57K45 - Higher-dimensional knots and links 57K50 - Low-dimensional manifolds of specific dimension 5 or higher 57K99 - Low-dimensional topology in specific dimensions 57Mxx - General low-dimensional topology 57M05 - Fundamental group, presentations, free differential calculus 57M07 - Topological methods in group theory 57M10 - Covering spaces and low-dimensional topology 57M12 - Low-dimensional topology of special (e.g., branched) coverings 57M15 - Relations of low-dimensional topology with graph theory 57M30 - Wild embeddings 57M50 - General geometric structures on low-dimensional manifolds 57M60 - Group actions on manifolds and cell complexes in low dimensions 57M99 - General low-dimensional topology 57Nxx - Topological manifolds 57N16 - Geometric structures on manifolds of high or arbitrary dimension 57N17 - Topology of topological vector spaces 57N20 - Topology of infinite-dimensional manifolds 57N25 - Shapes (aspects of topological manifolds) 57N30 - Engulfing in topological manifolds 57N35 - Embeddings and immersions in topological manifolds 57N37 - Isotopy and pseudo-isotopy 57N40 - Neighborhoods of submanifolds 57N45 - Flatness and tameness of topological manifolds 57N50 - (S^{n-1}subset E^n), Schoenflies problem 57N55 - Microbundles and block bundles 57N60 - Cellularity in topological manifolds 57N65 - Algebraic topology of manifolds 57N70 - Cobordism and concordance in topological manifolds 57N75 - General position and transversality 57N80 - Stratifications in topological manifolds 57N99 - Topological manifolds 57Pxx - Generalized manifolds 57P05 - Local properties of generalized manifolds 57P10 - Poincar� duality spaces 57P99 - Generalized manifolds 57Qxx - PL-topology 57Q05 - General topology of complexes 57Q10 - Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. 57Q12 - Wall finiteness obstruction for CW-complexes 57Q15 - Triangulating manifolds 57Q20 - Cobordism in PL-topology 57Q25 - Comparison of PL-structures: classification, Hauptvermutung 57Q30 - Engulfing 57Q35 - Embeddings and immersions in PL-topology 57Q37 - Isotopy in PL-topology 57Q40 - Regular neighborhoods in PL-topology 57Q50 - Microbundles and block bundles 57Q55 - Approximations in PL-topology 57Q60 - Cobordism and concordance in PL-topology 57Q65 - General position and transversality 57Q70 - Discrete Morse theory and related ideas in manifold topology 57Q91 - Equivariant PL-topology 57Q99 - PL-topology 57Rxx - Differential topology 57R05 - Triangulating 57R10 - Smoothing in differential topology 57R12 - Smooth approximations in differential topology 57R15 - Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) 57R17 - Symplectic and contact topology in high or arbitrary dimension 57R18 - Topology and geometry of orbifolds 57R19 - Algebraic topology on manifolds and differential topology 57R20 - Characteristic classes and numbers in differential topology 57R22 - Topology of vector bundles and fiber bundles 57R25 - Vector fields, frame fields in differential topology 57R27 - Controllability of vector fields on (C^infty) and real-analytic manifolds 57R30 - Foliations in differential topology; geometric theory 57R32 - Classifying spaces for foliations; Gelfand-Fuks cohomology 57R35 - Differentiable mappings in differential topology 57R40 - Embeddings in differential topology 57R42 - Immersions in differential topology 57R45 - Singularities of differentiable mappings in differential topology 57R50 - Differential topological aspects of diffeomorphisms 57R52 - Isotopy in differential topology 57R55 - Differentiable structures in differential topology 57R56 - Topological quantum field theories (aspects of differential topology) 57R57 - Applications of global analysis to structures on manifolds 57R58 - Floer homology 57R60 - Homotopy spheres, Poincar� conjecture 57R65 - Surgery and handlebodies 57R67 - Surgery obstructions, Wall groups 57R70 - Critical points and critical submanifolds in differential topology 57R75 - (mathrm{O})- and (mathrm{SO})-cobordism 57R77 - Complex cobordism ((mathrm{U})- and (mathrm{SU})-cobordism) 57R80 - (h)- and (s)-cobordism 57R85 - Equivariant cobordism 57R90 - Other types of cobordism 57R91 - Equivariant algebraic topology of manifolds 57R95 - Realizing cycles by submanifolds 57R99 - Differential topology 57Sxx - Topological transformation groups 57S05 - Topological properties of groups of homeomorphisms or diffeomorphisms 57S10 - Compact groups of homeomorphisms 57S12 - Toric topology 57S15 - Compact Lie groups of differentiable transformations 57S17 - Finite transformation groups 57S20 - Noncompact Lie groups of transformations 57S25 - Groups acting on specific manifolds 57S30 - Discontinuous groups of transformations 57S99 - Topological transformation groups 57Txx - Homology and homotopy of topological groups and related structures 57T05 - Hopf algebras (aspects of homology and homotopy of topological groups) 57T10 - Homology and cohomology of Lie groups 57T15 - Homology and cohomology of homogeneous spaces of Lie groups 57T20 - Homotopy groups of topological groups and homogeneous spaces 57T25 - Homology and cohomology of (H)-spaces 57T30 - Bar and cobar constructions 57T35 - Applications of Eilenberg-Moore spectral sequences 57T99 - Homology and homotopy of topological groups and related structures 57Zxx - Relations of manifolds and cell complexes with science and engineering 57Z05 - Relations of manifolds and cell complexes with physics 57Z10 - Relations of manifolds and cell complexes with biology 57Z15 - Relations of manifolds and cell complexes with chemistry 57Z20 - Relations of manifolds and cell complexes with engineering 57Z25 - Relations of manifolds and cell complexes with computer and data science 57Z99 - Relations of manifolds and cell complexes with science and engineering 58-XX - Global analysis, analysis on manifolds 58-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis 58-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis 58-02 - Research exposition (monographs, survey articles) pertaining to global analysis 58-03 - History of global analysis 58-04 - Software, source code, etc. for problems pertaining to global analysis 58-06 - Proceedings, conferences, collections, etc. pertaining to global analysis 58-08 - Computational methods for problems pertaining to global analysis 58-11 - Research data for problems pertaining to global analysis 58Axx - General theory of differentiable manifolds 58A03 - Topos-theoretic approach to differentiable manifolds 58A05 - Differentiable manifolds, foundations 58A07 - Real-analytic and Nash manifolds 58A10 - Differential forms in global analysis 58A12 - de Rham theory in global analysis 58A14 - Hodge theory in global analysis 58A15 - Exterior differential systems (Cartan theory) 58A17 - Pfaffian systems 58A20 - Jets in global analysis 58A25 - Currents in global analysis 58A30 - Vector distributions (subbundles of the tangent bundles) 58A32 - Natural bundles 58A35 - Stratified sets 58A40 - Differential spaces 58A50 - Supermanifolds and graded manifolds 58A99 - General theory of differentiable manifolds 58Bxx - Infinite-dimensional manifolds 58B05 - Homotopy and topological questions for infinite-dimensional manifolds 58B10 - Differentiability questions for infinite-dimensional manifolds 58B12 - Questions of holomorphy and infinite-dimensional manifolds 58B15 - Fredholm structures on infinite-dimensional manifolds 58B20 - Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds 58B25 - Group structures and generalizations on infinite-dimensional manifolds 58B32 - Geometry of quantum groups 58B34 - Noncommutative geometry (� la Connes) 58B99 - Infinite-dimensional manifolds 58Cxx - Calculus on manifolds; nonlinear operators 58C05 - Real-valued functions on manifolds 58C06 - Set-valued and function-space-valued mappings on manifolds 58C07 - Continuity properties of mappings on manifolds 58C10 - Holomorphic maps on manifolds 58C15 - Implicit function theorems; global Newton methods on manifolds 58C20 - Differentiation theory (Gateaux, Fr�chet, etc.) on manifolds 58C25 - Differentiable maps on manifolds 58C30 - Fixed-point theorems on manifolds 58C35 - Integration on manifolds; measures on manifolds 58C40 - Spectral theory; eigenvalue problems on manifolds 58C50 - Analysis on supermanifolds or graded manifolds 58C99 - Calculus on manifolds; nonlinear operators 58Dxx - Spaces and manifolds of mappings (including nonlinear versions of 46Exx) 58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds 58D07 - Groups and semigroups of nonlinear operators 58D10 - Spaces of embeddings and immersions 58D15 - Manifolds of mappings 58D17 - Manifolds of metrics (especially Riemannian) 58D19 - Group actions and symmetry properties 58D20 - Measures (Gaussian, cylindrical, etc.) on manifolds of maps 58D25 - Equations in function spaces; evolution equations 58D27 - Moduli problems for differential geometric structures 58D29 - Moduli problems for topological structures 58D30 - Applications of manifolds of mappings to the sciences 58D99 - Spaces and manifolds of mappings (including nonlinear versions of 46Exx) 58Exx - Variational problems in infinite-dimensional spaces 58E05 - Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces 58E07 - Variational problems in abstract bifurcation theory in infinite-dimensional spaces 58E09 - Group-invariant bifurcation theory in infinite-dimensional spaces 58E10 - Variational problems in applications to the theory of geodesics (problems in one independent variable) 58E11 - Critical metrics 58E12 - Variational problems concerning minimal surfaces (problems in two independent variables) 58E15 - Variational problems concerning extremal problems in several variables; Yang-Mills functionals 58E17 - Multiobjective variational problems, Pareto optimality, applications to economics, etc. 58E20 - Harmonic maps, etc. 58E25 - Applications of variational problems to control theory 58E30 - Variational principles in infinite-dimensional spaces 58E35 - Variational inequalities (global problems) in infinite-dimensional spaces 58E40 - Variational aspects of group actions in infinite-dimensional spaces 58E50 - Applications of variational problems in infinite-dimensional spaces to the sciences 58E99 - Variational problems in infinite-dimensional spaces 58Hxx - Pseudogroups, differentiable groupoids and general structures on manifolds 58H05 - Pseudogroups and differentiable groupoids 58H10 - Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) 58H15 - Deformations of general structures on manifolds 58H99 - Pseudogroups, differentiable groupoids and general structures on manifolds 58Jxx - Partial differential equations on manifolds; differential operators 58J05 - Elliptic equations on manifolds, general theory 58J10 - Differential complexes 58J15 - Relations of PDEs on manifolds with hyperfunctions 58J20 - Index theory and related fixed-point theorems on manifolds 58J22 - Exotic index theories on manifolds 58J26 - Elliptic genera 58J28 - Eta-invariants, Chern-Simons invariants 58J30 - Spectral flows 58J32 - Boundary value problems on manifolds 58J35 - Heat and other parabolic equation methods for PDEs on manifolds 58J37 - Perturbations of PDEs on manifolds; asymptotics 58J40 - Pseudodifferential and Fourier integral operators on manifolds 58J42 - Noncommutative global analysis, noncommutative residues 58J45 - Hyperbolic equations on manifolds 58J47 - Propagation of singularities; initial value problems on manifolds 58J50 - Spectral problems; spectral geometry; scattering theory on manifolds 58J51 - Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity 58J52 - Determinants and determinant bundles, analytic torsion 58J53 - Isospectrality 58J55 - Bifurcation theory for PDEs on manifolds 58J60 - Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) 58J65 - Diffusion processes and stochastic analysis on manifolds 58J70 - Invariance and symmetry properties for PDEs on manifolds 58J72 - Correspondences and other transformation methods (e.g., Lie-B�cklund) for PDEs on manifolds 58J90 - Applications of PDEs on manifolds 58J99 - Partial differential equations on manifolds; differential operators 58Kxx - Theory of singularities and catastrophe theory 58K05 - Critical points of functions and mappings on manifolds 58K10 - Monodromy on manifolds 58K15 - Topological properties of mappings on manifolds 58K20 - Algebraic and analytic properties of mappings on manifolds 58K25 - Stability theory for manifolds 58K30 - Global theory of singularities 58K35 - Catastrophe theory 58K40 - Classification; finite determinacy of map germs 58K45 - Singularities of vector fields, topological aspects 58K50 - Normal forms on manifolds 58K55 - Asymptotic behavior of solutions to equations on manifolds 58K60 - Deformation of singularities 58K65 - Topological invariants on manifolds 58K70 - Symmetries, equivariance on manifolds 58K99 - Theory of singularities and catastrophe theory 58Zxx - Applications of global analysis to the sciences 58Z05 - Applications of global analysis to the sciences 58Z99 - Applications of global analysis to the sciences 60-XX - Probability theory and stochastic processes 60-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to probability theory 60-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory 60-02 - Research exposition (monographs, survey articles) pertaining to probability theory 60-03 - History of probability theory 60-04 - Software, source code, etc. for problems pertaining to probability theory 60-06 - Proceedings, conferences, collections, etc. pertaining to probability theory 60-08 - Computational methods for problems pertaining to probability theory 60-11 - Research data for problems pertaining to probability theory 60Axx - Foundations of probability theory 60A05 - Axioms; other general questions in probability 60A10 - Probabilistic measure theory 60A86 - Fuzzy probability 60A99 - Foundations of probability theory 60Bxx - Probability theory on algebraic and topological structures 60B05 - Probability measures on topological spaces 60B10 - Convergence of probability measures 60B11 - Probability theory on linear topological spaces 60B12 - Limit theorems for vector-valued random variables (infinite-dimensional case) 60B15 - Probability measures on groups or semigroups, Fourier transforms, factorization 60B20 - Random matrices (probabilistic aspects) 60B99 - Probability theory on algebraic and topological structures 60Cxx - Combinatorial probability 60C05 - Combinatorial probability 60C99 - Combinatorial probability 60Dxx - Geometric probability and stochastic geometry 60D05 - Geometric probability and stochastic geometry 60D99 - Geometric probability and stochastic geometry 60Exx - Distribution theory 60E05 - Probability distributions: general theory 60E07 - Infinitely divisible distributions; stable distributions 60E10 - Characteristic functions; other transforms 60E15 - Inequalities; stochastic orderings 60E99 - Distribution theory 60Fxx - Limit theorems in probability theory 60F05 - Central limit and other weak theorems 60F10 - Large deviations 60F15 - Strong limit theorems 60F17 - Functional limit theorems; invariance principles 60F20 - Zero-one laws 60F25 - (L^p)-limit theorems 60F99 - Limit theorems in probability theory 60Gxx - Stochastic processes 60G05 - Foundations of stochastic processes 60G07 - General theory of stochastic processes 60G09 - Exchangeability for stochastic processes 60G10 - Stationary stochastic processes 60G12 - General second-order stochastic processes 60G15 - Gaussian processes 60G17 - Sample path properties 60G18 - Self-similar stochastic processes 60G20 - Generalized stochastic processes 60G22 - Fractional processes, including fractional Brownian motion 60G25 - Prediction theory (aspects of stochastic processes) 60G30 - Continuity and singularity of induced measures 60G35 - Signal detection and filtering (aspects of stochastic processes) 60G40 - Stopping times; optimal stopping problems; gambling theory 60G42 - Martingales with discrete parameter 60G44 - Martingales with continuous parameter 60G46 - Martingales and classical analysis 60G48 - Generalizations of martingales 60G50 - Sums of independent random variables; random walks 60G51 - Processes with independent increments; L�vy processes 60G52 - Stable stochastic processes 60G53 - Feller processes 60G55 - Point processes (e.g., Poisson, Cox, Hawkes processes) 60G57 - Random measures 60G60 - Random fields 60G65 - Nonlinear processes (e.g., (G)-Brownian motion, (G)-L�vy processes) 60G70 - Extreme value theory; extremal stochastic processes 60G99 - Stochastic processes 60Hxx - Stochastic analysis 60H05 - Stochastic integrals 60H07 - Stochastic calculus of variations and the Malliavin calculus 60H10 - Stochastic ordinary differential equations (aspects of stochastic analysis) 60H15 - Stochastic partial differential equations (aspects of stochastic analysis) 60H17 - Singular stochastic partial differential equations 60H20 - Stochastic integral equations 60H25 - Random operators and equations (aspects of stochastic analysis) 60H30 - Applications of stochastic analysis (to PDEs, etc.) 60H35 - Computational methods for stochastic equations (aspects of stochastic analysis) 60H40 - White noise theory 60H50 - Regularization by noise 60H99 - Stochastic analysis 60Jxx - Markov processes 60J05 - Discrete-time Markov processes on general state spaces 60J10 - Markov chains (discrete-time Markov processes on discrete state spaces) 60J20 - Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60J22 - Computational methods in Markov chains 60J25 - Continuous-time Markov processes on general state spaces 60J27 - Continuous-time Markov processes on discrete state spaces 60J28 - Applications of continuous-time Markov processes on discrete state spaces 60J35 - Transition functions, generators and resolvents 60J40 - Right processes 60J45 - Probabilistic potential theory 60J46 - Dirichlet form methods in Markov processes 60J50 - Boundary theory for Markov processes 60J55 - Local time and additive functionals 60J57 - Multiplicative functionals and Markov processes 60J60 - Diffusion processes 60J65 - Brownian motion 60J67 - Stochastic (Schramm-)Loewner evolution (SLE) 60J68 - Superprocesses 60J70 - Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60J74 - Jump processes on discrete state spaces 60J76 - Jump processes on general state spaces 60J80 - Branching processes (Galton-Watson, birth-and-death, etc.) 60J85 - Applications of branching processes 60J90 - Coalescent processes 60J95 - Applications of coalescent processes 60J99 - Markov processes 60Kxx - Special processes 60K05 - Renewal theory 60K10 - Applications of renewal theory (reliability, demand theory, etc.) 60K15 - Markov renewal processes, semi-Markov processes 60K20 - Applications of Markov renewal processes (reliability, queueing networks, etc.) 60K25 - Queueing theory (aspects of probability theory) 60K30 - Applications of queueing theory (congestion, allocation, storage, traffic, etc.) 60K35 - Interacting random processes; statistical mechanics type models; percolation theory 60K37 - Processes in random environments 60K40 - Other physical applications of random processes 60K50 - Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) 60K99 - Special processes 60Lxx - Rough analysis 60L10 - Signatures and data streams 60L20 - Rough paths 60L30 - Regularity structures 60L40 - Paracontrolled distributions and alternative approaches 60L50 - Rough partial differential equations 60L70 - Algebraic structures and computation 60L90 - Applications of rough analysis 60L99 - Rough analysis 62-XX - Statistics 62-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics 62-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics 62-02 - Research exposition (monographs, survey articles) pertaining to statistics 62-03 - History of statistics 62-04 - Software, source code, etc. for problems pertaining to statistics 62-06 - Proceedings, conferences, collections, etc. pertaining to statistics 62-08 - Computational methods for problems pertaining to statistics 62-11 - Research data for problems pertaining to statistics 62Axx - Foundational topics in statistics 62A01 - Foundations and philosophical topics in statistics 62A09 - Graphical methods in statistics 62A86 - Fuzzy analysis in statistics 62A99 - Foundational topics in statistics 62Bxx - Sufficiency and information 62B05 - Sufficient statistics and fields 62B10 - Statistical aspects of information-theoretic topics 62B11 - Information geometry (statistical aspects) 62B15 - Theory of statistical experiments 62B86 - Statistical aspects of fuzziness, sufficiency, and information 62B99 - Sufficiency and information 62Cxx - Statistical decision theory 62C05 - General considerations in statistical decision theory 62C07 - Complete class results in statistical decision theory 62C10 - Bayesian problems; characterization of Bayes procedures 62C12 - Empirical decision procedures; empirical Bayes procedures 62C15 - Admissibility in statistical decision theory 62C20 - Minimax procedures in statistical decision theory 62C25 - Compound decision problems in statistical decision theory 62C86 - Statistical decision theory and fuzziness 62C99 - Statistical decision theory 62Dxx - Statistical sampling theory and related topics 62D05 - Sampling theory, sample surveys 62D10 - Missing data 62D20 - Causal inference from observational studies 62D99 - Statistical sampling theory and related topics 62Exx - Statistical distribution theory 62E10 - Characterization and structure theory of statistical distributions 62E15 - Exact distribution theory in statistics 62E17 - Approximations to statistical distributions (nonasymptotic) 62E20 - Asymptotic distribution theory in statistics 62E86 - Fuzziness in connection with statistical distributions 62E99 - Statistical distribution theory 62Fxx - Parametric inference 62F03 - Parametric hypothesis testing 62F05 - Asymptotic properties of parametric tests 62F07 - Statistical ranking and selection procedures 62F10 - Point estimation 62F12 - Asymptotic properties of parametric estimators 62F15 - Bayesian inference 62F25 - Parametric tolerance and confidence regions 62F30 - Parametric inference under constraints 62F35 - Robustness and adaptive procedures (parametric inference) 62F40 - Bootstrap, jackknife and other resampling methods 62F86 - Parametric inference and fuzziness 62F99 - Parametric inference 62Gxx - Nonparametric inference 62G05 - Nonparametric estimation 62G07 - Density estimation 62G08 - Nonparametric regression and quantile regression 62G09 - Nonparametric statistical resampling methods 62G10 - Nonparametric hypothesis testing 62G15 - Nonparametric tolerance and confidence regions 62G20 - Asymptotic properties of nonparametric inference 62G30 - Order statistics; empirical distribution functions 62G32 - Statistics of extreme values; tail inference 62G35 - Nonparametric robustness 62G86 - Nonparametric inference and fuzziness 62G99 - Nonparametric inference 62Hxx - Multivariate analysis 62H05 - Characterization and structure theory for multivariate probability distributions; copulas 62H10 - Multivariate distribution of statistics 62H11 - Directional data; spatial statistics 62H12 - Estimation in multivariate analysis 62H15 - Hypothesis testing in multivariate analysis 62H17 - Contingency tables 62H20 - Measures of association (correlation, canonical correlation, etc.) 62H22 - Probabilistic graphical models 62H25 - Factor analysis and principal components; correspondence analysis 62H30 - Classification and discrimination; cluster analysis (statistical aspects) 62H35 - Image analysis in multivariate analysis 62H86 - Multivariate analysis and fuzziness 62H99 - Multivariate analysis 62Jxx - Linear inference, regression 62J02 - General nonlinear regression 62J05 - Linear regression; mixed models 62J07 - Ridge regression; shrinkage estimators (Lasso) 62J10 - Analysis of variance and covariance (ANOVA) 62J12 - Generalized linear models (logistic models) 62J15 - Paired and multiple comparisons; multiple testing 62J20 - Diagnostics, and linear inference and regression 62J86 - Fuzziness, and linear inference and regression 62J99 - Linear inference, regression 62Kxx - Design of statistical experiments 62K05 - Optimal statistical designs 62K10 - Statistical block designs 62K15 - Factorial statistical designs 62K20 - Response surface designs 62K25 - Robust parameter designs 62K86 - Fuzziness and design of statistical experiments 62K99 - Design of statistical experiments 62Lxx - Sequential statistical methods 62L05 - Sequential statistical design 62L10 - Sequential statistical analysis 62L12 - Sequential estimation 62L15 - Optimal stopping in statistics 62L20 - Stochastic approximation 62L86 - Fuzziness and sequential statistical methods 62L99 - Sequential statistical methods 62Mxx - Inference from stochastic processes 62M02 - Markov processes: hypothesis testing 62M05 - Markov processes: estimation; hidden Markov models 62M07 - Non-Markovian processes: hypothesis testing 62M09 - Non-Markovian processes: estimation 62M10 - Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M15 - Inference from stochastic processes and spectral analysis 62M20 - Inference from stochastic processes and prediction 62M30 - Inference from spatial processes 62M40 - Random fields; image analysis 62M45 - Neural nets and related approaches to inference from stochastic processes 62M86 - Inference from stochastic processes and fuzziness 62M99 - Inference from stochastic processes 62Nxx - Survival analysis and censored data 62N01 - Censored data models 62N02 - Estimation in survival analysis and censored data 62N03 - Testing in survival analysis and censored data 62N05 - Reliability and life testing 62N86 - Fuzziness, and survival analysis and censored data 62N99 - Survival analysis and censored data 62Pxx - Applications of statistics 62P05 - Applications of statistics to actuarial sciences and financial mathematics 62P10 - Applications of statistics to biology and medical sciences; meta analysis 62P12 - Applications of statistics to environmental and related topics 62P15 - Applications of statistics to psychology 62P20 - Applications of statistics to economics 62P25 - Applications of statistics to social sciences 62P30 - Applications of statistics in engineering and industry; control charts 62P35 - Applications of statistics to physics 62P99 - Applications of statistics 62Qxx - Statistical tables 62Q05 - Statistical tables 62Q99 - Statistical tables 62Rxx - Statistics on algebraic and topological structures 62R01 - Algebraic statistics 62R07 - Statistical aspects of big data and data science 62R10 - Functional data analysis 62R20 - Statistics on metric spaces 62R30 - Statistics on manifolds 62R40 - Topological data analysis 62R99 - Statistics on algebraic and topological structures 65-XX - Numerical analysis 65-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to numerical analysis 65-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis 65-02 - Research exposition (monographs, survey articles) pertaining to numerical analysis 65-03 - History of numerical analysis 65-04 - Software, source code, etc. for problems pertaining to numerical analysis 65-06 - Proceedings, conferences, collections, etc. pertaining to numerical analysis 65-11 - Research data for problems pertaining to numerical analysis 65Axx - Tables in numerical analysis 65A05 - Tables in numerical analysis 65A99 - Tables in numerical analysis 65Bxx - Acceleration of convergence in numerical analysis 65B05 - Extrapolation to the limit, deferred corrections 65B10 - Numerical summation of series 65B15 - Euler-Maclaurin formula in numerical analysis 65B99 - Acceleration of convergence in numerical analysis 65Cxx - Probabilistic methods, stochastic differential equations 65C05 - Monte Carlo methods 65C10 - Random number generation in numerical analysis 65C20 - Probabilistic models, generic numerical methods in probability and statistics 65C30 - Numerical solutions to stochastic differential and integral equations 65C35 - Stochastic particle methods 65C40 - Numerical analysis or methods applied to Markov chains 65C99 - Probabilistic methods, stochastic differential equations 65Dxx - Numerical approximation and computational geometry (primarily algorithms) 65D05 - Numerical interpolation 65D07 - Numerical computation using splines 65D10 - Numerical smoothing, curve fitting 65D12 - Numerical radial basis function approximation 65D15 - Algorithms for approximation of functions 65D17 - Computer-aided design (modeling of curves and surfaces) 65D18 - Numerical aspects of computer graphics, image analysis, and computational geometry 65D19 - Computational issues in computer and robotic vision 65D20 - Computation of special functions and constants, construction of tables 65D25 - Numerical differentiation 65D30 - Numerical integration 65D32 - Numerical quadrature and cubature formulas 65D40 - Numerical approximation of high-dimensional functions; sparse grids 65D99 - Numerical approximation and computational geometry (primarily algorithms) 65Exx - Numerical methods in complex analysis (potential theory, etc.) 65E05 - General theory of numerical methods in complex analysis (potential theory, etc.) 65E10 - Numerical methods in conformal mappings 65E99 - Numerical methods in complex analysis (potential theory, etc.) 65Fxx - Numerical linear algebra 65F05 - Direct numerical methods for linear systems and matrix inversion 65F08 - Preconditioners for iterative methods 65F10 - Iterative numerical methods for linear systems 65F15 - Numerical computation of eigenvalues and eigenvectors of matrices 65F18 - Numerical solutions to inverse eigenvalue problems 65F20 - Numerical solutions to overdetermined systems, pseudoinverses 65F22 - Ill-posedness and regularization problems in numerical linear algebra 65F25 - Orthogonalization in numerical linear algebra 65F35 - Numerical computation of matrix norms, conditioning, scaling 65F40 - Numerical computation of determinants 65F45 - Numerical methods for matrix equations 65F50 - Computational methods for sparse matrices 65F55 - Numerical methods for low-rank matrix approximation; matrix compression 65F60 - Numerical computation of matrix exponential and similar matrix functions 65F99 - Numerical linear algebra 65Gxx - Error analysis and interval analysis 65G20 - Algorithms with automatic result verification 65G30 - Interval and finite arithmetic 65G40 - General methods in interval analysis 65G50 - Roundoff error 65G99 - Error analysis and interval analysis 65Hxx - Nonlinear algebraic or transcendental equations 65H04 - Numerical computation of roots of polynomial equations 65H05 - Numerical computation of solutions to single equations 65H10 - Numerical computation of solutions to systems of equations 65H14 - Numerical algebraic geometry 65H17 - Numerical solution of nonlinear eigenvalue and eigenvector problems 65H20 - Global methods, including homotopy approaches to the numerical solution of nonlinear equations 65H99 - Nonlinear algebraic or transcendental equations 65Jxx - Numerical analysis in abstract spaces 65J05 - General theory of numerical analysis in abstract spaces 65J08 - Numerical solutions to abstract evolution equations 65J10 - Numerical solutions to equations with linear operators 65J15 - Numerical solutions to equations with nonlinear operators 65J20 - Numerical solutions of ill-posed problems in abstract spaces; regularization 65J22 - Numerical solution to inverse problems in abstract spaces 65J99 - Numerical analysis in abstract spaces 65Kxx - Numerical methods for mathematical programming, optimization and variational techniques 65K05 - Numerical mathematical programming methods 65K10 - Numerical optimization and variational techniques 65K15 - Numerical methods for variational inequalities and related problems 65K99 - Numerical methods for mathematical programming, optimization and variational techniques 65Lxx - Numerical methods for ordinary differential equations 65L03 - Numerical methods for functional-differential equations 65L04 - Numerical methods for stiff equations 65L05 - Numerical methods for initial value problems involving ordinary differential equations 65L06 - Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L07 - Numerical investigation of stability of solutions to ordinary differential equations 65L08 - Numerical solution of ill-posed problems involving ordinary differential equations 65L09 - Numerical solution of inverse problems involving ordinary differential equations 65L10 - Numerical solution of boundary value problems involving ordinary differential equations 65L11 - Numerical solution of singularly perturbed problems involving ordinary differential equations 65L12 - Finite difference and finite volume methods for ordinary differential equations 65L15 - Numerical solution of eigenvalue problems involving ordinary differential equations 65L20 - Stability and convergence of numerical methods for ordinary differential equations 65L50 - Mesh generation, refinement, and adaptive methods for ordinary differential equations 65L60 - Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 65L70 - Error bounds for numerical methods for ordinary differential equations 65L80 - Numerical methods for differential-algebraic equations 65L99 - Numerical methods for ordinary differential equations 65Mxx - Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 65M06 - Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M08 - Finite volume methods for initial value and initial-boundary value problems involving PDEs 65M12 - Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M15 - Error bounds for initial value and initial-boundary value problems involving PDEs 65M20 - Method of lines for initial value and initial-boundary value problems involving PDEs 65M22 - Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs 65M25 - Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs 65M30 - Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs 65M32 - Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs 65M38 - Boundary element methods for initial value and initial-boundary value problems involving PDEs 65M50 - Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 65M55 - Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs 65M60 - Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M70 - Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 65M75 - Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs 65M80 - Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs 65M85 - Fictitious domain methods for initial value and initial-boundary value problems involving PDEs 65M99 - Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 65Nxx - Numerical methods for partial differential equations, boundary value problems 65N06 - Finite difference methods for boundary value problems involving PDEs 65N08 - Finite volume methods for boundary value problems involving PDEs 65N12 - Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 - Error bounds for boundary value problems involving PDEs 65N20 - Numerical methods for ill-posed problems for boundary value problems involving PDEs 65N21 - Numerical methods for inverse problems for boundary value problems involving PDEs 65N22 - Numerical solution of discretized equations for boundary value problems involving PDEs 65N25 - Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N30 - Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N35 - Spectral, collocation and related methods for boundary value problems involving PDEs 65N38 - Boundary element methods for boundary value problems involving PDEs 65N40 - Method of lines for boundary value problems involving PDEs 65N45 - Method of contraction of the boundary for boundary value problems involving PDEs 65N50 - Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N55 - Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N75 - Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs 65N80 - Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs 65N85 - Fictitious domain methods for boundary value problems involving PDEs 65N99 - Numerical methods for partial differential equations, boundary value problems 65Pxx - Numerical problems in dynamical systems 65P10 - Numerical methods for Hamiltonian systems including symplectic integrators 65P20 - Numerical chaos 65P30 - Numerical bifurcation problems 65P40 - Numerical nonlinear stabilities in dynamical systems 65P99 - Numerical problems in dynamical systems 65Qxx - Numerical methods for difference and functional equations, recurrence relations 65Q10 - Numerical methods for difference equations 65Q20 - Numerical methods for functional equations 65Q30 - Numerical aspects of recurrence relations 65Q99 - Numerical methods for difference and functional equations, recurrence relations 65Rxx - Numerical methods for integral equations, integral transforms 65R10 - Numerical methods for integral transforms 65R15 - Numerical methods for eigenvalue problems in integral equations 65R20 - Numerical methods for integral equations 65R30 - Numerical methods for ill-posed problems for integral equations 65R32 - Numerical methods for inverse problems for integral equations 65R99 - Numerical methods for integral equations, integral transforms 65Sxx - Graphical methods in numerical analysis 65S05 - Graphical methods in numerical analysis 65S99 - Graphical methods in numerical analysis 65Txx - Numerical methods in Fourier analysis 65T40 - Numerical methods for trigonometric approximation and interpolation 65T50 - Numerical methods for discrete and fast Fourier transforms 65T60 - Numerical methods for wavelets 65T99 - Numerical methods in Fourier analysis 65Yxx - Computer aspects of numerical algorithms 65Y04 - Numerical algorithms for computer arithmetic, etc. 65Y05 - Parallel numerical computation 65Y10 - Numerical algorithms for specific classes of architectures 65Y15 - Packaged methods for numerical algorithms 65Y20 - Complexity and performance of numerical algorithms 65Y99 - Computer aspects of numerical algorithms 65Zxx - Applications to the sciences 65Z05 - Applications to the sciences 65Z99 - Applications to the sciences 68-XX - Computer science 68-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to computer science 68-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science 68-02 - Research exposition (monographs, survey articles) pertaining to computer science 68-03 - History of computer science 68-04 - Software, source code, etc. for problems pertaining to computer science 68-06 - Proceedings, conferences, collections, etc. pertaining to computer science 68-11 - Research data for problems pertaining to computer science 68Mxx - Computer system organization 68M01 - General theory of computer systems 68M07 - Mathematical problems of computer architecture 68M10 - Network design and communication in computer systems 68M11 - Internet topics 68M12 - Network protocols 68M14 - Distributed systems 68M15 - Reliability, testing and fault tolerance of networks and computer systems 68M18 - Wireless sensor networks as related to computer science 68M20 - Performance evaluation, queueing, and scheduling in the context of computer systems 68M25 - Computer security 68M99 - Computer system organization 68Nxx - Theory of software 68N01 - General topics in the theory of software 68N15 - Theory of programming languages 68N17 - Logic programming 68N18 - Functional programming and lambda calculus 68N19 - Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) 68N20 - Theory of compilers and interpreters 68N25 - Theory of operating systems 68N30 - Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) 68N99 - Theory of software 68Pxx - Theory of data 68P01 - General topics in the theory of data 68P05 - Data structures 68P10 - Searching and sorting 68P15 - Database theory 68P20 - Information storage and retrieval of data 68P25 - Data encryption (aspects in computer science) 68P27 - Privacy of data 68P30 - Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science) 68P99 - Theory of data 68Qxx - Theory of computing 68Q01 - General topics in the theory of computing 68Q04 - Classical models of computation (Turing machines, etc.) 68Q06 - Networks and circuits as models of computation; circuit complexity 68Q07 - Biologically inspired models of computation (DNA computing, membrane computing, etc.) 68Q09 - Other nonclassical models of computation 68Q10 - Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) 68Q11 - Communication complexity, information complexity 68Q12 - Quantum algorithms and complexity in the theory of computing 68Q15 - Complexity classes (hierarchies, relations among complexity classes, etc.) 68Q17 - Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 68Q19 - Descriptive complexity and finite models 68Q25 - Analysis of algorithms and problem complexity 68Q27 - Parameterized complexity, tractability and kernelization 68Q30 - Algorithmic information theory (Kolmogorov complexity, etc.) 68Q32 - Computational learning theory 68Q42 - Grammars and rewriting systems 68Q45 - Formal languages and automata 68Q55 - Semantics in the theory of computing 68Q60 - Specification and verification (program logics, model checking, etc.) 68Q65 - Abstract data types; algebraic specification 68Q70 - Algebraic theory of languages and automata 68Q80 - Cellular automata (computational aspects) 68Q85 - Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) 68Q87 - Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) 68Q99 - Theory of computing 68Rxx - Discrete mathematics in relation to computer science 68R01 - General topics of discrete mathematics in relation to computer science 68R05 - Combinatorics in computer science 68R07 - Computational aspects of satisfiability 68R10 - Graph theory (including graph drawing) in computer science 68R12 - Metric embeddings as related to computational problems and algorithms 68R15 - Combinatorics on words 68R99 - Discrete mathematics in relation to computer science 68Txx - Artificial intelligence 68T01 - General topics in artificial intelligence 68T05 - Learning and adaptive systems in artificial intelligence 68T07 - Artificial neural networks and deep learning 68T09 - Computational aspects of data analysis and big data 68T10 - Pattern recognition, speech recognition 68T20 - Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) 68T27 - Logic in artificial intelligence 68T30 - Knowledge representation 68T35 - Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence 68T37 - Reasoning under uncertainty in the context of artificial intelligence 68T40 - Artificial intelligence for robotics 68T42 - Agent technology and artificial intelligence 68T45 - Machine vision and scene understanding 68T50 - Natural language processing 68T99 - Artificial intelligence 68Uxx - Computing methodologies and applications 68U01 - General topics in computing methodologies 68U03 - Computational aspects of digital topology 68U05 - Computer graphics; computational geometry (digital and algorithmic aspects) 68U07 - Computer science aspects of computer-aided design 68U10 - Computing methodologies for image processing 68U15 - Computing methodologies for text processing; mathematical typography 68U35 - Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.) 68U99 - Computing methodologies and applications 68Vxx - Computer science support for mathematical research and practice 68V05 - Computer assisted proofs of proofs-by-exhaustion type 68V15 - Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.) 68V20 - Formalization of mathematics in connection with theorem provers 68V25 - Presentation and content markup for mathematics 68V30 - Mathematical knowledge management 68V35 - Digital mathematics libraries and repositories 68V99 - Computer science support for mathematical research and practice 68Wxx - Algorithms in computer science 68W01 - General topics in the theory of algorithms 68W05 - Nonnumerical algorithms 68W10 - Parallel algorithms in computer science 68W15 - Distributed algorithms 68W20 - Randomized algorithms 68W25 - Approximation algorithms 68W27 - Online algorithms; streaming algorithms 68W30 - Symbolic computation and algebraic computation 68W32 - Algorithms on strings 68W35 - Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.) 68W40 - Analysis of algorithms 68W50 - Evolutionary algorithms, genetic algorithms (computational aspects) 68W99 - Algorithms in computer science 70-XX - Mechanics of particles and systems 70-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of particles and systems 70-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems 70-02 - Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems 70-03 - History of mechanics of particles and systems 70-04 - Software, source code, etc. for problems pertaining to mechanics of particles and systems 70-05 - Experimental work for problems pertaining to mechanics of particles and systems 70-06 - Proceedings, conferences, collections, etc. pertaining to mechanics of particles and systems 70-08 - Computational methods for problems pertaining to mechanics of particles and systems 70-10 - Mathematical modeling or simulation for problems pertaining to mechanics of particles and systems 70-11 - Research data for problems pertaining to mechanics of particles and systems 70Axx - Axiomatics, foundations 70A05 - Axiomatics, foundations 70A99 - Axiomatics, foundations 70Bxx - Kinematics 70B05 - Kinematics of a particle 70B10 - Kinematics of a rigid body 70B15 - Kinematics of mechanisms and robots 70B99 - Kinematics 70Cxx - Statics 70C20 - Statics 70C99 - Statics 70Exx - Dynamics of a rigid body and of multibody systems 70E05 - Motion of the gyroscope 70E15 - Free motion of a rigid body 70E17 - Motion of a rigid body with a fixed point 70E18 - Motion of a rigid body in contact with a solid surface 70E20 - Perturbation methods for rigid body dynamics 70E40 - Integrable cases of motion in rigid body dynamics 70E45 - Higher-dimensional generalizations in rigid body dynamics 70E50 - Stability problems in rigid body dynamics 70E55 - Dynamics of multibody systems 70E60 - Robot dynamics and control of rigid bodies 70E99 - Dynamics of a rigid body and of multibody systems 70Fxx - Dynamics of a system of particles, including celestial mechanics 70F05 - Two-body problems 70F07 - Three-body problems 70F10 - (n)-body problems 70F15 - Celestial mechanics 70F16 - Collisions in celestial mechanics, regularization 70F17 - Inverse problems for systems of particles 70F20 - Holonomic systems related to the dynamics of a system of particles 70F25 - Nonholonomic systems related to the dynamics of a system of particles 70F35 - Collision of rigid or pseudo-rigid bodies 70F40 - Problems involving a system of particles with friction 70F45 - The dynamics of infinite particle systems 70F99 - Dynamics of a system of particles, including celestial mechanics 70Gxx - General models, approaches, and methods in mechanics of particles and systems 70G10 - Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics 70G40 - Topological and differential topological methods for problems in mechanics 70G45 - Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 70G55 - Algebraic geometry methods for problems in mechanics 70G60 - Dynamical systems methods for problems in mechanics 70G65 - Symmetries, Lie group and Lie algebra methods for problems in mechanics 70G70 - Functional analytic methods for problems in mechanics 70G75 - Variational methods for problems in mechanics 70G99 - General models, approaches, and methods in mechanics of particles and systems 70Hxx - Hamiltonian and Lagrangian mechanics 70H03 - Lagrange's equations 70H05 - Hamilton's equations 70H06 - Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics 70H07 - Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics 70H08 - Nearly integrable Hamiltonian systems, KAM theory 70H09 - Perturbation theories for problems in Hamiltonian and Lagrangian mechanics 70H11 - Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics 70H12 - Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics 70H14 - Stability problems for problems in Hamiltonian and Lagrangian mechanics 70H15 - Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics 70H20 - Hamilton-Jacobi equations in mechanics 70H25 - Hamilton's principle 70H30 - Other variational principles in mechanics 70H33 - Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics 70H40 - Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics 70H45 - Constrained dynamics, Dirac's theory of constraints 70H50 - Higher-order theories for problems in Hamiltonian and Lagrangian mechanics 70H99 - Hamiltonian and Lagrangian mechanics 70Jxx - Linear vibration theory 70J10 - Modal analysis in linear vibration theory 70J25 - Stability for problems in linear vibration theory 70J30 - Free motions in linear vibration theory 70J35 - Forced motions in linear vibration theory 70J40 - Parametric resonances in linear vibration theory 70J50 - Systems arising from the discretization of structural vibration problems 70J99 - Linear vibration theory 70Kxx - Nonlinear dynamics in mechanics 70K05 - Phase plane analysis, limit cycles for nonlinear problems in mechanics 70K20 - Stability for nonlinear problems in mechanics 70K25 - Free motions for nonlinear problems in mechanics 70K28 - Parametric resonances for nonlinear problems in mechanics 70K30 - Nonlinear resonances for nonlinear problems in mechanics 70K40 - Forced motions for nonlinear problems in mechanics 70K42 - Equilibria and periodic trajectories for nonlinear problems in mechanics 70K43 - Quasi-periodic motions and invariant tori for nonlinear problems in mechanics 70K44 - Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics 70K45 - Normal forms for nonlinear problems in mechanics 70K50 - Bifurcations and instability for nonlinear problems in mechanics 70K55 - Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics 70K60 - General perturbation schemes for nonlinear problems in mechanics 70K65 - Averaging of perturbations for nonlinear problems in mechanics 70K70 - Systems with slow and fast motions for nonlinear problems in mechanics 70K75 - Nonlinear modes 70K99 - Nonlinear dynamics in mechanics 70Lxx - Random and stochastic aspects of the mechanics of particles and systems 70L05 - Random vibrations in mechanics of particles and systems 70L10 - Stochastic geometric mechanics 70L99 - Random and stochastic aspects of the mechanics of particles and systems 70Mxx - Orbital mechanics 70M20 - Orbital mechanics 70M99 - Orbital mechanics 70Pxx - Variable mass, rockets 70P05 - Variable mass, rockets 70P99 - Variable mass, rockets 70Qxx - Control of mechanical systems 70Q05 - Control of mechanical systems 70Q99 - Control of mechanical systems 70Sxx - Classical field theories 70S05 - Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 70S10 - Symmetries and conservation laws in mechanics of particles and systems 70S15 - Yang-Mills and other gauge theories in mechanics of particles and systems 70S20 - More general nonquantum field theories in mechanics of particles and systems 70S99 - Classical field theories 74-XX - Mechanics of deformable solids 74-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of deformable solids 74-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids 74-02 - Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 74-03 - History of mechanics of deformable solids 74-04 - Software, source code, etc. for problems pertaining to mechanics of deformable solids 74-05 - Experimental work for problems pertaining to mechanics of deformable solids 74-06 - Proceedings, conferences, collections, etc. pertaining to mechanics of deformable solids 74-10 - Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids 74-11 - Research data for problems pertaining to mechanics of deformable solids 74Axx - Generalities, axiomatics, foundations of continuum mechanics of solids 74A05 - Kinematics of deformation 74A10 - Stress 74A15 - Thermodynamics in solid mechanics 74A20 - Theory of constitutive functions in solid mechanics 74A25 - Molecular, statistical, and kinetic theories in solid mechanics 74A30 - Nonsimple materials 74A35 - Polar materials 74A40 - Random materials and composite materials 74A45 - Theories of fracture and damage 74A50 - Structured surfaces and interfaces, coexistent phases 74A55 - Theories of friction (tribology) 74A60 - Micromechanical theories 74A65 - Reactive materials 74A70 - Peridynamics 74A99 - Generalities, axiomatics, foundations of continuum mechanics of solids 74Bxx - Elastic materials 74B05 - Classical linear elasticity 74B10 - Linear elasticity with initial stresses 74B15 - Equations linearized about a deformed state (small deformations superposed on large) 74B20 - Nonlinear elasticity 74B99 - Elastic materials 74Cxx - Plastic materials, materials of stress-rate and internal-variable type 74C05 - Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74C10 - Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) 74C15 - Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) 74C20 - Large-strain, rate-dependent theories of plasticity 74C99 - Plastic materials, materials of stress-rate and internal-variable type 74Dxx - Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) 74D05 - Linear constitutive equations for materials with memory 74D10 - Nonlinear constitutive equations for materials with memory 74D99 - Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) 74Exx - Material properties given special treatment 74E05 - Inhomogeneity in solid mechanics 74E10 - Anisotropy in solid mechanics 74E15 - Crystalline structure 74E20 - Granularity 74E25 - Texture in solid mechanics 74E30 - Composite and mixture properties 74E35 - Random structure in solid mechanics 74E40 - Chemical structure in solid mechanics 74E99 - Material properties given special treatment 74Fxx - Coupling of solid mechanics with other effects 74F05 - Thermal effects in solid mechanics 74F10 - Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74F15 - Electromagnetic effects in solid mechanics 74F20 - Mixture effects in solid mechanics 74F25 - Chemical and reactive effects in solid mechanics 74F99 - Coupling of solid mechanics with other effects 74Gxx - Equilibrium (steady-state) problems in solid mechanics 74G05 - Explicit solutions of equilibrium problems in solid mechanics 74G10 - Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics 74G15 - Numerical approximation of solutions of equilibrium problems in solid mechanics 74G22 - Existence of solutions of equilibrium problems in solid mechanics 74G30 - Uniqueness of solutions of equilibrium problems in solid mechanics 74G35 - Multiplicity of solutions of equilibrium problems in solid mechanics 74G40 - Regularity of solutions of equilibrium problems in solid mechanics 74G45 - Bounds for solutions of equilibrium problems in solid mechanics 74G50 - Saint-Venant's principle 74G55 - Qualitative behavior of solutions of equilibrium problems in solid mechanics 74G60 - Bifurcation and buckling 74G65 - Energy minimization in equilibrium problems in solid mechanics 74G70 - Stress concentrations, singularities in solid mechanics 74G75 - Inverse problems in equilibrium solid mechanics 74G99 - Equilibrium (steady-state) problems in solid mechanics 74Hxx - Dynamical problems in solid mechanics 74H05 - Explicit solutions of dynamical problems in solid mechanics 74H10 - Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics 74H15 - Numerical approximation of solutions of dynamical problems in solid mechanics 74H20 - Existence of solutions of dynamical problems in solid mechanics 74H25 - Uniqueness of solutions of dynamical problems in solid mechanics 74H30 - Regularity of solutions of dynamical problems in solid mechanics 74H35 - Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics 74H40 - Long-time behavior of solutions for dynamical problems in solid mechanics 74H45 - Vibrations in dynamical problems in solid mechanics 74H50 - Random vibrations in dynamical problems in solid mechanics 74H55 - Stability of dynamical problems in solid mechanics 74H60 - Dynamical bifurcation of solutions to dynamical problems in solid mechanics 74H65 - Chaotic behavior of solutions to dynamical problems in solid mechanics 74H75 - Inverse problems in dynamical solid mechanics 74H80 - Energy minimization in dynamical problems in solid mechanics 74H99 - Dynamical problems in solid mechanics 74Jxx - Waves in solid mechanics 74J05 - Linear waves in solid mechanics 74J10 - Bulk waves in solid mechanics 74J15 - Surface waves in solid mechanics 74J20 - Wave scattering in solid mechanics 74J25 - Inverse problems for waves in solid mechanics 74J30 - Nonlinear waves in solid mechanics 74J35 - Solitary waves in solid mechanics 74J40 - Shocks and related discontinuities in solid mechanics 74J99 - Waves in solid mechanics 74Kxx - Thin bodies, structures 74K05 - Strings 74K10 - Rods (beams, columns, shafts, arches, rings, etc.) 74K15 - Membranes 74K20 - Plates 74K25 - Shells 74K30 - Junctions 74K35 - Thin films 74K99 - Thin bodies, structures 74Lxx - Special subfields of solid mechanics 74L05 - Geophysical solid mechanics 74L10 - Soil and rock mechanics 74L15 - Biomechanical solid mechanics 74L99 - Special subfields of solid mechanics 74Mxx - Special kinds of problems in solid mechanics 74M05 - Control, switches and devices (``smart materials'') in solid mechanics 74M10 - Friction in solid mechanics 74M15 - Contact in solid mechanics 74M20 - Impact in solid mechanics 74M25 - Micromechanics of solids 74M99 - Special kinds of problems in solid mechanics 74Nxx - Phase transformations in solids 74N05 - Crystals in solids 74N10 - Displacive transformations in solids 74N15 - Analysis of microstructure in solids 74N20 - Dynamics of phase boundaries in solids 74N25 - Transformations involving diffusion in solids 74N30 - Problems involving hysteresis in solids 74N99 - Phase transformations in solids 74Pxx - Optimization problems in solid mechanics 74P05 - Compliance or weight optimization in solid mechanics 74P10 - Optimization of other properties in solid mechanics 74P15 - Topological methods for optimization problems in solid mechanics 74P20 - Geometrical methods for optimization problems in solid mechanics 74P99 - Optimization problems in solid mechanics 74Qxx - Homogenization, determination of effective properties in solid mechanics 74Q05 - Homogenization in equilibrium problems of solid mechanics 74Q10 - Homogenization and oscillations in dynamical problems of solid mechanics 74Q15 - Effective constitutive equations in solid mechanics 74Q20 - Bounds on effective properties in solid mechanics 74Q99 - Homogenization, determination of effective properties in solid mechanics 74Rxx - Fracture and damage 74R05 - Brittle damage 74R10 - Brittle fracture 74R15 - High-velocity fracture 74R20 - Anelastic fracture and damage 74R99 - Fracture and damage 74Sxx - Numerical and other methods in solid mechanics 74S05 - Finite element methods applied to problems in solid mechanics 74S10 - Finite volume methods applied to problems in solid mechanics 74S15 - Boundary element methods applied to problems in solid mechanics 74S20 - Finite difference methods applied to problems in solid mechanics 74S22 - Isogeometric methods applied to problems in solid mechanics 74S25 - Spectral and related methods applied to problems in solid mechanics 74S40 - Applications of fractional calculus in solid mechanics 74S50 - Applications of graph theory in solid mechanics 74S60 - Stochastic and other probabilistic methods applied to problems in solid mechanics 74S70 - Complex-variable methods applied to problems in solid mechanics 74S99 - Numerical and other methods in solid mechanics 76-XX - Fluid mechanics 76-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to fluid mechanics 76-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics 76-02 - Research exposition (monographs, survey articles) pertaining to fluid mechanics 76-03 - History of fluid mechanics 76-04 - Software, source code, etc. for problems pertaining to fluid mechanics 76-05 - Experimental work for problems pertaining to fluid mechanics 76-06 - Proceedings, conferences, collections, etc. pertaining to fluid mechanics 76-10 - Mathematical modeling or simulation for problems pertaining to fluid mechanics 76-11 - Research data for problems pertaining to fluid mechanics 76Axx - Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena 76A02 - Foundations of fluid mechanics 76A05 - Non-Newtonian fluids 76A10 - Viscoelastic fluids 76A15 - Liquid crystals 76A20 - Thin fluid films 76A25 - Superfluids (classical aspects) 76A30 - Traffic and pedestrian flow models 76A99 - Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena 76Bxx - Incompressible inviscid fluids 76B03 - Existence, uniqueness, and regularity theory for incompressible inviscid fluids 76B07 - Free-surface potential flows for incompressible inviscid fluids 76B10 - Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 76B15 - Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76B20 - Ship waves 76B25 - Solitary waves for incompressible inviscid fluids 76B45 - Capillarity (surface tension) for incompressible inviscid fluids 76B47 - Vortex flows for incompressible inviscid fluids 76B55 - Internal waves for incompressible inviscid fluids 76B70 - Stratification effects in inviscid fluids 76B75 - Flow control and optimization for incompressible inviscid fluids 76B99 - Incompressible inviscid fluids 76Dxx - Incompressible viscous fluids 76D03 - Existence, uniqueness, and regularity theory for incompressible viscous fluids 76D05 - Navier-Stokes equations for incompressible viscous fluids 76D06 - Statistical solutions of Navier-Stokes and related equations 76D07 - Stokes and related (Oseen, etc.) flows 76D08 - Lubrication theory 76D09 - Viscous-inviscid interaction 76D10 - Boundary-layer theory, separation and reattachment, higher-order effects 76D17 - Viscous vortex flows 76D25 - Wakes and jets 76D27 - Other free boundary flows; Hele-Shaw flows 76D33 - Waves for incompressible viscous fluids 76D45 - Capillarity (surface tension) for incompressible viscous fluids 76D50 - Stratification effects in viscous fluids 76D55 - Flow control and optimization for incompressible viscous fluids 76D99 - Incompressible viscous fluids 76Exx - Hydrodynamic stability 76E05 - Parallel shear flows in hydrodynamic stability 76E06 - Convection in hydrodynamic stability 76E07 - Rotation in hydrodynamic stability 76E09 - Stability and instability of nonparallel flows in hydrodynamic stability 76E15 - Absolute and convective instability and stability in hydrodynamic stability 76E17 - Interfacial stability and instability in hydrodynamic stability 76E19 - Compressibility effects in hydrodynamic stability 76E20 - Stability and instability of geophysical and astrophysical flows 76E25 - Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 76E30 - Nonlinear effects in hydrodynamic stability 76E99 - Hydrodynamic stability 76Fxx - Turbulence 76F02 - Fundamentals of turbulence 76F05 - Isotropic turbulence; homogeneous turbulence 76F06 - Transition to turbulence 76F10 - Shear flows and turbulence 76F20 - Dynamical systems approach to turbulence 76F25 - Turbulent transport, mixing 76F30 - Renormalization and other field-theoretical methods for turbulence 76F35 - Convective turbulence 76F40 - Turbulent boundary layers 76F45 - Stratification effects in turbulence 76F50 - Compressibility effects in turbulence 76F55 - Statistical turbulence modeling 76F60 - (k)-(varepsilon) modeling in turbulence 76F65 - Direct numerical and large eddy simulation of turbulence 76F70 - Control of turbulent flows 76F80 - Turbulent combustion; reactive turbulence 76F99 - Turbulence 76Gxx - General aerodynamics and subsonic flows 76G25 - General aerodynamics and subsonic flows 76G99 - General aerodynamics and subsonic flows 76Hxx - Transonic flows 76H05 - Transonic flows 76H99 - Transonic flows 76Jxx - Supersonic flows 76J20 - Supersonic flows 76J99 - Supersonic flows 76Kxx - Hypersonic flows 76K05 - Hypersonic flows 76K99 - Hypersonic flows 76Lxx - Shock waves and blast waves in fluid mechanics 76L05 - Shock waves and blast waves in fluid mechanics 76L99 - Shock waves and blast waves in fluid mechanics 76Mxx - Basic methods in fluid mechanics 76M10 - Finite element methods applied to problems in fluid mechanics 76M12 - Finite volume methods applied to problems in fluid mechanics 76M15 - Boundary element methods applied to problems in fluid mechanics 76M20 - Finite difference methods applied to problems in fluid mechanics 76M21 - Inverse problems in fluid mechanics 76M22 - Spectral methods applied to problems in fluid mechanics 76M23 - Vortex methods applied to problems in fluid mechanics 76M27 - Visualization algorithms applied to problems in fluid mechanics 76M28 - Particle methods and lattice-gas methods 76M30 - Variational methods applied to problems in fluid mechanics 76M35 - Stochastic analysis applied to problems in fluid mechanics 76M40 - Complex variables methods applied to problems in fluid mechanics 76M45 - Asymptotic methods, singular perturbations applied to problems in fluid mechanics 76M50 - Homogenization applied to problems in fluid mechanics 76M55 - Dimensional analysis and similarity applied to problems in fluid mechanics 76M60 - Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics 76M99 - Basic methods in fluid mechanics 76Nxx - Compressible fluids and gas dynamics 76N06 - Compressible Navier-Stokes equations 76N10 - Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76N15 - Gas dynamics (general theory) 76N17 - Viscous-inviscid interaction for compressible fluids and gas dynamics 76N20 - Boundary-layer theory for compressible fluids and gas dynamics 76N25 - Flow control and optimization for compressible fluids and gas dynamics 76N30 - Waves in compressible fluids 76N99 - Compressible fluids and gas dynamics 76Pxx - Rarefied gas flows, Boltzmann equation in fluid mechanics 76P05 - Rarefied gas flows, Boltzmann equation in fluid mechanics 76P99 - Rarefied gas flows, Boltzmann equation in fluid mechanics 76Qxx - Hydro- and aero-acoustics 76Q05 - Hydro- and aero-acoustics 76Q99 - Hydro- and aero-acoustics 76Rxx - Diffusion and convection 76R05 - Forced convection 76R10 - Free convection 76R50 - Diffusion 76R99 - Diffusion and convection 76Sxx - Flows in porous media; filtration; seepage 76S05 - Flows in porous media; filtration; seepage 76S99 - Flows in porous media; filtration; seepage 76Txx - Multiphase and multicomponent flows 76T06 - Liquid-liquid two component flows 76T10 - Liquid-gas two-phase flows, bubbly flows 76T15 - Dusty-gas two-phase flows 76T17 - Two gas multicomponent flows 76T20 - Suspensions 76T25 - Granular flows 76T30 - Three or more component flows 76T99 - Multiphase and multicomponent flows 76Uxx - Rotating fluids 76U05 - General theory of rotating fluids 76U60 - Geophysical flows 76U65 - Rossby waves 76U99 - Rotating fluids 76Vxx - Reaction effects in flows 76V05 - Reaction effects in flows 76V99 - Reaction effects in flows 76Wxx - Magnetohydrodynamics and electrohydrodynamics 76W05 - Magnetohydrodynamics and electrohydrodynamics 76W99 - Magnetohydrodynamics and electrohydrodynamics 76Xxx - Ionized gas flow in electromagnetic fields; plasmic flow 76X05 - Ionized gas flow in electromagnetic fields; plasmic flow 76X99 - Ionized gas flow in electromagnetic fields; plasmic flow 76Yxx - Quantum hydrodynamics and relativistic hydrodynamics 76Y05 - Quantum hydrodynamics and relativistic hydrodynamics 76Y99 - Quantum hydrodynamics and relativistic hydrodynamics 76Zxx - Biological fluid mechanics 76Z05 - Physiological flows 76Z10 - Biopropulsion in water and in air 76Z99 - Biological fluid mechanics 78-XX - Optics, electromagnetic theory 78-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to optics and electromagnetic theory 78-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory 78-02 - Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory 78-03 - History of optics and electromagnetic theory 78-04 - Software, source code, etc. for problems pertaining to optics and electromagnetic theory 78-05 - Experimental work for problems pertaining to optics and electromagnetic theory 78-06 - Proceedings, conferences, collections, etc. pertaining to optics and electromagnetic theory 78-10 - Mathematical modeling or simulation for problems pertaining to optics and electromagnetic theory 78-11 - Research data for problems pertaining to optics and electromagnetic theory 78Axx - General topics in optics and electromagnetic theory 78A02 - Foundations in optics and electromagnetic theory 78A05 - Geometric optics 78A10 - Physical optics 78A15 - Electron optics 78A20 - Space charge waves 78A25 - Electromagnetic theory (general) 78A30 - Electro- and magnetostatics 78A35 - Motion of charged particles 78A37 - Ion traps 78A40 - Waves and radiation in optics and electromagnetic theory 78A45 - Diffraction, scattering 78A46 - Inverse problems (including inverse scattering) in optics and electromagnetic theory 78A48 - Composite media; random media in optics and electromagnetic theory 78A50 - Antennas, waveguides in optics and electromagnetic theory 78A55 - Technical applications of optics and electromagnetic theory 78A57 - Electrochemistry 78A60 - Lasers, masers, optical bistability, nonlinear optics 78A70 - Biological applications of optics and electromagnetic theory 78A97 - Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in Section 78-XX) 78A99 - General topics in optics and electromagnetic theory 78Mxx - Basic methods for problems in optics and electromagnetic theory 78M05 - Method of moments applied to problems in optics and electromagnetic theory 78M10 - Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78M12 - Finite volume methods, finite integration techniques applied to problems in optics and electromagnetic theory 78M15 - Boundary element methods applied to problems in optics and electromagnetic theory 78M16 - Multipole methods applied to problems in optics and electromagnetic theory 78M20 - Finite difference methods applied to problems in optics and electromagnetic theory 78M22 - Spectral, collocation and related methods applied to problems in optics and electromagnetic theory 78M30 - Variational methods applied to problems in optics and electromagnetic theory 78M31 - Monte Carlo methods applied to problems in optics and electromagnetic theory 78M32 - Neural and heuristic methods applied to problems in optics and electromagnetic theory 78M34 - Model reduction in optics and electromagnetic theory 78M35 - Asymptotic analysis in optics and electromagnetic theory 78M40 - Homogenization in optics and electromagnetic theory 78M50 - Optimization problems in optics and electromagnetic theory 78M99 - Basic methods for problems in optics and electromagnetic theory 80-XX - Classical thermodynamics, heat transfer 80-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to classical thermodynamics 80-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics 80-02 - Research exposition (monographs, survey articles) pertaining to classical thermodynamics 80-03 - History of classical thermodynamics 80-04 - Software, source code, etc. for problems pertaining to classical thermodynamics 80-05 - Experimental work for problems pertaining to classical thermodynamics 80-06 - Proceedings, conferences, collections, etc. pertaining to classical thermodynamics 80-10 - Mathematical modeling or simulation for problems pertaining to classical thermodynamics 80-11 - Research data for problems pertaining to classical thermodynamics 80Axx - Thermodynamics and heat transfer 80A05 - Foundations of thermodynamics and heat transfer 80A10 - Classical and relativistic thermodynamics 80A17 - Thermodynamics of continua 80A19 - Diffusive and convective heat and mass transfer, heat flow 80A21 - Radiative heat transfer 80A22 - Stefan problems, phase changes, etc. 80A23 - Inverse problems in thermodynamics and heat transfer 80A25 - Combustion 80A30 - Chemical kinetics in thermodynamics and heat transfer 80A32 - Chemically reacting flows 80A50 - Chemistry (general) in thermodynamics and heat transfer 80A99 - Thermodynamics and heat transfer 80Mxx - Basic methods in thermodynamics and heat transfer 80M10 - Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer 80M12 - Finite volume methods applied to problems in thermodynamics and heat transfer 80M15 - Boundary element methods applied to problems in thermodynamics and heat transfer 80M20 - Finite difference methods applied to problems in thermodynamics and heat transfer 80M22 - Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer 80M30 - Variational methods applied to problems in thermodynamics and heat transfer 80M31 - Monte Carlo methods applied to problems in thermodynamics and heat transfer 80M35 - Asymptotic analysis for problems in thermodynamics and heat transfer 80M40 - Homogenization for problems in thermodynamics and heat transfer 80M50 - Optimization problems in thermodynamics and heat transfer 80M60 - Stochastic analysis in thermodynamics and heat transfer 80M99 - Basic methods in thermodynamics and heat transfer 81-XX - Quantum theory 81-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to quantum theory 81-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory 81-02 - Research exposition (monographs, survey articles) pertaining to quantum theory 81-03 - History of quantum theory 81-04 - Software, source code, etc. for problems pertaining to quantum theory 81-05 - Experimental work for problems pertaining to quantum theory 81-06 - Proceedings, conferences, collections, etc. pertaining to quantum theory 81-08 - Computational methods for problems pertaining to quantum theory 81-10 - Mathematical modeling or simulation for problems pertaining to quantum theory 81-11 - Research data for problems pertaining to quantum theory 81Pxx - Foundations, quantum information and its processing, quantum axioms, and philosophy 81P05 - General and philosophical questions in quantum theory 81P10 - Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 81P13 - Contextuality in quantum theory 81P15 - Quantum measurement theory, state operations, state preparations 81P16 - Quantum state spaces, operational and probabilistic concepts 81P17 - Quantum entropies 81P18 - Quantum state tomography, quantum state discrimination 81P20 - Stochastic mechanics (including stochastic electrodynamics) 81P40 - Quantum coherence, entanglement, quantum correlations 81P42 - Entanglement measures, concurrencies, separability criteria 81P43 - Quantum discord 81P45 - Quantum information, communication, networks (quantum-theoretic aspects) 81P47 - Quantum channels, fidelity 81P48 - LOCC, teleportation, dense coding, remote state operations, distillation 81P50 - Quantum state estimation, approximate cloning 81P55 - Special bases (entangled, mutual unbiased, etc.) 81P65 - Quantum gates 81P68 - Quantum computation 81P70 - Quantum coding (general) 81P73 - Computational stability and error-correcting codes for quantum computation and communication processing 81P94 - Quantum cryptography (quantum-theoretic aspects) 81P99 - Foundations, quantum information and its processing, quantum axioms, and philosophy 81Qxx - General mathematical topics and methods in quantum theory 81Q05 - Closed and approximate solutions to the Schr�dinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81Q10 - Selfadjoint operator theory in quantum theory, including spectral analysis 81Q12 - Nonselfadjoint operator theory in quantum theory including creation and destruction operators 81Q15 - Perturbation theories for operators and differential equations in quantum theory 81Q20 - Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 81Q30 - Feynman integrals and graphs; applications of algebraic topology and algebraic geometry 81Q35 - Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices 81Q37 - Quantum dots, waveguides, ratchets, etc. 81Q40 - Bethe-Salpeter and other integral equations arising in quantum theory 81Q50 - Quantum chaos 81Q60 - Supersymmetry and quantum mechanics 81Q65 - Alternative quantum mechanics (including hidden variables, etc.) 81Q70 - Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory 81Q80 - Special quantum systems, such as solvable systems 81Q93 - Quantum control 81Q99 - General mathematical topics and methods in quantum theory 81Rxx - Groups and algebras in quantum theory 81R05 - Finite-dimensional groups and algebras motivated by physics and their representations 81R10 - Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations 81R12 - Groups and algebras in quantum theory and relations with integrable systems 81R15 - Operator algebra methods applied to problems in quantum theory 81R20 - Covariant wave equations in quantum theory, relativistic quantum mechanics 81R25 - Spinor and twistor methods applied to problems in quantum theory 81R30 - Coherent states 81R40 - Symmetry breaking in quantum theory 81R50 - Quantum groups and related algebraic methods applied to problems in quantum theory 81R60 - Noncommutative geometry in quantum theory 81R99 - Groups and algebras in quantum theory 81Sxx - General quantum mechanics and problems of quantization 81S05 - Commutation relations and statistics as related to quantum mechanics (general) 81S07 - Uncertainty relations, also entropic 81S08 - Canonical quantization 81S10 - Geometry and quantization, symplectic methods 81S20 - Stochastic quantization 81S22 - Open systems, reduced dynamics, master equations, decoherence 81S25 - Quantum stochastic calculus 81S30 - Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics 81S40 - Path integrals in quantum mechanics 81S99 - General quantum mechanics and problems of quantization 81Txx - Quantum field theory; related classical field theories 81T05 - Axiomatic quantum field theory; operator algebras 81T08 - Constructive quantum field theory 81T10 - Model quantum field theories 81T11 - Higher spin theories 81T12 - Effective quantum field theories 81T13 - Yang-Mills and other gauge theories in quantum field theory 81T15 - Perturbative methods of renormalization applied to problems in quantum field theory 81T16 - Nonperturbative methods of renormalization applied to problems in quantum field theory 81T17 - Renormalization group methods applied to problems in quantum field theory 81T18 - Feynman diagrams 81T20 - Quantum field theory on curved space or space-time backgrounds 81T25 - Quantum field theory on lattices 81T27 - Continuum limits in quantum field theory 81T28 - Thermal quantum field theory 81T30 - String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T32 - Matrix models and tensor models for quantum field theory 81T33 - Dimensional compactification in quantum field theory 81T35 - Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) 81T40 - Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81T45 - Topological field theories in quantum mechanics 81T50 - Anomalies in quantum field theory 81T55 - Casimir effect in quantum field theory 81T60 - Supersymmetric field theories in quantum mechanics 81T70 - Quantization in field theory; cohomological methods 81T75 - Noncommutative geometry methods in quantum field theory 81T99 - Quantum field theory; related classical field theories 81Uxx - Quantum scattering theory 81U05 - (2)-body potential quantum scattering theory 81U10 - (n)-body potential quantum scattering theory 81U15 - Exactly and quasi-solvable systems arising in quantum theory 81U20 - (S)-matrix theory, etc. in quantum theory 81U24 - Resonances in quantum scattering theory 81U26 - Tunneling in quantum theory 81U30 - Dispersion theory, dispersion relations arising in quantum theory 81U35 - Inelastic and multichannel quantum scattering 81U40 - Inverse scattering problems in quantum theory 81U90 - Particle decays 81U99 - Quantum scattering theory 81Vxx - Applications of quantum theory to specific physical systems 81V05 - Strong interaction, including quantum chromodynamics 81V10 - Electromagnetic interaction; quantum electrodynamics 81V15 - Weak interaction in quantum theory 81V17 - Gravitational interaction in quantum theory 81V19 - Other fundamental interactions in quantum theory 81V22 - Unified quantum theories 81V25 - Other elementary particle theory in quantum theory 81V27 - Anyons 81V35 - Nuclear physics 81V45 - Atomic physics 81V55 - Molecular physics 81V60 - Mono-, di- and multipole moments (EM and other), gyromagnetic relations 81V65 - Quantum dots as quasi particles 81V70 - Many-body theory; quantum Hall effect 81V72 - Particle exchange symmetries in quantum theory (general) 81V73 - Bosonic systems in quantum theory 81V74 - Fermionic systems in quantum theory 81V80 - Quantum optics 81V99 - Applications of quantum theory to specific physical systems 82-XX - Statistical mechanics, structure of matter 82-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistical mechanics 82-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics 82-02 - Research exposition (monographs, survey articles) pertaining to statistical mechanics 82-03 - History of statistical mechanics 82-04 - Software, source code, etc. for problems pertaining to statistical mechanics 82-05 - Experimental work for problems pertaining to statistical mechanics 82-06 - Proceedings, conferences, collections, etc. pertaining to statistical mechanics 82-10 - Mathematical modeling or simulation for problems pertaining to statistical mechanics 82-11 - Research data for problems pertaining to statistical mechanics 82Bxx - Equilibrium statistical mechanics 82B03 - Foundations of equilibrium statistical mechanics 82B05 - Classical equilibrium statistical mechanics (general) 82B10 - Quantum equilibrium statistical mechanics (general) 82B20 - Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B21 - Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics 82B23 - Exactly solvable models; Bethe ansatz 82B24 - Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics 82B26 - Phase transitions (general) in equilibrium statistical mechanics 82B27 - Critical phenomena in equilibrium statistical mechanics 82B28 - Renormalization group methods in equilibrium statistical mechanics 82B30 - Statistical thermodynamics 82B31 - Stochastic methods applied to problems in equilibrium statistical mechanics 82B35 - Irreversible thermodynamics, including Onsager-Machlup theory 82B40 - Kinetic theory of gases in equilibrium statistical mechanics 82B41 - Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 82B43 - Percolation 82B44 - Disordered systems (random Ising models, random Schr�dinger operators, etc.) in equilibrium statistical mechanics 82B99 - Equilibrium statistical mechanics 82Cxx - Time-dependent statistical mechanics (dynamic and nonequilibrium) 82C03 - Foundations of time-dependent statistical mechanics 82C05 - Classical dynamic and nonequilibrium statistical mechanics (general) 82C10 - Quantum dynamics and nonequilibrium statistical mechanics (general) 82C20 - Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 82C21 - Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics 82C22 - Interacting particle systems in time-dependent statistical mechanics 82C23 - Exactly solvable dynamic models in time-dependent statistical mechanics 82C24 - Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics 82C26 - Dynamic and nonequilibrium phase transitions (general) in statistical mechanics 82C27 - Dynamic critical phenomena in statistical mechanics 82C28 - Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics 82C31 - Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics 82C32 - Neural nets applied to problems in time-dependent statistical mechanics 82C35 - Irreversible thermodynamics, including Onsager-Machlup theory 82C40 - Kinetic theory of gases in time-dependent statistical mechanics 82C41 - Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics 82C43 - Time-dependent percolation in statistical mechanics 82C44 - Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics 82C70 - Transport processes in time-dependent statistical mechanics 82C99 - Time-dependent statistical mechanics (dynamic and nonequilibrium) 82Dxx - Applications of statistical mechanics to specific types of physical systems 82D03 - Statistical mechanics in condensed matter (general) 82D05 - Statistical mechanics of gases 82D10 - Statistical mechanics of plasmas 82D15 - Statistical mechanics of liquids 82D20 - Statistical mechanics of solids 82D25 - Statistical mechanics of crystals 82D30 - Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) 82D35 - Statistical mechanics of metals 82D37 - Statistical mechanics of semiconductors 82D40 - Statistical mechanics of magnetic materials 82D45 - Statistical mechanics of ferroelectrics 82D50 - Statistical mechanics of superfluids 82D55 - Statistical mechanics of superconductors 82D60 - Statistical mechanics of polymers 82D75 - Nuclear reactor theory; neutron transport 82D77 - Quantum waveguides, quantum wires 82D80 - Statistical mechanics of nanostructures and nanoparticles 82D99 - Applications of statistical mechanics to specific types of physical systems 82Mxx - Basic methods in statistical mechanics 82M10 - Finite element, Galerkin and related methods applied to problems in statistical mechanics 82M12 - Finite volume methods applied to problems in statistical mechanics 82M15 - Boundary element methods applied to problems in statistical mechanics 82M20 - Finite difference methods applied to problems in statistical mechanics 82M22 - Spectral, collocation and related (meshless) methods applied to problems in statistical mechanics 82M30 - Variational methods applied to problems in statistical mechanics 82M31 - Monte Carlo methods applied to problems in statistical mechanics 82M36 - Computational density functional analysis in statistical mechanics 82M37 - Computational molecular dynamics in statistical mechanics 82M60 - Stochastic analysis in statistical mechanics 82M99 - Basic methods in statistical mechanics 83-XX - Relativity and gravitational theory 83-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to relativity and gravitational theory 83-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory 83-02 - Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory 83-03 - History of relativity and gravitational theory 83-04 - Software, source code, etc. for problems pertaining to relativity and gravitational theory 83-05 - Experimental work for problems pertaining to relativity and gravitational theory 83-06 - Proceedings, conferences, collections, etc. pertaining to relativity and gravitational theory 83-08 - Computational methods for problems pertaining to relativity and gravitational theory 83-10 - Mathematical modeling or simulation for problems pertaining to relativity and gravitational theory 83-11 - Research data for problems pertaining to relativity and gravitational theory 83Axx - Special relativity 83A05 - Special relativity 83A99 - Special relativity 83Bxx - Observational and experimental questions in relativity and gravitational theory 83B05 - Observational and experimental questions in relativity and gravitational theory 83B99 - Observational and experimental questions in relativity and gravitational theory 83Cxx - General relativity 83C05 - Einstein's equations (general structure, canonical formalism, Cauchy problems) 83C10 - Equations of motion in general relativity and gravitational theory 83C15 - Exact solutions to problems in general relativity and gravitational theory 83C20 - Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory 83C22 - Einstein-Maxwell equations 83C25 - Approximation procedures, weak fields in general relativity and gravitational theory 83C27 - Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory 83C30 - Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory 83C35 - Gravitational waves 83C40 - Gravitational energy and conservation laws; groups of motions 83C45 - Quantization of the gravitational field 83C47 - Methods of quantum field theory in general relativity and gravitational theory 83C50 - Electromagnetic fields in general relativity and gravitational theory 83C55 - Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) 83C56 - Dark matter and dark energy 83C57 - Black holes 83C60 - Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism 83C65 - Methods of noncommutative geometry in general relativity 83C75 - Space-time singularities, cosmic censorship, etc. 83C80 - Analogues of general relativity in lower dimensions 83C99 - General relativity 83Dxx - Relativistic gravitational theories other than Einstein's, including asymmetric field theories 83D05 - Relativistic gravitational theories other than Einstein's, including asymmetric field theories 83D99 - Relativistic gravitational theories other than Einstein's, including asymmetric field theories 83Exx - Unified, higher-dimensional and super field theories 83E05 - Geometrodynamics and the holographic principle 83E15 - Kaluza-Klein and other higher-dimensional theories 83E30 - String and superstring theories in gravitational theory 83E50 - Supergravity 83E99 - Unified, higher-dimensional and super field theories 83Fxx - Relativistic cosmology 83F05 - Relativistic cosmology 83F99 - Relativistic cosmology 85-XX - Astronomy and astrophysics 85-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to astronomy and astrophysics 85-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to astronomy and astrophysics 85-02 - Research exposition (monographs, survey articles) pertaining to astronomy and astrophysics 85-03 - History of astronomy and astrophysics 85-04 - Software, source code, etc. for problems pertaining to astronomy and astrophysics 85-05 - Experimental work for problems pertaining to astronomy and astrophysics 85-06 - Proceedings, conferences, collections, etc. pertaining to astronomy and astrophysics 85-08 - Computational methods for problems pertaining to astronomy and astrophysics 85-10 - Mathematical modeling or simulation for problems pertaining to astronomy and astrophysics 85-11 - Research data for problems pertaining to astronomy and astrophysics 85Axx - Astronomy and astrophysics 85A04 - General questions in astronomy and astrophysics 85A05 - Galactic and stellar dynamics 85A15 - Galactic and stellar structure 85A20 - Planetary atmospheres 85A25 - Radiative transfer in astronomy and astrophysics 85A30 - Hydrodynamic and hydromagnetic problems in astronomy and astrophysics 85A35 - Statistical astronomy 85A40 - Astrophysical cosmology 85A99 - Astronomy and astrophysics 86-XX - Geophysics 86-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geophysics 86-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geophysics 86-02 - Research exposition (monographs, survey articles) pertaining to geophysics 86-03 - History of geophysics 86-04 - Software, source code, etc. for problems pertaining to geophysics 86-05 - Experimental work for problems pertaining to geophysics 86-06 - Proceedings, conferences, collections, etc. pertaining to geophysics 86-08 - Computational methods for problems pertaining to geophysics 86-10 - Mathematical modeling or simulation for problems pertaining to geophysics 86-11 - Research data for problems pertaining to geophysics 86Axx - Geophysics 86A04 - General questions in geophysics 86A05 - Hydrology, hydrography, oceanography 86A08 - Climate science and climate modeling 86A10 - Meteorology and atmospheric physics 86A15 - Seismology (including tsunami modeling), earthquakes 86A20 - Potentials, prospecting 86A22 - Inverse problems in geophysics 86A25 - Geo-electricity and geomagnetism 86A30 - Geodesy, mapping problems 86A32 - Geostatistics 86A40 - Glaciology 86A60 - Geological problems 86A70 - Vulcanology; magma and lava flow 86A99 - Geophysics 90-XX - Operations research, mathematical programming 90-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operations research and mathematical programming 90-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming 90-02 - Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming 90-03 - History of operations research and mathematical programming 90-04 - Software, source code, etc. for problems pertaining to operations research and mathematical programming 90-05 - Experimental work for problems pertaining to operations research and mathematical programming 90-06 - Proceedings, conferences, collections, etc. pertaining to operations research and mathematical programming 90-08 - Computational methods for problems pertaining to operations research and mathematical programming 90-10 - Mathematical modeling or simulation for problems pertaining to operations research and mathematical programming 90-11 - Research data for problems pertaining to operations research and mathematical programming 90Bxx - Operations research and management science 90B05 - Inventory, storage, reservoirs 90B06 - Transportation, logistics and supply chain management 90B10 - Deterministic network models in operations research 90B15 - Stochastic network models in operations research 90B18 - Communication networks in operations research 90B20 - Traffic problems in operations research 90B22 - Queues and service in operations research 90B25 - Reliability, availability, maintenance, inspection in operations research 90B30 - Production models 90B35 - Deterministic scheduling theory in operations research 90B36 - Stochastic scheduling theory in operations research 90B40 - Search theory 90B50 - Management decision making, including multiple objectives 90B60 - Marketing, advertising 90B70 - Theory of organizations, manpower planning in operations research 90B80 - Discrete location and assignment 90B85 - Continuous location 90B90 - Case-oriented studies in operations research 90B99 - Operations research and management science 90Cxx - Mathematical programming 90C05 - Linear programming 90C06 - Large-scale problems in mathematical programming 90C08 - Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) 90C09 - Boolean programming 90C10 - Integer programming 90C11 - Mixed integer programming 90C15 - Stochastic programming 90C17 - Robustness in mathematical programming 90C20 - Quadratic programming 90C22 - Semidefinite programming 90C23 - Polynomial optimization 90C24 - Tropical optimization (e.g., max-plus optimization) 90C25 - Convex programming 90C26 - Nonconvex programming, global optimization 90C27 - Combinatorial optimization 90C29 - Multi-objective and goal programming 90C30 - Nonlinear programming 90C31 - Sensitivity, stability, parametric optimization 90C32 - Fractional programming 90C33 - Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C34 - Semi-infinite programming 90C35 - Programming involving graphs or networks 90C39 - Dynamic programming 90C40 - Markov and semi-Markov decision processes 90C46 - Optimality conditions and duality in mathematical programming 90C47 - Minimax problems in mathematical programming 90C48 - Programming in abstract spaces 90C49 - Extreme-point and pivoting methods 90C51 - Interior-point methods 90C52 - Methods of reduced gradient type 90C53 - Methods of quasi-Newton type 90C55 - Methods of successive quadratic programming type 90C56 - Derivative-free methods and methods using generalized derivatives 90C57 - Polyhedral combinatorics, branch-and-bound, branch-and-cut 90C59 - Approximation methods and heuristics in mathematical programming 90C60 - Abstract computational complexity for mathematical programming problems 90C70 - Fuzzy and other nonstochastic uncertainty mathematical programming 90C90 - Applications of mathematical programming 90C99 - Mathematical programming 91-XX - Game theory, economics, finance, and other social and behavioral sciences 91-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to game theory, economics, and finance 91-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance 91-02 - Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance 91-03 - History of game theory, economics, and finance 91-04 - Software, source code, etc. for problems pertaining to game theory, economics, and finance 91-05 - Experimental work for problems pertaining to game theory, economics, and finance 91-06 - Proceedings, conferences, collections, etc. pertaining to game theory, economics, and finance 91-08 - Computational methods for problems pertaining to game theory, economics, and finance 91-10 - Mathematical modeling or simulation for problems pertaining to game theory, economics, and finance 91-11 - Research data for problems pertaining to game theory, economics, and finance 91Axx - Game theory 91A05 - 2-person games 91A06 - (n)-person games, (n>2) 91A07 - Games with infinitely many players 91A10 - Noncooperative games 91A11 - Equilibrium refinements 91A12 - Cooperative games 91A14 - Potential and congestion games 91A15 - Stochastic games, stochastic differential games 91A16 - Mean field games (aspects of game theory) 91A18 - Games in extensive form 91A20 - Multistage and repeated games 91A22 - Evolutionary games 91A23 - Differential games (aspects of game theory) 91A24 - Positional games (pursuit and evasion, etc.) 91A25 - Dynamic games 91A26 - Rationality and learning in game theory 91A27 - Games with incomplete information, Bayesian games 91A28 - Signaling and communication in game theory 91A30 - Utility theory for games 91A35 - Decision theory for games 91A40 - Other game-theoretic models 91A43 - Games involving graphs 91A44 - Games involving topology, set theory, or logic 91A46 - Combinatorial games 91A50 - Discrete-time games 91A55 - Games of timing 91A60 - Probabilistic games; gambling 91A65 - Hierarchical games (including Stackelberg games) 91A68 - Algorithmic game theory and complexity 91A70 - Spaces of games 91A80 - Applications of game theory 91A81 - Quantum games 91A86 - Game theory and fuzziness 91A90 - Experimental studies 91A99 - Game theory 91Bxx - Mathematical economics 91B02 - Fundamental topics (basic mathematics, methodology; applicable to economics in general) 91B03 - Mechanism design theory 91B05 - Risk models (general) 91B06 - Decision theory 91B08 - Individual preferences 91B10 - Group preferences 91B12 - Voting theory 91B14 - Social choice 91B15 - Welfare economics 91B16 - Utility theory 91B18 - Public goods 91B24 - Microeconomic theory (price theory and economic markets) 91B26 - Auctions, bargaining, bidding and selling, and other market models 91B32 - Resource and cost allocation (including fair division, apportionment, etc.) 91B38 - Production theory, theory of the firm 91B39 - Labor markets 91B41 - Contract theory (moral hazard, adverse selection) 91B42 - Consumer behavior, demand theory 91B43 - Principal-agent models 91B44 - Economics of information 91B50 - General equilibrium theory 91B51 - Dynamic stochastic general equilibrium theory 91B52 - Special types of economic equilibria 91B54 - Special types of economic markets (including Cournot, Bertrand) 91B55 - Economic dynamics 91B60 - Trade models 91B62 - Economic growth models 91B64 - Macroeconomic theory (monetary models, models of taxation) 91B66 - Multisectoral models in economics 91B68 - Matching models 91B69 - Heterogeneous agent models 91B70 - Stochastic models in economics 91B72 - Spatial models in economics 91B74 - Economic models of real-world systems (e.g., electricity markets, etc.) 91B76 - Environmental economics (natural resource models, harvesting, pollution, etc.) 91B80 - Applications of statistical and quantum mechanics to economics (econophysics) 91B82 - Statistical methods; economic indices and measures 91B84 - Economic time series analysis 91B86 - Mathematical economics and fuzziness 91B99 - Mathematical economics 91Cxx - Social and behavioral sciences: general topics 91C05 - Measurement theory in the social and behavioral sciences 91C15 - One- and multidimensional scaling in the social and behavioral sciences 91C20 - Clustering in the social and behavioral sciences 91C99 - Social and behavioral sciences: general topics 91Dxx - Mathematical sociology (including anthropology) 91D10 - Models of societies, social and urban evolution 91D15 - Social learning 91D20 - Mathematical geography and demography 91D25 - Spatial models in sociology 91D30 - Social networks; opinion dynamics 91D35 - Manpower systems in sociology 91D99 - Mathematical sociology (including anthropology) 91Exx - Mathematical psychology 91E10 - Cognitive psychology 91E30 - Psychophysics and psychophysiology; perception 91E40 - Memory and learning in psychology 91E45 - Measurement and performance in psychology 91E99 - Mathematical psychology 91Fxx - Other social and behavioral sciences (mathematical treatment) 91F10 - History, political science 91F20 - Linguistics 91F99 - Other social and behavioral sciences (mathematical treatment) 91Gxx - Actuarial science and mathematical finance 91G05 - Actuarial mathematics 91G10 - Portfolio theory 91G15 - Financial markets 91G20 - Derivative securities (option pricing, hedging, etc.) 91G30 - Interest rates, asset pricing, etc. (stochastic models) 91G40 - Credit risk 91G45 - Financial networks (including contagion, systemic risk, regulation) 91G50 - Corporate finance (dividends, real options, etc.) 91G60 - Numerical methods (including Monte Carlo methods) 91G70 - Statistical methods; risk measures 91G80 - Financial applications of other theories 91G99 - Actuarial science and mathematical finance 92-XX - Biology and other natural sciences 92-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to biology 92-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology 92-02 - Research exposition (monographs, survey articles) pertaining to biology 92-03 - History of biology 92-04 - Software, source code, etc. for problems pertaining to biology 92-05 - Experimental work for problems pertaining to biology 92-06 - Proceedings, conferences, collections, etc. pertaining to biology 92-08 - Computational methods for problems pertaining to biology 92-10 - Mathematical modeling or simulation for problems pertaining to biology 92-11 - Research data for problems pertaining to biology 92Bxx - Mathematical biology in general 92B05 - General biology and biomathematics 92B10 - Taxonomy, cladistics, statistics in mathematical biology 92B15 - General biostatistics 92B20 - Neural networks for/in biological studies, artificial life and related topics 92B25 - Biological rhythms and synchronization 92B99 - Mathematical biology in general 92Cxx - Physiological, cellular and medical topics 92C05 - Biophysics 92C10 - Biomechanics 92C15 - Developmental biology, pattern formation 92C17 - Cell movement (chemotaxis, etc.) 92C20 - Neural biology 92C30 - Physiology (general) 92C32 - Pathology, pathophysiology 92C35 - Physiological flow 92C37 - Cell biology 92C40 - Biochemistry, molecular biology 92C42 - Systems biology, networks 92C45 - Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) 92C47 - Biosensors (not for medical applications) 92C50 - Medical applications (general) 92C55 - Biomedical imaging and signal processing 92C60 - Medical epidemiology 92C70 - Microbiology 92C75 - Biotechnology 92C80 - Plant biology 92C99 - Physiological, cellular and medical topics 92Dxx - Genetics and population dynamics 92D10 - Genetics and epigenetics 92D15 - Problems related to evolution 92D20 - Protein sequences, DNA sequences 92D25 - Population dynamics (general) 92D30 - Epidemiology 92D40 - Ecology 92D45 - Pest management 92D50 - Animal behavior 92D99 - Genetics and population dynamics 92Exx - Chemistry 92E10 - Molecular structure (graph-theoretic methods, methods of differential topology, etc.) 92E20 - Classical flows, reactions, etc. in chemistry 92E99 - Chemistry 92Fxx - Other natural sciences (mathematical treatment) 92F05 - Other natural sciences (mathematical treatment) 92F99 - Other natural sciences (mathematical treatment) 93-XX - Systems theory; control 93-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to systems and control theory 93-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory 93-02 - Research exposition (monographs, survey articles) pertaining to systems and control theory 93-03 - History of systems and control theory 93-04 - Software, source code, etc. for problems pertaining to systems and control theory 93-05 - Experimental work for problems pertaining to systems and control theory 93-06 - Proceedings, conferences, collections, etc. pertaining to systems and control theory 93-08 - Computational methods for problems pertaining to systems and control theory 93-10 - Mathematical modeling or simulation for problems pertaining to systems and control theory 93-11 - Research data for problems pertaining to systems and control theory 93Axx - General systems theory 93A05 - Axiomatic systems theory 93A10 - General systems 93A13 - Hierarchical systems 93A14 - Decentralized systems 93A15 - Large-scale systems 93A16 - Multi-agent systems 93A99 - General systems theory 93Bxx - Controllability, observability, and system structure 93B03 - Attainable sets, reachability 93B05 - Controllability 93B07 - Observability 93B10 - Canonical structure 93B11 - System structure simplification 93B12 - Variable structure systems 93B15 - Realizations from input-output data 93B17 - Transformations 93B18 - Linearizations 93B20 - Minimal systems representations 93B24 - Topological methods 93B25 - Algebraic methods 93B27 - Geometric methods 93B28 - Operator-theoretic methods 93B30 - System identification 93B35 - Sensitivity (robustness) 93B36 - (H^infty)-control 93B45 - Model predictive control 93B47 - Iterative learning control 93B50 - Synthesis problems 93B51 - Design techniques (robust design, computer-aided design, etc.) 93B52 - Feedback control 93B53 - Observers 93B55 - Pole and zero placement problems 93B60 - Eigenvalue problems 93B70 - Networked control 93B99 - Controllability, observability, and system structure 93Cxx - Model systems in control theory 93C05 - Linear systems in control theory 93C10 - Nonlinear systems in control theory 93C15 - Control/observation systems governed by ordinary differential equations 93C20 - Control/observation systems governed by partial differential equations 93C23 - Control/observation systems governed by functional-differential equations 93C25 - Control/observation systems in abstract spaces 93C27 - Impulsive control/observation systems 93C28 - Positive control/observation systems 93C29 - Boolean control/observation systems 93C30 - Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93C35 - Multivariable systems, multidimensional control systems 93C40 - Adaptive control/observation systems 93C41 - Control/observation systems with incomplete information 93C42 - Fuzzy control/observation systems 93C43 - Delay control/observation systems 93C55 - Discrete-time control/observation systems 93C57 - Sampled-data control/observation systems 93C62 - Digital control/observation systems 93C65 - Discrete event control/observation systems 93C70 - Time-scale analysis and singular perturbations in control/observation systems 93C73 - Perturbations in control/observation systems 93C80 - Frequency-response methods in control theory 93C83 - Control/observation systems involving computers (process control, etc.) 93C85 - Automated systems (robots, etc.) in control theory 93C95 - Application models in control theory 93C99 - Model systems in control theory 93Dxx - Stability of control systems 93D05 - Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory 93D09 - Robust stability 93D10 - Popov-type stability of feedback systems 93D15 - Stabilization of systems by feedback 93D20 - Asymptotic stability in control theory 93D21 - Adaptive or robust stabilization 93D23 - Exponential stability 93D25 - Input-output approaches in control theory 93D30 - Lyapunov and storage functions 93D40 - Finite-time stability 93D50 - Consensus 93D99 - Stability of control systems 93Exx - Stochastic systems and control 93E03 - Stochastic systems in control theory (general) 93E10 - Estimation and detection in stochastic control theory 93E11 - Filtering in stochastic control theory 93E12 - Identification in stochastic control theory 93E14 - Data smoothing in stochastic control theory 93E15 - Stochastic stability in control theory 93E20 - Optimal stochastic control 93E24 - Least squares and related methods for stochastic control systems 93E35 - Stochastic learning and adaptive control 93E99 - Stochastic systems and control 94-XX - Information and communication theory, circuits 94-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to information and communication theory 94-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory 94-02 - Research exposition (monographs, survey articles) pertaining to information and communication theory 94-03 - History of information and communication theory 94-04 - Software, source code, etc. for problems pertaining to information and communication theory 94-05 - Experimental work for problems pertaining to information and communication theory 94-06 - Proceedings, conferences, collections, etc. pertaining to information and communication theory 94-08 - Computational methods for problems pertaining to information and communication theory 94-10 - Mathematical modeling or simulation for problems pertaining to information and communication theory 94-11 - Research data for problems pertaining to information and communication theory 94Axx - Communication, information 94A05 - Communication theory 94A08 - Image processing (compression, reconstruction, etc.) in information and communication theory 94A11 - Application of orthogonal and other special functions 94A12 - Signal theory (characterization, reconstruction, filtering, etc.) 94A13 - Detection theory in information and communication theory 94A14 - Modulation and demodulation in information and communication theory 94A15 - Information theory (general) 94A16 - Informational aspects of data analysis and big data 94A17 - Measures of information, entropy 94A20 - Sampling theory in information and communication theory 94A24 - Coding theorems (Shannon theory) 94A29 - Source coding 94A34 - Rate-distortion theory in information and communication theory 94A40 - Channel models (including quantum) in information and communication theory 94A45 - Prefix, length-variable, comma-free codes 94A50 - Theory of questionnaires 94A55 - Shift register sequences and sequences over finite alphabets in information and communication theory 94A60 - Cryptography 94A62 - Authentication, digital signatures and secret sharing 94A99 - Communication, information 94Bxx - Theory of error-correcting codes and error-detecting codes 94B05 - Linear codes (general theory) 94B10 - Convolutional codes 94B12 - Combined modulation schemes (including trellis codes) in coding theory 94B15 - Cyclic codes 94B20 - Burst-correcting codes 94B25 - Combinatorial codes 94B27 - Geometric methods (including applications of algebraic geometry) applied to coding theory 94B30 - Majority codes 94B35 - Decoding 94B40 - Arithmetic codes 94B50 - Synchronization error-correcting codes 94B60 - Other types of codes 94B65 - Bounds on codes 94B70 - Error probability in coding theory 94B75 - Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory 94B99 - Theory of error-correcting codes and error-detecting codes 94Cxx - Circuits, networks 94C05 - Analytic circuit theory 94C11 - Switching theory, applications of Boolean algebras to circuits and networks 94C12 - Fault detection; testing in circuits and networks 94C15 - Applications of graph theory to circuits and networks 94C30 - Applications of design theory to circuits and networks 94C60 - Circuits in qualitative investigation and simulation of models 94C99 - Circuits, networks 94Dxx - Miscellaneous topics in information and communication theory 94D05 - Fuzzy sets and logic (in connection with information, communication, or circuits theory) 94D10 - Boolean functions 94D99 - Miscellaneous topics in information and communication theory 97-XX - Mathematics education 97-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematics education 97-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education 97-02 - Research exposition (monographs, survey articles) pertaining to mathematics education 97-03 - History of mathematics education 97-06 - Proceedings, conferences, collections, etc. pertaining to mathematics education 97-11 - Research data for problems pertaining to mathematics education 97Axx - History and society (aspects of mathematics education) 97A30 - History in mathematics education 97A40 - Mathematics education and society 97A99 - History and society (aspects of mathematics education) 97Bxx - Educational policy and systems 97B10 - Mathematics educational research and planning 97B20 - Educational policy for general education 97B30 - Educational policy for vocational education 97B40 - Educational policy for higher education 97B50 - Mathematics teacher education 97B60 - Educational policy for adult and further education 97B70 - Syllabuses, educational standards 97B99 - Educational policy and systems 97Cxx - Psychology of mathematics education, research in mathematics education 97C10 - Comprehensive works on psychology of mathematics education 97C20 - Affective behavior and mathematics education 97C30 - Cognitive processes, learning theories (aspects of mathematics education) 97C40 - Intelligence and aptitudes (aspects of mathematics education) 97C50 - Language and verbal communities (aspects of mathematics education) 97C60 - Sociological aspects of learning (aspects of mathematics education) 97C70 - Teaching-learning processes in mathematics education 97C99 - Psychology of mathematics education, research in mathematics education 97Dxx - Education and instruction in mathematics 97D10 - Comprehensive works and comparative studies on education and instruction in mathematics 97D20 - Philosophical and theoretical contributions (didactics of mathematics) 97D30 - Objectives and goals of mathematics teaching 97D40 - Mathematics teaching methods and classroom techniques 97D50 - Teaching mathematical problem solving and heuristic strategies 97D60 - Student assessment, achievement control, and rating (aspects of mathematics education) 97D70 - Learning difficulties and student errors (aspects of mathematics education) 97D80 - Mathematics teaching units and draft lessons 97D99 - Education and instruction in mathematics 97Exx - Education of foundations of mathematics 97E10 - Comprehensive works on education of foundations of mathematics 97E20 - Philosophy and mathematics (educational aspects) 97E30 - Logic (educational aspects) 97E40 - Language of mathematics (educational aspects) 97E50 - Reasoning and proving in the mathematics classroom 97E60 - Sets, relations, set theory (educational aspects) 97E99 - Education of foundations of mathematics 97Fxx - Education of arithmetic and number theory 97F10 - Comprehensive works on education of arithmetic and number theory 97F20 - Pre-numerical stage, concept of numbers 97F30 - Natural numbers (educational aspects) 97F40 - Integers, rational numbers (educational aspects) 97F50 - Real numbers, complex numbers (educational aspects) 97F60 - Number theory (educational aspects) 97F70 - Measures and units (educational aspects) 97F80 - Ratio and proportion, percentages (educational aspects) 97F90 - Real-life mathematics, practical arithmetic (educational aspects) 97F99 - Education of arithmetic and number theory 97Gxx - Geometry education 97G10 - Comprehensive works on geometry education 97G20 - Informal geometry (educational aspects) 97G30 - Area and volume (educational aspects) 97G40 - Plane and solid geometry (educational aspects) 97G50 - Transformation geometry (educational aspects) 97G60 - Plane and spherical trigonometry (educational aspects) 97G70 - Analytic geometry, vector algebra (educational aspects) 97G80 - Descriptive geometry (educational aspects) 97G99 - Geometry education 97Hxx - Algebra education 97H10 - Comprehensive works on algebra education 97H20 - Elementary algebra (educational aspects) 97H30 - Equations and inequalities (educational aspects) 97H40 - Groups, rings, fields (educational aspects) 97H50 - Ordered algebraic structures (educational aspects) 97H60 - Linear algebra (educational aspects) 97H99 - Algebra education 97Ixx - Analysis education 97I10 - Comprehensive works on analysis education 97I20 - Mappings and functions (educational aspects) 97I30 - Sequences and series (educational aspects) 97I40 - Differential calculus (educational aspects) 97I50 - Integral calculus (educational aspects) 97I60 - Functions of several variables (educational aspects) 97I70 - Functional equations (educational aspects) 97I80 - Complex analysis (educational aspects) 97I99 - Analysis education 97Kxx - Education of combinatorics, graph theory, probability theory, and statistics 97K10 - Comprehensive works on combinatorics, graph theory, and probability (educational aspects) 97K20 - Combinatorics (educational aspects) 97K30 - Graph theory (educational aspects) 97K40 - Descriptive statistics (educational aspects) 97K50 - Probability theory (educational aspects) 97K60 - Distributions and stochastic processes (educational aspects) 97K70 - Foundations and methodology of statistics (educational aspects) 97K80 - Applied statistics (educational aspects) 97K99 - Education of combinatorics, graph theory, probability theory, and statistics 97Mxx - Education of mathematical modeling and applications of mathematics 97M10 - Modeling and interdisciplinarity (aspects of mathematics education) 97M20 - Mathematics in vocational training and career education 97M30 - Financial and insurance mathematics (aspects of mathematics education) 97M40 - Operations research, economics (aspects of mathematics education) 97M50 - Physics, astronomy, technology, engineering (aspects of mathematics education) 97M60 - Biology, chemistry, medicine (aspects of mathematics education) 97M70 - Behavioral and social sciences (aspects of mathematics education) 97M80 - Arts, music, language, architecture (aspects of mathematics education) 97M99 - Education of mathematical modeling and applications of mathematics 97Nxx - Education of numerical mathematics 97N10 - Comprehensive works on education of numerical mathematics 97N20 - Rounding, estimation, theory of errors (educational aspects) 97N30 - Numerical algebra (educational aspects) 97N40 - Numerical analysis (educational aspects) 97N50 - Interpolation and approximation (educational aspects) 97N60 - Mathematical programming (educational aspects) 97N70 - Discrete mathematics (educational aspects) 97N80 - Mathematical software, computer programs (educational aspects) 97N99 - Education of numerical mathematics 97Pxx - Computer science (educational aspects) 97P10 - Comprehensive works on computer science (educational aspects) 97P20 - Theoretical computer science (educational aspects) 97P30 - Systems, databases (educational aspects) 97P40 - Programming languages (educational aspects) 97P50 - Programming techniques (educational aspects) 97P80 - Artificial intelligence (educational aspects) 97P99 - Computer science (educational aspects) 97Uxx - Educational material and media and educational technology in mathematics education 97U10 - Comprehensive works on educational material and media and educational technology in mathematics education 97U20 - Textbooks, textbook research (aspects of mathematics education) 97U30 - Teachers' manuals and planning aids (aspects of mathematics education) 97U40 - Problem books, competitions, examinations (aspects of mathematics education) 97U50 - Computer-assisted instruction, e-learning (aspects of mathematics education) 97U60 - Manipulative materials (aspects of mathematics education) 97U70 - Technological tools, calculators (aspects of mathematics education) 97U80 - Audiovisual media (aspects of mathematics education) 97U99 - Educational material and media and educational technology in mathematics education
Champs secondaires
Choisir
00-XX - General and overarching topics; collections 00-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general 00-02 - Research exposition (monographs, survey articles) pertaining to mathematics in general 00Axx - General and miscellaneous specific topics 00A05 - Mathematics in general 00A06 - Mathematics for nonmathematicians (engineering, social sciences, etc.) 00A07 - Problem books 00A08 - Recreational mathematics 00A09 - Popularization of mathematics 00A15 - Bibliographies for mathematics in general 00A17 - External book reviews 00A20 - Dictionaries and other general reference works 00A22 - Formularies 00A27 - Lists of open problems 00A30 - Philosophy of mathematics 00A35 - Methodology of mathematics 00A64 - Mathematics and literature 00A65 - Mathematics and music 00A66 - Mathematics and visual arts 00A67 - Mathematics and architecture 00A69 - General applied mathematics 00A71 - General theory of mathematical modeling 00A72 - General theory of simulation 00A79 - Physics 00A99 - General and miscellaneous specific topics 00Bxx - Conference proceedings and collections of articles 00B05 - Collections of abstracts of lectures 00B10 - Collections of articles of general interest 00B15 - Collections of articles of miscellaneous specific interest 00B20 - Proceedings of conferences of general interest 00B25 - Proceedings of conferences of miscellaneous specific interest 00B30 - Festschriften 00B50 - Collections of translated articles of general interest 00B55 - Collections of translated articles of miscellaneous specific interest 00B60 - Collections of reprinted articles 00B99 - Conference proceedings and collections of articles 01-XX - History and biography 01-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography 01-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography 01-02 - Research exposition (monographs, survey articles) pertaining to history and biography 01-06 - Proceedings, conferences, collections, etc. pertaining to history and biography 01-11 - Research data for problems pertaining to history and biography 01Axx - History of mathematics and mathematicians 01A05 - General histories, source books 01A07 - Ethnomathematics (general) 01A10 - History of mathematics in Paleolithic and Neolithic times 01A11 - History of mathematics of the indigenous cultures of Africa, Asia, and Oceania 01A12 - History of mathematics of the indigenous cultures of the Americas 01A15 - History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.) 01A16 - History of Egyptian mathematics 01A17 - History of Babylonian mathematics 01A20 - History of Greek and Roman mathematics 01A25 - History of Chinese mathematics 01A27 - History of Japanese mathematics 01A29 - History of East and Southeast Asian mathematics (non-Chinese, non-Japanese) 01A30 - History of mathematics in the Golden Age of Islam 01A32 - History of Indian mathematics 01A35 - History of mathematics in Late Antiquity and medieval Europe 01A40 - History of mathematics in the 15th and 16th centuries, Renaissance 01A45 - History of mathematics in the 17th century 01A50 - History of mathematics in the 18th century 01A55 - History of mathematics in the 19th century 01A60 - History of mathematics in the 20th century 01A61 - History of mathematics in the 21st century 01A65 - Development of contemporary mathematics 01A67 - Future perspectives in mathematics 01A70 - Biographies, obituaries, personalia, bibliographies 01A72 - Schools of mathematics 01A73 - History of mathematics at specific universities 01A74 - History of mathematics at institutions and academies (non-university) 01A75 - Collected or selected works; reprintings or translations of classics 01A80 - Sociology (and profession) of mathematics 01A85 - Historiography 01A90 - Bibliographic studies 01A99 - History of mathematics and mathematicians 03-XX - Mathematical logic and foundations 03-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations 03-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations 03-02 - Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations 03-03 - History of mathematical logic and foundations 03-04 - Software, source code, etc. for problems pertaining to mathematical logic and foundations 03-06 - Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations 03-08 - Computational methods for problems pertaining to mathematical logic and foundations 03-11 - Research data for problems pertaining to mathematical logic and foundations 03Axx - Philosophical aspects of logic and foundations 03A05 - Philosophical and critical aspects of logic and foundations 03A10 - Logic in the philosophy of science 03A99 - Philosophical aspects of logic and foundations 03Bxx - General logic 03B05 - Classical propositional logic 03B10 - Classical first-order logic 03B16 - Higher-order logic 03B20 - Subsystems of classical logic (including intuitionistic logic) 03B22 - Abstract deductive systems 03B25 - Decidability of theories and sets of sentences 03B30 - Foundations of classical theories (including reverse mathematics) 03B35 - Mechanization of proofs and logical operations 03B38 - Type theory 03B40 - Combinatory logic and lambda calculus 03B42 - Logics of knowledge and belief (including belief change) 03B44 - Temporal logic 03B45 - Modal logic (including the logic of norms) 03B47 - Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) 03B48 - Probability and inductive logic 03B50 - Many-valued logic 03B52 - Fuzzy logic; logic of vagueness 03B53 - Paraconsistent logics 03B55 - Intermediate logics 03B60 - Other nonclassical logic 03B62 - Combined logics 03B65 - Logic of natural languages 03B70 - Logic in computer science 03B80 - Other applications of logic 03B99 - General logic 03Cxx - Model theory 03C05 - Equational classes, universal algebra in model theory 03C07 - Basic properties of first-order languages and structures 03C10 - Quantifier elimination, model completeness, and related topics 03C13 - Model theory of finite structures 03C15 - Model theory of denumerable and separable structures 03C20 - Ultraproducts and related constructions 03C25 - Model-theoretic forcing 03C30 - Other model constructions 03C35 - Categoricity and completeness of theories 03C40 - Interpolation, preservation, definability 03C45 - Classification theory, stability, and related concepts in model theory 03C48 - Abstract elementary classes and related topics 03C50 - Models with special properties (saturated, rigid, etc.) 03C52 - Properties of classes of models 03C55 - Set-theoretic model theory 03C57 - Computable structure theory, computable model theory 03C60 - Model-theoretic algebra 03C62 - Models of arithmetic and set theory 03C64 - Model theory of ordered structures; o-minimality 03C65 - Models of other mathematical theories 03C66 - Continuous model theory, model theory of metric structures 03C68 - Other classical first-order model theory 03C70 - Logic on admissible sets 03C75 - Other infinitary logic 03C80 - Logic with extra quantifiers and operators 03C85 - Second- and higher-order model theory 03C90 - Nonclassical models (Boolean-valued, sheaf, etc.) 03C95 - Abstract model theory 03C98 - Applications of model theory 03C99 - Model theory 03Dxx - Computability and recursion theory 03D03 - Thue and Post systems, etc. 03D05 - Automata and formal grammars in connection with logical questions 03D10 - Turing machines and related notions 03D15 - Complexity of computation (including implicit computational complexity) 03D20 - Recursive functions and relations, subrecursive hierarchies 03D25 - Recursively (computably) enumerable sets and degrees 03D28 - Other Turing degree structures 03D30 - Other degrees and reducibilities in computability and recursion theory 03D32 - Algorithmic randomness and dimension 03D35 - Undecidability and degrees of sets of sentences 03D40 - Word problems, etc. in computability and recursion theory 03D45 - Theory of numerations, effectively presented structures 03D50 - Recursive equivalence types of sets and structures, isols 03D55 - Hierarchies of computability and definability 03D60 - Computability and recursion theory on ordinals, admissible sets, etc. 03D65 - Higher-type and set recursion theory 03D70 - Inductive definability 03D75 - Abstract and axiomatic computability and recursion theory 03D78 - Computation over the reals, computable analysis 03D80 - Applications of computability and recursion theory 03D99 - Computability and recursion theory 03Exx - Set theory 03E02 - Partition relations 03E04 - Ordered sets and their cofinalities; pcf theory 03E05 - Other combinatorial set theory 03E10 - Ordinal and cardinal numbers 03E15 - Descriptive set theory 03E17 - Cardinal characteristics of the continuum 03E20 - Other classical set theory (including functions, relations, and set algebra) 03E25 - Axiom of choice and related propositions 03E30 - Axiomatics of classical set theory and its fragments 03E35 - Consistency and independence results 03E40 - Other aspects of forcing and Boolean-valued models 03E45 - Inner models, including constructibility, ordinal definability, and core models 03E47 - Other notions of set-theoretic definability 03E50 - Continuum hypothesis and Martin's axiom 03E55 - Large cardinals 03E57 - Generic absoluteness and forcing axioms 03E60 - Determinacy principles 03E65 - Other set-theoretic hypotheses and axioms 03E70 - Nonclassical and second-order set theories 03E72 - Theory of fuzzy sets, etc. 03E75 - Applications of set theory 03E99 - Set theory 03Fxx - Proof theory and constructive mathematics 03F03 - Proof theory in general (including proof-theoretic semantics) 03F05 - Cut-elimination and normal-form theorems 03F07 - Structure of proofs 03F10 - Functionals in proof theory 03F15 - Recursive ordinals and ordinal notations 03F20 - Complexity of proofs 03F25 - Relative consistency and interpretations 03F30 - First-order arithmetic and fragments 03F35 - Second- and higher-order arithmetic and fragments 03F40 - G�del numberings and issues of incompleteness 03F45 - Provability logics and related algebras (e.g., diagonalizable algebras) 03F50 - Metamathematics of constructive systems 03F52 - Proof-theoretic aspects of linear logic and other substructural logics 03F55 - Intuitionistic mathematics 03F60 - Constructive and recursive analysis 03F65 - Other constructive mathematics 03F99 - Proof theory and constructive mathematics 03Gxx - Algebraic logic 03G05 - Logical aspects of Boolean algebras 03G10 - Logical aspects of lattices and related structures 03G12 - Quantum logic 03G15 - Cylindric and polyadic algebras; relation algebras 03G20 - Logical aspects of ?ukasiewicz and Post algebras 03G25 - Other algebras related to logic 03G27 - Abstract algebraic logic 03G30 - Categorical logic, topoi 03G99 - Algebraic logic 03Hxx - Nonstandard models 03H05 - Nonstandard models in mathematics 03H10 - Other applications of nonstandard models (economics, physics, etc.) 03H15 - Nonstandard models of arithmetic 03H99 - Nonstandard models 05-XX - Combinatorics 05-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics 05-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics 05-02 - Research exposition (monographs, survey articles) pertaining to combinatorics 05-03 - History of combinatorics 05-04 - Software, source code, etc. for problems pertaining to combinatorics 05-06 - Proceedings, conferences, collections, etc. pertaining to combinatorics 05-08 - Computational methods for problems pertaining to combinatorics 05-11 - Research data for problems pertaining to combinatorics 05Axx - Enumerative combinatorics 05A05 - Permutations, words, matrices 05A10 - Factorials, binomial coefficients, combinatorial functions 05A15 - Exact enumeration problems, generating functions 05A16 - Asymptotic enumeration 05A17 - Combinatorial aspects of partitions of integers 05A18 - Partitions of sets 05A19 - Combinatorial identities, bijective combinatorics 05A20 - Combinatorial inequalities 05A30 - (q)-calculus and related topics 05A40 - Umbral calculus 05A99 - Enumerative combinatorics 05Bxx - Designs and configurations 05B05 - Combinatorial aspects of block designs 05B07 - Triple systems 05B10 - Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) 05B15 - Orthogonal arrays, Latin squares, Room squares 05B20 - Combinatorial aspects of matrices (incidence, Hadamard, etc.) 05B25 - Combinatorial aspects of finite geometries 05B30 - Other designs, configurations 05B35 - Combinatorial aspects of matroids and geometric lattices 05B40 - Combinatorial aspects of packing and covering 05B45 - Combinatorial aspects of tessellation and tiling problems 05B50 - Polyominoes 05B99 - Designs and configurations 05Cxx - Graph theory 05C05 - Trees 05C07 - Vertex degrees 05C09 - Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) 05C10 - Planar graphs; geometric and topological aspects of graph theory 05C12 - Distance in graphs 05C15 - Coloring of graphs and hypergraphs 05C17 - Perfect graphs 05C20 - Directed graphs (digraphs), tournaments 05C21 - Flows in graphs 05C22 - Signed and weighted graphs 05C25 - Graphs and abstract algebra (groups, rings, fields, etc.) 05C30 - Enumeration in graph theory 05C31 - Graph polynomials 05C35 - Extremal problems in graph theory 05C38 - Paths and cycles 05C40 - Connectivity 05C42 - Density (toughness, etc.) 05C45 - Eulerian and Hamiltonian graphs 05C48 - Expander graphs 05C50 - Graphs and linear algebra (matrices, eigenvalues, etc.) 05C51 - Graph designs and isomorphic decomposition 05C55 - Generalized Ramsey theory 05C57 - Games on graphs (graph-theoretic aspects) 05C60 - Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C62 - Graph representations (geometric and intersection representations, etc.) 05C63 - Infinite graphs 05C65 - Hypergraphs 05C69 - Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C70 - Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C72 - Fractional graph theory, fuzzy graph theory 05C75 - Structural characterization of families of graphs 05C76 - Graph operations (line graphs, products, etc.) 05C78 - Graph labelling (graceful graphs, bandwidth, etc.) 05C80 - Random graphs (graph-theoretic aspects) 05C81 - Random walks on graphs 05C82 - Small world graphs, complex networks (graph-theoretic aspects) 05C83 - Graph minors 05C85 - Graph algorithms (graph-theoretic aspects) 05C90 - Applications of graph theory 05C92 - Chemical graph theory 05C99 - Graph theory 05Dxx - Extremal combinatorics 05D05 - Extremal set theory 05D10 - Ramsey theory 05D15 - Transversal (matching) theory 05D40 - Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) 05D99 - Extremal combinatorics 05Exx - Algebraic combinatorics 05E05 - Symmetric functions and generalizations 05E10 - Combinatorial aspects of representation theory 05E14 - Combinatorial aspects of algebraic geometry 05E16 - Combinatorial aspects of groups and algebras 05E18 - Group actions on combinatorial structures 05E30 - Association schemes, strongly regular graphs 05E40 - Combinatorial aspects of commutative algebra 05E45 - Combinatorial aspects of simplicial complexes 05E99 - Algebraic combinatorics 06-XX - Order, lattices, ordered algebraic structures 06-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered structures 06-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures 06-02 - Research exposition (monographs, survey articles) pertaining to ordered structures 06-03 - History of ordered structures 06-04 - Software, source code, etc. for problems pertaining to ordered structures 06-06 - Proceedings, conferences, collections, etc. pertaining to ordered structures 06-08 - Computational methods for problems pertaining to ordered structures 06-11 - Research data for problems pertaining to ordered structures 06Axx - Ordered sets 06A05 - Total orders 06A06 - Partial orders, general 06A07 - Combinatorics of partially ordered sets 06A11 - Algebraic aspects of posets 06A12 - Semilattices 06A15 - Galois correspondences, closure operators (in relation to ordered sets) 06A75 - Generalizations of ordered sets 06A99 - Ordered sets 06Bxx - Lattices 06B05 - Structure theory of lattices 06B10 - Lattice ideals, congruence relations 06B15 - Representation theory of lattices 06B20 - Varieties of lattices 06B23 - Complete lattices, completions 06B25 - Free lattices, projective lattices, word problems 06B30 - Topological lattices 06B35 - Continuous lattices and posets, applications 06B75 - Generalizations of lattices 06B99 - Lattices 06Cxx - Modular lattices, complemented lattices 06C05 - Modular lattices, Desarguesian lattices 06C10 - Semimodular lattices, geometric lattices 06C15 - Complemented lattices, orthocomplemented lattices and posets 06C20 - Complemented modular lattices, continuous geometries 06C99 - Modular lattices, complemented lattices 06Dxx - Distributive lattices 06D05 - Structure and representation theory of distributive lattices 06D10 - Complete distributivity 06D15 - Pseudocomplemented lattices 06D20 - Heyting algebras (lattice-theoretic aspects) 06D22 - Frames, locales 06D25 - Post algebras (lattice-theoretic aspects) 06D30 - De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) 06D35 - MV-algebras 06D50 - Lattices and duality 06D72 - Fuzzy lattices (soft algebras) and related topics 06D75 - Other generalizations of distributive lattices 06D99 - Distributive lattices 06Exx - Boolean algebras (Boolean rings) 06E05 - Structure theory of Boolean algebras 06E10 - Chain conditions, complete algebras 06E15 - Stone spaces (Boolean spaces) and related structures 06E20 - Ring-theoretic properties of Boolean algebras 06E25 - Boolean algebras with additional operations (diagonalizable algebras, etc.) 06E30 - Boolean functions 06E75 - Generalizations of Boolean algebras 06E99 - Boolean algebras (Boolean rings) 06Fxx - Ordered structures 06F05 - Ordered semigroups and monoids 06F07 - Quantales 06F10 - Noether lattices 06F15 - Ordered groups 06F20 - Ordered abelian groups, Riesz groups, ordered linear spaces 06F25 - Ordered rings, algebras, modules 06F30 - Ordered topological structures 06F35 - BCK-algebras, BCI-algebras 06F99 - Ordered structures 08-XX - General algebraic systems 08-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general algebraic systems 08-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems 08-02 - Research exposition (monographs, survey articles) pertaining to general algebraic systems 08-03 - History of general algebraic systems 08-04 - Software, source code, etc. for problems pertaining to general algebraic systems 08-06 - Proceedings, conferences, collections, etc. pertaining to general algebraic systems 08-08 - Computational methods for problems pertaining to general algebraic systems 08-11 - Research data for problems pertaining to general algebraic systems 08Axx - Algebraic structures 08A02 - Relational systems, laws of composition 08A05 - Structure theory of algebraic structures 08A30 - Subalgebras, congruence relations 08A35 - Automorphisms and endomorphisms of algebraic structures 08A40 - Operations and polynomials in algebraic structures, primal algebras 08A45 - Equational compactness 08A50 - Word problems (aspects of algebraic structures) 08A55 - Partial algebras 08A60 - Unary algebras 08A62 - Finitary algebras 08A65 - Infinitary algebras 08A68 - Heterogeneous algebras 08A70 - Applications of universal algebra in computer science 08A72 - Fuzzy algebraic structures 08A99 - Algebraic structures 08Bxx - Varieties 08B05 - Equational logic, Mal'tsev conditions 08B10 - Congruence modularity, congruence distributivity 08B15 - Lattices of varieties 08B20 - Free algebras 08B25 - Products, amalgamated products, and other kinds of limits and colimits 08B26 - Subdirect products and subdirect irreducibility 08B30 - Injectives, projectives 08B99 - Varieties 08Cxx - Other classes of algebras 08C05 - Categories of algebras 08C10 - Axiomatic model classes 08C15 - Quasivarieties 08C20 - Natural dualities for classes of algebras 08C99 - Other classes of algebras 11-XX - Number theory 11-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory 11-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 11-02 - Research exposition (monographs, survey articles) pertaining to number theory 11-03 - History of number theory 11-04 - Software, source code, etc. for problems pertaining to number theory 11-06 - Proceedings, conferences, collections, etc. pertaining to number theory 11-11 - Research data for problems pertaining to number theory 11Axx - Elementary number theory 11A05 - Multiplicative structure; Euclidean algorithm; greatest common divisors 11A07 - Congruences; primitive roots; residue systems 11A15 - Power residues, reciprocity 11A25 - Arithmetic functions; related numbers; inversion formulas 11A41 - Primes 11A51 - Factorization; primality 11A55 - Continued fractions 11A63 - Radix representation; digital problems 11A67 - Other number representations 11A99 - Elementary number theory 11Bxx - Sequences and sets 11B05 - Density, gaps, topology 11B13 - Additive bases, including sumsets 11B25 - Arithmetic progressions 11B30 - Arithmetic combinatorics; higher degree uniformity 11B34 - Representation functions 11B37 - Recurrences 11B39 - Fibonacci and Lucas numbers and polynomials and generalizations 11B50 - Sequences (mod (m)) 11B57 - Farey sequences; the sequences (1^k, 2^k, dots) 11B65 - Binomial coefficients; factorials; (q)-identities 11B68 - Bernoulli and Euler numbers and polynomials 11B73 - Bell and Stirling numbers 11B75 - Other combinatorial number theory 11B83 - Special sequences and polynomials 11B85 - Automata sequences 11B99 - Sequences and sets 11Cxx - Polynomials and matrices 11C08 - Polynomials in number theory 11C20 - Matrices, determinants in number theory 11C99 - Polynomials and matrices 11Dxx - Diophantine equations 11D04 - Linear Diophantine equations 11D07 - The Frobenius problem 11D09 - Quadratic and bilinear Diophantine equations 11D25 - Cubic and quartic Diophantine equations 11D41 - Higher degree equations; Fermat's equation 11D45 - Counting solutions of Diophantine equations 11D57 - Multiplicative and norm form equations 11D59 - Thue-Mahler equations 11D61 - Exponential Diophantine equations 11D68 - Rational numbers as sums of fractions 11D72 - Diophantine equations in many variables 11D75 - Diophantine inequalities 11D79 - Congruences in many variables 11D85 - Representation problems 11D88 - (p)-adic and power series fields 11D99 - Diophantine equations 11Exx - Forms and linear algebraic groups 11E04 - Quadratic forms over general fields 11E08 - Quadratic forms over local rings and fields 11E10 - Forms over real fields 11E12 - Quadratic forms over global rings and fields 11E16 - General binary quadratic forms 11E20 - General ternary and quaternary quadratic forms; forms of more than two variables 11E25 - Sums of squares and representations by other particular quadratic forms 11E39 - Bilinear and Hermitian forms 11E41 - Class numbers of quadratic and Hermitian forms 11E45 - Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) 11E57 - Classical groups 11E70 - (K)-theory of quadratic and Hermitian forms 11E72 - Galois cohomology of linear algebraic groups 11E76 - Forms of degree higher than two 11E81 - Algebraic theory of quadratic forms; Witt groups and rings 11E88 - Quadratic spaces; Clifford algebras 11E95 - (p)-adic theory 11E99 - Forms and linear algebraic groups 11Fxx - Discontinuous groups and automorphic forms 11F03 - Modular and automorphic functions 11F06 - Structure of modular groups and generalizations; arithmetic groups 11F11 - Holomorphic modular forms of integral weight 11F12 - Automorphic forms, one variable 11F20 - Dedekind eta function, Dedekind sums 11F22 - Relationship to Lie algebras and finite simple groups 11F23 - Relations with algebraic geometry and topology 11F25 - Hecke-Petersson operators, differential operators (one variable) 11F27 - Theta series; Weil representation; theta correspondences 11F30 - Fourier coefficients of automorphic forms 11F32 - Modular correspondences, etc. 11F33 - Congruences for modular and (p)-adic modular forms 11F37 - Forms of half-integer weight; nonholomorphic modular forms 11F41 - Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F46 - Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11F50 - Jacobi forms 11F52 - Modular forms associated to Drinfel'd modules 11F55 - Other groups and their modular and automorphic forms (several variables) 11F60 - Hecke-Petersson operators, differential operators (several variables) 11F66 - Langlands (L)-functions; one variable Dirichlet series and functional equations 11F67 - Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols 11F68 - Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 11F70 - Representation-theoretic methods; automorphic representations over local and global fields 11F72 - Spectral theory; trace formulas (e.g., that of Selberg) 11F75 - Cohomology of arithmetic groups 11F77 - Automorphic forms and their relations with perfectoid spaces 11F80 - Galois representations 11F85 - (p)-adic theory, local fields 11F99 - Discontinuous groups and automorphic forms 11Gxx - Arithmetic algebraic geometry (Diophantine geometry) 11G05 - Elliptic curves over global fields 11G07 - Elliptic curves over local fields 11G09 - Drinfel'd modules; higher-dimensional motives, etc. 11G10 - Abelian varieties of dimension (> 1) 11G15 - Complex multiplication and moduli of abelian varieties 11G16 - Elliptic and modular units 11G18 - Arithmetic aspects of modular and Shimura varieties 11G20 - Curves over finite and local fields 11G25 - Varieties over finite and local fields 11G30 - Curves of arbitrary genus or genus (e 1) over global fields 11G32 - Arithmetic aspects of dessins d'enfants, Bely? theory 11G35 - Varieties over global fields 11G40 - (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11G42 - Arithmetic mirror symmetry 11G45 - Geometric class field theory 11G50 - Heights 11G55 - Polylogarithms and relations with (K)-theory 11G99 - Arithmetic algebraic geometry (Diophantine geometry) 11Hxx - Geometry of numbers 11H06 - Lattices and convex bodies (number-theoretic aspects) 11H16 - Nonconvex bodies 11H31 - Lattice packing and covering (number-theoretic aspects) 11H46 - Products of linear forms 11H50 - Minima of forms 11H55 - Quadratic forms (reduction theory, extreme forms, etc.) 11H56 - Automorphism groups of lattices 11H60 - Mean value and transfer theorems 11H71 - Relations with coding theory 11H99 - Geometry of numbers 11Jxx - Diophantine approximation, transcendental number theory 11J04 - Homogeneous approximation to one number 11J06 - Markov and Lagrange spectra and generalizations 11J13 - Simultaneous homogeneous approximation, linear forms 11J17 - Approximation by numbers from a fixed field 11J20 - Inhomogeneous linear forms 11J25 - Diophantine inequalities 11J54 - Small fractional parts of polynomials and generalizations 11J61 - Approximation in non-Archimedean valuations 11J68 - Approximation to algebraic numbers 11J70 - Continued fractions and generalizations 11J71 - Distribution modulo one 11J72 - Irrationality; linear independence over a field 11J81 - Transcendence (general theory) 11J82 - Measures of irrationality and of transcendence 11J83 - Metric theory 11J85 - Algebraic independence; Gel'fond's method 11J86 - Linear forms in logarithms; Baker's method 11J87 - Schmidt Subspace Theorem and applications 11J89 - Transcendence theory of elliptic and abelian functions 11J91 - Transcendence theory of other special functions 11J93 - Transcendence theory of Drinfel'd and (t)-modules 11J95 - Results involving abelian varieties 11J97 - Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) 11J99 - Diophantine approximation, transcendental number theory 11Kxx - Probabilistic theory: distribution modulo (1); metric theory of algorithms 11K06 - General theory of distribution modulo (1) 11K16 - Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 11K31 - Special sequences 11K36 - Well-distributed sequences and other variations 11K38 - Irregularities of distribution, discrepancy 11K41 - Continuous, (p)-adic and abstract analogues 11K45 - Pseudo-random numbers; Monte Carlo methods 11K50 - Metric theory of continued fractions 11K55 - Metric theory of other algorithms and expansions; measure and Hausdorff dimension 11K60 - Diophantine approximation in probabilistic number theory 11K65 - Arithmetic functions in probabilistic number theory 11K70 - Harmonic analysis and almost periodicity in probabilistic number theory 11K99 - Probabilistic theory: distribution modulo (1); metric theory of algorithms 11Lxx - Exponential sums and character sums 11L03 - Trigonometric and exponential sums (general theory) 11L05 - Gauss and Kloosterman sums; generalizations 11L07 - Estimates on exponential sums 11L10 - Jacobsthal and Brewer sums; other complete character sums 11L15 - Weyl sums 11L20 - Sums over primes 11L26 - Sums over arbitrary intervals 11L40 - Estimates on character sums 11L99 - Exponential sums and character sums 11Mxx - Zeta and (L)-functions: analytic theory 11M06 - (zeta (s)) and (L(s, chi)) 11M20 - Real zeros of (L(s, chi)); results on (L(1, chi)) 11M26 - Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses 11M32 - Multiple Dirichlet series and zeta functions and multizeta values 11M35 - Hurwitz and Lerch zeta functions 11M36 - Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) 11M38 - Zeta and (L)-functions in characteristic (p) 11M41 - Other Dirichlet series and zeta functions 11M45 - Tauberian theorems 11M50 - Relations with random matrices 11M55 - Relations with noncommutative geometry 11M99 - Zeta and (L)-functions: analytic theory 11Nxx - Multiplicative number theory 11N05 - Distribution of primes 11N13 - Primes in congruence classes 11N25 - Distribution of integers with specified multiplicative constraints 11N30 - Tur�n theory 11N32 - Primes represented by polynomials; other multiplicative structures of polynomial values 11N35 - Sieves 11N36 - Applications of sieve methods 11N37 - Asymptotic results on arithmetic functions 11N45 - Asymptotic results on counting functions for algebraic and topological structures 11N56 - Rate of growth of arithmetic functions 11N60 - Distribution functions associated with additive and positive multiplicative functions 11N64 - Other results on the distribution of values or the characterization of arithmetic functions 11N69 - Distribution of integers in special residue classes 11N75 - Applications of automorphic functions and forms to multiplicative problems 11N80 - Generalized primes and integers 11N99 - Multiplicative number theory 11Pxx - Additive number theory; partitions 11P05 - Waring's problem and variants 11P21 - Lattice points in specified regions 11P32 - Goldbach-type theorems; other additive questions involving primes 11P55 - Applications of the Hardy-Littlewood method 11P70 - Inverse problems of additive number theory, including sumsets 11P81 - Elementary theory of partitions 11P82 - Analytic theory of partitions 11P83 - Partitions; congruences and congruential restrictions 11P84 - Partition identities; identities of Rogers-Ramanujan type 11P99 - Additive number theory; partitions 11Rxx - Algebraic number theory: global fields 11R04 - Algebraic numbers; rings of algebraic integers 11R06 - PV-numbers and generalizations; other special algebraic numbers; Mahler measure 11R09 - Polynomials (irreducibility, etc.) 11R11 - Quadratic extensions 11R16 - Cubic and quartic extensions 11R18 - Cyclotomic extensions 11R20 - Other abelian and metabelian extensions 11R21 - Other number fields 11R23 - Iwasawa theory 11R27 - Units and factorization 11R29 - Class numbers, class groups, discriminants 11R32 - Galois theory 11R33 - Integral representations related to algebraic numbers; Galois module structure of rings of integers 11R34 - Galois cohomology 11R37 - Class field theory 11R39 - Langlands-Weil conjectures, nonabelian class field theory 11R42 - Zeta functions and (L)-functions of number fields 11R44 - Distribution of prime ideals 11R45 - Density theorems 11R47 - Other analytic theory 11R52 - Quaternion and other division algebras: arithmetic, zeta functions 11R54 - Other algebras and orders, and their zeta and (L)-functions 11R56 - Ad�le rings and groups 11R58 - Arithmetic theory of algebraic function fields 11R59 - Zeta functions and (L)-functions of function fields 11R60 - Cyclotomic function fields (class groups, Bernoulli objects, etc.) 11R65 - Class groups and Picard groups of orders 11R70 - (K)-theory of global fields 11R80 - Totally real fields 11R99 - Algebraic number theory: global fields 11Sxx - Algebraic number theory: local fields 11S05 - Polynomials 11S15 - Ramification and extension theory 11S20 - Galois theory 11S23 - Integral representations 11S25 - Galois cohomology 11S31 - Class field theory; (p)-adic formal groups 11S37 - Langlands-Weil conjectures, nonabelian class field theory 11S40 - Zeta functions and (L)-functions 11S45 - Algebras and orders, and their zeta functions 11S70 - (K)-theory of local fields 11S80 - Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) 11S82 - Non-Archimedean dynamical systems 11S85 - Other nonanalytic theory 11S90 - Prehomogeneous vector spaces 11S99 - Algebraic number theory: local fields 11Txx - Finite fields and commutative rings (number-theoretic aspects) 11T06 - Polynomials over finite fields 11T22 - Cyclotomy 11T23 - Exponential sums 11T24 - Other character sums and Gauss sums 11T30 - Structure theory for finite fields and commutative rings (number-theoretic aspects) 11T55 - Arithmetic theory of polynomial rings over finite fields 11T60 - Finite upper half-planes 11T71 - Algebraic coding theory; cryptography (number-theoretic aspects) 11T99 - Finite fields and commutative rings (number-theoretic aspects) 11Uxx - Connections of number theory and logic 11U05 - Decidability (number-theoretic aspects) 11U07 - Ultraproducts (number-theoretic aspects) 11U09 - Model theory (number-theoretic aspects) 11U10 - Nonstandard arithmetic (number-theoretic aspects) 11U99 - Connections of number theory and logic 11Yxx - Computational number theory 11Y05 - Factorization 11Y11 - Primality 11Y16 - Number-theoretic algorithms; complexity 11Y35 - Analytic computations 11Y40 - Algebraic number theory computations 11Y50 - Computer solution of Diophantine equations 11Y55 - Calculation of integer sequences 11Y60 - Evaluation of number-theoretic constants 11Y65 - Continued fraction calculations (number-theoretic aspects) 11Y70 - Values of arithmetic functions; tables 11Y99 - Computational number theory 11Zxx - Miscellaneous applications of number theory 11Z05 - Miscellaneous applications of number theory 11Z99 - Miscellaneous applications of number theory 12-XX - Field theory and polynomials 12-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory 12-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory 12-02 - Research exposition (monographs, survey articles) pertaining to field theory 12-03 - History of field theory 12-04 - Software, source code, etc. for problems pertaining to field theory 12-06 - Proceedings, conferences, collections, etc. pertaining to field theory 12-08 - Computational methods for problems pertaining to field theory 12-11 - Research data for problems pertaining to field theory 12Dxx - Real and complex fields 12D05 - Polynomials in real and complex fields: factorization 12D10 - Polynomials in real and complex fields: location of zeros (algebraic theorems) 12D15 - Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 12D99 - Real and complex fields 12Exx - General field theory 12E05 - Polynomials in general fields (irreducibility, etc.) 12E10 - Special polynomials in general fields 12E12 - Equations in general fields 12E15 - Skew fields, division rings 12E20 - Finite fields (field-theoretic aspects) 12E25 - Hilbertian fields; Hilbert's irreducibility theorem 12E30 - Field arithmetic 12E99 - General field theory 12Fxx - Field extensions 12F05 - Algebraic field extensions 12F10 - Separable extensions, Galois theory 12F12 - Inverse Galois theory 12F15 - Inseparable field extensions 12F20 - Transcendental field extensions 12F99 - Field extensions 12Gxx - Homological methods (field theory) 12G05 - Galois cohomology 12G10 - Cohomological dimension of fields 12G99 - Homological methods (field theory) 12Hxx - Differential and difference algebra 12H05 - Differential algebra 12H10 - Difference algebra 12H20 - Abstract differential equations 12H25 - (p)-adic differential equations 12H99 - Differential and difference algebra 12Jxx - Topological fields 12J05 - Normed fields 12J10 - Valued fields 12J12 - Formally (p)-adic fields 12J15 - Ordered fields 12J17 - Topological semifields 12J20 - General valuation theory for fields 12J25 - Non-Archimedean valued fields 12J27 - Krasner-Tate algebras 12J99 - Topological fields 12Kxx - Generalizations of fields 12K05 - Near-fields 12K10 - Semifields 12K99 - Generalizations of fields 12Lxx - Connections between field theory and logic 12L05 - Decidability and field theory 12L10 - Ultraproducts and field theory 12L12 - Model theory of fields 12L15 - Nonstandard arithmetic and field theory 12L99 - Connections between field theory and logic 13-XX - Commutative algebra 13-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra 13-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra 13-02 - Research exposition (monographs, survey articles) pertaining to commutative algebra 13-03 - History of commutative algebra 13-04 - Software, source code, etc. for problems pertaining to commutative algebra 13-06 - Proceedings, conferences, collections, etc. pertaining to commutative algebra 13-11 - Research data for problems pertaining to commutative algebra 13Axx - General commutative ring theory 13A02 - Graded rings 13A05 - Divisibility and factorizations in commutative rings 13A15 - Ideals and multiplicative ideal theory in commutative rings 13A18 - Valuations and their generalizations for commutative rings 13A30 - Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13A35 - Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure 13A50 - Actions of groups on commutative rings; invariant theory 13A70 - General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) 13A99 - General commutative ring theory 13Bxx - Commutative ring extensions and related topics 13B02 - Extension theory of commutative rings 13B05 - Galois theory and commutative ring extensions 13B10 - Morphisms of commutative rings 13B21 - Integral dependence in commutative rings; going up, going down 13B22 - Integral closure of commutative rings and ideals 13B25 - Polynomials over commutative rings 13B30 - Rings of fractions and localization for commutative rings 13B35 - Completion of commutative rings 13B40 - �tale and flat extensions; Henselization; Artin approximation 13B99 - Commutative ring extensions and related topics 13Cxx - Theory of modules and ideals in commutative rings 13C05 - Structure, classification theorems for modules and ideals in commutative rings 13C10 - Projective and free modules and ideals in commutative rings 13C11 - Injective and flat modules and ideals in commutative rings 13C12 - Torsion modules and ideals in commutative rings 13C13 - Other special types of modules and ideals in commutative rings 13C14 - Cohen-Macaulay modules 13C15 - Dimension theory, depth, related commutative rings (catenary, etc.) 13C20 - Class groups 13C40 - Linkage, complete intersections and determinantal ideals 13C60 - Module categories and commutative rings 13C70 - Theory of modules and ideals in commutative rings described by combinatorial properties 13C99 - Theory of modules and ideals in commutative rings 13Dxx - Homological methods in commutative ring theory 13D02 - Syzygies, resolutions, complexes and commutative rings 13D03 - (Co)homology of commutative rings and algebras (e.g., Hochschild, Andr�-Quillen, cyclic, dihedral, etc.) 13D05 - Homological dimension and commutative rings 13D07 - Homological functors on modules of commutative rings (Tor, Ext, etc.) 13D09 - Derived categories and commutative rings 13D10 - Deformations and infinitesimal methods in commutative ring theory 13D15 - Grothendieck groups, (K)-theory and commutative rings 13D22 - Homological conjectures (intersection theorems) in commutative ring theory 13D30 - Torsion theory for commutative rings 13D40 - Hilbert-Samuel and Hilbert-Kunz functions; Poincar� series 13D45 - Local cohomology and commutative rings 13D99 - Homological methods in commutative ring theory 13Exx - Chain conditions, finiteness conditions in commutative ring theory 13E05 - Commutative Noetherian rings and modules 13E10 - Commutative Artinian rings and modules, finite-dimensional algebras 13E15 - Commutative rings and modules of finite generation or presentation; number of generators 13E99 - Chain conditions, finiteness conditions in commutative ring theory 13Fxx - Arithmetic rings and other special commutative rings 13F05 - Dedekind, Pr�fer, Krull and Mori rings and their generalizations 13F07 - Euclidean rings and generalizations 13F10 - Principal ideal rings 13F15 - Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) 13F20 - Polynomial rings and ideals; rings of integer-valued polynomials 13F25 - Formal power series rings 13F30 - Valuation rings 13F35 - Witt vectors and related rings 13F40 - Excellent rings 13F45 - Seminormal rings 13F50 - Rings with straightening laws, Hodge algebras 13F55 - Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes 13F60 - Cluster algebras 13F65 - Commutative rings defined by binomial ideals, toric rings, etc. 13F70 - Other commutative rings defined by combinatorial properties 13F99 - Arithmetic rings and other special commutative rings 13Gxx - Integral domains 13G05 - Integral domains 13G99 - Integral domains 13Hxx - Local rings and semilocal rings 13H05 - Regular local rings 13H10 - Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 13H15 - Multiplicity theory and related topics 13H99 - Local rings and semilocal rings 13Jxx - Topological rings and modules 13J05 - Power series rings 13J07 - Analytical algebras and rings 13J10 - Complete rings, completion 13J15 - Henselian rings 13J20 - Global topological rings 13J25 - Ordered rings 13J30 - Real algebra 13J99 - Topological rings and modules 13Lxx - Applications of logic to commutative algebra 13L05 - Applications of logic to commutative algebra 13L99 - Applications of logic to commutative algebra 13Mxx - Finite commutative rings 13M05 - Structure of finite commutative rings 13M10 - Polynomials and finite commutative rings 13M99 - Finite commutative rings 13Nxx - Differential algebra 13N05 - Modules of differentials 13N10 - Commutative rings of differential operators and their modules 13N15 - Derivations and commutative rings 13N99 - Differential algebra 13Pxx - Computational aspects and applications of commutative rings 13P05 - Polynomials, factorization in commutative rings 13P10 - Gr�bner bases; other bases for ideals and modules (e.g., Janet and border bases) 13P15 - Solving polynomial systems; resultants 13P20 - Computational homological algebra 13P25 - Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 13P99 - Computational aspects and applications of commutative rings 14-XX - Algebraic geometry 14-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry 14-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry 14-02 - Research exposition (monographs, survey articles) pertaining to algebraic geometry 14-03 - History of algebraic geometry 14-04 - Software, source code, etc. for problems pertaining to algebraic geometry 14-06 - Proceedings, conferences, collections, etc. pertaining to algebraic geometry 14-11 - Research data for problems pertaining to algebraic geometry 14Axx - Foundations of algebraic geometry 14A05 - Relevant commutative algebra 14A10 - Varieties and morphisms 14A15 - Schemes and morphisms 14A20 - Generalizations (algebraic spaces, stacks) 14A21 - Logarithmic algebraic geometry, log schemes 14A22 - Noncommutative algebraic geometry 14A23 - Geometry over the field with one element 14A25 - Elementary questions in algebraic geometry 14A30 - Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) 14A99 - Foundations of algebraic geometry 14Bxx - Local theory in algebraic geometry 14B05 - Singularities in algebraic geometry 14B07 - Deformations of singularities 14B10 - Infinitesimal methods in algebraic geometry 14B12 - Local deformation theory, Artin approximation, etc. 14B15 - Local cohomology and algebraic geometry 14B20 - Formal neighborhoods in algebraic geometry 14B25 - Local structure of morphisms in algebraic geometry: �tale, flat, etc. 14B99 - Local theory in algebraic geometry 14Cxx - Cycles and subschemes 14C05 - Parametrization (Chow and Hilbert schemes) 14C15 - (Equivariant) Chow groups and rings; motives 14C17 - Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14C20 - Divisors, linear systems, invertible sheaves 14C21 - Pencils, nets, webs in algebraic geometry 14C22 - Picard groups 14C25 - Algebraic cycles 14C30 - Transcendental methods, Hodge theory (algebro-geometric aspects) 14C34 - Torelli problem 14C35 - Applications of methods of algebraic (K)-theory in algebraic geometry 14C40 - Riemann-Roch theorems 14C99 - Cycles and subschemes 14Dxx - Families, fibrations in algebraic geometry 14D05 - Structure of families (Picard-Lefschetz, monodromy, etc.) 14D06 - Fibrations, degenerations in algebraic geometry 14D07 - Variation of Hodge structures (algebro-geometric aspects) 14D10 - Arithmetic ground fields (finite, local, global) and families or fibrations 14D15 - Formal methods and deformations in algebraic geometry 14D20 - Algebraic moduli problems, moduli of vector bundles 14D21 - Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 14D22 - Fine and coarse moduli spaces 14D23 - Stacks and moduli problems 14D24 - Geometric Langlands program (algebro-geometric aspects) 14D99 - Families, fibrations in algebraic geometry 14Exx - Birational geometry 14E05 - Rational and birational maps 14E07 - Birational automorphisms, Cremona group and generalizations 14E08 - Rationality questions in algebraic geometry 14E15 - Global theory and resolution of singularities (algebro-geometric aspects) 14E16 - McKay correspondence 14E18 - Arcs and motivic integration 14E20 - Coverings in algebraic geometry 14E22 - Ramification problems in algebraic geometry 14E25 - Embeddings in algebraic geometry 14E30 - Minimal model program (Mori theory, extremal rays) 14E99 - Birational geometry 14Fxx - (Co)homology theory in algebraic geometry 14F06 - Sheaves in algebraic geometry 14F08 - Derived categories of sheaves, dg categories, and related constructions in algebraic geometry 14F10 - Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14F17 - Vanishing theorems in algebraic geometry 14F18 - Multiplier ideals 14F20 - �tale and other Grothendieck topologies and (co)homologies 14F22 - Brauer groups of schemes 14F25 - Classical real and complex (co)homology in algebraic geometry 14F30 - (p)-adic cohomology, crystalline cohomology 14F35 - Homotopy theory and fundamental groups in algebraic geometry 14F40 - de Rham cohomology and algebraic geometry 14F42 - Motivic cohomology; motivic homotopy theory 14F43 - Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14F45 - Topological properties in algebraic geometry 14F99 - (Co)homology theory in algebraic geometry 14Gxx - Arithmetic problems in algebraic geometry; Diophantine geometry 14G05 - Rational points 14G10 - Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 14G12 - Hasse principle, weak and strong approximation, Brauer-Manin obstruction 14G15 - Finite ground fields in algebraic geometry 14G17 - Positive characteristic ground fields in algebraic geometry 14G20 - Local ground fields in algebraic geometry 14G22 - Rigid analytic geometry 14G25 - Global ground fields in algebraic geometry 14G27 - Other nonalgebraically closed ground fields in algebraic geometry 14G32 - Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) 14G35 - Modular and Shimura varieties 14G40 - Arithmetic varieties and schemes; Arakelov theory; heights 14G45 - Perfectoid spaces and mixed characteristic 14G50 - Applications to coding theory and cryptography of arithmetic geometry 14G99 - Arithmetic problems in algebraic geometry; Diophantine geometry 14Hxx - Curves in algebraic geometry 14H05 - Algebraic functions and function fields in algebraic geometry 14H10 - Families, moduli of curves (algebraic) 14H15 - Families, moduli of curves (analytic) 14H20 - Singularities of curves, local rings 14H25 - Arithmetic ground fields for curves 14H30 - Coverings of curves, fundamental group 14H37 - Automorphisms of curves 14H40 - Jacobians, Prym varieties 14H42 - Theta functions and curves; Schottky problem 14H45 - Special algebraic curves and curves of low genus 14H50 - Plane and space curves 14H51 - Special divisors on curves (gonality, Brill-Noether theory) 14H52 - Elliptic curves 14H55 - Riemann surfaces; Weierstrass points; gap sequences 14H57 - Dessins d'enfants theory 14H60 - Vector bundles on curves and their moduli 14H70 - Relationships between algebraic curves and integrable systems 14H81 - Relationships between algebraic curves and physics 14H99 - Curves in algebraic geometry 14Jxx - Surfaces and higher-dimensional varieties 14J10 - Families, moduli, classification: algebraic theory 14J15 - Moduli, classification: analytic theory; relations with modular forms 14J17 - Singularities of surfaces or higher-dimensional varieties 14J20 - Arithmetic ground fields for surfaces or higher-dimensional varieties 14J25 - Special surfaces 14J26 - Rational and ruled surfaces 14J27 - Elliptic surfaces, elliptic or Calabi-Yau fibrations 14J28 - (K3) surfaces and Enriques surfaces 14J29 - Surfaces of general type 14J30 - (3)-folds 14J32 - Calabi-Yau manifolds (algebro-geometric aspects) 14J33 - Mirror symmetry (algebro-geometric aspects) 14J35 - (4)-folds 14J40 - (n)-folds ((n>4)) 14J42 - Holomorphic symplectic varieties, hyper-K�hler varieties 14J45 - Fano varieties 14J50 - Automorphisms of surfaces and higher-dimensional varieties 14J60 - Vector bundles on surfaces and higher-dimensional varieties, and their moduli 14J70 - Hypersurfaces and algebraic geometry 14J80 - Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) 14J81 - Relationships between surfaces, higher-dimensional varieties, and physics 14J99 - Surfaces and higher-dimensional varieties 14Kxx - Abelian varieties and schemes 14K02 - Isogeny 14K05 - Algebraic theory of abelian varieties 14K10 - Algebraic moduli of abelian varieties, classification 14K12 - Subvarieties of abelian varieties 14K15 - Arithmetic ground fields for abelian varieties 14K20 - Analytic theory of abelian varieties; abelian integrals and differentials 14K22 - Complex multiplication and abelian varieties 14K25 - Theta functions and abelian varieties 14K30 - Picard schemes, higher Jacobians 14K99 - Abelian varieties and schemes 14Lxx - Algebraic groups 14L05 - Formal groups, (p)-divisible groups 14L10 - Group varieties 14L15 - Group schemes 14L17 - Affine algebraic groups, hyperalgebra constructions 14L24 - Geometric invariant theory 14L30 - Group actions on varieties or schemes (quotients) 14L35 - Classical groups (algebro-geometric aspects) 14L40 - Other algebraic groups (geometric aspects) 14L99 - Algebraic groups 14Mxx - Special varieties 14M05 - Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14M06 - Linkage 14M07 - Low codimension problems in algebraic geometry 14M10 - Complete intersections 14M12 - Determinantal varieties 14M15 - Grassmannians, Schubert varieties, flag manifolds 14M17 - Homogeneous spaces and generalizations 14M20 - Rational and unirational varieties 14M22 - Rationally connected varieties 14M25 - Toric varieties, Newton polyhedra, Okounkov bodies 14M27 - Compactifications; symmetric and spherical varieties 14M30 - Supervarieties 14M35 - Character varieties 14M99 - Special varieties 14Nxx - Projective and enumerative algebraic geometry 14N05 - Projective techniques in algebraic geometry 14N07 - Secant varieties, tensor rank, varieties of sums of powers 14N10 - Enumerative problems (combinatorial problems) in algebraic geometry 14N15 - Classical problems, Schubert calculus 14N20 - Configurations and arrangements of linear subspaces 14N25 - Varieties of low degree 14N30 - Adjunction problems 14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 14N99 - Projective and enumerative algebraic geometry 14Pxx - Real algebraic and real-analytic geometry 14P05 - Real algebraic sets 14P10 - Semialgebraic sets and related spaces 14P15 - Real-analytic and semi-analytic sets 14P20 - Nash functions and manifolds 14P25 - Topology of real algebraic varieties 14P99 - Real algebraic and real-analytic geometry 14Qxx - Computational aspects in algebraic geometry 14Q05 - Computational aspects of algebraic curves 14Q10 - Computational aspects of algebraic surfaces 14Q15 - Computational aspects of higher-dimensional varieties 14Q20 - Effectivity, complexity and computational aspects of algebraic geometry 14Q25 - Computational algebraic geometry over arithmetic ground fields 14Q30 - Computational real algebraic geometry 14Q65 - Geometric aspects of numerical algebraic geometry 14Q99 - Computational aspects in algebraic geometry 14Rxx - Affine geometry 14R05 - Classification of affine varieties 14R10 - Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 14R15 - Jacobian problem 14R20 - Group actions on affine varieties 14R25 - Affine fibrations 14R99 - Affine geometry 14Txx - Tropical geometry 14T10 - Foundations of tropical geometry and relations with algebra 14T15 - Combinatorial aspects of tropical varieties 14T20 - Geometric aspects of tropical varieties 14T25 - Arithmetic aspects of tropical varieties 14T90 - Applications of tropical geometry 14T99 - Tropical geometry 15-XX - Linear and multilinear algebra; matrix theory 15-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to linear algebra 15-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra 15-02 - Research exposition (monographs, survey articles) pertaining to linear algebra 15-03 - History of linear algebra 15-04 - Software, source code, etc. for problems pertaining to linear algebra 15-06 - Proceedings, conferences, collections, etc. pertaining to linear algebra 15-11 - Research data for problems pertaining to linear algebra 15Axx - Basic linear algebra 15A03 - Vector spaces, linear dependence, rank, lineability 15A04 - Linear transformations, semilinear transformations 15A06 - Linear equations (linear algebraic aspects) 15A09 - Theory of matrix inversion and generalized inverses 15A10 - Applications of generalized inverses 15A12 - Conditioning of matrices 15A15 - Determinants, permanents, traces, other special matrix functions 15A16 - Matrix exponential and similar functions of matrices 15A18 - Eigenvalues, singular values, and eigenvectors 15A20 - Diagonalization, Jordan forms 15A21 - Canonical forms, reductions, classification 15A22 - Matrix pencils 15A23 - Factorization of matrices 15A24 - Matrix equations and identities 15A27 - Commutativity of matrices 15A29 - Inverse problems in linear algebra 15A30 - Algebraic systems of matrices 15A39 - Linear inequalities of matrices 15A42 - Inequalities involving eigenvalues and eigenvectors 15A45 - Miscellaneous inequalities involving matrices 15A54 - Matrices over function rings in one or more variables 15A60 - Norms of matrices, numerical range, applications of functional analysis to matrix theory 15A63 - Quadratic and bilinear forms, inner products 15A66 - Clifford algebras, spinors 15A67 - Applications of Clifford algebras to physics, etc. 15A69 - Multilinear algebra, tensor calculus 15A72 - Vector and tensor algebra, theory of invariants 15A75 - Exterior algebra, Grassmann algebras 15A78 - Other algebras built from modules 15A80 - Max-plus and related algebras 15A83 - Matrix completion problems 15A86 - Linear preserver problems 15A99 - Basic linear algebra 15Bxx - Special matrices 15B05 - Toeplitz, Cauchy, and related matrices 15B10 - Orthogonal matrices 15B15 - Fuzzy matrices 15B30 - Matrix Lie algebras 15B33 - Matrices over special rings (quaternions, finite fields, etc.) 15B34 - Boolean and Hadamard matrices 15B35 - Sign pattern matrices 15B36 - Matrices of integers 15B48 - Positive matrices and their generalizations; cones of matrices 15B51 - Stochastic matrices 15B52 - Random matrices (algebraic aspects) 15B57 - Hermitian, skew-Hermitian, and related matrices 15B99 - Special matrices 16-XX - Associative rings and algebras 16-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras 16-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras 16-02 - Research exposition (monographs, survey articles) pertaining to associative rings and algebras 16-03 - History of associative rings and algebras 16-04 - Software, source code, etc. for problems pertaining to associative rings and algebras 16-06 - Proceedings, conferences, collections, etc. pertaining to associative rings and algebras 16-11 - Research data for problems pertaining to associative rings and algebras 16Bxx - General and miscellaneous 16B50 - Category-theoretic methods and results in associative algebras (except as in 16D90) 16B70 - Applications of logic in associative algebras 16B99 - General and miscellaneous 16Dxx - Modules, bimodules and ideals in associative algebras 16D10 - General module theory in associative algebras 16D20 - Bimodules in associative algebras 16D25 - Ideals in associative algebras 16D30 - Infinite-dimensional simple rings (except as in 16Kxx) 16D40 - Free, projective, and flat modules and ideals in associative algebras 16D50 - Injective modules, self-injective associative rings 16D60 - Simple and semisimple modules, primitive rings and ideals in associative algebras 16D70 - Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) 16D80 - Other classes of modules and ideals in associative algebras 16D90 - Module categories in associative algebras 16D99 - Modules, bimodules and ideals in associative algebras 16Exx - Homological methods in associative algebras 16E05 - Syzygies, resolutions, complexes in associative algebras 16E10 - Homological dimension in associative algebras 16E20 - Grothendieck groups, (K)-theory, etc. 16E30 - Homological functors on modules (Tor, Ext, etc.) in associative algebras 16E35 - Derived categories and associative algebras 16E40 - (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) 16E45 - Differential graded algebras and applications (associative algebraic aspects) 16E50 - von Neumann regular rings and generalizations (associative algebraic aspects) 16E60 - Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. 16E65 - Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 16E99 - Homological methods in associative algebras 16Gxx - Representation theory of associative rings and algebras 16G10 - Representations of associative Artinian rings 16G20 - Representations of quivers and partially ordered sets 16G30 - Representations of orders, lattices, algebras over commutative rings 16G50 - Cohen-Macaulay modules in associative algebras 16G60 - Representation type (finite, tame, wild, etc.) of associative algebras 16G70 - Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 16G99 - Representation theory of associative rings and algebras 16Hxx - Associative algebras and orders 16H05 - Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16H10 - Orders in separable algebras 16H15 - Commutative orders 16H20 - Lattices over orders 16H99 - Associative algebras and orders 16Kxx - Division rings and semisimple Artin rings 16K20 - Finite-dimensional division rings 16K40 - Infinite-dimensional and general division rings 16K50 - Brauer groups (algebraic aspects) 16K99 - Division rings and semisimple Artin rings 16Lxx - Local rings and generalizations 16L30 - Noncommutative local and semilocal rings, perfect rings 16L60 - Quasi-Frobenius rings 16L99 - Local rings and generalizations 16Nxx - Radicals and radical properties of associative rings 16N20 - Jacobson radical, quasimultiplication 16N40 - Nil and nilpotent radicals, sets, ideals, associative rings 16N60 - Prime and semiprime associative rings 16N80 - General radicals and associative rings 16N99 - Radicals and radical properties of associative rings 16Pxx - Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras 16P10 - Finite rings and finite-dimensional associative algebras 16P20 - Artinian rings and modules (associative rings and algebras) 16P40 - Noetherian rings and modules (associative rings and algebras) 16P50 - Localization and associative Noetherian rings 16P60 - Chain conditions on annihilators and summands: Goldie-type conditions 16P70 - Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) 16P90 - Growth rate, Gelfand-Kirillov dimension 16P99 - Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras 16Rxx - Rings with polynomial identity 16R10 - (T)-ideals, identities, varieties of associative rings and algebras 16R20 - Semiprime p.i. rings, rings embeddable in matrices over commutative rings 16R30 - Trace rings and invariant theory (associative rings and algebras) 16R40 - Identities other than those of matrices over commutative rings 16R50 - Other kinds of identities (generalized polynomial, rational, involution) 16R60 - Functional identities (associative rings and algebras) 16R99 - Rings with polynomial identity 16Sxx - Associative rings and algebras arising under various constructions 16S10 - Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 16S15 - Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) 16S20 - Centralizing and normalizing extensions 16S30 - Universal enveloping algebras of Lie algebras 16S32 - Rings of differential operators (associative algebraic aspects) 16S34 - Group rings 16S35 - Twisted and skew group rings, crossed products 16S36 - Ordinary and skew polynomial rings and semigroup rings 16S37 - Quadratic and Koszul algebras 16S38 - Rings arising from noncommutative algebraic geometry 16S40 - Smash products of general Hopf actions 16S50 - Endomorphism rings; matrix rings 16S60 - Associative rings of functions, subdirect products, sheaves of rings 16S70 - Extensions of associative rings by ideals 16S80 - Deformations of associative rings 16S85 - Associative rings of fractions and localizations 16S88 - Leavitt path algebras 16S90 - Torsion theories; radicals on module categories (associative algebraic aspects) 16S99 - Associative rings and algebras arising under various constructions 16Txx - Hopf algebras, quantum groups and related topics 16T05 - Hopf algebras and their applications 16T10 - Bialgebras 16T15 - Coalgebras and comodules; corings 16T20 - Ring-theoretic aspects of quantum groups 16T25 - Yang-Baxter equations 16T30 - Connections of Hopf algebras with combinatorics 16T99 - Hopf algebras, quantum groups and related topics 16Uxx - Conditions on elements 16U10 - Integral domains (associative rings and algebras) 16U20 - Ore rings, multiplicative sets, Ore localization 16U30 - Divisibility, noncommutative UFDs 16U40 - Idempotent elements (associative rings and algebras) 16U60 - Units, groups of units (associative rings and algebras) 16U70 - Center, normalizer (invariant elements) (associative rings and algebras) 16U80 - Generalizations of commutativity (associative rings and algebras) 16U90 - Generalized inverses (associative rings and algebras) 16U99 - Conditions on elements 16Wxx - Associative rings and algebras with additional structure 16W10 - Rings with involution; Lie, Jordan and other nonassociative structures 16W20 - Automorphisms and endomorphisms 16W22 - Actions of groups and semigroups; invariant theory (associative rings and algebras) 16W25 - Derivations, actions of Lie algebras 16W50 - Graded rings and modules (associative rings and algebras) 16W55 - ``Super'' (or ``skew'') structure 16W60 - Valuations, completions, formal power series and related constructions (associative rings and algebras) 16W70 - Filtered associative rings; filtrational and graded techniques 16W80 - Topological and ordered rings and modules 16W99 - Associative rings and algebras with additional structure 16Yxx - Generalizations 16Y20 - Hyperrings 16Y30 - Near-rings 16Y60 - Semirings 16Y80 - (Gamma) and fuzzy structures 16Y99 - Generalizations 16Zxx - Computational aspects of associative rings 16Z05 - Computational aspects of associative rings (general theory) 16Z10 - Gr�bner-Shirshov bases 16Z99 - Computational aspects of associative rings 17-XX - Nonassociative rings and algebras 17-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to nonassociative rings and algebras 17-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras 17-02 - Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras 17-03 - History of nonassociative rings and algebras 17-04 - Software, source code, etc. for problems pertaining to nonassociative rings and algebras 17-06 - Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras 17-08 - Computational methods for problems pertaining to nonassociative rings and algebras 17-11 - Research data for problems pertaining to nonassociative rings and algebras 17Axx - General nonassociative rings 17A01 - General theory of nonassociative rings and algebras 17A05 - Power-associative rings 17A15 - Noncommutative Jordan algebras 17A20 - Flexible algebras 17A30 - Nonassociative algebras satisfying other identities 17A32 - Leibniz algebras 17A35 - Nonassociative division algebras 17A36 - Automorphisms, derivations, other operators (nonassociative rings and algebras) 17A40 - Ternary compositions 17A42 - Other (n)-ary compositions ((n ge 3)) 17A45 - Quadratic algebras (but not quadratic Jordan algebras) 17A50 - Free nonassociative algebras 17A60 - Structure theory for nonassociative algebras 17A61 - Gr�bner-Shirshov bases in nonassociative algebras 17A65 - Radical theory (nonassociative rings and algebras) 17A70 - Superalgebras 17A75 - Composition algebras 17A80 - Valued algebras 17A99 - General nonassociative rings 17Bxx - Lie algebras and Lie superalgebras 17B01 - Identities, free Lie (super)algebras 17B05 - Structure theory for Lie algebras and superalgebras 17B08 - Coadjoint orbits; nilpotent varieties 17B10 - Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B15 - Representations of Lie algebras and Lie superalgebras, analytic theory 17B20 - Simple, semisimple, reductive (super)algebras 17B22 - Root systems 17B25 - Exceptional (super)algebras 17B30 - Solvable, nilpotent (super)algebras 17B35 - Universal enveloping (super)algebras 17B37 - Quantum groups (quantized enveloping algebras) and related deformations 17B38 - Yang-Baxter equations and Rota-Baxter operators 17B40 - Automorphisms, derivations, other operators for Lie algebras and super algebras 17B45 - Lie algebras of linear algebraic groups 17B50 - Modular Lie (super)algebras 17B55 - Homological methods in Lie (super)algebras 17B56 - Cohomology of Lie (super)algebras 17B60 - Lie (super)algebras associated with other structures (associative, Jordan, etc.) 17B61 - Hom-Lie and related algebras 17B62 - Lie bialgebras; Lie coalgebras 17B63 - Poisson algebras 17B65 - Infinite-dimensional Lie (super)algebras 17B66 - Lie algebras of vector fields and related (super) algebras 17B67 - Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B68 - Virasoro and related algebras 17B69 - Vertex operators; vertex operator algebras and related structures 17B70 - Graded Lie (super)algebras 17B75 - Color Lie (super)algebras 17B80 - Applications of Lie algebras and superalgebras to integrable systems 17B81 - Applications of Lie (super)algebras to physics, etc. 17B99 - Lie algebras and Lie superalgebras 17Cxx - Jordan algebras (algebras, triples and pairs) 17C05 - Identities and free Jordan structures 17C10 - Structure theory for Jordan algebras 17C17 - Radicals in Jordan algebras 17C20 - Simple, semisimple Jordan algebras 17C27 - Idempotents, Peirce decompositions 17C30 - Associated groups, automorphisms of Jordan algebras 17C36 - Associated manifolds of Jordan algebras 17C37 - Associated geometries of Jordan algebras 17C40 - Exceptional Jordan structures 17C50 - Jordan structures associated with other structures 17C55 - Finite-dimensional structures of Jordan algebras 17C60 - Division algebras and Jordan algebras 17C65 - Jordan structures on Banach spaces and algebras 17C70 - Super structures 17C90 - Applications of Jordan algebras to physics, etc. 17C99 - Jordan algebras (algebras, triples and pairs) 17Dxx - Other nonassociative rings and algebras 17D05 - Alternative rings 17D10 - Mal'tsev rings and algebras 17D15 - Right alternative rings 17D20 - ((gamma, delta))-rings, including ((1,-1))-rings 17D25 - Lie-admissible algebras 17D30 - (non-Lie) Hom algebras and topics 17D92 - Genetic algebras 17D99 - Other nonassociative rings and algebras 18-XX - Category theory; homological algebra 18-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory 18-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory 18-02 - Research exposition (monographs, survey articles) pertaining to category theory 18-03 - History of category theory 18-04 - Software, source code, etc. for problems pertaining to category theory 18-06 - Proceedings, conferences, collections, etc. pertaining to category theory 18-08 - Computational methods for problems pertaining to category theory 18-11 - Research data for problems pertaining to category theory 18Axx - General theory of categories and functors 18A05 - Definitions and generalizations in theory of categories 18A10 - Graphs, diagram schemes, precategories 18A15 - Foundations, relations to logic and deductive systems 18A20 - Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18A22 - Special properties of functors (faithful, full, etc.) 18A23 - Natural morphisms, dinatural morphisms 18A25 - Functor categories, comma categories 18A30 - Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 18A32 - Factorization systems, substructures, quotient structures, congruences, amalgams 18A35 - Categories admitting limits (complete categories), functors preserving limits, completions 18A40 - Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18A50 - Graded categories (general) 18A99 - General theory of categories and functors 18Bxx - Special categories 18B05 - Categories of sets, characterizations 18B10 - Categories of spans/cospans, relations, or partial maps 18B15 - Embedding theorems, universal categories 18B20 - Categories of machines, automata 18B25 - Topoi 18B35 - Preorders, orders, domains and lattices (viewed as categories) 18B40 - Groupoids, semigroupoids, semigroups, groups (viewed as categories) 18B50 - Extensive, distributive, and adhesive categories 18B99 - Special categories 18Cxx - Categories and theories 18C05 - Equational categories 18C10 - Theories (e.g., algebraic theories), structure, and semantics 18C15 - Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads 18C20 - Eilenberg-Moore and Kleisli constructions for monads 18C30 - Sketches and generalizations 18C35 - Accessible and locally presentable categories 18C40 - Structured objects in a category (group objects, etc.) 18C50 - Categorical semantics of formal languages 18C99 - Categories and theories 18Dxx - Categorical structures 18D15 - Closed categories (closed monoidal and Cartesian closed categories, etc.) 18D20 - Enriched categories (over closed or monoidal categories) 18D25 - Actions of a monoidal category, tensorial strength 18D30 - Fibered categories 18D40 - Internal categories and groupoids 18D60 - Profunctors (= correspondences, distributors, modules) 18D65 - Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads) 18D70 - Formal category theory 18D99 - Categorical structures 18Exx - Categorical algebra 18E05 - Preadditive, additive categories 18E08 - Regular categories, Barr-exact categories 18E10 - Abelian categories, Grothendieck categories 18E13 - Protomodular categories, semi-abelian categories, Mal'tsev categories 18E20 - Categorical embedding theorems 18E35 - Localization of categories, calculus of fractions 18E40 - Torsion theories, radicals 18E45 - Definable subcategories and connections with model theory 18E50 - Categorical Galois theory 18E99 - Categorical algebra 18Fxx - Categories in geometry and topology 18F05 - Local categories and functors 18F10 - Grothendieck topologies and Grothendieck topoi 18F15 - Abstract manifolds and fiber bundles (category-theoretic aspects) 18F20 - Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) 18F25 - Algebraic (K)-theory and (L)-theory (category-theoretic aspects) 18F30 - Grothendieck groups (category-theoretic aspects) 18F40 - Synthetic differential geometry, tangent categories, differential categories 18F50 - Goodwillie calculus and functor calculus 18F60 - Categories of topological spaces and continuous mappings 18F70 - Frames and locales, pointfree topology, Stone duality 18F75 - Quantales 18F99 - Categories in geometry and topology 18Gxx - Homological algebra in category theory, derived categories and functors 18G05 - Projectives and injectives (category-theoretic aspects) 18G10 - Resolutions; derived functors (category-theoretic aspects) 18G15 - Ext and Tor, generalizations, K�nneth formula (category-theoretic aspects) 18G20 - Homological dimension (category-theoretic aspects) 18G25 - Relative homological algebra, projective classes (category-theoretic aspects) 18G31 - Simplicial modules and Dold-Kan correspondence 18G35 - Chain complexes (category-theoretic aspects), dg categories 18G40 - Spectral sequences, hypercohomology 18G45 - 2-groups, crossed modules, crossed complexes 18G50 - Nonabelian homological algebra (category-theoretic aspects) 18G65 - Stable module categories 18G70 - (A_{infty})-categories, relations with homological mirror symmetry 18G80 - Derived categories, triangulated categories 18G85 - Graph complexes and graph homology 18G90 - Other (co)homology theories (category-theoretic aspects) 18G99 - Homological algebra in category theory, derived categories and functors 18Mxx - Monoidal categories and operads 18M05 - Monoidal categories, symmetric monoidal categories 18M10 - Traced monoidal categories, compact closed categories, star-autonomous categories 18M15 - Braided monoidal categories and ribbon categories 18M20 - Fusion categories, modular tensor categories, modular functors 18M25 - Tannakian categories 18M30 - String diagrams and graphical calculi 18M35 - Categories of networks and processes, compositionality 18M40 - Dagger categories, categorical quantum mechanics 18M45 - Categorical aspects of linear logic 18M50 - Bimonoidal, skew-monoidal, duoidal categories 18M60 - Operads (general) 18M65 - Non-symmetric operads, multicategories, generalized multicategories 18M70 - Algebraic operads, cooperads, and Koszul duality 18M75 - Topological and simplicial operads 18M80 - Species, Hopf monoids, operads in combinatorics 18M85 - Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads 18M90 - Globular operads 18M99 - Monoidal categories and operads 18Nxx - Higher categories and homotopical algebra 18N10 - 2-categories, bicategories, double categories 18N15 - 2-dimensional monad theory 18N20 - Tricategories, weak (n)-categories, coherence, semi-strictification 18N25 - Categorification 18N30 - Strict omega-categories, computads, polygraphs 18N40 - Homotopical algebra, Quillen model categories, derivators 18N45 - Categories of fibrations, relations to (K)-theory, relations to type theory 18N50 - Simplicial sets, simplicial objects 18N55 - Localizations (e.g., simplicial localization, Bousfield localization) 18N60 - ((infty,1))-categories (quasi-categories, Segal spaces, etc.); (infty)-topoi, stable (infty)-categories 18N65 - ((infty, n))-categories and ((infty,infty))-categories 18N70 - (infty)-operads and higher algebra 18N99 - Higher categories and homotopical algebra 19-XX - (K)-theory 19-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to (K)-theory 19-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to (K)-theory 19-02 - Research exposition (monographs, survey articles) pertaining to (K)-theory 19-03 - History of (K)-theory 19-04 - Software, source code, etc. for problems pertaining to (K)-theory 19-06 - Proceedings, conferences, collections, etc. pertaining to (K)-theory 19-08 - Computational methods for problems pertaining to (K)-theory 19-11 - Research data for problems pertaining to (K)-theory 19Axx - Grothendieck groups and (K_0) 19A13 - Stability for projective modules 19A15 - Efficient generation of modules 19A22 - Frobenius induction, Burnside and representation rings 19A31 - (K_0) of group rings and orders 19A49 - (K_0) of other rings 19A99 - Grothendieck groups and (K_0) 19Bxx - Whitehead groups and (K_1) 19B10 - Stable range conditions 19B14 - Stability for linear groups 19B28 - (K_1) of group rings and orders 19B37 - Congruence subgroup problems 19B99 - Whitehead groups and (K_1) 19Cxx - Steinberg groups and (K_2) 19C09 - Central extensions and Schur multipliers 19C20 - Symbols, presentations and stability of (K_2) 19C30 - (K_2) and the Brauer group 19C40 - Excision for (K_2) 19C99 - Steinberg groups and (K_2) 19Dxx - Higher algebraic (K)-theory 19D06 - (Q)- and plus-constructions 19D10 - Algebraic (K)-theory of spaces 19D23 - Symmetric monoidal categories 19D25 - Karoubi-Villamayor-Gersten (K)-theory 19D35 - Negative (K)-theory, NK and Nil 19D45 - Higher symbols, Milnor (K)-theory 19D50 - Computations of higher (K)-theory of rings 19D55 - (K)-theory and homology; cyclic homology and cohomology 19D99 - Higher algebraic (K)-theory 19Exx - (K)-theory in geometry 19E08 - (K)-theory of schemes 19E15 - Algebraic cycles and motivic cohomology ((K)-theoretic aspects) 19E20 - Relations of (K)-theory with cohomology theories 19E99 - (K)-theory in geometry 19Fxx - (K)-theory in number theory 19F05 - Generalized class field theory ((K)-theoretic aspects) 19F15 - Symbols and arithmetic ((K)-theoretic aspects) 19F27 - �tale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) 19F99 - (K)-theory in number theory 19Gxx - (K)-theory of forms 19G05 - Stability for quadratic modules 19G12 - Witt groups of rings 19G24 - (L)-theory of group rings 19G38 - Hermitian (K)-theory, relations with (K)-theory of rings 19G99 - (K)-theory of forms 19Jxx - Obstructions from topology 19J05 - Finiteness and other obstructions in (K_0) 19J10 - Whitehead (and related) torsion 19J25 - Surgery obstructions ((K)-theoretic aspects) 19J35 - Obstructions to group actions ((K)-theoretic aspects) 19J99 - Obstructions from topology 19Kxx - (K)-theory and operator algebras 19K14 - (K_0) as an ordered group, traces 19K33 - Ext and (K)-homology 19K35 - Kasparov theory ((KK)-theory) 19K56 - Index theory 19K99 - (K)-theory and operator algebras 19Lxx - Topological (K)-theory 19L10 - Riemann-Roch theorems, Chern characters 19L20 - (J)-homomorphism, Adams operations 19L41 - Connective (K)-theory, cobordism 19L47 - Equivariant (K)-theory 19L50 - Twisted (K)-theory; differential (K)-theory 19L64 - Geometric applications of topological (K)-theory 19L99 - Topological (K)-theory 19Mxx - Miscellaneous applications of (K)-theory 19M05 - Miscellaneous applications of (K)-theory 19M99 - Miscellaneous applications of (K)-theory 20-XX - Group theory and generalizations 20-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to group theory 20-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory 20-02 - Research exposition (monographs, survey articles) pertaining to group theory 20-03 - History of group theory 20-04 - Software, source code, etc. for problems pertaining to group theory 20-06 - Proceedings, conferences, collections, etc. pertaining to group theory 20-08 - Computational methods for problems pertaining to group theory 20-11 - Research data for problems pertaining to group theory 20Axx - Foundations 20A05 - Axiomatics and elementary properties of groups 20A10 - Metamathematical considerations in group theory 20A15 - Applications of logic to group theory 20A99 - Foundations 20Bxx - Permutation groups 20B05 - General theory for finite permutation groups 20B07 - General theory for infinite permutation groups 20B10 - Characterization theorems for permutation groups 20B15 - Primitive groups 20B20 - Multiply transitive finite groups 20B22 - Multiply transitive infinite groups 20B25 - Finite automorphism groups of algebraic, geometric, or combinatorial structures 20B27 - Infinite automorphism groups 20B30 - Symmetric groups 20B35 - Subgroups of symmetric groups 20B99 - Permutation groups 20Cxx - Representation theory of groups 20C05 - Group rings of finite groups and their modules (group-theoretic aspects) 20C07 - Group rings of infinite groups and their modules (group-theoretic aspects) 20C08 - Hecke algebras and their representations 20C10 - Integral representations of finite groups 20C11 - (p)-adic representations of finite groups 20C12 - Integral representations of infinite groups 20C15 - Ordinary representations and characters 20C20 - Modular representations and characters 20C25 - Projective representations and multipliers 20C30 - Representations of finite symmetric groups 20C32 - Representations of infinite symmetric groups 20C33 - Representations of finite groups of Lie type 20C34 - Representations of sporadic groups 20C35 - Applications of group representations to physics and other areas of science 20C99 - Representation theory of groups 20Dxx - Abstract finite groups 20D05 - Finite simple groups and their classification 20D06 - Simple groups: alternating groups and groups of Lie type 20D08 - Simple groups: sporadic groups 20D10 - Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks 20D15 - Finite nilpotent groups, (p)-groups 20D20 - Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure 20D25 - Special subgroups (Frattini, Fitting, etc.) 20D30 - Series and lattices of subgroups 20D35 - Subnormal subgroups of abstract finite groups 20D40 - Products of subgroups of abstract finite groups 20D45 - Automorphisms of abstract finite groups 20D60 - Arithmetic and combinatorial problems involving abstract finite groups 20D99 - Abstract finite groups 20Exx - Structure and classification of infinite or finite groups 20E05 - Free nonabelian groups 20E06 - Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20E07 - Subgroup theorems; subgroup growth 20E08 - Groups acting on trees 20E10 - Quasivarieties and varieties of groups 20E15 - Chains and lattices of subgroups, subnormal subgroups 20E18 - Limits, profinite groups 20E22 - Extensions, wreath products, and other compositions of groups 20E25 - Local properties of groups 20E26 - Residual properties and generalizations; residually finite groups 20E28 - Maximal subgroups 20E32 - Simple groups 20E34 - General structure theorems for groups 20E36 - Automorphisms of infinite groups 20E42 - Groups with a (BN)-pair; buildings 20E45 - Conjugacy classes for groups 20E99 - Structure and classification of infinite or finite groups 20Fxx - Special aspects of infinite or finite groups 20F05 - Generators, relations, and presentations of groups 20F06 - Cancellation theory of groups; application of van Kampen diagrams 20F10 - Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 20F11 - Groups of finite Morley rank 20F12 - Commutator calculus 20F14 - Derived series, central series, and generalizations for groups 20F16 - Solvable groups, supersolvable groups 20F17 - Formations of groups, Fitting classes 20F18 - Nilpotent groups 20F19 - Generalizations of solvable and nilpotent groups 20F22 - Other classes of groups defined by subgroup chains 20F24 - FC-groups and their generalizations 20F28 - Automorphism groups of groups 20F29 - Representations of groups as automorphism groups of algebraic systems 20F34 - Fundamental groups and their automorphisms (group-theoretic aspects) 20F36 - Braid groups; Artin groups 20F38 - Other groups related to topology or analysis 20F40 - Associated Lie structures for groups 20F45 - Engel conditions 20F50 - Periodic groups; locally finite groups 20F55 - Reflection and Coxeter groups (group-theoretic aspects) 20F60 - Ordered groups (group-theoretic aspects) 20F65 - Geometric group theory 20F67 - Hyperbolic groups and nonpositively curved groups 20F69 - Asymptotic properties of groups 20F70 - Algebraic geometry over groups; equations over groups 20F99 - Special aspects of infinite or finite groups 20Gxx - Linear algebraic groups and related topics 20G05 - Representation theory for linear algebraic groups 20G07 - Structure theory for linear algebraic groups 20G10 - Cohomology theory for linear algebraic groups 20G15 - Linear algebraic groups over arbitrary fields 20G20 - Linear algebraic groups over the reals, the complexes, the quaternions 20G25 - Linear algebraic groups over local fields and their integers 20G30 - Linear algebraic groups over global fields and their integers 20G35 - Linear algebraic groups over ad�les and other rings and schemes 20G40 - Linear algebraic groups over finite fields 20G41 - Exceptional groups 20G42 - Quantum groups (quantized function algebras) and their representations 20G43 - Schur and (q)-Schur algebras 20G44 - Kac-Moody groups 20G45 - Applications of linear algebraic groups to the sciences 20G99 - Linear algebraic groups and related topics 20Hxx - Other groups of matrices 20H05 - Unimodular groups, congruence subgroups (group-theoretic aspects) 20H10 - Fuchsian groups and their generalizations (group-theoretic aspects) 20H15 - Other geometric groups, including crystallographic groups 20H20 - Other matrix groups over fields 20H25 - Other matrix groups over rings 20H30 - Other matrix groups over finite fields 20H99 - Other groups of matrices 20Jxx - Connections of group theory with homological algebra and category theory 20J05 - Homological methods in group theory 20J06 - Cohomology of groups 20J15 - Category of groups 20J99 - Connections of group theory with homological algebra and category theory 20Kxx - Abelian groups 20K01 - Finite abelian groups 20K10 - Torsion groups, primary groups and generalized primary groups 20K15 - Torsion-free groups, finite rank 20K20 - Torsion-free groups, infinite rank 20K21 - Mixed groups 20K25 - Direct sums, direct products, etc. for abelian groups 20K27 - Subgroups of abelian groups 20K30 - Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups 20K35 - Extensions of abelian groups 20K40 - Homological and categorical methods for abelian groups 20K45 - Topological methods for abelian groups 20K99 - Abelian groups 20Lxx - Groupoids (i.e. small categories in which all morphisms are isomorphisms) 20L05 - Groupoids (i.e. small categories in which all morphisms are isomorphisms) 20L99 - Groupoids (i.e. small categories in which all morphisms are isomorphisms) 20Mxx - Semigroups 20M05 - Free semigroups, generators and relations, word problems 20M07 - Varieties and pseudovarieties of semigroups 20M10 - General structure theory for semigroups 20M11 - Radical theory for semigroups 20M12 - Ideal theory for semigroups 20M13 - Arithmetic theory of semigroups 20M14 - Commutative semigroups 20M15 - Mappings of semigroups 20M17 - Regular semigroups 20M18 - Inverse semigroups 20M19 - Orthodox semigroups 20M20 - Semigroups of transformations, relations, partitions, etc. 20M25 - Semigroup rings, multiplicative semigroups of rings 20M30 - Representation of semigroups; actions of semigroups on sets 20M32 - Algebraic monoids 20M35 - Semigroups in automata theory, linguistics, etc. 20M50 - Connections of semigroups with homological algebra and category theory 20M75 - Generalizations of semigroups 20M99 - Semigroups 20Nxx - Other generalizations of groups 20N02 - Sets with a single binary operation (groupoids) 20N05 - Loops, quasigroups 20N10 - Ternary systems (heaps, semiheaps, heapoids, etc.) 20N15 - (n)-ary systems ((nge 3)) 20N20 - Hypergroups 20N25 - Fuzzy groups 20N99 - Other generalizations of groups 20Pxx - Probabilistic methods in group theory 20P05 - Probabilistic methods in group theory 20P99 - Probabilistic methods in group theory 22-XX - Topological groups, Lie groups 22-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to topological groups 22-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups 22-02 - Research exposition (monographs, survey articles) pertaining to topological groups 22-03 - History of topological groups 22-04 - Software, source code, etc. for problems pertaining to topological groups 22-06 - Proceedings, conferences, collections, etc. pertaining to topological groups 22-08 - Computational methods for problems pertaining to topological groups 22-11 - Research data for problems pertaining to topological groups 22Axx - Topological and differentiable algebraic systems 22A05 - Structure of general topological groups 22A10 - Analysis on general topological groups 22A15 - Structure of topological semigroups 22A20 - Analysis on topological semigroups 22A22 - Topological groupoids (including differentiable and Lie groupoids) 22A25 - Representations of general topological groups and semigroups 22A26 - Topological semilattices, lattices and applications 22A30 - Other topological algebraic systems and their representations 22A99 - Topological and differentiable algebraic systems 22Bxx - Locally compact abelian groups (LCA groups) 22B05 - General properties and structure of LCA groups 22B10 - Structure of group algebras of LCA groups 22B99 - Locally compact abelian groups (LCA groups) 22Cxx - Compact groups 22C05 - Compact groups 22C99 - Compact groups 22Dxx - Locally compact groups and their algebras 22D05 - General properties and structure of locally compact groups 22D10 - Unitary representations of locally compact groups 22D12 - Other representations of locally compact groups 22D15 - Group algebras of locally compact groups 22D20 - Representations of group algebras 22D25 - (C^*)-algebras and (W^*)-algebras in relation to group representations 22D30 - Induced representations for locally compact groups 22D35 - Duality theorems for locally compact groups 22D40 - Ergodic theory on groups 22D45 - Automorphism groups of locally compact groups 22D50 - Rigidity in locally compact groups 22D55 - Kazhdan's property (T), the Haagerup property, and generalizations 22D99 - Locally compact groups and their algebras 22Exx - Lie groups 22E05 - Local Lie groups 22E10 - General properties and structure of complex Lie groups 22E15 - General properties and structure of real Lie groups 22E20 - General properties and structure of other Lie groups 22E25 - Nilpotent and solvable Lie groups 22E27 - Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) 22E30 - Analysis on real and complex Lie groups 22E35 - Analysis on (p)-adic Lie groups 22E40 - Discrete subgroups of Lie groups 22E41 - Continuous cohomology of Lie groups 22E43 - Structure and representation of the Lorentz group 22E45 - Representations of Lie and linear algebraic groups over real fields: analytic methods 22E46 - Semisimple Lie groups and their representations 22E47 - Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) 22E50 - Representations of Lie and linear algebraic groups over local fields 22E55 - Representations of Lie and linear algebraic groups over global fields and ad�le rings 22E57 - Geometric Langlands program: representation-theoretic aspects 22E60 - Lie algebras of Lie groups 22E65 - Infinite-dimensional Lie groups and their Lie algebras: general properties 22E66 - Analysis on and representations of infinite-dimensional Lie groups 22E67 - Loop groups and related constructions, group-theoretic treatment 22E70 - Applications of Lie groups to the sciences; explicit representations 22E99 - Lie groups 22Fxx - Noncompact transformation groups 22F05 - General theory of group and pseudogroup actions 22F10 - Measurable group actions 22F30 - Homogeneous spaces 22F50 - Groups as automorphisms of other structures 22F99 - Noncompact transformation groups 26-XX - Real functions 26-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions 26-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions 26-02 - Research exposition (monographs, survey articles) pertaining to real functions 26-03 - History of real functions 26-04 - Software, source code, etc. for problems pertaining to real functions 26-06 - Proceedings, conferences, collections, etc. pertaining to real functions 26-08 - Computational methods for problems pertaining to real functions 26-11 - Research data for problems pertaining to real functions 26Axx - Functions of one variable 26A03 - Foundations: limits and generalizations, elementary topology of the line 26A06 - One-variable calculus 26A09 - Elementary functions 26A12 - Rate of growth of functions, orders of infinity, slowly varying functions 26A15 - Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 26A16 - Lipschitz (H�lder) classes 26A18 - Iteration of real functions in one variable 26A21 - Classification of real functions; Baire classification of sets and functions 26A24 - Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems 26A27 - Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives 26A30 - Singular functions, Cantor functions, functions with other special properties 26A33 - Fractional derivatives and integrals 26A36 - Antidifferentiation 26A39 - Denjoy and Perron integrals, other special integrals 26A42 - Integrals of Riemann, Stieltjes and Lebesgue type 26A45 - Functions of bounded variation, generalizations 26A46 - Absolutely continuous real functions in one variable 26A48 - Monotonic functions, generalizations 26A51 - Convexity of real functions in one variable, generalizations 26A99 - Functions of one variable 26Bxx - Functions of several variables 26B05 - Continuity and differentiation questions 26B10 - Implicit function theorems, Jacobians, transformations with several variables 26B12 - Calculus of vector functions 26B15 - Integration of real functions of several variables: length, area, volume 26B20 - Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) 26B25 - Convexity of real functions of several variables, generalizations 26B30 - Absolutely continuous real functions of several variables, functions of bounded variation 26B35 - Special properties of functions of several variables, H�lder conditions, etc. 26B40 - Representation and superposition of functions 26B99 - Functions of several variables 26Cxx - Polynomials, rational functions in real analysis 26C05 - Real polynomials: analytic properties, etc. 26C10 - Real polynomials: location of zeros 26C15 - Real rational functions 26C99 - Polynomials, rational functions in real analysis 26Dxx - Inequalities in real analysis 26D05 - Inequalities for trigonometric functions and polynomials 26D07 - Inequalities involving other types of functions 26D10 - Inequalities involving derivatives and differential and integral operators 26D15 - Inequalities for sums, series and integrals 26D20 - Other analytical inequalities 26D99 - Inequalities in real analysis 26Exx - Miscellaneous topics in real functions 26E05 - Real-analytic functions 26E10 - (C^infty)-functions, quasi-analytic functions 26E15 - Calculus of functions on infinite-dimensional spaces 26E20 - Calculus of functions taking values in infinite-dimensional spaces 26E25 - Set-valued functions 26E30 - Non-Archimedean analysis 26E35 - Nonstandard analysis 26E40 - Constructive real analysis 26E50 - Fuzzy real analysis 26E60 - Means 26E70 - Real analysis on time scales or measure chains 26E99 - Miscellaneous topics in real functions 28-XX - Measure and integration 28-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration 28-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration 28-02 - Research exposition (monographs, survey articles) pertaining to measure and integration 28-03 - History of measure and integration 28-04 - Software, source code, etc. for problems pertaining to measure and integration 28-06 - Proceedings, conferences, collections, etc. pertaining to measure and integration 28-08 - Computational methods for problems pertaining to measure and integration 28-11 - Research data for problems pertaining to measure and integration 28Axx - Classical measure theory 28A05 - Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets 28A10 - Real- or complex-valued set functions 28A12 - Contents, measures, outer measures, capacities 28A15 - Abstract differentiation theory, differentiation of set functions 28A20 - Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 28A25 - Integration with respect to measures and other set functions 28A33 - Spaces of measures, convergence of measures 28A35 - Measures and integrals in product spaces 28A50 - Integration and disintegration of measures 28A51 - Lifting theory 28A60 - Measures on Boolean rings, measure algebras 28A75 - Length, area, volume, other geometric measure theory 28A78 - Hausdorff and packing measures 28A80 - Fractals 28A99 - Classical measure theory 28Bxx - Set functions, measures and integrals with values in abstract spaces 28B05 - Vector-valued set functions, measures and integrals 28B10 - Group- or semigroup-valued set functions, measures and integrals 28B15 - Set functions, measures and integrals with values in ordered spaces 28B20 - Set-valued set functions and measures; integration of set-valued functions; measurable selections 28B99 - Set functions, measures and integrals with values in abstract spaces 28Cxx - Set functions and measures on spaces with additional structure 28C05 - Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures 28C10 - Set functions and measures on topological groups or semigroups, Haar measures, invariant measures 28C15 - Set functions and measures on topological spaces (regularity of measures, etc.) 28C20 - Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) 28C99 - Set functions and measures on spaces with additional structure 28Dxx - Measure-theoretic ergodic theory 28D05 - Measure-preserving transformations 28D10 - One-parameter continuous families of measure-preserving transformations 28D15 - General groups of measure-preserving transformations 28D20 - Entropy and other invariants 28D99 - Measure-theoretic ergodic theory 28Exx - Miscellaneous topics in measure theory 28E05 - Nonstandard measure theory 28E10 - Fuzzy measure theory 28E15 - Other connections with logic and set theory 28E99 - Miscellaneous topics in measure theory 30-XX - Functions of a complex variable 30-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable 30-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable 30-02 - Research exposition (monographs, survey articles) pertaining to functions of a complex variable 30-03 - History of functions of a complex variable 30-04 - Software, source code, etc. for problems pertaining to functions of a complex variable 30-06 - Proceedings, conferences, collections, etc. pertaining to functions of a complex variable 30-08 - Computational methods for problems pertaining to functions of a complex variable 30-11 - Research data for problems pertaining to functions of a complex variable 30Axx - General properties of functions of one complex variable 30A05 - Monogenic and polygenic functions of one complex variable 30A10 - Inequalities in the complex plane 30A99 - General properties of functions of one complex variable 30Bxx - Series expansions of functions of one complex variable 30B10 - Power series (including lacunary series) in one complex variable 30B20 - Random power series in one complex variable 30B30 - Boundary behavior of power series in one complex variable; over-convergence 30B40 - Analytic continuation of functions of one complex variable 30B50 - Dirichlet series, exponential series and other series in one complex variable 30B60 - Completeness problems, closure of a system of functions of one complex variable 30B70 - Continued fractions; complex-analytic aspects 30B99 - Series expansions of functions of one complex variable 30Cxx - Geometric function theory 30C10 - Polynomials and rational functions of one complex variable 30C15 - Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) 30C20 - Conformal mappings of special domains 30C25 - Covering theorems in conformal mapping theory 30C30 - Schwarz-Christoffel-type mappings 30C35 - General theory of conformal mappings 30C40 - Kernel functions in one complex variable and applications 30C45 - Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C50 - Coefficient problems for univalent and multivalent functions of one complex variable 30C55 - General theory of univalent and multivalent functions of one complex variable 30C62 - Quasiconformal mappings in the complex plane 30C65 - Quasiconformal mappings in (mathbb{R}^n), other generalizations 30C70 - Extremal problems for conformal and quasiconformal mappings, variational methods 30C75 - Extremal problems for conformal and quasiconformal mappings, other methods 30C80 - Maximum principle, Schwarz's lemma, Lindel�f principle, analogues and generalizations; subordination 30C85 - Capacity and harmonic measure in the complex plane 30C99 - Geometric function theory 30Dxx - Entire and meromorphic functions of one complex variable, and related topics 30D05 - Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 30D10 - Representations of entire functions of one complex variable by series and integrals 30D15 - Special classes of entire functions of one complex variable and growth estimates 30D20 - Entire functions of one complex variable (general theory) 30D30 - Meromorphic functions of one complex variable (general theory) 30D35 - Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D40 - Cluster sets, prime ends, boundary behavior 30D45 - Normal functions of one complex variable, normal families 30D60 - Quasi-analytic and other classes of functions of one complex variable 30D99 - Entire and meromorphic functions of one complex variable, and related topics 30Exx - Miscellaneous topics of analysis in the complex plane 30E05 - Moment problems and interpolation problems in the complex plane 30E10 - Approximation in the complex plane 30E15 - Asymptotic representations in the complex plane 30E20 - Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane 30E25 - Boundary value problems in the complex plane 30E99 - Miscellaneous topics of analysis in the complex plane 30Fxx - Riemann surfaces 30F10 - Compact Riemann surfaces and uniformization 30F15 - Harmonic functions on Riemann surfaces 30F20 - Classification theory of Riemann surfaces 30F25 - Ideal boundary theory for Riemann surfaces 30F30 - Differentials on Riemann surfaces 30F35 - Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) 30F40 - Kleinian groups (aspects of compact Riemann surfaces and uniformization) 30F45 - Conformal metrics (hyperbolic, Poincar�, distance functions) 30F50 - Klein surfaces 30F60 - Teichm�ller theory for Riemann surfaces 30F99 - Riemann surfaces 30Gxx - Generalized function theory 30G06 - Non-Archimedean function theory 30G12 - Finely holomorphic functions and topological function theory 30G20 - Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) 30G25 - Discrete analytic functions 30G30 - Other generalizations of analytic functions (including abstract-valued functions) 30G35 - Functions of hypercomplex variables and generalized variables 30G99 - Generalized function theory 30Hxx - Spaces and algebras of analytic functions of one complex variable 30H05 - Spaces of bounded analytic functions of one complex variable 30H10 - Hardy spaces 30H15 - Nevanlinna spaces and Smirnov spaces 30H20 - Bergman spaces and Fock spaces 30H25 - Besov spaces and (Q_p)-spaces 30H30 - Bloch spaces 30H35 - BMO-spaces 30H40 - Zygmund spaces 30H45 - de Branges-Rovnyak spaces 30H50 - Algebras of analytic functions of one complex variable 30H80 - Corona theorems 30H99 - Spaces and algebras of analytic functions of one complex variable 30Jxx - Function theory on the disc 30J05 - Inner functions of one complex variable 30J10 - Blaschke products 30J15 - Singular inner functions of one complex variable 30J99 - Function theory on the disc 30Kxx - Universal holomorphic functions of one complex variable 30K05 - Universal Taylor series in one complex variable 30K10 - Universal Dirichlet series in one complex variable 30K15 - Universal functions of one complex variable 30K20 - Compositional universality 30K99 - Universal holomorphic functions of one complex variable 30Lxx - Analysis on metric spaces 30L05 - Geometric embeddings of metric spaces 30L10 - Quasiconformal mappings in metric spaces 30L15 - Inequalities in metric spaces 30L99 - Analysis on metric spaces 31-XX - Potential theory 31-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to potential theory 31-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory 31-02 - Research exposition (monographs, survey articles) pertaining to potential theory 31-03 - History of potential theory 31-04 - Software, source code, etc. for problems pertaining to potential theory 31-06 - Proceedings, conferences, collections, etc. pertaining to potential theory 31-08 - Computational methods for problems pertaining to potential theory 31-11 - Research data for problems pertaining to potential theory 31Axx - Two-dimensional potential theory 31A05 - Harmonic, subharmonic, superharmonic functions in two dimensions 31A10 - Integral representations, integral operators, integral equations methods in two dimensions 31A15 - Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions 31A20 - Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions 31A25 - Boundary value and inverse problems for harmonic functions in two dimensions 31A30 - Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions 31A35 - Connections of harmonic functions with differential equations in two dimensions 31A99 - Two-dimensional potential theory 31Bxx - Higher-dimensional potential theory 31B05 - Harmonic, subharmonic, superharmonic functions in higher dimensions 31B10 - Integral representations, integral operators, integral equations methods in higher dimensions 31B15 - Potentials and capacities, extremal length and related notions in higher dimensions 31B20 - Boundary value and inverse problems for harmonic functions in higher dimensions 31B25 - Boundary behavior of harmonic functions in higher dimensions 31B30 - Biharmonic and polyharmonic equations and functions in higher dimensions 31B35 - Connections of harmonic functions with differential equations in higher dimensions 31B99 - Higher-dimensional potential theory 31Cxx - Generalizations of potential theory 31C05 - Harmonic, subharmonic, superharmonic functions on other spaces 31C10 - Pluriharmonic and plurisubharmonic functions 31C12 - Potential theory on Riemannian manifolds and other spaces 31C15 - Potentials and capacities on other spaces 31C20 - Discrete potential theory 31C25 - Dirichlet forms 31C35 - Martin boundary theory 31C40 - Fine potential theory; fine properties of sets and functions 31C45 - Other generalizations (nonlinear potential theory, etc.) 31C99 - Generalizations of potential theory 31Dxx - Axiomatic potential theory 31D05 - Axiomatic potential theory 31D99 - Axiomatic potential theory 31Exx - Potential theory on fractals and metric spaces 31E05 - Potential theory on fractals and metric spaces 31E99 - Potential theory on fractals and metric spaces 32-XX - Several complex variables and analytic spaces 32-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces 32-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces 32-02 - Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces 32-03 - History of several complex variables and analytic spaces 32-04 - Software, source code, etc. for problems pertaining to several complex variables and analytic spaces 32-06 - Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces 32-08 - Computational methods for problems pertaining to several complex variables and analytic spaces 32-11 - Research data for problems pertaining to several complex variables and analytic spaces 32Axx - Holomorphic functions of several complex variables 32A05 - Power series, series of functions of several complex variables 32A08 - Polynomials and rational functions of several complex variables 32A10 - Holomorphic functions of several complex variables 32A12 - Multifunctions of several complex variables 32A15 - Entire functions of several complex variables 32A17 - Special families of functions of several complex variables 32A18 - Bloch functions, normal functions of several complex variables 32A19 - Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.) 32A20 - Meromorphic functions of several complex variables 32A22 - Nevanlinna theory; growth estimates; other inequalities of several complex variables 32A25 - Integral representations; canonical kernels (Szeg?, Bergman, etc.) 32A26 - Integral representations, constructed kernels (e.g., Cauchy, Fantappi�-type kernels) 32A27 - Residues for several complex variables 32A30 - Other generalizations of function theory of one complex variable 32A35 - (H^p)-spaces, Nevanlinna spaces of functions in several complex variables 32A36 - Bergman spaces of functions in several complex variables 32A37 - Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 32A38 - Algebras of holomorphic functions of several complex variables 32A40 - Boundary behavior of holomorphic functions of several complex variables 32A45 - Hyperfunctions 32A50 - Harmonic analysis of several complex variables 32A55 - Singular integrals of functions in several complex variables 32A60 - Zero sets of holomorphic functions of several complex variables 32A65 - Banach algebra techniques applied to functions of several complex variables 32A70 - Functional analysis techniques applied to functions of several complex variables 32A99 - Holomorphic functions of several complex variables 32Bxx - Local analytic geometry 32B05 - Analytic algebras and generalizations, preparation theorems 32B10 - Germs of analytic sets, local parametrization 32B15 - Analytic subsets of affine space 32B20 - Semi-analytic sets, subanalytic sets, and generalizations 32B25 - Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions 32B99 - Local analytic geometry 32Cxx - Analytic spaces 32C05 - Real-analytic manifolds, real-analytic spaces 32C07 - Real-analytic sets, complex Nash functions 32C09 - Embedding of real-analytic manifolds 32C11 - Complex supergeometry 32C15 - Complex spaces 32C18 - Topology of analytic spaces 32C20 - Normal analytic spaces 32C22 - Embedding of analytic spaces 32C25 - Analytic subsets and submanifolds 32C30 - Integration on analytic sets and spaces, currents 32C35 - Analytic sheaves and cohomology groups 32C36 - Local cohomology of analytic spaces 32C37 - Duality theorems for analytic spaces 32C38 - Sheaves of differential operators and their modules, (D)-modules 32C55 - The Levi problem in complex spaces; generalizations 32C81 - Applications of analytic spaces to physics and other areas of science 32C99 - Analytic spaces 32Dxx - Analytic continuation 32D05 - Domains of holomorphy 32D10 - Envelopes of holomorphy 32D15 - Continuation of analytic objects in several complex variables 32D20 - Removable singularities in several complex variables 32D26 - Riemann domains 32D99 - Analytic continuation 32Exx - Holomorphic convexity 32E05 - Holomorphically convex complex spaces, reduction theory 32E10 - Stein spaces 32E20 - Polynomial convexity, rational convexity, meromorphic convexity in several complex variables 32E30 - Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs 32E35 - Global boundary behavior of holomorphic functions of several complex variables 32E40 - The Levi problem 32E99 - Holomorphic convexity 32Fxx - Geometric convexity in several complex variables 32F10 - (q)-convexity, (q)-concavity 32F17 - Other notions of convexity in relation to several complex variables 32F18 - Finite-type conditions for the boundary of a domain 32F27 - Topological consequences of geometric convexity 32F32 - Analytical consequences of geometric convexity (vanishing theorems, etc.) 32F45 - Invariant metrics and pseudodistances in several complex variables 32F99 - Geometric convexity in several complex variables 32Gxx - Deformations of analytic structures 32G05 - Deformations of complex structures 32G07 - Deformations of special (e.g., CR) structures 32G08 - Deformations of fiber bundles 32G10 - Deformations of submanifolds and subspaces 32G13 - Complex-analytic moduli problems 32G15 - Moduli of Riemann surfaces, Teichm�ller theory (complex-analytic aspects in several variables) 32G20 - Period matrices, variation of Hodge structure; degenerations 32G34 - Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) 32G81 - Applications of deformations of analytic structures to the sciences 32G99 - Deformations of analytic structures 32Hxx - Holomorphic mappings and correspondences 32H02 - Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 32H04 - Meromorphic mappings in several complex variables 32H12 - Boundary uniqueness of mappings in several complex variables 32H25 - Picard-type theorems and generalizations for several complex variables 32H30 - Value distribution theory in higher dimensions 32H35 - Proper holomorphic mappings, finiteness theorems 32H40 - Boundary regularity of mappings in several complex variables 32H50 - Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables 32H99 - Holomorphic mappings and correspondences 32Jxx - Compact analytic spaces 32J05 - Compactification of analytic spaces 32J10 - Algebraic dependence theorems 32J15 - Compact complex surfaces 32J17 - Compact complex (3)-folds 32J18 - Compact complex (n)-folds 32J25 - Transcendental methods of algebraic geometry (complex-analytic aspects) 32J27 - Compact K�hler manifolds: generalizations, classification 32J81 - Applications of compact analytic spaces to the sciences 32J99 - Compact analytic spaces 32Kxx - Generalizations of analytic spaces 32K05 - Banach analytic manifolds and spaces 32K07 - Formal and graded complex spaces 32K12 - Holomorphic maps with infinite-dimensional arguments or values 32K15 - Differentiable functions on analytic spaces, differentiable spaces 32K99 - Generalizations of analytic spaces 32Lxx - Holomorphic fiber spaces 32L05 - Holomorphic bundles and generalizations 32L10 - Sheaves and cohomology of sections of holomorphic vector bundles, general results 32L15 - Bundle convexity 32L20 - Vanishing theorems 32L25 - Twistor theory, double fibrations (complex-analytic aspects) 32L81 - Applications of holomorphic fiber spaces to the sciences 32L99 - Holomorphic fiber spaces 32Mxx - Complex spaces with a group of automorphisms 32M05 - Complex Lie groups, group actions on complex spaces 32M10 - Homogeneous complex manifolds 32M12 - Almost homogeneous manifolds and spaces 32M15 - Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) 32M17 - Automorphism groups of (mathbb{C}^n) and affine manifolds 32M18 - Automorphism groups of other complex spaces 32M25 - Complex vector fields, holomorphic foliations, (mathbb{C})-actions 32M99 - Complex spaces with a group of automorphisms 32Nxx - Automorphic functions 32N05 - General theory of automorphic functions of several complex variables 32N10 - Automorphic forms in several complex variables 32N15 - Automorphic functions in symmetric domains 32N99 - Automorphic functions 32Pxx - Non-Archimedean analysis 32P05 - Non-Archimedean analysis 32P99 - Non-Archimedean analysis 32Qxx - Complex manifolds 32Q02 - Special domains (Reinhardt, Hartogs, circular, tube, etc.) in (mathbb{C}^n) and complex manifolds 32Q05 - Negative curvature complex manifolds 32Q10 - Positive curvature complex manifolds 32Q15 - K�hler manifolds 32Q20 - K�hler-Einstein manifolds 32Q25 - Calabi-Yau theory (complex-analytic aspects) 32Q26 - Notions of stability for complex manifolds 32Q28 - Stein manifolds 32Q30 - Uniformization of complex manifolds 32Q35 - Complex manifolds as subdomains of Euclidean space 32Q40 - Embedding theorems for complex manifolds 32Q45 - Hyperbolic and Kobayashi hyperbolic manifolds 32Q55 - Topological aspects of complex manifolds 32Q56 - Oka principle and Oka manifolds 32Q57 - Classification theorems for complex manifolds 32Q60 - Almost complex manifolds 32Q65 - Pseudoholomorphic curves 32Q99 - Complex manifolds 32Sxx - Complex singularities 32S05 - Local complex singularities 32S10 - Invariants of analytic local rings 32S15 - Equisingularity (topological and analytic) 32S20 - Global theory of complex singularities; cohomological properties 32S22 - Relations with arrangements of hyperplanes 32S25 - Complex surface and hypersurface singularities 32S30 - Deformations of complex singularities; vanishing cycles 32S35 - Mixed Hodge theory of singular varieties (complex-analytic aspects) 32S40 - Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) 32S45 - Modifications; resolution of singularities (complex-analytic aspects) 32S50 - Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants 32S55 - Milnor fibration; relations with knot theory 32S60 - Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 32S65 - Singularities of holomorphic vector fields and foliations 32S70 - Other operations on complex singularities 32S99 - Complex singularities 32Txx - Pseudoconvex domains 32T05 - Domains of holomorphy 32T15 - Strongly pseudoconvex domains 32T20 - Worm domains 32T25 - Finite-type domains 32T27 - Geometric and analytic invariants on weakly pseudoconvex boundaries 32T35 - Exhaustion functions 32T40 - Peak functions 32T99 - Pseudoconvex domains 32Uxx - Pluripotential theory 32U05 - Plurisubharmonic functions and generalizations 32U10 - Plurisubharmonic exhaustion functions 32U15 - General pluripotential theory 32U20 - Capacity theory and generalizations 32U25 - Lelong numbers 32U30 - Removable sets in pluripotential theory 32U35 - Plurisubharmonic extremal functions, pluricomplex Green functions 32U40 - Currents 32U99 - Pluripotential theory 32Vxx - CR manifolds 32V05 - CR structures, CR operators, and generalizations 32V10 - CR functions 32V15 - CR manifolds as boundaries of domains 32V20 - Analysis on CR manifolds 32V25 - Extension of functions and other analytic objects from CR manifolds 32V30 - Embeddings of CR manifolds 32V35 - Finite-type conditions on CR manifolds 32V40 - Real submanifolds in complex manifolds 32V99 - CR manifolds 32Wxx - Differential operators in several variables 32W05 - (overlinepartial) and (overlinepartial)-Neumann operators 32W10 - (overlinepartial_b) and (overlinepartial_b)-Neumann operators 32W20 - Complex Monge-Amp�re operators 32W25 - Pseudodifferential operators in several complex variables 32W30 - Heat kernels in several complex variables 32W50 - Other partial differential equations of complex analysis in several variables 32W99 - Differential operators in several variables 33-XX - Special functions 33-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions 33-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions 33-02 - Research exposition (monographs, survey articles) pertaining to special functions 33-03 - History of special functions 33-04 - Software, source code, etc. for problems pertaining to special functions 33-06 - Proceedings, conferences, collections, etc. pertaining to special functions 33-11 - Research data for problems pertaining to special functions 33Bxx - Elementary classical functions 33B10 - Exponential and trigonometric functions 33B15 - Gamma, beta and polygamma functions 33B20 - Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) 33B30 - Higher logarithm functions 33B99 - Elementary classical functions 33Cxx - Hypergeometric functions 33C05 - Classical hypergeometric functions, ({}_2F_1) 33C10 - Bessel and Airy functions, cylinder functions, ({}_0F_1) 33C15 - Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) 33C20 - Generalized hypergeometric series, ({}_pF_q) 33C45 - Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 33C47 - Other special orthogonal polynomials and functions 33C50 - Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable 33C52 - Orthogonal polynomials and functions associated with root systems 33C55 - Spherical harmonics 33C60 - Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) 33C65 - Appell, Horn and Lauricella functions 33C67 - Hypergeometric functions associated with root systems 33C70 - Other hypergeometric functions and integrals in several variables 33C75 - Elliptic integrals as hypergeometric functions 33C80 - Connections of hypergeometric functions with groups and algebras, and related topics 33C90 - Applications of hypergeometric functions 33C99 - Hypergeometric functions 33Dxx - Basic hypergeometric functions 33D05 - (q)-gamma functions, (q)-beta functions and integrals 33D15 - Basic hypergeometric functions in one variable, ({}_rphi_s) 33D45 - Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D50 - Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 33D52 - Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) 33D60 - Basic hypergeometric integrals and functions defined by them 33D65 - Bibasic functions and multiple bases 33D67 - Basic hypergeometric functions associated with root systems 33D70 - Other basic hypergeometric functions and integrals in several variables 33D80 - Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics 33D90 - Applications of basic hypergeometric functions 33D99 - Basic hypergeometric functions 33Exx - Other special functions 33E05 - Elliptic functions and integrals 33E10 - Lam�, Mathieu, and spheroidal wave functions 33E12 - Mittag-Leffler functions and generalizations 33E15 - Other wave functions 33E17 - Painlev�-type functions 33E20 - Other functions defined by series and integrals 33E30 - Other functions coming from differential, difference and integral equations 33E50 - Special functions in characteristic (p) (gamma functions, etc.) 33E99 - Other special functions 33Fxx - Computational aspects of special functions 33F05 - Numerical approximation and evaluation of special functions 33F10 - Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) 33F99 - Computational aspects of special functions 34-XX - Ordinary differential equations 34-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations 34-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations 34-02 - Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34-03 - History of ordinary differential equations 34-04 - Software, source code, etc. for problems pertaining to ordinary differential equations 34-06 - Proceedings, conferences, collections, etc. pertaining to ordinary differential equations 34-11 - Research data for problems pertaining to ordinary differential equations 34Axx - General theory for ordinary differential equations 34A05 - Explicit solutions, first integrals of ordinary differential equations 34A06 - Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) 34A07 - Fuzzy ordinary differential equations 34A08 - Fractional ordinary differential equations 34A09 - Implicit ordinary differential equations, differential-algebraic equations 34A12 - Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A25 - Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A26 - Geometric methods in ordinary differential equations 34A30 - Linear ordinary differential equations and systems 34A33 - Ordinary lattice differential equations 34A34 - Nonlinear ordinary differential equations and systems 34A35 - Ordinary differential equations of infinite order 34A36 - Discontinuous ordinary differential equations 34A37 - Ordinary differential equations with impulses 34A38 - Hybrid systems of ordinary differential equations 34A40 - Differential inequalities involving functions of a single real variable 34A45 - Theoretical approximation of solutions to ordinary differential equations 34A55 - Inverse problems involving ordinary differential equations 34A60 - Ordinary differential inclusions 34A99 - General theory for ordinary differential equations 34Bxx - Boundary value problems for ordinary differential equations 34B05 - Linear boundary value problems for ordinary differential equations 34B07 - Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter 34B08 - Parameter dependent boundary value problems for ordinary differential equations 34B09 - Boundary eigenvalue problems for ordinary differential equations 34B10 - Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 - Nonlinear boundary value problems for ordinary differential equations 34B16 - Singular nonlinear boundary value problems for ordinary differential equations 34B18 - Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B20 - Weyl theory and its generalizations for ordinary differential equations 34B24 - Sturm-Liouville theory 34B27 - Green's functions for ordinary differential equations 34B30 - Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34B37 - Boundary value problems with impulses for ordinary differential equations 34B40 - Boundary value problems on infinite intervals for ordinary differential equations 34B45 - Boundary value problems on graphs and networks for ordinary differential equations 34B60 - Applications of boundary value problems involving ordinary differential equations 34B99 - Boundary value problems for ordinary differential equations 34Cxx - Qualitative theory for ordinary differential equations 34C05 - Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C07 - Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations 34C08 - Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 34C10 - Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C11 - Growth and boundedness of solutions to ordinary differential equations 34C12 - Monotone systems involving ordinary differential equations 34C14 - Symmetries, invariants of ordinary differential equations 34C15 - Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C20 - Transformation and reduction of ordinary differential equations and systems, normal forms 34C23 - Bifurcation theory for ordinary differential equations 34C25 - Periodic solutions to ordinary differential equations 34C26 - Relaxation oscillations for ordinary differential equations 34C27 - Almost and pseudo-almost periodic solutions to ordinary differential equations 34C28 - Complex behavior and chaotic systems of ordinary differential equations 34C29 - Averaging method for ordinary differential equations 34C37 - Homoclinic and heteroclinic solutions to ordinary differential equations 34C40 - Ordinary differential equations and systems on manifolds 34C41 - Equivalence and asymptotic equivalence of ordinary differential equations 34C45 - Invariant manifolds for ordinary differential equations 34C46 - Multifrequency systems of ordinary differential equations 34C55 - Hysteresis for ordinary differential equations 34C60 - Qualitative investigation and simulation of ordinary differential equation models 34C99 - Qualitative theory for ordinary differential equations 34Dxx - Stability theory for ordinary differential equations 34D05 - Asymptotic properties of solutions to ordinary differential equations 34D06 - Synchronization of solutions to ordinary differential equations 34D08 - Characteristic and Lyapunov exponents of ordinary differential equations 34D09 - Dichotomy, trichotomy of solutions to ordinary differential equations 34D10 - Perturbations of ordinary differential equations 34D15 - Singular perturbations of ordinary differential equations 34D20 - Stability of solutions to ordinary differential equations 34D23 - Global stability of solutions to ordinary differential equations 34D30 - Structural stability and analogous concepts of solutions to ordinary differential equations 34D35 - Stability of manifolds of solutions to ordinary differential equations 34D45 - Attractors of solutions to ordinary differential equations 34D99 - Stability theory for ordinary differential equations 34Exx - Asymptotic theory for ordinary differential equations 34E05 - Asymptotic expansions of solutions to ordinary differential equations 34E10 - Perturbations, asymptotics of solutions to ordinary differential equations 34E13 - Multiple scale methods for ordinary differential equations 34E15 - Singular perturbations for ordinary differential equations 34E17 - Canard solutions to ordinary differential equations 34E18 - Methods of nonstandard analysis for ordinary differential equations 34E20 - Singular perturbations, turning point theory, WKB methods for ordinary differential equations 34E99 - Asymptotic theory for ordinary differential equations 34Fxx - Ordinary differential equations and systems with randomness 34F05 - Ordinary differential equations and systems with randomness 34F10 - Bifurcation of solutions to ordinary differential equations involving randomness 34F15 - Resonance phenomena for ordinary differential equations involving randomness 34F99 - Ordinary differential equations and systems with randomness 34Gxx - Differential equations in abstract spaces 34G10 - Linear differential equations in abstract spaces 34G20 - Nonlinear differential equations in abstract spaces 34G25 - Evolution inclusions 34G99 - Differential equations in abstract spaces 34Hxx - Control problems involving ordinary differential equations 34H05 - Control problems involving ordinary differential equations 34H10 - Chaos control for problems involving ordinary differential equations 34H15 - Stabilization of solutions to ordinary differential equations 34H20 - Bifurcation control of ordinary differential equations 34H99 - Control problems involving ordinary differential equations 34Kxx - Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34K04 - Symmetries, invariants of functional-differential equations 34K05 - General theory of functional-differential equations 34K06 - Linear functional-differential equations 34K07 - Theoretical approximation of solutions to functional-differential equations 34K08 - Spectral theory of functional-differential operators 34K09 - Functional-differential inclusions 34K10 - Boundary value problems for functional-differential equations 34K11 - Oscillation theory of functional-differential equations 34K12 - Growth, boundedness, comparison of solutions to functional-differential equations 34K13 - Periodic solutions to functional-differential equations 34K14 - Almost and pseudo-almost periodic solutions to functional-differential equations 34K16 - Heteroclinic and homoclinic orbits of functional-differential equations 34K17 - Transformation and reduction of functional-differential equations and systems, normal forms 34K18 - Bifurcation theory of functional-differential equations 34K19 - Invariant manifolds of functional-differential equations 34K20 - Stability theory of functional-differential equations 34K21 - Stationary solutions of functional-differential equations 34K23 - Complex (chaotic) behavior of solutions to functional-differential equations 34K24 - Synchronization of functional-differential equations 34K25 - Asymptotic theory of functional-differential equations 34K26 - Singular perturbations of functional-differential equations 34K27 - Perturbations of functional-differential equations 34K29 - Inverse problems for functional-differential equations 34K30 - Functional-differential equations in abstract spaces 34K31 - Lattice functional-differential equations 34K32 - Implicit functional-differential equations 34K33 - Averaging for functional-differential equations 34K34 - Hybrid systems of functional-differential equations 34K35 - Control problems for functional-differential equations 34K36 - Fuzzy functional-differential equations 34K37 - Functional-differential equations with fractional derivatives 34K38 - Functional-differential inequalities 34K39 - Discontinuous functional-differential equations 34K40 - Neutral functional-differential equations 34K41 - Functional-differential equations in the complex domain 34K42 - Functional-differential equations on time scales or measure chains 34K43 - Functional-differential equations with state-dependent arguments 34K45 - Functional-differential equations with impulses 34K50 - Stochastic functional-differential equations 34K60 - Qualitative investigation and simulation of models involving functional-differential equations 34K99 - Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34Lxx - Ordinary differential operators 34L05 - General spectral theory of ordinary differential operators 34L10 - Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators 34L15 - Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators 34L16 - Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators 34L20 - Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators 34L25 - Scattering theory, inverse scattering involving ordinary differential operators 34L30 - Nonlinear ordinary differential operators 34L40 - Particular ordinary differential operators (Dirac, one-dimensional Schr�dinger, etc.) 34L99 - Ordinary differential operators 34Mxx - Ordinary differential equations in the complex domain 34M03 - Linear ordinary differential equations and systems in the complex domain 34M04 - Nonlinear ordinary differential equations and systems in the complex domain 34M05 - Entire and meromorphic solutions to ordinary differential equations in the complex domain 34M10 - Oscillation, growth of solutions to ordinary differential equations in the complex domain 34M15 - Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain 34M25 - Formal solutions and transform techniques for ordinary differential equations in the complex domain 34M30 - Asymptotics and summation methods for ordinary differential equations in the complex domain 34M35 - Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms 34M40 - Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain 34M45 - Ordinary differential equations on complex manifolds 34M46 - Spectral theory for ordinary differential operators in the complex domain 34M50 - Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain 34M55 - Painlev� and other special ordinary differential equations in the complex domain; classification, hierarchies 34M56 - Isomonodromic deformations for ordinary differential equations in the complex domain 34M60 - Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) 34M65 - Topological structure of trajectories of ordinary differential equations in the complex domain 34M99 - Ordinary differential equations in the complex domain 34Nxx - Dynamic equations on time scales or measure chains 34N05 - Dynamic equations on time scales or measure chains 34N99 - Dynamic equations on time scales or measure chains 35-XX - Partial differential equations 35-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations 35-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations 35-02 - Research exposition (monographs, survey articles) pertaining to partial differential equations 35-03 - History of partial differential equations 35-04 - Software, source code, etc. for problems pertaining to partial differential equations 35-06 - Proceedings, conferences, collections, etc. pertaining to partial differential equations 35-11 - Research data for problems pertaining to partial differential equations 35Axx - General topics in partial differential equations 35A01 - Existence problems for PDEs: global existence, local existence, non-existence 35A02 - Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35A08 - Fundamental solutions to PDEs 35A09 - Classical solutions to PDEs 35A10 - Cauchy-Kovalevskaya theorems 35A15 - Variational methods applied to PDEs 35A16 - Topological and monotonicity methods applied to PDEs 35A17 - Parametrices in context of PDEs 35A18 - Wave front sets in context of PDEs 35A20 - Analyticity in context of PDEs 35A21 - Singularity in context of PDEs 35A22 - Transform methods (e.g., integral transforms) applied to PDEs 35A23 - Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals 35A24 - Methods of ordinary differential equations applied to PDEs 35A25 - Other special methods applied to PDEs 35A27 - Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs 35A30 - Geometric theory, characteristics, transformations in context of PDEs 35A35 - Theoretical approximation in context of PDEs 35A99 - General topics in partial differential equations 35Bxx - Qualitative properties of solutions to partial differential equations 35B05 - Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B06 - Symmetries, invariants, etc. in context of PDEs 35B07 - Axially symmetric solutions to PDEs 35B08 - Entire solutions to PDEs 35B09 - Positive solutions to PDEs 35B10 - Periodic solutions to PDEs 35B15 - Almost and pseudo-almost periodic solutions to PDEs 35B20 - Perturbations in context of PDEs 35B25 - Singular perturbations in context of PDEs 35B27 - Homogenization in context of PDEs; PDEs in media with periodic structure 35B30 - Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B32 - Bifurcations in context of PDEs 35B33 - Critical exponents in context of PDEs 35B34 - Resonance in context of PDEs 35B35 - Stability in context of PDEs 35B36 - Pattern formations in context of PDEs 35B38 - Critical points of functionals in context of PDEs (e.g., energy functionals) 35B40 - Asymptotic behavior of solutions to PDEs 35B41 - Attractors 35B42 - Inertial manifolds 35B44 - Blow-up in context of PDEs 35B45 - A priori estimates in context of PDEs 35B50 - Maximum principles in context of PDEs 35B51 - Comparison principles in context of PDEs 35B53 - Liouville theorems and Phragm�n-Lindel�f theorems in context of PDEs 35B60 - Continuation and prolongation of solutions to PDEs 35B65 - Smoothness and regularity of solutions to PDEs 35B99 - Qualitative properties of solutions to partial differential equations 35Cxx - Representations of solutions to partial differential equations 35C05 - Solutions to PDEs in closed form 35C06 - Self-similar solutions to PDEs 35C07 - Traveling wave solutions 35C08 - Soliton solutions 35C09 - Trigonometric solutions to PDEs 35C10 - Series solutions to PDEs 35C11 - Polynomial solutions to PDEs 35C15 - Integral representations of solutions to PDEs 35C20 - Asymptotic expansions of solutions to PDEs 35C99 - Representations of solutions to partial differential equations 35Dxx - Generalized solutions to partial differential equations 35D30 - Weak solutions to PDEs 35D35 - Strong solutions to PDEs 35D40 - Viscosity solutions to PDEs 35D99 - Generalized solutions to partial differential equations 35Exx - Partial differential equations and systems of partial differential equations with constant coefficients 35E05 - Fundamental solutions to PDEs and systems of PDEs with constant coefficients 35E10 - Convexity properties of solutions to PDEs with constant coefficients 35E15 - Initial value problems for PDEs and systems of PDEs with constant coefficients 35E20 - General theory of PDEs and systems of PDEs with constant coefficients 35E99 - Partial differential equations and systems of partial differential equations with constant coefficients 35Fxx - General first-order partial differential equations and systems of first-order partial differential equations 35F05 - Linear first-order PDEs 35F10 - Initial value problems for linear first-order PDEs 35F15 - Boundary value problems for linear first-order PDEs 35F16 - Initial-boundary value problems for linear first-order PDEs 35F20 - Nonlinear first-order PDEs 35F21 - Hamilton-Jacobi equations 35F25 - Initial value problems for nonlinear first-order PDEs 35F30 - Boundary value problems for nonlinear first-order PDEs 35F31 - Initial-boundary value problems for nonlinear first-order PDEs 35F35 - Systems of linear first-order PDEs 35F40 - Initial value problems for systems of linear first-order PDEs 35F45 - Boundary value problems for systems of linear first-order PDEs 35F46 - Initial-boundary value problems for systems of linear first-order PDEs 35F50 - Systems of nonlinear first-order PDEs 35F55 - Initial value problems for systems of nonlinear first-order PDEs 35F60 - Boundary value problems for systems of nonlinear first-order PDEs 35F61 - Initial-boundary value problems for systems of nonlinear first-order PDEs 35F99 - General first-order partial differential equations and systems of first-order partial differential equations 35Gxx - General higher-order partial differential equations and systems of higher-order partial differential equations 35G05 - Linear higher-order PDEs 35G10 - Initial value problems for linear higher-order PDEs 35G15 - Boundary value problems for linear higher-order PDEs 35G16 - Initial-boundary value problems for linear higher-order PDEs 35G20 - Nonlinear higher-order PDEs 35G25 - Initial value problems for nonlinear higher-order PDEs 35G30 - Boundary value problems for nonlinear higher-order PDEs 35G31 - Initial-boundary value problems for nonlinear higher-order PDEs 35G35 - Systems of linear higher-order PDEs 35G40 - Initial value problems for systems of linear higher-order PDEs 35G45 - Boundary value problems for systems of linear higher-order PDEs 35G46 - Initial-boundary value problems for systems of linear higher-order PDEs 35G50 - Systems of nonlinear higher-order PDEs 35G55 - Initial value problems for systems of nonlinear higher-order PDEs 35G60 - Boundary value problems for systems of nonlinear higher-order PDEs 35G61 - Initial-boundary value problems for systems of nonlinear higher-order PDEs 35G99 - General higher-order partial differential equations and systems of higher-order partial differential equations 35Hxx - Close-to-elliptic equations 35H10 - Hypoelliptic equations 35H20 - Subelliptic equations 35H30 - Quasielliptic equations 35H99 - Close-to-elliptic equations 35Jxx - Elliptic equations and elliptic systems 35J05 - Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35J08 - Green's functions for elliptic equations 35J10 - Schr�dinger operator, Schr�dinger equation 35J15 - Second-order elliptic equations 35J20 - Variational methods for second-order elliptic equations 35J25 - Boundary value problems for second-order elliptic equations 35J30 - Higher-order elliptic equations 35J35 - Variational methods for higher-order elliptic equations 35J40 - Boundary value problems for higher-order elliptic equations 35J46 - First-order elliptic systems 35J47 - Second-order elliptic systems 35J48 - Higher-order elliptic systems 35J50 - Variational methods for elliptic systems 35J56 - Boundary value problems for first-order elliptic systems 35J57 - Boundary value problems for second-order elliptic systems 35J58 - Boundary value problems for higher-order elliptic systems 35J60 - Nonlinear elliptic equations 35J61 - Semilinear elliptic equations 35J62 - Quasilinear elliptic equations 35J65 - Nonlinear boundary value problems for linear elliptic equations 35J66 - Nonlinear boundary value problems for nonlinear elliptic equations 35J67 - Boundary values of solutions to elliptic equations and elliptic systems 35J70 - Degenerate elliptic equations 35J75 - Singular elliptic equations 35J86 - Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators 35J87 - Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators 35J88 - Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators 35J91 - Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian 35J92 - Quasilinear elliptic equations with (p)-Laplacian 35J93 - Quasilinear elliptic equations with mean curvature operator 35J94 - Elliptic equations with infinity-Laplacian 35J96 - Monge-Amp�re equations 35J99 - Elliptic equations and elliptic systems 35Kxx - Parabolic equations and parabolic systems 35K05 - Heat equation 35K08 - Heat kernel 35K10 - Second-order parabolic equations 35K15 - Initial value problems for second-order parabolic equations 35K20 - Initial-boundary value problems for second-order parabolic equations 35K25 - Higher-order parabolic equations 35K30 - Initial value problems for higher-order parabolic equations 35K35 - Initial-boundary value problems for higher-order parabolic equations 35K40 - Second-order parabolic systems 35K41 - Higher-order parabolic systems 35K45 - Initial value problems for second-order parabolic systems 35K46 - Initial value problems for higher-order parabolic systems 35K51 - Initial-boundary value problems for second-order parabolic systems 35K52 - Initial-boundary value problems for higher-order parabolic systems 35K55 - Nonlinear parabolic equations 35K57 - Reaction-diffusion equations 35K58 - Semilinear parabolic equations 35K59 - Quasilinear parabolic equations 35K60 - Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35K61 - Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 35K65 - Degenerate parabolic equations 35K67 - Singular parabolic equations 35K70 - Ultraparabolic equations, pseudoparabolic equations, etc. 35K85 - Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators 35K86 - Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators 35K87 - Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators 35K90 - Abstract parabolic equations 35K91 - Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian 35K92 - Quasilinear parabolic equations with (p)-Laplacian 35K93 - Quasilinear parabolic equations with mean curvature operator 35K96 - Parabolic Monge-Amp�re equations 35K99 - Parabolic equations and parabolic systems 35Lxx - Hyperbolic equations and hyperbolic systems 35L02 - First-order hyperbolic equations 35L03 - Initial value problems for first-order hyperbolic equations 35L04 - Initial-boundary value problems for first-order hyperbolic equations 35L05 - Wave equation 35L10 - Second-order hyperbolic equations 35L15 - Initial value problems for second-order hyperbolic equations 35L20 - Initial-boundary value problems for second-order hyperbolic equations 35L25 - Higher-order hyperbolic equations 35L30 - Initial value problems for higher-order hyperbolic equations 35L35 - Initial-boundary value problems for higher-order hyperbolic equations 35L40 - First-order hyperbolic systems 35L45 - Initial value problems for first-order hyperbolic systems 35L50 - Initial-boundary value problems for first-order hyperbolic systems 35L51 - Second-order hyperbolic systems 35L52 - Initial value problems for second-order hyperbolic systems 35L53 - Initial-boundary value problems for second-order hyperbolic systems 35L55 - Higher-order hyperbolic systems 35L56 - Initial value problems for higher-order hyperbolic systems 35L57 - Initial-boundary value problems for higher-order hyperbolic systems 35L60 - First-order nonlinear hyperbolic equations 35L65 - Hyperbolic conservation laws 35L67 - Shocks and singularities for hyperbolic equations 35L70 - Second-order nonlinear hyperbolic equations 35L71 - Second-order semilinear hyperbolic equations 35L72 - Second-order quasilinear hyperbolic equations 35L75 - Higher-order nonlinear hyperbolic equations 35L76 - Higher-order semilinear hyperbolic equations 35L77 - Higher-order quasilinear hyperbolic equations 35L80 - Degenerate hyperbolic equations 35L81 - Singular hyperbolic equations 35L82 - Pseudohyperbolic equations 35L85 - Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators 35L86 - Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators 35L87 - Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators 35L90 - Abstract hyperbolic equations 35L99 - Hyperbolic equations and hyperbolic systems 35Mxx - Partial differential equations of mixed type and mixed-type systems of partial differential equations 35M10 - PDEs of mixed type 35M11 - Initial value problems for PDEs of mixed type 35M12 - Boundary value problems for PDEs of mixed type 35M13 - Initial-boundary value problems for PDEs of mixed type 35M30 - Mixed-type systems of PDEs 35M31 - Initial value problems for mixed-type systems of PDEs 35M32 - Boundary value problems for mixed-type systems of PDEs 35M33 - Initial-boundary value problems for mixed-type systems of PDEs 35M85 - Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type 35M86 - Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type 35M87 - Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type 35M99 - Partial differential equations of mixed type and mixed-type systems of partial differential equations 35Nxx - Overdetermined problems for partial differential equations and systems of partial differential equations 35N05 - Overdetermined systems of PDEs with constant coefficients 35N10 - Overdetermined systems of PDEs with variable coefficients 35N15 - (overlinepartial)-Neumann problems and formal complexes in context of PDEs 35N20 - Overdetermined initial value problems for PDEs and systems of PDEs 35N25 - Overdetermined boundary value problems for PDEs and systems of PDEs 35N30 - Overdetermined initial-boundary value problems for PDEs and systems of PDEs 35N99 - Overdetermined problems for partial differential equations and systems of partial differential equations 35Pxx - Spectral theory and eigenvalue problems for partial differential equations 35P05 - General topics in linear spectral theory for PDEs 35P10 - Completeness of eigenfunctions and eigenfunction expansions in context of PDEs 35P15 - Estimates of eigenvalues in context of PDEs 35P20 - Asymptotic distributions of eigenvalues in context of PDEs 35P25 - Scattering theory for PDEs 35P30 - Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35P99 - Spectral theory and eigenvalue problems for partial differential equations 35Qxx - Partial differential equations of mathematical physics and other areas of application 35Q05 - Euler-Poisson-Darboux equations 35Q07 - Fuchsian PDEs 35Q15 - Riemann-Hilbert problems in context of PDEs 35Q20 - Boltzmann equations 35Q30 - Navier-Stokes equations 35Q31 - Euler equations 35Q35 - PDEs in connection with fluid mechanics 35Q40 - PDEs in connection with quantum mechanics 35Q41 - Time-dependent Schr�dinger equations and Dirac equations 35Q49 - Transport equations 35Q51 - Soliton equations 35Q53 - KdV equations (Korteweg-de Vries equations) 35Q55 - NLS equations (nonlinear Schr�dinger equations) 35Q56 - Ginzburg-Landau equations 35Q60 - PDEs in connection with optics and electromagnetic theory 35Q61 - Maxwell equations 35Q62 - PDEs in connection with statistics 35Q68 - PDEs in connection with computer science 35Q70 - PDEs in connection with mechanics of particles and systems of particles 35Q74 - PDEs in connection with mechanics of deformable solids 35Q75 - PDEs in connection with relativity and gravitational theory 35Q76 - Einstein equations 35Q79 - PDEs in connection with classical thermodynamics and heat transfer 35Q81 - PDEs in connection with semiconductor devices 35Q82 - PDEs in connection with statistical mechanics 35Q83 - Vlasov equations 35Q84 - Fokker-Planck equations 35Q85 - PDEs in connection with astronomy and astrophysics 35Q86 - PDEs in connection with geophysics 35Q89 - PDEs in connection with mean field game theory 35Q90 - PDEs in connection with mathematical programming 35Q91 - PDEs in connection with game theory, economics, social and behavioral sciences 35Q92 - PDEs in connection with biology, chemistry and other natural sciences 35Q93 - PDEs in connection with control and optimization 35Q94 - PDEs in connection with information and communication 35Q99 - Partial differential equations of mathematical physics and other areas of application 35Rxx - Miscellaneous topics in partial differential equations 35R01 - PDEs on manifolds 35R02 - PDEs on graphs and networks (ramified or polygonal spaces) 35R03 - PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. 35R05 - PDEs with low regular coefficients and/or low regular data 35R06 - PDEs with measure 35R07 - PDEs on time scales 35R09 - Integro-partial differential equations 35R10 - Partial functional-differential equations 35R11 - Fractional partial differential equations 35R12 - Impulsive partial differential equations 35R13 - Fuzzy partial differential equations 35R15 - PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) 35R20 - Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) 35R25 - Ill-posed problems for PDEs 35R30 - Inverse problems for PDEs 35R35 - Free boundary problems for PDEs 35R37 - Moving boundary problems for PDEs 35R45 - Partial differential inequalities and systems of partial differential inequalities 35R50 - PDEs of infinite order 35R60 - PDEs with randomness, stochastic partial differential equations 35R70 - PDEs with multivalued right-hand sides 35R99 - Miscellaneous topics in partial differential equations 35Sxx - Pseudodifferential operators and other generalizations of partial differential operators 35S05 - Pseudodifferential operators as generalizations of partial differential operators 35S10 - Initial value problems for PDEs with pseudodifferential operators 35S15 - Boundary value problems for PDEs with pseudodifferential operators 35S16 - Initial-boundary value problems for PDEs with pseudodifferential operators 35S30 - Fourier integral operators applied to PDEs 35S35 - Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc. 35S50 - Paradifferential operators as generalizations of partial differential operators in context of PDEs 35S99 - Pseudodifferential operators and other generalizations of partial differential operators 37-XX - Dynamical systems and ergodic theory 37-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to dynamical systems and ergodic theory 37-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory 37-02 - Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory 37-03 - History of dynamical systems and ergodic theory 37-04 - Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory 37-06 - Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory 37-11 - Research data for problems pertaining to dynamical systems and ergodic theory 37Axx - Ergodic theory 37A05 - Dynamical aspects of measure-preserving transformations 37A10 - Dynamical systems involving one-parameter continuous families of measure-preserving transformations 37A15 - General groups of measure-preserving transformations and dynamical systems 37A17 - Homogeneous flows 37A20 - Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations 37A25 - Ergodicity, mixing, rates of mixing 37A30 - Ergodic theorems, spectral theory, Markov operators 37A35 - Entropy and other invariants, isomorphism, classification in ergodic theory 37A40 - Nonsingular (and infinite-measure preserving) transformations 37A44 - Relations between ergodic theory and number theory 37A46 - Relations between ergodic theory and harmonic analysis 37A50 - Dynamical systems and their relations with probability theory and stochastic processes 37A55 - Dynamical systems and the theory of (C^*)-algebras 37A60 - Dynamical aspects of statistical mechanics 37A99 - Ergodic theory 37Bxx - Topological dynamics 37B02 - Dynamics in general topological spaces 37B05 - Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 37B10 - Symbolic dynamics 37B15 - Dynamical aspects of cellular automata 37B20 - Notions of recurrence and recurrent behavior in topological dynamical systems 37B25 - Stability of topological dynamical systems 37B30 - Index theory for dynamical systems, Morse-Conley indices 37B35 - Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems 37B40 - Topological entropy 37B45 - Continua theory in dynamics 37B51 - Multidimensional shifts of finite type 37B52 - Tiling dynamics 37B55 - Topological dynamics of nonautonomous systems 37B65 - Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems 37B99 - Topological dynamics 37Cxx - Smooth dynamical systems: general theory 37C05 - Dynamical systems involving smooth mappings and diffeomorphisms 37C10 - Dynamics induced by flows and semiflows 37C15 - Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 37C20 - Generic properties, structural stability of dynamical systems 37C25 - Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 37C27 - Periodic orbits of vector fields and flows 37C29 - Homoclinic and heteroclinic orbits for dynamical systems 37C30 - Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 37C35 - Orbit growth in dynamical systems 37C40 - Smooth ergodic theory, invariant measures for smooth dynamical systems 37C45 - Dimension theory of smooth dynamical systems 37C50 - Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics 37C55 - Periodic and quasi-periodic flows and diffeomorphisms 37C60 - Nonautonomous smooth dynamical systems 37C65 - Monotone flows as dynamical systems 37C70 - Attractors and repellers of smooth dynamical systems and their topological structure 37C75 - Stability theory for smooth dynamical systems 37C79 - Symmetries and invariants of dynamical systems 37C81 - Equivariant dynamical systems 37C83 - Dynamical systems with singularities (billiards, etc.) 37C85 - Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) 37C86 - Foliations generated by dynamical systems 37C99 - Smooth dynamical systems: general theory 37Dxx - Dynamical systems with hyperbolic behavior 37D05 - Dynamical systems with hyperbolic orbits and sets 37D10 - Invariant manifold theory for dynamical systems 37D15 - Morse-Smale systems 37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37D30 - Partially hyperbolic systems and dominated splittings 37D35 - Thermodynamic formalism, variational principles, equilibrium states for dynamical systems 37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 37D45 - Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37D99 - Dynamical systems with hyperbolic behavior 37Exx - Low-dimensional dynamical systems 37E05 - Dynamical systems involving maps of the interval 37E10 - Dynamical systems involving maps of the circle 37E15 - Combinatorial dynamics (types of periodic orbits) 37E20 - Universality and renormalization of dynamical systems 37E25 - Dynamical systems involving maps of trees and graphs 37E30 - Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37E35 - Flows on surfaces 37E40 - Dynamical aspects of twist maps 37E45 - Rotation numbers and vectors 37E99 - Low-dimensional dynamical systems 37Fxx - Dynamical systems over complex numbers 37F05 - Dynamical systems involving relations and correspondences in one complex variable 37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets 37F12 - Critical orbits for holomorphic dynamical systems 37F15 - Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems 37F20 - Combinatorics and topology in relation with holomorphic dynamical systems 37F25 - Renormalization of holomorphic dynamical systems 37F31 - Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics 37F32 - Fuchsian and Kleinian groups as dynamical systems 37F34 - Teichm�ller theory; moduli spaces of holomorphic dynamical systems 37F35 - Conformal densities and Hausdorff dimension for holomorphic dynamical systems 37F40 - Geometric limits in holomorphic dynamics 37F44 - Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps 37F46 - Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets 37F50 - Small divisors, rotation domains and linearization in holomorphic dynamics 37F75 - Dynamical aspects of holomorphic foliations and vector fields 37F80 - Higher-dimensional holomorphic and meromorphic dynamics 37F99 - Dynamical systems over complex numbers 37Gxx - Local and nonlocal bifurcation theory for dynamical systems 37G05 - Normal forms for dynamical systems 37G10 - Bifurcations of singular points in dynamical systems 37G15 - Bifurcations of limit cycles and periodic orbits in dynamical systems 37G20 - Hyperbolic singular points with homoclinic trajectories in dynamical systems 37G25 - Bifurcations connected with nontransversal intersection in dynamical systems 37G30 - Infinite nonwandering sets arising in bifurcations of dynamical systems 37G35 - Dynamical aspects of attractors and their bifurcations 37G40 - Dynamical aspects of symmetries, equivariant bifurcation theory 37G99 - Local and nonlocal bifurcation theory for dynamical systems 37Hxx - Random dynamical systems 37H05 - General theory of random and stochastic dynamical systems 37H10 - Generation, random and stochastic difference and differential equations 37H12 - Random iteration 37H15 - Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents 37H20 - Bifurcation theory for random and stochastic dynamical systems 37H30 - Stability theory for random and stochastic dynamical systems 37H99 - Random dynamical systems 37Jxx - Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37J06 - General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants 37J11 - Symplectic and canonical mappings 37J12 - Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems 37J20 - Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems 37J25 - Stability problems for finite-dimensional Hamiltonian and Lagrangian systems 37J30 - Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) 37J35 - Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37J37 - Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures 37J38 - Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions 37J39 - Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) 37J40 - Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion 37J46 - Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems 37J51 - Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods 37J55 - Contact systems 37J60 - Nonholonomic dynamical systems 37J65 - Nonautonomous Hamiltonian dynamical systems (Painlev� equations, etc.) 37J70 - Completely integrable discrete dynamical systems 37J99 - Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37Kxx - Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems 37K06 - General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws 37K10 - Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K15 - Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 37K20 - Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions 37K25 - Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry 37K30 - Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures 37K35 - Lie-B�cklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 37K40 - Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 37K45 - Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems 37K50 - Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 37K55 - Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems 37K58 - Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems 37K60 - Lattice dynamics; integrable lattice equations 37K65 - Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics 37K99 - Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems 37Lxx - Infinite-dimensional dissipative dynamical systems 37L05 - General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 37L10 - Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems 37L15 - Stability problems for infinite-dimensional dissipative dynamical systems 37L20 - Symmetries of infinite-dimensional dissipative dynamical systems 37L25 - Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 37L30 - Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 37L40 - Invariant measures for infinite-dimensional dissipative dynamical systems 37L45 - Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems 37L50 - Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems 37L55 - Infinite-dimensional random dynamical systems; stochastic equations 37L60 - Lattice dynamics and infinite-dimensional dissipative dynamical systems 37L65 - Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems 37L99 - Infinite-dimensional dissipative dynamical systems 37Mxx - Approximation methods and numerical treatment of dynamical systems 37M05 - Simulation of dynamical systems 37M10 - Time series analysis of dynamical systems 37M15 - Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems 37M20 - Computational methods for bifurcation problems in dynamical systems 37M21 - Computational methods for invariant manifolds of dynamical systems 37M22 - Computational methods for attractors of dynamical systems 37M25 - Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) 37M99 - Approximation methods and numerical treatment of dynamical systems 37Nxx - Applications of dynamical systems 37N05 - Dynamical systems in classical and celestial mechanics 37N10 - Dynamical systems in fluid mechanics, oceanography and meteorology 37N15 - Dynamical systems in solid mechanics 37N20 - Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 37N25 - Dynamical systems in biology 37N30 - Dynamical systems in numerical analysis 37N35 - Dynamical systems in control 37N40 - Dynamical systems in optimization and economics 37N99 - Applications of dynamical systems 37Pxx - Arithmetic and non-Archimedean dynamical systems 37P05 - Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 37P10 - Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps 37P15 - Dynamical systems over global ground fields 37P20 - Dynamical systems over non-Archimedean local ground fields 37P25 - Dynamical systems over finite ground fields 37P30 - Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems 37P35 - Arithmetic properties of periodic points 37P40 - Non-Archimedean Fatou and Julia sets 37P45 - Families and moduli spaces in arithmetic and non-Archimedean dynamical systems 37P50 - Dynamical systems on Berkovich spaces 37P55 - Arithmetic dynamics on general algebraic varieties 37P99 - Arithmetic and non-Archimedean dynamical systems 39-XX - Difference and functional equations 39-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to difference and functional equations 39-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations 39-02 - Research exposition (monographs, survey articles) pertaining to difference and functional equations 39-03 - History of difference and functional equations 39-04 - Software, source code, etc. for problems pertaining to difference and functional equations 39-06 - Proceedings, conferences, collections, etc. pertaining to difference and functional equations 39-08 - Computational methods for problems pertaining to difference and functional equations 39-11 - Research data for problems pertaining to difference and functional equations 39Axx - Difference equations 39A05 - General theory of difference equations 39A06 - Linear difference equations 39A10 - Additive difference equations 39A12 - Discrete version of topics in analysis 39A13 - Difference equations, scaling ((q)-differences) 39A14 - Partial difference equations 39A20 - Multiplicative and other generalized difference equations 39A21 - Oscillation theory for difference equations 39A22 - Growth, boundedness, comparison of solutions to difference equations 39A23 - Periodic solutions of difference equations 39A24 - Almost periodic solutions of difference equations 39A26 - Fuzzy difference equations 39A27 - Boundary value problems for difference equations 39A28 - Bifurcation theory for difference equations 39A30 - Stability theory for difference equations 39A33 - Chaotic behavior of solutions of difference equations 39A36 - Integrable difference and lattice equations; integrability tests 39A45 - Difference equations in the complex domain 39A50 - Stochastic difference equations 39A60 - Applications of difference equations 39A70 - Difference operators 39A99 - Difference equations 39Bxx - Functional equations and inequalities 39B05 - General theory of functional equations and inequalities 39B12 - Iteration theory, iterative and composite equations 39B22 - Functional equations for real functions 39B32 - Functional equations for complex functions 39B42 - Matrix and operator functional equations 39B52 - Functional equations for functions with more general domains and/or ranges 39B55 - Orthogonal additivity and other conditional functional equations 39B62 - Functional inequalities, including subadditivity, convexity, etc. 39B72 - Systems of functional equations and inequalities 39B82 - Stability, separation, extension, and related topics for functional equations 39B99 - Functional equations and inequalities 40-XX - Sequences, series, summability 40-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability 40-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability 40-02 - Research exposition (monographs, survey articles) pertaining to sequences, series, summability 40-03 - History of sequences, series, summability 40-04 - Software, source code, etc. for problems pertaining to sequences, series, summability 40-06 - Proceedings, conferences, collections, etc. pertaining to sequences, series, summability 40-08 - Computational methods for problems pertaining to sequences, series, summability 40-11 - Research data for problems pertaining to sequences, series, summability 40Axx - Convergence and divergence of infinite limiting processes 40A05 - Convergence and divergence of series and sequences 40A10 - Convergence and divergence of integrals 40A15 - Convergence and divergence of continued fractions 40A20 - Convergence and divergence of infinite products 40A25 - Approximation to limiting values (summation of series, etc.) 40A30 - Convergence and divergence of series and sequences of functions 40A35 - Ideal and statistical convergence 40A99 - Convergence and divergence of infinite limiting processes 40Bxx - Multiple sequences and series 40B05 - Multiple sequences and series 40B99 - Multiple sequences and series 40Cxx - General summability methods 40C05 - Matrix methods for summability 40C10 - Integral methods for summability 40C15 - Function-theoretic methods (including power series methods and semicontinuous methods) for summability 40C99 - General summability methods 40Dxx - Direct theorems on summability 40D05 - General theorems on summability 40D09 - Structure of summability fields 40D10 - Tauberian constants and oscillation limits in summability theory 40D15 - Convergence factors and summability factors 40D20 - Summability and bounded fields of methods 40D25 - Inclusion and equivalence theorems in summability theory 40D99 - Direct theorems on summability 40Exx - Inversion theorems 40E05 - Tauberian theorems 40E10 - Growth estimates 40E15 - Lacunary inversion theorems 40E20 - Tauberian constants 40E99 - Inversion theorems 40Fxx - Absolute and strong summability 40F05 - Absolute and strong summability 40F99 - Absolute and strong summability 40Gxx - Special methods of summability 40G05 - Ces�ro, Euler, N�rlund and Hausdorff methods 40G10 - Abel, Borel and power series methods 40G15 - Summability methods using statistical convergence 40G99 - Special methods of summability 40Hxx - Functional analytic methods in summability 40H05 - Functional analytic methods in summability 40H99 - Functional analytic methods in summability 40Jxx - Summability in abstract structures 40J05 - Summability in abstract structures 40J99 - Summability in abstract structures 41-XX - Approximations and expansions 41-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to approximations and expansions 41-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to approximations and expansions 41-02 - Research exposition (monographs, survey articles) pertaining to approximations and expansions 41-03 - History of approximations and expansions 41-04 - Software, source code, etc. for problems pertaining to approximations and expansions 41-06 - Proceedings, conferences, collections, etc. pertaining to approximations and expansions 41-11 - Research data for problems pertaining to approximations and expansions 41Axx - Approximations and expansions 41A05 - Interpolation in approximation theory 41A10 - Approximation by polynomials 41A15 - Spline approximation 41A17 - Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) 41A20 - Approximation by rational functions 41A21 - Pad� approximation 41A25 - Rate of convergence, degree of approximation 41A27 - Inverse theorems in approximation theory 41A28 - Simultaneous approximation 41A29 - Approximation with constraints 41A30 - Approximation by other special function classes 41A35 - Approximation by operators (in particular, by integral operators) 41A36 - Approximation by positive operators 41A40 - Saturation in approximation theory 41A44 - Best constants in approximation theory 41A45 - Approximation by arbitrary linear expressions 41A46 - Approximation by arbitrary nonlinear expressions; widths and entropy 41A50 - Best approximation, Chebyshev systems 41A52 - Uniqueness of best approximation 41A55 - Approximate quadratures 41A58 - Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) 41A60 - Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 41A63 - Multidimensional problems 41A65 - Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A80 - Remainders in approximation formulas 41A81 - Weighted approximation 41A99 - Approximations and expansions 42-XX - Harmonic analysis on Euclidean spaces 42-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to harmonic analysis on Euclidean spaces 42-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces 42-02 - Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces 42-03 - History of harmonic analysis on Euclidean spaces 42-04 - Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces 42-06 - Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces 42-08 - Computational methods for problems pertaining to harmonic analysis on Euclidean spaces 42-11 - Research data for problems pertaining to harmonic analysis on Euclidean spaces 42Axx - Harmonic analysis in one variable 42A05 - Trigonometric polynomials, inequalities, extremal problems 42A10 - Trigonometric approximation 42A15 - Trigonometric interpolation 42A16 - Fourier coefficients, Fourier series of functions with special properties, special Fourier series 42A20 - Convergence and absolute convergence of Fourier and trigonometric series 42A24 - Summability and absolute summability of Fourier and trigonometric series 42A32 - Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) 42A38 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42A45 - Multipliers in one variable harmonic analysis 42A50 - Conjugate functions, conjugate series, singular integrals 42A55 - Lacunary series of trigonometric and other functions; Riesz products 42A61 - Probabilistic methods for one variable harmonic analysis 42A63 - Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization 42A65 - Completeness of sets of functions in one variable harmonic analysis 42A70 - Trigonometric moment problems in one variable harmonic analysis 42A75 - Classical almost periodic functions, mean periodic functions 42A82 - Positive definite functions in one variable harmonic analysis 42A85 - Convolution, factorization for one variable harmonic analysis 42A99 - Harmonic analysis in one variable 42Bxx - Harmonic analysis in several variables 42B05 - Fourier series and coefficients in several variables 42B08 - Summability in several variables 42B10 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42B15 - Multipliers for harmonic analysis in several variables 42B20 - Singular and oscillatory integrals (Calder�n-Zygmund, etc.) 42B25 - Maximal functions, Littlewood-Paley theory 42B30 - (H^p)-spaces 42B35 - Function spaces arising in harmonic analysis 42B37 - Harmonic analysis and PDEs 42B99 - Harmonic analysis in several variables 42Cxx - Nontrigonometric harmonic analysis 42C05 - Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42C15 - General harmonic expansions, frames 42C20 - Other transformations of harmonic type 42C25 - Uniqueness and localization for orthogonal series 42C30 - Completeness of sets of functions in nontrigonometric harmonic analysis 42C40 - Nontrigonometric harmonic analysis involving wavelets and other special systems 42C99 - Nontrigonometric harmonic analysis 43-XX - Abstract harmonic analysis 43-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to abstract harmonic analysis 43-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to abstract harmonic analysis 43-02 - Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis 43-03 - History of abstract harmonic analysis 43-04 - Software, source code, etc. for problems pertaining to abstract harmonic analysis 43-06 - Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis 43-08 - Computational methods for problems pertaining to abstract harmonic analysis 43-11 - Research data for problems pertaining to abstract harmonic analysis 43Axx - Abstract harmonic analysis 43A05 - Measures on groups and semigroups, etc. 43A07 - Means on groups, semigroups, etc.; amenable groups 43A10 - Measure algebras on groups, semigroups, etc. 43A15 - (L^p)-spaces and other function spaces on groups, semigroups, etc. 43A17 - Analysis on ordered groups, (H^p)-theory 43A20 - (L^1)-algebras on groups, semigroups, etc. 43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A25 - Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 43A30 - Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A32 - Other transforms and operators of Fourier type 43A35 - Positive definite functions on groups, semigroups, etc. 43A40 - Character groups and dual objects 43A45 - Spectral synthesis on groups, semigroups, etc. 43A46 - Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 43A50 - Convergence of Fourier series and of inverse transforms 43A55 - Summability methods on groups, semigroups, etc. 43A60 - Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 43A62 - Harmonic analysis on hypergroups 43A65 - Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) 43A70 - Analysis on specific locally compact and other abelian groups 43A75 - Harmonic analysis on specific compact groups 43A77 - Harmonic analysis on general compact groups 43A80 - Analysis on other specific Lie groups 43A85 - Harmonic analysis on homogeneous spaces 43A90 - Harmonic analysis and spherical functions 43A95 - Categorical methods for abstract harmonic analysis 43A99 - Abstract harmonic analysis 44-XX - Integral transforms, operational calculus 44-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral transforms 44-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms 44-02 - Research exposition (monographs, survey articles) pertaining to integral transforms 44-03 - History of integral transforms 44-04 - Software, source code, etc. for problems pertaining to integral transforms 44-06 - Proceedings, conferences, collections, etc. pertaining to integral transforms 44-11 - Research data for problems pertaining to integral transforms 44Axx - Integral transforms, operational calculus 44A05 - General integral transforms 44A10 - Laplace transform 44A12 - Radon transform 44A15 - Special integral transforms (Legendre, Hilbert, etc.) 44A20 - Integral transforms of special functions 44A30 - Multiple integral transforms 44A35 - Convolution as an integral transform 44A40 - Calculus of Mikusi?ski and other operational calculi 44A45 - Classical operational calculus 44A55 - Discrete operational calculus 44A60 - Moment problems 44A99 - Integral transforms, operational calculus 45-XX - Integral equations 45-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral equations 45-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral equations 45-02 - Research exposition (monographs, survey articles) pertaining to integral equations 45-03 - History of integral equations 45-04 - Software, source code, etc. for problems pertaining to integral equations 45-06 - Proceedings, conferences, collections, etc. pertaining to integral equations 45-11 - Research data for problems pertaining to integral equations 45Axx - Linear integral equations 45A05 - Linear integral equations 45A99 - Linear integral equations 45Bxx - Fredholm integral equations 45B05 - Fredholm integral equations 45B99 - Fredholm integral equations 45Cxx - Eigenvalue problems for integral equations 45C05 - Eigenvalue problems for integral equations 45C99 - Eigenvalue problems for integral equations 45Dxx - Volterra integral equations 45D05 - Volterra integral equations 45D99 - Volterra integral equations 45Exx - Singular integral equations 45E05 - Integral equations with kernels of Cauchy type 45E10 - Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) 45E99 - Singular integral equations 45Fxx - Systems of linear integral equations 45F05 - Systems of nonsingular linear integral equations 45F10 - Dual, triple, etc., integral and series equations 45F15 - Systems of singular linear integral equations 45F99 - Systems of linear integral equations 45Gxx - Nonlinear integral equations 45G05 - Singular nonlinear integral equations 45G10 - Other nonlinear integral equations 45G15 - Systems of nonlinear integral equations 45G99 - Nonlinear integral equations 45Hxx - Integral equations with miscellaneous special kernels 45H05 - Integral equations with miscellaneous special kernels 45H99 - Integral equations with miscellaneous special kernels 45Jxx - Integro-ordinary differential equations 45J05 - Integro-ordinary differential equations 45J99 - Integro-ordinary differential equations 45Kxx - Integro-partial differential equations 45K05 - Integro-partial differential equations 45K99 - Integro-partial differential equations 45Lxx - Theoretical approximation of solutions to integral equations 45L05 - Theoretical approximation of solutions to integral equations 45L99 - Theoretical approximation of solutions to integral equations 45Mxx - Qualitative behavior of solutions to integral equations 45M05 - Asymptotics of solutions to integral equations 45M10 - Stability theory for integral equations 45M15 - Periodic solutions of integral equations 45M20 - Positive solutions of integral equations 45M99 - Qualitative behavior of solutions to integral equations 45Nxx - Abstract integral equations, integral equations in abstract spaces 45N05 - Abstract integral equations, integral equations in abstract spaces 45N99 - Abstract integral equations, integral equations in abstract spaces 45Pxx - Integral operators 45P05 - Integral operators 45P99 - Integral operators 45Qxx - Inverse problems for integral equations 45Q05 - Inverse problems for integral equations 45Q99 - Inverse problems for integral equations 45Rxx - Random integral equations 45R05 - Random integral equations 45R99 - Random integral equations 46-XX - Functional analysis 46-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analysis 46-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis 46-02 - Research exposition (monographs, survey articles) pertaining to functional analysis 46-03 - History of functional analysis 46-04 - Software, source code, etc. for problems pertaining to functional analysis 46-06 - Proceedings, conferences, collections, etc. pertaining to functional analysis 46-08 - Computational methods for problems pertaining to functional analysis 46-11 - Research data for problems pertaining to functional analysis 46Axx - Topological linear spaces and related structures 46A03 - General theory of locally convex spaces 46A04 - Locally convex Fr�chet spaces and (DF)-spaces 46A08 - Barrelled spaces, bornological spaces 46A11 - Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 46A13 - Spaces defined by inductive or projective limits (LB, LF, etc.) 46A16 - Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46A17 - Bornologies and related structures; Mackey convergence, etc. 46A19 - Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) 46A20 - Duality theory for topological vector spaces 46A22 - Theorems of Hahn-Banach type; extension and lifting of functionals and operators 46A25 - Reflexivity and semi-reflexivity 46A30 - Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) 46A32 - Spaces of linear operators; topological tensor products; approximation properties 46A35 - Summability and bases in topological vector spaces 46A40 - Ordered topological linear spaces, vector lattices 46A45 - Sequence spaces (including K�the sequence spaces) 46A50 - Compactness in topological linear spaces; angelic spaces, etc. 46A55 - Convex sets in topological linear spaces; Choquet theory 46A61 - Graded Fr�chet spaces and tame operators 46A63 - Topological invariants ((DN), ((Omega)), etc.) for locally convex spaces 46A70 - Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 46A80 - Modular spaces 46A99 - Topological linear spaces and related structures 46Bxx - Normed linear spaces and Banach spaces; Banach lattices 46B03 - Isomorphic theory (including renorming) of Banach spaces 46B04 - Isometric theory of Banach spaces 46B06 - Asymptotic theory of Banach spaces 46B07 - Local theory of Banach spaces 46B08 - Ultraproduct techniques in Banach space theory 46B09 - Probabilistic methods in Banach space theory 46B10 - Duality and reflexivity in normed linear and Banach spaces 46B15 - Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces 46B20 - Geometry and structure of normed linear spaces 46B22 - Radon-Nikod�m, Kre?n-Milman and related properties 46B25 - Classical Banach spaces in the general theory 46B26 - Nonseparable Banach spaces 46B28 - Spaces of operators; tensor products; approximation properties 46B40 - Ordered normed spaces 46B42 - Banach lattices 46B45 - Banach sequence spaces 46B50 - Compactness in Banach (or normed) spaces 46B70 - Interpolation between normed linear spaces 46B80 - Nonlinear classification of Banach spaces; nonlinear quotients 46B85 - Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science 46B87 - Lineability in functional analysis 46B99 - Normed linear spaces and Banach spaces; Banach lattices 46Cxx - Inner product spaces and their generalizations, Hilbert spaces 46C05 - Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 46C07 - Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) 46C15 - Characterizations of Hilbert spaces 46C20 - Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) 46C50 - Generalizations of inner products (semi-inner products, partial inner products, etc.) 46C99 - Inner product spaces and their generalizations, Hilbert spaces 46Exx - Linear function spaces and their duals 46E05 - Lattices of continuous, differentiable or analytic functions 46E10 - Topological linear spaces of continuous, differentiable or analytic functions 46E15 - Banach spaces of continuous, differentiable or analytic functions 46E20 - Hilbert spaces of continuous, differentiable or analytic functions 46E22 - Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) 46E25 - Rings and algebras of continuous, differentiable or analytic functions 46E27 - Spaces of measures 46E30 - Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, K�the function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35 - Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems 46E36 - Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces 46E39 - Sobolev (and similar kinds of) spaces of functions of discrete variables 46E40 - Spaces of vector- and operator-valued functions 46E50 - Spaces of differentiable or holomorphic functions on infinite-dimensional spaces 46E99 - Linear function spaces and their duals 46Fxx - Distributions, generalized functions, distribution spaces 46F05 - Topological linear spaces of test functions, distributions and ultradistributions 46F10 - Operations with distributions and generalized functions 46F12 - Integral transforms in distribution spaces 46F15 - Hyperfunctions, analytic functionals 46F20 - Distributions and ultradistributions as boundary values of analytic functions 46F25 - Distributions on infinite-dimensional spaces 46F30 - Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 46F99 - Distributions, generalized functions, distribution spaces 46Gxx - Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) 46G05 - Derivatives of functions in infinite-dimensional spaces 46G10 - Vector-valued measures and integration 46G12 - Measures and integration on abstract linear spaces 46G15 - Functional analytic lifting theory 46G20 - Infinite-dimensional holomorphy 46G25 - (Spaces of) multilinear mappings, polynomials 46G99 - Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) 46Hxx - Topological algebras, normed rings and algebras, Banach algebras 46H05 - General theory of topological algebras 46H10 - Ideals and subalgebras 46H15 - Representations of topological algebras 46H20 - Structure, classification of topological algebras 46H25 - Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46H30 - Functional calculus in topological algebras 46H35 - Topological algebras of operators 46H40 - Automatic continuity 46H70 - Nonassociative topological algebras 46H99 - Topological algebras, normed rings and algebras, Banach algebras 46Jxx - Commutative Banach algebras and commutative topological algebras 46J05 - General theory of commutative topological algebras 46J10 - Banach algebras of continuous functions, function algebras 46J15 - Banach algebras of differentiable or analytic functions, (H^p)-spaces 46J20 - Ideals, maximal ideals, boundaries 46J25 - Representations of commutative topological algebras 46J30 - Subalgebras of commutative topological algebras 46J40 - Structure and classification of commutative topological algebras 46J45 - Radical Banach algebras 46J99 - Commutative Banach algebras and commutative topological algebras 46Kxx - Topological (rings and) algebras with an involution 46K05 - General theory of topological algebras with involution 46K10 - Representations of topological algebras with involution 46K15 - Hilbert algebras 46K50 - Nonselfadjoint (sub)algebras in algebras with involution 46K70 - Nonassociative topological algebras with an involution 46K99 - Topological (rings and) algebras with an involution 46Lxx - Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) 46L05 - General theory of (C^*)-algebras 46L06 - Tensor products of (C^*)-algebras 46L07 - Operator spaces and completely bounded maps 46L08 - (C^*)-modules 46L09 - Free products of (C^*)-algebras 46L10 - General theory of von Neumann algebras 46L30 - States of selfadjoint operator algebras 46L35 - Classifications of (C^*)-algebras 46L36 - Classification of factors 46L37 - Subfactors and their classification 46L40 - Automorphisms of selfadjoint operator algebras 46L45 - Decomposition theory for (C^*)-algebras 46L51 - Noncommutative measure and integration 46L52 - Noncommutative function spaces 46L53 - Noncommutative probability and statistics 46L54 - Free probability and free operator algebras 46L55 - Noncommutative dynamical systems 46L57 - Derivations, dissipations and positive semigroups in (C^*)-algebras 46L60 - Applications of selfadjoint operator algebras to physics 46L65 - Quantizations, deformations for selfadjoint operator algebras 46L67 - Quantum groups (operator algebraic aspects) 46L70 - Nonassociative selfadjoint operator algebras 46L80 - (K)-theory and operator algebras (including cyclic theory) 46L85 - Noncommutative topology 46L87 - Noncommutative differential geometry 46L89 - Other ``noncommutative'' mathematics based on (C^*)-algebra theory 46L99 - Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) 46Mxx - Methods of category theory in functional analysis 46M05 - Tensor products in functional analysis 46M07 - Ultraproducts in functional analysis 46M10 - Projective and injective objects in functional analysis 46M15 - Categories, functors in functional analysis 46M18 - Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 46M20 - Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 46M35 - Abstract interpolation of topological vector spaces 46M40 - Inductive and projective limits in functional analysis 46M99 - Methods of category theory in functional analysis 46Nxx - Miscellaneous applications of functional analysis 46N10 - Applications of functional analysis in optimization, convex analysis, mathematical programming, economics 46N20 - Applications of functional analysis to differential and integral equations 46N30 - Applications of functional analysis in probability theory and statistics 46N40 - Applications of functional analysis in numerical analysis 46N50 - Applications of functional analysis in quantum physics 46N55 - Applications of functional analysis in statistical physics 46N60 - Applications of functional analysis in biology and other sciences 46N99 - Miscellaneous applications of functional analysis 46Sxx - Other (nonclassical) types of functional analysis 46S05 - Quaternionic functional analysis 46S10 - Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis 46S20 - Nonstandard functional analysis 46S30 - Constructive functional analysis 46S40 - Fuzzy functional analysis 46S50 - Functional analysis in probabilistic metric linear spaces 46S60 - Functional analysis on superspaces (supermanifolds) or graded spaces 46S99 - Other (nonclassical) types of functional analysis 46Txx - Nonlinear functional analysis 46T05 - Infinite-dimensional manifolds 46T10 - Manifolds of mappings 46T12 - Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds 46T20 - Continuous and differentiable maps in nonlinear functional analysis 46T25 - Holomorphic maps in nonlinear functional analysis 46T30 - Distributions and generalized functions on nonlinear spaces 46T99 - Nonlinear functional analysis 47-XX - Operator theory 47-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operator theory 47-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory 47-02 - Research exposition (monographs, survey articles) pertaining to operator theory 47-03 - History of operator theory 47-04 - Software, source code, etc. for problems pertaining to operator theory 47-06 - Proceedings, conferences, collections, etc. pertaining to operator theory 47-08 - Computational methods for problems pertaining to operator theory 47-11 - Research data for problems pertaining to operator theory 47Axx - General theory of linear operators 47A05 - General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A06 - Linear relations (multivalued linear operators) 47A07 - Forms (bilinear, sesquilinear, multilinear) 47A08 - Operator matrices 47A10 - Spectrum, resolvent 47A11 - Local spectral properties of linear operators 47A12 - Numerical range, numerical radius 47A13 - Several-variable operator theory (spectral, Fredholm, etc.) 47A15 - Invariant subspaces of linear operators 47A16 - Cyclic vectors, hypercyclic and chaotic operators 47A20 - Dilations, extensions, compressions of linear operators 47A25 - Spectral sets of linear operators 47A30 - Norms (inequalities, more than one norm, etc.) of linear operators 47A35 - Ergodic theory of linear operators 47A40 - Scattering theory of linear operators 47A45 - Canonical models for contractions and nonselfadjoint linear operators 47A46 - Chains (nests) of projections or of invariant subspaces, integrals along chains, etc. 47A48 - Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. 47A50 - Equations and inequalities involving linear operators, with vector unknowns 47A52 - Linear operators and ill-posed problems, regularization 47A53 - (Semi-) Fredholm operators; index theories 47A55 - Perturbation theory of linear operators 47A56 - Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 47A57 - Linear operator methods in interpolation, moment and extension problems 47A58 - Linear operator approximation theory 47A60 - Functional calculus for linear operators 47A62 - Equations involving linear operators, with operator unknowns 47A63 - Linear operator inequalities 47A64 - Operator means involving linear operators, shorted linear operators, etc. 47A65 - Structure theory of linear operators 47A66 - Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators 47A67 - Representation theory of linear operators 47A68 - Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators 47A70 - (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces 47A75 - Eigenvalue problems for linear operators 47A80 - Tensor products of linear operators 47A99 - General theory of linear operators 47Bxx - Special classes of linear operators 47B01 - Operators on Banach spaces 47B02 - Operators on Hilbert spaces (general) 47B06 - Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators 47B07 - Linear operators defined by compactness properties 47B10 - Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) 47B12 - Sectorial operators 47B13 - Cowen-Douglas operators 47B15 - Hermitian and normal operators (spectral measures, functional calculus, etc.) 47B20 - Subnormal operators, hyponormal operators, etc. 47B25 - Linear symmetric and selfadjoint operators (unbounded) 47B28 - Nonselfadjoint operators 47B32 - Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) 47B33 - Linear composition operators 47B34 - Kernel operators 47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B36 - Jacobi (tridiagonal) operators (matrices) and generalizations 47B37 - Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B38 - Linear operators on function spaces (general) 47B39 - Linear difference operators 47B40 - Spectral operators, decomposable operators, well-bounded operators, etc. 47B44 - Linear accretive operators, dissipative operators, etc. 47B47 - Commutators, derivations, elementary operators, etc. 47B48 - Linear operators on Banach algebras 47B49 - Transformers, preservers (linear operators on spaces of linear operators) 47B50 - Linear operators on spaces with an indefinite metric 47B60 - Linear operators on ordered spaces 47B65 - Positive linear operators and order-bounded operators 47B80 - Random linear operators 47B90 - Operator theory and harmonic analysis 47B91 - Operators on complex function spaces 47B92 - Operators on real function spaces 47B93 - Operators arising in mathematical physics 47B99 - Special classes of linear operators 47Cxx - Individual linear operators as elements of algebraic systems 47C05 - Linear operators in algebras 47C10 - Linear operators in ({}^*)-algebras 47C15 - Linear operators in (C^*)- or von Neumann algebras 47C99 - Individual linear operators as elements of algebraic systems 47Dxx - Groups and semigroups of linear operators, their generalizations and applications 47D03 - Groups and semigroups of linear operators 47D06 - One-parameter semigroups and linear evolution equations 47D07 - Markov semigroups and applications to diffusion processes 47D08 - Schr�dinger and Feynman-Kac semigroups 47D09 - Operator sine and cosine functions and higher-order Cauchy problems 47D60 - (C)-semigroups, regularized semigroups 47D62 - Integrated semigroups 47D99 - Groups and semigroups of linear operators, their generalizations and applications 47Exx - Ordinary differential operators 47E05 - General theory of ordinary differential operators 47E07 - Functional-differential and differential-difference operators 47E99 - Ordinary differential operators 47Fxx - Partial differential operators 47F05 - General theory of partial differential operators 47F10 - Elliptic operators and their generalizations 47F99 - Partial differential operators 47Gxx - Integral, integro-differential, and pseudodifferential operators 47G10 - Integral operators 47G20 - Integro-differential operators 47G30 - Pseudodifferential operators 47G40 - Potential operators 47G99 - Integral, integro-differential, and pseudodifferential operators 47Hxx - Nonlinear operators and their properties 47H04 - Set-valued operators 47H05 - Monotone operators and generalizations 47H06 - Nonlinear accretive operators, dissipative operators, etc. 47H07 - Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 47H08 - Measures of noncompactness and condensing mappings, (K)-set contractions, etc. 47H09 - Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. 47H10 - Fixed-point theorems 47H11 - Degree theory for nonlinear operators 47H14 - Perturbations of nonlinear operators 47H20 - Semigroups of nonlinear operators 47H25 - Nonlinear ergodic theorems 47H30 - Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) 47H40 - Random nonlinear operators 47H60 - Multilinear and polynomial operators 47H99 - Nonlinear operators and their properties 47Jxx - Equations and inequalities involving nonlinear operators 47J05 - Equations involving nonlinear operators (general) 47J06 - Nonlinear ill-posed problems 47J07 - Abstract inverse mapping and implicit function theorems involving nonlinear operators 47J10 - Nonlinear spectral theory, nonlinear eigenvalue problems 47J15 - Abstract bifurcation theory involving nonlinear operators 47J20 - Variational and other types of inequalities involving nonlinear operators (general) 47J22 - Variational and other types of inclusions 47J25 - Iterative procedures involving nonlinear operators 47J26 - Fixed-point iterations 47J30 - Variational methods involving nonlinear operators 47J35 - Nonlinear evolution equations 47J40 - Equations with nonlinear hysteresis operators 47J99 - Equations and inequalities involving nonlinear operators 47Lxx - Linear spaces and algebras of operators 47L05 - Linear spaces of operators 47L07 - Convex sets and cones of operators 47L10 - Algebras of operators on Banach spaces and other topological linear spaces 47L15 - Operator algebras with symbol structure 47L20 - Operator ideals 47L22 - Ideals of polynomials and of multilinear mappings in operator theory 47L25 - Operator spaces (= matricially normed spaces) 47L30 - Abstract operator algebras on Hilbert spaces 47L35 - Nest algebras, CSL algebras 47L40 - Limit algebras, subalgebras of (C^*)-algebras 47L45 - Dual algebras; weakly closed singly generated operator algebras 47L50 - Dual spaces of operator algebras 47L55 - Representations of (nonselfadjoint) operator algebras 47L60 - Algebras of unbounded operators; partial algebras of operators 47L65 - Crossed product algebras (analytic crossed products) 47L70 - Nonassociative nonselfadjoint operator algebras 47L75 - Other nonselfadjoint operator algebras 47L80 - Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) 47L90 - Applications of operator algebras to the sciences 47L99 - Linear spaces and algebras of operators 47Nxx - Miscellaneous applications of operator theory 47N10 - Applications of operator theory in optimization, convex analysis, mathematical programming, economics 47N20 - Applications of operator theory to differential and integral equations 47N30 - Applications of operator theory in probability theory and statistics 47N40 - Applications of operator theory in numerical analysis 47N50 - Applications of operator theory in the physical sciences 47N60 - Applications of operator theory in chemistry and life sciences 47N70 - Applications of operator theory in systems, signals, circuits, and control theory 47N99 - Miscellaneous applications of operator theory 47Sxx - Other (nonclassical) types of operator theory 47S05 - Quaternionic operator theory 47S10 - Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory 47S20 - Nonstandard operator theory 47S30 - Constructive operator theory 47S40 - Fuzzy operator theory 47S50 - Operator theory in probabilistic metric linear spaces 47S99 - Other (nonclassical) types of operator theory 49-XX - Calculus of variations and optimal control; optimization 49-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to calculus of variations and optimal control 49-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control 49-02 - Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control 49-03 - History of calculus of variations and optimal control 49-04 - Software, source code, etc. for problems pertaining to calculus of variations and optimal control 49-06 - Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control 49-11 - Research data for problems pertaining to calculus of variations and optimal control 49Jxx - Existence theories in calculus of variations and optimal control 49J05 - Existence theories for free problems in one independent variable 49J10 - Existence theories for free problems in two or more independent variables 49J15 - Existence theories for optimal control problems involving ordinary differential equations 49J20 - Existence theories for optimal control problems involving partial differential equations 49J21 - Existence theories for optimal control problems involving relations other than differential equations 49J27 - Existence theories for problems in abstract spaces 49J30 - Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 49J35 - Existence of solutions for minimax problems 49J40 - Variational inequalities 49J45 - Methods involving semicontinuity and convergence; relaxation 49J50 - Fr�chet and Gateaux differentiability in optimization 49J52 - Nonsmooth analysis 49J53 - Set-valued and variational analysis 49J55 - Existence of optimal solutions to problems involving randomness 49J99 - Existence theories in calculus of variations and optimal control 49Kxx - Optimality conditions 49K05 - Optimality conditions for free problems in one independent variable 49K10 - Optimality conditions for free problems in two or more independent variables 49K15 - Optimality conditions for problems involving ordinary differential equations 49K20 - Optimality conditions for problems involving partial differential equations 49K21 - Optimality conditions for problems involving relations other than differential equations 49K27 - Optimality conditions for problems in abstract spaces 49K30 - Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 49K35 - Optimality conditions for minimax problems 49K40 - Sensitivity, stability, well-posedness 49K45 - Optimality conditions for problems involving randomness 49K99 - Optimality conditions 49Lxx - Hamilton-Jacobi theories 49L12 - Hamilton-Jacobi equations in optimal control and differential games 49L20 - Dynamic programming in optimal control and differential games 49L25 - Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 49L99 - Hamilton-Jacobi theories 49Mxx - Numerical methods in optimal control 49M05 - Numerical methods based on necessary conditions 49M15 - Newton-type methods 49M20 - Numerical methods of relaxation type 49M25 - Discrete approximations in optimal control 49M27 - Decomposition methods 49M29 - Numerical methods involving duality 49M37 - Numerical methods based on nonlinear programming 49M41 - PDE constrained optimization (numerical aspects) 49M99 - Numerical methods in optimal control 49Nxx - Miscellaneous topics in calculus of variations and optimal control 49N05 - Linear optimal control problems 49N10 - Linear-quadratic optimal control problems 49N15 - Duality theory (optimization) 49N20 - Periodic optimal control problems 49N25 - Impulsive optimal control problems 49N30 - Problems with incomplete information (optimization) 49N35 - Optimal feedback synthesis 49N45 - Inverse problems in optimal control 49N60 - Regularity of solutions in optimal control 49N70 - Differential games and control 49N75 - Pursuit and evasion games 49N80 - Mean field games and control 49N90 - Applications of optimal control and differential games 49N99 - Miscellaneous topics in calculus of variations and optimal control 49Qxx - Manifolds and measure-geometric topics 49Q05 - Minimal surfaces and optimization 49Q10 - Optimization of shapes other than minimal surfaces 49Q12 - Sensitivity analysis for optimization problems on manifolds 49Q15 - Geometric measure and integration theory, integral and normal currents in optimization 49Q20 - Variational problems in a geometric measure-theoretic setting 49Q22 - Optimal transportation 49Q99 - Manifolds and measure-geometric topics 49Rxx - Variational methods for eigenvalues of operators 49R05 - Variational methods for eigenvalues of operators 49R99 - Variational methods for eigenvalues of operators 49Sxx - Variational principles of physics 49S05 - Variational principles of physics 49S99 - Variational principles of physics 51-XX - Geometry 51-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry 51-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry 51-02 - Research exposition (monographs, survey articles) pertaining to geometry 51-03 - History of geometry 51-04 - Software, source code, etc. for problems pertaining to geometry 51-06 - Proceedings, conferences, collections, etc. pertaining to geometry 51-08 - Computational methods for problems pertaining to geometry 51-11 - Research data for problems pertaining to geometry 51Axx - Linear incidence geometry 51A05 - General theory of linear incidence geometry and projective geometries 51A10 - Homomorphism, automorphism and dualities in linear incidence geometry 51A15 - Linear incidence geometric structures with parallelism 51A20 - Configuration theorems in linear incidence geometry 51A25 - Algebraization in linear incidence geometry 51A30 - Desarguesian and Pappian geometries 51A35 - Non-Desarguesian affine and projective planes 51A40 - Translation planes and spreads in linear incidence geometry 51A45 - Incidence structures embeddable into projective geometries 51A50 - Polar geometry, symplectic spaces, orthogonal spaces 51A99 - Linear incidence geometry 51Bxx - Nonlinear incidence geometry 51B05 - General theory of nonlinear incidence geometry 51B10 - M�bius geometries 51B15 - Laguerre geometries 51B20 - Minkowski geometries in nonlinear incidence geometry 51B25 - Lie geometries in nonlinear incidence geometry 51B99 - Nonlinear incidence geometry 51Cxx - Ring geometry (Hjelmslev, Barbilian, etc.) 51C05 - Ring geometry (Hjelmslev, Barbilian, etc.) 51C99 - Ring geometry (Hjelmslev, Barbilian, etc.) 51Dxx - Geometric closure systems 51D05 - Abstract (Maeda) geometries 51D10 - Abstract geometries with exchange axiom 51D15 - Abstract geometries with parallelism 51D20 - Combinatorial geometries and geometric closure systems 51D25 - Lattices of subspaces and geometric closure systems 51D30 - Continuous geometries, geometric closure systems and related topics 51D99 - Geometric closure systems 51Exx - Finite geometry and special incidence structures 51E05 - General block designs in finite geometry 51E10 - Steiner systems in finite geometry 51E12 - Generalized quadrangles and generalized polygons in finite geometry 51E14 - Finite partial geometries (general), nets, partial spreads 51E15 - Finite affine and projective planes (geometric aspects) 51E20 - Combinatorial structures in finite projective spaces 51E21 - Blocking sets, ovals, (k)-arcs 51E22 - Linear codes and caps in Galois spaces 51E23 - Spreads and packing problems in finite geometry 51E24 - Buildings and the geometry of diagrams 51E25 - Other finite nonlinear geometries 51E26 - Other finite linear geometries 51E30 - Other finite incidence structures (geometric aspects) 51E99 - Finite geometry and special incidence structures 51Fxx - Metric geometry 51F05 - Absolute planes in metric geometry 51F10 - Absolute spaces in metric geometry 51F15 - Reflection groups, reflection geometries 51F20 - Congruence and orthogonality in metric geometry 51F25 - Orthogonal and unitary groups in metric geometry 51F30 - Lipschitz and coarse geometry of metric spaces 51F99 - Metric geometry 51Gxx - Ordered geometries (ordered incidence structures, etc.) 51G05 - Ordered geometries (ordered incidence structures, etc.) 51G99 - Ordered geometries (ordered incidence structures, etc.) 51Hxx - Topological geometry 51H05 - General theory of topological geometry 51H10 - Topological linear incidence structures 51H15 - Topological nonlinear incidence structures 51H20 - Topological geometries on manifolds 51H25 - Geometries with differentiable structure 51H30 - Geometries with algebraic manifold structure 51H99 - Topological geometry 51Jxx - Incidence groups 51J05 - General theory of incidence groups 51J10 - Projective incidence groups 51J15 - Kinematic spaces 51J20 - Representation by near-fields and near-algebras 51J99 - Incidence groups 51Kxx - Distance geometry 51K05 - General theory of distance geometry 51K10 - Synthetic differential geometry 51K99 - Distance geometry 51Lxx - Geometric order structures 51L05 - Geometry of orders of nondifferentiable curves 51L10 - Directly differentiable curves in geometric order structures 51L15 - (n)-vertex theorems via direct methods 51L20 - Geometry of orders of surfaces 51L99 - Geometric order structures 51Mxx - Real and complex geometry 51M04 - Elementary problems in Euclidean geometries 51M05 - Euclidean geometries (general) and generalizations 51M09 - Elementary problems in hyperbolic and elliptic geometries 51M10 - Hyperbolic and elliptic geometries (general) and generalizations 51M15 - Geometric constructions in real or complex geometry 51M16 - Inequalities and extremum problems in real or complex geometry 51M20 - Polyhedra and polytopes; regular figures, division of spaces 51M25 - Length, area and volume in real or complex geometry 51M30 - Line geometries and their generalizations 51M35 - Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) 51M99 - Real and complex geometry 51Nxx - Analytic and descriptive geometry 51N05 - Descriptive geometry 51N10 - Affine analytic geometry 51N15 - Projective analytic geometry 51N20 - Euclidean analytic geometry 51N25 - Analytic geometry with other transformation groups 51N30 - Geometry of classical groups 51N35 - Questions of classical algebraic geometry 51N99 - Analytic and descriptive geometry 51Pxx - Classical or axiomatic geometry and physics 51P05 - Classical or axiomatic geometry and physics 51P99 - Classical or axiomatic geometry and physics 52-XX - Convex and discrete geometry 52-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to convex and discrete geometry 52-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry 52-02 - Research exposition (monographs, survey articles) pertaining to convex and discrete geometry 52-03 - History of convex and discrete geometry 52-04 - Software, source code, etc. for problems pertaining to convex and discrete geometry 52-06 - Proceedings, conferences, collections, etc. pertaining to convex and discrete geometry 52-08 - Computational methods for problems pertaining to convex and discrete geometry 52-11 - Research data for problems pertaining to convex and discrete geometry 52Axx - General convexity 52A01 - Axiomatic and generalized convexity 52A05 - Convex sets without dimension restrictions (aspects of convex geometry) 52A07 - Convex sets in topological vector spaces (aspects of convex geometry) 52A10 - Convex sets in (2) dimensions (including convex curves) 52A15 - Convex sets in (3) dimensions (including convex surfaces) 52A20 - Convex sets in (n) dimensions (including convex hypersurfaces) 52A21 - Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) 52A22 - Random convex sets and integral geometry (aspects of convex geometry) 52A23 - Asymptotic theory of convex bodies 52A27 - Approximation by convex sets 52A30 - Variants of convex sets (star-shaped, ((m, n))-convex, etc.) 52A35 - Helly-type theorems and geometric transversal theory 52A37 - Other problems of combinatorial convexity 52A38 - Length, area, volume and convex sets (aspects of convex geometry) 52A39 - Mixed volumes and related topics in convex geometry 52A40 - Inequalities and extremum problems involving convexity in convex geometry 52A41 - Convex functions and convex programs in convex geometry 52A55 - Spherical and hyperbolic convexity 52A99 - General convexity 52Bxx - Polytopes and polyhedra 52B05 - Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) 52B10 - Three-dimensional polytopes 52B11 - (n)-dimensional polytopes 52B12 - Special polytopes (linear programming, centrally symmetric, etc.) 52B15 - Symmetry properties of polytopes 52B20 - Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 52B22 - Shellability for polytopes and polyhedra 52B35 - Gale and other diagrams 52B40 - Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) 52B45 - Dissections and valuations (Hilbert's third problem, etc.) 52B55 - Computational aspects related to convexity 52B60 - Isoperimetric problems for polytopes 52B70 - Polyhedral manifolds 52B99 - Polytopes and polyhedra 52Cxx - Discrete geometry 52C05 - Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) 52C07 - Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) 52C10 - Erd?s problems and related topics of discrete geometry 52C15 - Packing and covering in (2) dimensions (aspects of discrete geometry) 52C17 - Packing and covering in (n) dimensions (aspects of discrete geometry) 52C20 - Tilings in (2) dimensions (aspects of discrete geometry) 52C22 - Tilings in (n) dimensions (aspects of discrete geometry) 52C23 - Quasicrystals and aperiodic tilings in discrete geometry 52C25 - Rigidity and flexibility of structures (aspects of discrete geometry) 52C26 - Circle packings and discrete conformal geometry 52C30 - Planar arrangements of lines and pseudolines (aspects of discrete geometry) 52C35 - Arrangements of points, flats, hyperplanes (aspects of discrete geometry) 52C40 - Oriented matroids in discrete geometry 52C45 - Combinatorial complexity of geometric structures 52C99 - Discrete geometry 53-XX - Differential geometry 53-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to differential geometry 53-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry 53-02 - Research exposition (monographs, survey articles) pertaining to differential geometry 53-03 - History of differential geometry 53-04 - Software, source code, etc. for problems pertaining to differential geometry 53-06 - Proceedings, conferences, collections, etc. pertaining to differential geometry 53-08 - Computational methods for problems pertaining to differential geometry 53-11 - Research data for problems pertaining to differential geometry 53Axx - Classical differential geometry 53A04 - Curves in Euclidean and related spaces 53A05 - Surfaces in Euclidean and related spaces 53A07 - Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces 53A10 - Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53A15 - Affine differential geometry 53A17 - Differential geometric aspects in kinematics 53A20 - Projective differential geometry 53A25 - Differential line geometry 53A31 - Differential geometry of submanifolds of M�bius space 53A35 - Non-Euclidean differential geometry 53A40 - Other special differential geometries 53A45 - Differential geometric aspects in vector and tensor analysis 53A55 - Differential invariants (local theory), geometric objects 53A60 - Differential geometry of webs 53A70 - Discrete differential geometry 53A99 - Classical differential geometry 53Bxx - Local differential geometry 53B05 - Linear and affine connections 53B10 - Projective connections 53B12 - Differential geometric aspects of statistical manifolds and information geometry 53B15 - Other connections 53B20 - Local Riemannian geometry 53B21 - Methods of local Riemannian geometry 53B25 - Local submanifolds 53B30 - Local differential geometry of Lorentz metrics, indefinite metrics 53B35 - Local differential geometry of Hermitian and K�hlerian structures 53B40 - Local differential geometry of Finsler spaces and generalizations (areal metrics) 53B50 - Applications of local differential geometry to the sciences 53B99 - Local differential geometry 53Cxx - Global differential geometry 53C05 - Connections (general theory) 53C07 - Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) 53C08 - Differential geometric aspects of gerbes and differential characters 53C10 - (G)-structures 53C12 - Foliations (differential geometric aspects) 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C17 - Sub-Riemannian geometry 53C18 - Conformal structures on manifolds 53C20 - Global Riemannian geometry, including pinching 53C21 - Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C22 - Geodesics in global differential geometry 53C23 - Global geometric and topological methods (� la Gromov); differential geometric analysis on metric spaces 53C24 - Rigidity results 53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C26 - Hyper-K�hler and quaternionic K�hler geometry, ``special'' geometry 53C27 - Spin and Spin({}^c) geometry 53C28 - Twistor methods in differential geometry 53C29 - Issues of holonomy in differential geometry 53C30 - Differential geometry of homogeneous manifolds 53C35 - Differential geometry of symmetric spaces 53C38 - Calibrations and calibrated geometries 53C40 - Global submanifolds 53C42 - Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C43 - Differential geometric aspects of harmonic maps 53C45 - Global surface theory (convex surfaces � la A. D. Aleksandrov) 53C50 - Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C55 - Global differential geometry of Hermitian and K�hlerian manifolds 53C56 - Other complex differential geometry 53C60 - Global differential geometry of Finsler spaces and generalizations (areal metrics) 53C65 - Integral geometry 53C70 - Direct methods ((G)-spaces of Busemann, etc.) 53C75 - Geometric orders, order geometry 53C80 - Applications of global differential geometry to the sciences 53C99 - Global differential geometry 53Dxx - Symplectic geometry, contact geometry 53D05 - Symplectic manifolds (general theory) 53D10 - Contact manifolds (general theory) 53D12 - Lagrangian submanifolds; Maslov index 53D15 - Almost contact and almost symplectic manifolds 53D17 - Poisson manifolds; Poisson groupoids and algebroids 53D18 - Generalized geometries (� la Hitchin) 53D20 - Momentum maps; symplectic reduction 53D22 - Canonical transformations in symplectic and contact geometry 53D25 - Geodesic flows in symplectic geometry and contact geometry 53D30 - Symplectic structures of moduli spaces 53D35 - Global theory of symplectic and contact manifolds 53D37 - Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category 53D40 - Symplectic aspects of Floer homology and cohomology 53D42 - Symplectic field theory; contact homology 53D45 - Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 53D50 - Geometric quantization 53D55 - Deformation quantization, star products 53D99 - Symplectic geometry, contact geometry 53Exx - Geometric evolution equations 53E10 - Flows related to mean curvature 53E20 - Ricci flows 53E30 - Flows related to complex manifolds (e.g., K�hler-Ricci flows, Chern-Ricci flows) 53E40 - Higher-order geometric flows 53E50 - Flows related to symplectic and contact structures 53E99 - Geometric evolution equations 53Zxx - Applications of differential geometry to sciences and engineering 53Z05 - Applications of differential geometry to physics 53Z10 - Applications of differential geometry to biology 53Z15 - Applications of differential geometry to chemistry 53Z30 - Applications of differential geometry to engineering 53Z50 - Applications of differential geometry to data and computer science 53Z99 - Applications of differential geometry to sciences and engineering 54-XX - General topology 54-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general topology 54-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology 54-02 - Research exposition (monographs, survey articles) pertaining to general topology 54-03 - History of general topology 54-04 - Software, source code, etc. for problems pertaining to general topology 54-06 - Proceedings, conferences, collections, etc. pertaining to general topology 54-08 - Computational methods for problems pertaining to general topology 54-11 - Research data for problems pertaining to general topology 54Axx - Generalities in topology 54A05 - Topological spaces and generalizations (closure spaces, etc.) 54A10 - Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54A15 - Syntopogeneous structures 54A20 - Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54A25 - Cardinality properties (cardinal functions and inequalities, discrete subsets) 54A35 - Consistency and independence results in general topology 54A40 - Fuzzy topology 54A99 - Generalities in topology 54Bxx - Basic constructions in general topology 54B05 - Subspaces in general topology 54B10 - Product spaces in general topology 54B15 - Quotient spaces, decompositions in general topology 54B17 - Adjunction spaces and similar constructions in general topology 54B20 - Hyperspaces in general topology 54B30 - Categorical methods in general topology 54B35 - Spectra in general topology 54B40 - Presheaves and sheaves in general topology 54B99 - Basic constructions in general topology 54Cxx - Maps and general types of topological spaces defined by maps 54C05 - Continuous maps 54C08 - Weak and generalized continuity 54C10 - Special maps on topological spaces (open, closed, perfect, etc.) 54C15 - Retraction 54C20 - Extension of maps 54C25 - Embedding 54C30 - Real-valued functions in general topology 54C35 - Function spaces in general topology 54C40 - Algebraic properties of function spaces in general topology 54C45 - (C)- and (C^*)-embedding 54C50 - Topology of special sets defined by functions 54C55 - Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 54C56 - Shape theory in general topology 54C60 - Set-valued maps in general topology 54C65 - Selections in general topology 54C70 - Entropy in general topology 54C99 - Maps and general types of topological spaces defined by maps 54Dxx - Fairly general properties of topological spaces 54D05 - Connected and locally connected spaces (general aspects) 54D10 - Lower separation axioms ((T_0)--(T_3), etc.) 54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 - Noncompact covering properties (paracompact, Lindel�f, etc.) 54D25 - ``(P)-minimal'' and ``(P)-closed'' spaces 54D30 - Compactness 54D35 - Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54D40 - Remainders in general topology 54D45 - Local compactness, (sigma)-compactness 54D50 - (k)-spaces 54D55 - Sequential spaces 54D60 - Realcompactness and realcompactification 54D65 - Separability of topological spaces 54D70 - Base properties of topological spaces 54D80 - Special constructions of topological spaces (spaces of ultrafilters, etc.) 54D99 - Fairly general properties of topological spaces 54Exx - Topological spaces with richer structures 54E05 - Proximity structures and generalizations 54E15 - Uniform structures and generalizations 54E17 - Nearness spaces 54E18 - (p)-spaces, (M)-spaces, (sigma)-spaces, etc. 54E20 - Stratifiable spaces, cosmic spaces, etc. 54E25 - Semimetric spaces 54E30 - Moore spaces 54E35 - Metric spaces, metrizability 54E40 - Special maps on metric spaces 54E45 - Compact (locally compact) metric spaces 54E50 - Complete metric spaces 54E52 - Baire category, Baire spaces 54E55 - Bitopologies 54E70 - Probabilistic metric spaces 54E99 - Topological spaces with richer structures 54Fxx - Special properties of topological spaces 54F05 - Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 54F15 - Continua and generalizations 54F16 - Hyperspaces of continua 54F17 - Inverse limits of set-valued functions 54F35 - Higher-dimensional local connectedness 54F45 - Dimension theory in general topology 54F50 - Topological spaces of dimension (leq 1); curves, dendrites 54F55 - Unicoherence, multicoherence 54F65 - Topological characterizations of particular spaces 54F99 - Special properties of topological spaces 54Gxx - Peculiar topological spaces 54G05 - Extremally disconnected spaces, (F)-spaces, etc. 54G10 - (P)-spaces 54G12 - Scattered spaces 54G15 - Pathological topological spaces 54G20 - Counterexamples in general topology 54G99 - Peculiar topological spaces 54Hxx - Connections of general topology with other structures, applications 54H05 - Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 54H10 - Topological representations of algebraic systems 54H11 - Topological groups (topological aspects) 54H12 - Topological lattices, etc. (topological aspects) 54H13 - Topological fields, rings, etc. (topological aspects) 54H15 - Transformation groups and semigroups (topological aspects) 54H25 - Fixed-point and coincidence theorems (topological aspects) 54H30 - Applications of general topology to computer science (e.g., digital topology, image processing) 54H99 - Connections of general topology with other structures, applications 54Jxx - Nonstandard topology 54J05 - Nonstandard topology 54J99 - Nonstandard topology 55-XX - Algebraic topology 55-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic topology 55-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology 55-02 - Research exposition (monographs, survey articles) pertaining to algebraic topology 55-03 - History of algebraic topology 55-04 - Software, source code, etc. for problems pertaining to algebraic topology 55-06 - Proceedings, conferences, collections, etc. pertaining to algebraic topology 55-08 - Computational methods for problems pertaining to algebraic topology 55-11 - Research data for problems pertaining to algebraic topology 55Mxx - Classical topics in algebraic topology 55M05 - Duality in algebraic topology 55M10 - Dimension theory in algebraic topology 55M15 - Absolute neighborhood retracts 55M20 - Fixed points and coincidences in algebraic topology 55M25 - Degree, winding number 55M30 - Lyusternik-Shnirel'man category of a space, topological complexity � la Farber, topological robotics (topological aspects) 55M35 - Finite groups of transformations in algebraic topology (including Smith theory) 55M99 - Classical topics in algebraic topology 55Nxx - Homology and cohomology theories in algebraic topology 55N05 - ?ech types 55N07 - Steenrod-Sitnikov homologies 55N10 - Singular homology and cohomology theory 55N15 - Topological (K)-theory 55N20 - Generalized (extraordinary) homology and cohomology theories in algebraic topology 55N22 - Bordism and cobordism theories and formal group laws in algebraic topology 55N25 - Homology with local coefficients, equivariant cohomology 55N30 - Sheaf cohomology in algebraic topology 55N31 - Persistent homology and applications, topological data analysis 55N32 - Orbifold cohomology 55N33 - Intersection homology and cohomology in algebraic topology 55N34 - Elliptic cohomology 55N35 - Other homology theories in algebraic topology 55N40 - Axioms for homology theory and uniqueness theorems in algebraic topology 55N45 - Products and intersections in homology and cohomology 55N91 - Equivariant homology and cohomology in algebraic topology 55N99 - Homology and cohomology theories in algebraic topology 55Pxx - Homotopy theory 55P05 - Homotopy extension properties, cofibrations in algebraic topology 55P10 - Homotopy equivalences in algebraic topology 55P15 - Classification of homotopy type 55P20 - Eilenberg-Mac Lane spaces 55P25 - Spanier-Whitehead duality 55P30 - Eckmann-Hilton duality 55P35 - Loop spaces 55P40 - Suspensions 55P42 - Stable homotopy theory, spectra 55P43 - Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) 55P45 - (H)-spaces and duals 55P47 - Infinite loop spaces 55P48 - Loop space machines and operads in algebraic topology 55P50 - String topology 55P55 - Shape theory 55P57 - Proper homotopy theory 55P60 - Localization and completion in homotopy theory 55P62 - Rational homotopy theory 55P65 - Homotopy functors in algebraic topology 55P91 - Equivariant homotopy theory in algebraic topology 55P92 - Relations between equivariant and nonequivariant homotopy theory in algebraic topology 55P99 - Homotopy theory 55Qxx - Homotopy groups 55Q05 - Homotopy groups, general; sets of homotopy classes 55Q07 - Shape groups 55Q10 - Stable homotopy groups 55Q15 - Whitehead products and generalizations 55Q20 - Homotopy groups of wedges, joins, and simple spaces 55Q25 - Hopf invariants 55Q35 - Operations in homotopy groups 55Q40 - Homotopy groups of spheres 55Q45 - Stable homotopy of spheres 55Q50 - (J)-morphism 55Q51 - (v_n)-periodicity 55Q52 - Homotopy groups of special spaces 55Q55 - Cohomotopy groups 55Q70 - Homotopy groups of special types 55Q91 - Equivariant homotopy groups 55Q99 - Homotopy groups 55Rxx - Fiber spaces and bundles in algebraic topology 55R05 - Fiber spaces in algebraic topology 55R10 - Fiber bundles in algebraic topology 55R12 - Transfer for fiber spaces and bundles in algebraic topology 55R15 - Classification of fiber spaces or bundles in algebraic topology 55R20 - Spectral sequences and homology of fiber spaces in algebraic topology 55R25 - Sphere bundles and vector bundles in algebraic topology 55R35 - Classifying spaces of groups and (H)-spaces in algebraic topology 55R37 - Maps between classifying spaces in algebraic topology 55R40 - Homology of classifying spaces and characteristic classes in algebraic topology 55R45 - Homology and homotopy of (Bmathrm{O}) and (Bmathrm{U}); Bott periodicity 55R50 - Stable classes of vector space bundles in algebraic topology and relations to (K)-theory 55R55 - Fiberings with singularities in algebraic topology 55R60 - Microbundles and block bundles in algebraic topology 55R65 - Generalizations of fiber spaces and bundles in algebraic topology 55R70 - Fibrewise topology 55R80 - Discriminantal varieties and configuration spaces in algebraic topology 55R91 - Equivariant fiber spaces and bundles in algebraic topology 55R99 - Fiber spaces and bundles in algebraic topology 55Sxx - Operations and obstructions in algebraic topology 55S05 - Primary cohomology operations in algebraic topology 55S10 - Steenrod algebra 55S12 - Dyer-Lashof operations 55S15 - Symmetric products and cyclic products in algebraic topology 55S20 - Secondary and higher cohomology operations in algebraic topology 55S25 - (K)-theory operations and generalized cohomology operations in algebraic topology 55S30 - Massey products 55S35 - Obstruction theory in algebraic topology 55S36 - Extension and compression of mappings in algebraic topology 55S37 - Classification of mappings in algebraic topology 55S40 - Sectioning fiber spaces and bundles in algebraic topology 55S45 - Postnikov systems, (k)-invariants 55S91 - Equivariant operations and obstructions in algebraic topology 55S99 - Operations and obstructions in algebraic topology 55Txx - Spectral sequences in algebraic topology 55T05 - General theory of spectral sequences in algebraic topology 55T10 - Serre spectral sequences 55T15 - Adams spectral sequences 55T20 - Eilenberg-Moore spectral sequences 55T25 - Generalized cohomology and spectral sequences in algebraic topology 55T99 - Spectral sequences in algebraic topology 55Uxx - Applied homological algebra and category theory in algebraic topology 55U05 - Abstract complexes in algebraic topology 55U10 - Simplicial sets and complexes in algebraic topology 55U15 - Chain complexes in algebraic topology 55U20 - Universal coefficient theorems, Bockstein operator 55U25 - Homology of a product, K�nneth formula 55U30 - Duality in applied homological algebra and category theory (aspects of algebraic topology) 55U35 - Abstract and axiomatic homotopy theory in algebraic topology 55U40 - Topological categories, foundations of homotopy theory 55U99 - Applied homological algebra and category theory in algebraic topology 57-XX - Manifolds and cell complexes 57-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes 57-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes 57-02 - Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes 57-03 - History of manifolds and cell complexes 57-04 - Software, source code, etc. for problems pertaining to manifolds and cell complexes 57-06 - Proceedings, conferences, collections, etc. pertaining to manifolds and cell complexes 57-08 - Computational methods for problems pertaining to manifolds and cell complexes 57-11 - Research data for problems pertaining to manifolds and cell complexes 57Kxx - Low-dimensional topology in specific dimensions 57K10 - Knot theory 57K12 - Generalized knots (virtual knots, welded knots, quandles, etc.) 57K14 - Knot polynomials 57K16 - Finite-type and quantum invariants, topological quantum field theories (TQFT) 57K18 - Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) 57K20 - 2-dimensional topology (including mapping class groups of surfaces, Teichm�ller theory, curve complexes, etc.) 57K30 - General topology of 3-manifolds 57K31 - Invariants of 3-manifolds (including skein modules, character varieties) 57K32 - Hyperbolic 3-manifolds 57K33 - Contact structures in 3 dimensions 57K35 - Other geometric structures on 3-manifolds 57K40 - General topology of 4-manifolds 57K41 - Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants) 57K43 - Symplectic structures in 4 dimensions 57K45 - Higher-dimensional knots and links 57K50 - Low-dimensional manifolds of specific dimension 5 or higher 57K99 - Low-dimensional topology in specific dimensions 57Mxx - General low-dimensional topology 57M05 - Fundamental group, presentations, free differential calculus 57M07 - Topological methods in group theory 57M10 - Covering spaces and low-dimensional topology 57M12 - Low-dimensional topology of special (e.g., branched) coverings 57M15 - Relations of low-dimensional topology with graph theory 57M30 - Wild embeddings 57M50 - General geometric structures on low-dimensional manifolds 57M60 - Group actions on manifolds and cell complexes in low dimensions 57M99 - General low-dimensional topology 57Nxx - Topological manifolds 57N16 - Geometric structures on manifolds of high or arbitrary dimension 57N17 - Topology of topological vector spaces 57N20 - Topology of infinite-dimensional manifolds 57N25 - Shapes (aspects of topological manifolds) 57N30 - Engulfing in topological manifolds 57N35 - Embeddings and immersions in topological manifolds 57N37 - Isotopy and pseudo-isotopy 57N40 - Neighborhoods of submanifolds 57N45 - Flatness and tameness of topological manifolds 57N50 - (S^{n-1}subset E^n), Schoenflies problem 57N55 - Microbundles and block bundles 57N60 - Cellularity in topological manifolds 57N65 - Algebraic topology of manifolds 57N70 - Cobordism and concordance in topological manifolds 57N75 - General position and transversality 57N80 - Stratifications in topological manifolds 57N99 - Topological manifolds 57Pxx - Generalized manifolds 57P05 - Local properties of generalized manifolds 57P10 - Poincar� duality spaces 57P99 - Generalized manifolds 57Qxx - PL-topology 57Q05 - General topology of complexes 57Q10 - Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. 57Q12 - Wall finiteness obstruction for CW-complexes 57Q15 - Triangulating manifolds 57Q20 - Cobordism in PL-topology 57Q25 - Comparison of PL-structures: classification, Hauptvermutung 57Q30 - Engulfing 57Q35 - Embeddings and immersions in PL-topology 57Q37 - Isotopy in PL-topology 57Q40 - Regular neighborhoods in PL-topology 57Q50 - Microbundles and block bundles 57Q55 - Approximations in PL-topology 57Q60 - Cobordism and concordance in PL-topology 57Q65 - General position and transversality 57Q70 - Discrete Morse theory and related ideas in manifold topology 57Q91 - Equivariant PL-topology 57Q99 - PL-topology 57Rxx - Differential topology 57R05 - Triangulating 57R10 - Smoothing in differential topology 57R12 - Smooth approximations in differential topology 57R15 - Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) 57R17 - Symplectic and contact topology in high or arbitrary dimension 57R18 - Topology and geometry of orbifolds 57R19 - Algebraic topology on manifolds and differential topology 57R20 - Characteristic classes and numbers in differential topology 57R22 - Topology of vector bundles and fiber bundles 57R25 - Vector fields, frame fields in differential topology 57R27 - Controllability of vector fields on (C^infty) and real-analytic manifolds 57R30 - Foliations in differential topology; geometric theory 57R32 - Classifying spaces for foliations; Gelfand-Fuks cohomology 57R35 - Differentiable mappings in differential topology 57R40 - Embeddings in differential topology 57R42 - Immersions in differential topology 57R45 - Singularities of differentiable mappings in differential topology 57R50 - Differential topological aspects of diffeomorphisms 57R52 - Isotopy in differential topology 57R55 - Differentiable structures in differential topology 57R56 - Topological quantum field theories (aspects of differential topology) 57R57 - Applications of global analysis to structures on manifolds 57R58 - Floer homology 57R60 - Homotopy spheres, Poincar� conjecture 57R65 - Surgery and handlebodies 57R67 - Surgery obstructions, Wall groups 57R70 - Critical points and critical submanifolds in differential topology 57R75 - (mathrm{O})- and (mathrm{SO})-cobordism 57R77 - Complex cobordism ((mathrm{U})- and (mathrm{SU})-cobordism) 57R80 - (h)- and (s)-cobordism 57R85 - Equivariant cobordism 57R90 - Other types of cobordism 57R91 - Equivariant algebraic topology of manifolds 57R95 - Realizing cycles by submanifolds 57R99 - Differential topology 57Sxx - Topological transformation groups 57S05 - Topological properties of groups of homeomorphisms or diffeomorphisms 57S10 - Compact groups of homeomorphisms 57S12 - Toric topology 57S15 - Compact Lie groups of differentiable transformations 57S17 - Finite transformation groups 57S20 - Noncompact Lie groups of transformations 57S25 - Groups acting on specific manifolds 57S30 - Discontinuous groups of transformations 57S99 - Topological transformation groups 57Txx - Homology and homotopy of topological groups and related structures 57T05 - Hopf algebras (aspects of homology and homotopy of topological groups) 57T10 - Homology and cohomology of Lie groups 57T15 - Homology and cohomology of homogeneous spaces of Lie groups 57T20 - Homotopy groups of topological groups and homogeneous spaces 57T25 - Homology and cohomology of (H)-spaces 57T30 - Bar and cobar constructions 57T35 - Applications of Eilenberg-Moore spectral sequences 57T99 - Homology and homotopy of topological groups and related structures 57Zxx - Relations of manifolds and cell complexes with science and engineering 57Z05 - Relations of manifolds and cell complexes with physics 57Z10 - Relations of manifolds and cell complexes with biology 57Z15 - Relations of manifolds and cell complexes with chemistry 57Z20 - Relations of manifolds and cell complexes with engineering 57Z25 - Relations of manifolds and cell complexes with computer and data science 57Z99 - Relations of manifolds and cell complexes with science and engineering 58-XX - Global analysis, analysis on manifolds 58-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis 58-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis 58-02 - Research exposition (monographs, survey articles) pertaining to global analysis 58-03 - History of global analysis 58-04 - Software, source code, etc. for problems pertaining to global analysis 58-06 - Proceedings, conferences, collections, etc. pertaining to global analysis 58-08 - Computational methods for problems pertaining to global analysis 58-11 - Research data for problems pertaining to global analysis 58Axx - General theory of differentiable manifolds 58A03 - Topos-theoretic approach to differentiable manifolds 58A05 - Differentiable manifolds, foundations 58A07 - Real-analytic and Nash manifolds 58A10 - Differential forms in global analysis 58A12 - de Rham theory in global analysis 58A14 - Hodge theory in global analysis 58A15 - Exterior differential systems (Cartan theory) 58A17 - Pfaffian systems 58A20 - Jets in global analysis 58A25 - Currents in global analysis 58A30 - Vector distributions (subbundles of the tangent bundles) 58A32 - Natural bundles 58A35 - Stratified sets 58A40 - Differential spaces 58A50 - Supermanifolds and graded manifolds 58A99 - General theory of differentiable manifolds 58Bxx - Infinite-dimensional manifolds 58B05 - Homotopy and topological questions for infinite-dimensional manifolds 58B10 - Differentiability questions for infinite-dimensional manifolds 58B12 - Questions of holomorphy and infinite-dimensional manifolds 58B15 - Fredholm structures on infinite-dimensional manifolds 58B20 - Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds 58B25 - Group structures and generalizations on infinite-dimensional manifolds 58B32 - Geometry of quantum groups 58B34 - Noncommutative geometry (� la Connes) 58B99 - Infinite-dimensional manifolds 58Cxx - Calculus on manifolds; nonlinear operators 58C05 - Real-valued functions on manifolds 58C06 - Set-valued and function-space-valued mappings on manifolds 58C07 - Continuity properties of mappings on manifolds 58C10 - Holomorphic maps on manifolds 58C15 - Implicit function theorems; global Newton methods on manifolds 58C20 - Differentiation theory (Gateaux, Fr�chet, etc.) on manifolds 58C25 - Differentiable maps on manifolds 58C30 - Fixed-point theorems on manifolds 58C35 - Integration on manifolds; measures on manifolds 58C40 - Spectral theory; eigenvalue problems on manifolds 58C50 - Analysis on supermanifolds or graded manifolds 58C99 - Calculus on manifolds; nonlinear operators 58Dxx - Spaces and manifolds of mappings (including nonlinear versions of 46Exx) 58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds 58D07 - Groups and semigroups of nonlinear operators 58D10 - Spaces of embeddings and immersions 58D15 - Manifolds of mappings 58D17 - Manifolds of metrics (especially Riemannian) 58D19 - Group actions and symmetry properties 58D20 - Measures (Gaussian, cylindrical, etc.) on manifolds of maps 58D25 - Equations in function spaces; evolution equations 58D27 - Moduli problems for differential geometric structures 58D29 - Moduli problems for topological structures 58D30 - Applications of manifolds of mappings to the sciences 58D99 - Spaces and manifolds of mappings (including nonlinear versions of 46Exx) 58Exx - Variational problems in infinite-dimensional spaces 58E05 - Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces 58E07 - Variational problems in abstract bifurcation theory in infinite-dimensional spaces 58E09 - Group-invariant bifurcation theory in infinite-dimensional spaces 58E10 - Variational problems in applications to the theory of geodesics (problems in one independent variable) 58E11 - Critical metrics 58E12 - Variational problems concerning minimal surfaces (problems in two independent variables) 58E15 - Variational problems concerning extremal problems in several variables; Yang-Mills functionals 58E17 - Multiobjective variational problems, Pareto optimality, applications to economics, etc. 58E20 - Harmonic maps, etc. 58E25 - Applications of variational problems to control theory 58E30 - Variational principles in infinite-dimensional spaces 58E35 - Variational inequalities (global problems) in infinite-dimensional spaces 58E40 - Variational aspects of group actions in infinite-dimensional spaces 58E50 - Applications of variational problems in infinite-dimensional spaces to the sciences 58E99 - Variational problems in infinite-dimensional spaces 58Hxx - Pseudogroups, differentiable groupoids and general structures on manifolds 58H05 - Pseudogroups and differentiable groupoids 58H10 - Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) 58H15 - Deformations of general structures on manifolds 58H99 - Pseudogroups, differentiable groupoids and general structures on manifolds 58Jxx - Partial differential equations on manifolds; differential operators 58J05 - Elliptic equations on manifolds, general theory 58J10 - Differential complexes 58J15 - Relations of PDEs on manifolds with hyperfunctions 58J20 - Index theory and related fixed-point theorems on manifolds 58J22 - Exotic index theories on manifolds 58J26 - Elliptic genera 58J28 - Eta-invariants, Chern-Simons invariants 58J30 - Spectral flows 58J32 - Boundary value problems on manifolds 58J35 - Heat and other parabolic equation methods for PDEs on manifolds 58J37 - Perturbations of PDEs on manifolds; asymptotics 58J40 - Pseudodifferential and Fourier integral operators on manifolds 58J42 - Noncommutative global analysis, noncommutative residues 58J45 - Hyperbolic equations on manifolds 58J47 - Propagation of singularities; initial value problems on manifolds 58J50 - Spectral problems; spectral geometry; scattering theory on manifolds 58J51 - Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity 58J52 - Determinants and determinant bundles, analytic torsion 58J53 - Isospectrality 58J55 - Bifurcation theory for PDEs on manifolds 58J60 - Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) 58J65 - Diffusion processes and stochastic analysis on manifolds 58J70 - Invariance and symmetry properties for PDEs on manifolds 58J72 - Correspondences and other transformation methods (e.g., Lie-B�cklund) for PDEs on manifolds 58J90 - Applications of PDEs on manifolds 58J99 - Partial differential equations on manifolds; differential operators 58Kxx - Theory of singularities and catastrophe theory 58K05 - Critical points of functions and mappings on manifolds 58K10 - Monodromy on manifolds 58K15 - Topological properties of mappings on manifolds 58K20 - Algebraic and analytic properties of mappings on manifolds 58K25 - Stability theory for manifolds 58K30 - Global theory of singularities 58K35 - Catastrophe theory 58K40 - Classification; finite determinacy of map germs 58K45 - Singularities of vector fields, topological aspects 58K50 - Normal forms on manifolds 58K55 - Asymptotic behavior of solutions to equations on manifolds 58K60 - Deformation of singularities 58K65 - Topological invariants on manifolds 58K70 - Symmetries, equivariance on manifolds 58K99 - Theory of singularities and catastrophe theory 58Zxx - Applications of global analysis to the sciences 58Z05 - Applications of global analysis to the sciences 58Z99 - Applications of global analysis to the sciences 60-XX - Probability theory and stochastic processes 60-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to probability theory 60-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory 60-02 - Research exposition (monographs, survey articles) pertaining to probability theory 60-03 - History of probability theory 60-04 - Software, source code, etc. for problems pertaining to probability theory 60-06 - Proceedings, conferences, collections, etc. pertaining to probability theory 60-08 - Computational methods for problems pertaining to probability theory 60-11 - Research data for problems pertaining to probability theory 60Axx - Foundations of probability theory 60A05 - Axioms; other general questions in probability 60A10 - Probabilistic measure theory 60A86 - Fuzzy probability 60A99 - Foundations of probability theory 60Bxx - Probability theory on algebraic and topological structures 60B05 - Probability measures on topological spaces 60B10 - Convergence of probability measures 60B11 - Probability theory on linear topological spaces 60B12 - Limit theorems for vector-valued random variables (infinite-dimensional case) 60B15 - Probability measures on groups or semigroups, Fourier transforms, factorization 60B20 - Random matrices (probabilistic aspects) 60B99 - Probability theory on algebraic and topological structures 60Cxx - Combinatorial probability 60C05 - Combinatorial probability 60C99 - Combinatorial probability 60Dxx - Geometric probability and stochastic geometry 60D05 - Geometric probability and stochastic geometry 60D99 - Geometric probability and stochastic geometry 60Exx - Distribution theory 60E05 - Probability distributions: general theory 60E07 - Infinitely divisible distributions; stable distributions 60E10 - Characteristic functions; other transforms 60E15 - Inequalities; stochastic orderings 60E99 - Distribution theory 60Fxx - Limit theorems in probability theory 60F05 - Central limit and other weak theorems 60F10 - Large deviations 60F15 - Strong limit theorems 60F17 - Functional limit theorems; invariance principles 60F20 - Zero-one laws 60F25 - (L^p)-limit theorems 60F99 - Limit theorems in probability theory 60Gxx - Stochastic processes 60G05 - Foundations of stochastic processes 60G07 - General theory of stochastic processes 60G09 - Exchangeability for stochastic processes 60G10 - Stationary stochastic processes 60G12 - General second-order stochastic processes 60G15 - Gaussian processes 60G17 - Sample path properties 60G18 - Self-similar stochastic processes 60G20 - Generalized stochastic processes 60G22 - Fractional processes, including fractional Brownian motion 60G25 - Prediction theory (aspects of stochastic processes) 60G30 - Continuity and singularity of induced measures 60G35 - Signal detection and filtering (aspects of stochastic processes) 60G40 - Stopping times; optimal stopping problems; gambling theory 60G42 - Martingales with discrete parameter 60G44 - Martingales with continuous parameter 60G46 - Martingales and classical analysis 60G48 - Generalizations of martingales 60G50 - Sums of independent random variables; random walks 60G51 - Processes with independent increments; L�vy processes 60G52 - Stable stochastic processes 60G53 - Feller processes 60G55 - Point processes (e.g., Poisson, Cox, Hawkes processes) 60G57 - Random measures 60G60 - Random fields 60G65 - Nonlinear processes (e.g., (G)-Brownian motion, (G)-L�vy processes) 60G70 - Extreme value theory; extremal stochastic processes 60G99 - Stochastic processes 60Hxx - Stochastic analysis 60H05 - Stochastic integrals 60H07 - Stochastic calculus of variations and the Malliavin calculus 60H10 - Stochastic ordinary differential equations (aspects of stochastic analysis) 60H15 - Stochastic partial differential equations (aspects of stochastic analysis) 60H17 - Singular stochastic partial differential equations 60H20 - Stochastic integral equations 60H25 - Random operators and equations (aspects of stochastic analysis) 60H30 - Applications of stochastic analysis (to PDEs, etc.) 60H35 - Computational methods for stochastic equations (aspects of stochastic analysis) 60H40 - White noise theory 60H50 - Regularization by noise 60H99 - Stochastic analysis 60Jxx - Markov processes 60J05 - Discrete-time Markov processes on general state spaces 60J10 - Markov chains (discrete-time Markov processes on discrete state spaces) 60J20 - Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60J22 - Computational methods in Markov chains 60J25 - Continuous-time Markov processes on general state spaces 60J27 - Continuous-time Markov processes on discrete state spaces 60J28 - Applications of continuous-time Markov processes on discrete state spaces 60J35 - Transition functions, generators and resolvents 60J40 - Right processes 60J45 - Probabilistic potential theory 60J46 - Dirichlet form methods in Markov processes 60J50 - Boundary theory for Markov processes 60J55 - Local time and additive functionals 60J57 - Multiplicative functionals and Markov processes 60J60 - Diffusion processes 60J65 - Brownian motion 60J67 - Stochastic (Schramm-)Loewner evolution (SLE) 60J68 - Superprocesses 60J70 - Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60J74 - Jump processes on discrete state spaces 60J76 - Jump processes on general state spaces 60J80 - Branching processes (Galton-Watson, birth-and-death, etc.) 60J85 - Applications of branching processes 60J90 - Coalescent processes 60J95 - Applications of coalescent processes 60J99 - Markov processes 60Kxx - Special processes 60K05 - Renewal theory 60K10 - Applications of renewal theory (reliability, demand theory, etc.) 60K15 - Markov renewal processes, semi-Markov processes 60K20 - Applications of Markov renewal processes (reliability, queueing networks, etc.) 60K25 - Queueing theory (aspects of probability theory) 60K30 - Applications of queueing theory (congestion, allocation, storage, traffic, etc.) 60K35 - Interacting random processes; statistical mechanics type models; percolation theory 60K37 - Processes in random environments 60K40 - Other physical applications of random processes 60K50 - Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) 60K99 - Special processes 60Lxx - Rough analysis 60L10 - Signatures and data streams 60L20 - Rough paths 60L30 - Regularity structures 60L40 - Paracontrolled distributions and alternative approaches 60L50 - Rough partial differential equations 60L70 - Algebraic structures and computation 60L90 - Applications of rough analysis 60L99 - Rough analysis 62-XX - Statistics 62-00 - General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics 62-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics 62-02 - Research exposition (monographs, survey articles) pertaining to statistics 62-03 - History of statistics 62-04 - Software, source code, etc. for problems pertaining to statistics 62-06 - Proceedings, conferences, collections, etc. pertaining to statistics 62-08 - Computational methods for problems pertaining to statistics 62-11 - Research data for problems pertaining to statistics 62Axx - Foundational topics in statistics 62A01 - Foundations and philosophical topics in statistics 62A09 - Graphical methods in statistics 62A86 - Fuzzy analysis in statistics 62A99 - Foundational topics in statistics 62Bxx - Sufficiency and information 62B05 - Sufficient statistics and fields 62B10 - Statistical aspects of information-theoretic topics 62B11 - Information geometry (statistical aspects) 62B15 - Theory of statistical experiments 62B86 - Statistical aspects of fuzziness, sufficiency, and information 62B99 - Sufficiency and information 62Cxx - Statistical decision theory 62C05 - General considerations in statistical decision theory 62C07 - Complete class results in statistical decision theory 62C10 - Bayesian problems; characterization of Bayes procedures 62C12 - Empirical decision procedures; empirical Bayes procedures 62C15 - Admissibility in statistical decision theory 62C20 - Minimax procedures in statistical decision theory 62C25 - Compound decision problems in statistical decision theory 62C86 - Statistical decision theory and fuzziness 62C99 - Statistical decision theory 62Dxx - Statistical sampling theory and related topics 62D05 - Sampling theory, sample surveys 62D10 - Missing data 62D20 - Causal inference from observational studies 62D99 - Statistical sampling theory and related topics 62Exx - Statistical distribution theory 62E10 - Characterization and structure theory of statistical distributions 62E15 - Exact distribution theory in statistics 62E17 - Approximations to statistical distributions (nonasymptotic) 62E20 - Asymptotic distribution theory in statistics 62E86 - Fuzziness in connection with statistical distributions 62E99 - Statistical distribution theory 62Fxx - Parametric inference 62F03 - Parametric hypothesis testing 62F05 - Asymptotic properties of parametric tests 62F07 - Statistical
