AMS数学主题分类表（2020版）.pdf

MSC2020-Mathematics Subject Classification System Associate Editors of Mathematical Reviews and zbMATH 00 General and overarching topics; collections 45 Integral equations 01 History and biography 46 Functional analysis 03 Mathematical logic and foundations 47 Operator theory 05 Combinatorics 49 Calculus of variations and optimal control; optimization 06 Order, lattices, ordered algebraic structures 51 Geometry 08 General algebraic systems 52 Convex and discrete geometry 11 Number theory 53 Differential geometry 12 Field theory and polynomials 54 General topology 13 Commutative algebra 55 Algebraic topology 14 Algebraic geometry 57 Manifolds and cell complexes 15 Linear and multilinear algebra; matrix theory 58 Global analysis, analysis on manifolds 16 Associative rings and algebras 60 Probability theory and stochastic processes 17 Nonassociative rings and algebras 62 Statistics 18 Category theory; homological algebra 65 Numerical analysis 19 K-theory 68 Computer science 20 Group theory and generalizations 70 Mechanics of particles and systems 22 Topological groups, Lie groups 74 Mechanics of deformable solids 26 Real functions 76 Fluid mechanics 28 Measure and integration 78 Optics, electromagnetic theory 30 Functions of a complex variable 80 Classical thermodynamics, heat transfer 31 Potential theory 81 Quantum theory 32 Several complex variables and analytic spaces 33 Special functions 82 Statistical mechanics, structure of matter 34 Ordinary differential equations 83 Relativity and gravitational theory 35 Partial differential equations 85 Astronomy and astrophysics 37 Dynamical systems and ergodic theory 86 Geophysics 39 Difference and functional equations 90 Operations research, mathematical programming 40 Sequences, series, summability 91 Game theory, economics, social and behavioral sciences 41 Approximations and expansions 92 Biology and other natural sciences 42 Harmonic analysis on Euclidean spaces 93 Systems theory; control 43 Abstract harmonic analysis 94 Information and communication, circuits 44 Integral transforms, operational calculus 97 Mathematics education © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 1 This document is a printed form of MSC2020, an MSC revision produced jointly by the editorial staffs of Mathematical Reviews (MR) and Zentralblatt für Mathematik (zbMATH) in consultation with the mathematical community. The goals of this revision of the Mathematics Subject Classification (MSC) were set out in the announcement of it and call for comments by the Executive Editor of MR and the Chief Editor of zbMATH in July 2016. This document results from the MSC revision process that has been going on since then. MSC2020 will be fully deployed from January 2020. The editors of MR and zbMATH deploying this revision therefore ask for feedback on remaining errors to help in this work, which should be given through e-mail to feedback@msc2020.org. They are grateful for the many suggestions that were received previously, which have greatly influenced what we have. 2 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. How to use the Mathematics Subject Classification [MSC] The main purpose of the classification of items in the mathematical literature using the Mathematics Subject Classification scheme is to help users find the items of present or potential interest to them as readily as possible—in products derived from the Mathematical Reviews Database (MRDB) such as MathSciNet, in Zentralblatt MATH (zbMATH), or anywhere else where this classification scheme is used. An item in the mathematical literature should be classified so as to attract the attention of all those possibly interested in it. The item may be something that falls squarely within one clear area of the MSC, or it may involve several areas. Ideally, the MSC codes attached to an item should represent the subjects to which the item contains a contribution. The classification should serve both those closely concerned with specific subject areas, and those familiar enough with subjects to apply their results and methods elsewhere, inside or outside of mathematics. It will be extremely useful for both users and classifiers to familiarize themselves with the entire classification system and thus to become aware of all the classifications of possible interest to them. Every item in the MRDB or zbMATH receives precisely one primary classification, which is simply the MSC code that describes its principal contribution. When an item contains several principal contributions to different areas, the primary classification should cover the most important among them. A paper or book may be assigned one or several secondary classification numbers to cover any remaining principal contributions, ancillary results, motivation or origin of the matters discussed, intended or potential field of application, or other significant aspects worthy of notice. The principal contribution is meant to be the one including the most important part of the work actually done in the item. For example, a paper whose main overall content is the solution of a problem in graph theory, which arose in computer science and whose solution is (perhaps) at present only of interest to computer scientists, would have a primary classification in 05C (Graph Theory) with one or more secondary classifications in 68 (Computer Science); conversely, a paper whose overall content lies mainly in computer science should receive a primary classification in 68, even if it makes heavy use of graph theory and proves several new graph-theoretic results along the way. There are two types of cross-references given at the end of many of the MSC2020 entries in the MSC. The first type is in braces: “{For A, see X}”; if this appears in section Y, it means that contributions described by A should usually be assigned the classification code X, not Y. The other type of cross-reference merely points out related classifications; it is in brackets: “[See also ... ]”, “[See mainly ... ]”, etc., and the classification codes listed in the brackets may, but need not, be included in the classification codes of a paper, or they may be used in place of the classification where the cross-reference is given. The classifier must judge which classification is the most appropriate for the paper at hand. 3 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 00-XX General and overarching 00Bxx Conference proceedings and collections of articles topics; collections 00-01 Introductory exposition (textbooks, tutorial pa- 00B05 Collections of abstracts of lectures pers, etc.) pertaining to mathematics in general 00B10 Collections of articles of general interest 00-02 Research exposition (monographs, survey articles) pertaining to mathematics in general 00B15 Collections of articles of miscellaneous specific interest 00Axx General and miscellaneous specific topics 00B20 Proceedings of conferences of general interest 00A05 Mathematics in general 00A06 Mathematics for nonmathematicians (engineer- 00B25 Proceedings of conferences of miscellaneous speing, social sciences, etc.) cific interest 00A07 Problem books {For open problems, see 00A27} 00B30 Festschriften 00A08 Recreational mathematics 00B50 Collections of translated articles of general interest 00A09 Popularization of mathematics 00A15 Bibliographies for mathematics in general [See also 01A70 and the classification number –00 in the 00B55 Collections of translated articles of miscellaneous other sections] specific interest 00A17 External book reviews 00A20 Dictionaries and other general reference works 00B60 Collections of reprinted articles [See also 01A75] [See also the classification number –00 in the other sections] 00B99 None of the above, but in this section 00A22 Formularies 00A27 Lists of open problems 01-XX History and biography [See 00A30 Philosophy of mathematics [See also 03A05] also the classification number –03 00A35 Methodology of mathematics {For mathematics in the other sections] education, see 97-XX} 01-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography 00A64 Mathematics and literature 00A65 Mathematics and music 00A66 Mathematics and visual arts 01-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography 00A67 Mathematics and architecture 00A69 General applied mathematics {For physics, see 00A79 and Sections 70 through 86} 01-02 Research exposition (monographs, survey articles) pertaining to history and biography 00A71 General theory of mathematical modeling 01-06 Proceedings, conferences, collections, etc. taining to history and biography 00A72 General theory of simulation 00A79 Physics (Use more specific entries from Sections 70 through 86 when possible) 01-11 Research data for problems pertaining to history and biography 00A99 None of the above, but in this section 4 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. per- 01Axx History of mathematics and math- 01A74 History of mathematics at institutions and academies (non-university) ematicians 01A05 General histories, source books 01A75 Collected or selected works; reprintings or translations of classics [See also 00B60] 01A07 Ethnomathematics, general 01A10 History of mathematics in Paleolithic and Ne- 01A80 Sociology (and profession) of mathematics olithic times 01A85 Historiography 01A11 History of mathematics of the indigenous cul01A90 Bibliographic studies tures of Africa, Asia, and Oceania 01A12 History of mathematics of the indigenous cul- 01A99 None of the above, but in this section tures of the Americas 01A15 History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.) 03-XX Mathematical foundations 01A16 History of mathematics in Ancient Egypt logic and 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations 01A20 History of mathematics in Ancient Greece and Rome 03-01 Introductory exposition (textbooks, tutorial pa01A25 History of mathematics in China pers, etc.) pertaining to mathematical logic and foundations 01A27 History of mathematics in Japan 01A17 History of mathematics in Ancient Babylon 03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations 01A29 History of mathematics in Southeast Asia 01A30 History of mathematics in the Golden Age of Is03-03 History of mathematical logic and foundations lam [Consider also classification numbers pertaining to 01A32 History of mathematics in India Section 01] 01A35 History of mathematics in late antiquity and me03-04 Software, source code, etc. for problems pertaindieval Europe ing to mathematical logic and foundations 01A40 History of mathematics in the 15th and 16th cen03-06 Proceedings, conferences, collections, etc. perturies, Renaissance taining to mathematical logic and foundations 01A45 History of mathematics in the 17th century 03-08 Computational methods for problems pertaining 01A50 History of mathematics in the 18th century to mathematical logic and foundations 01A55 History of mathematics in the 19th century 03-11 Research data for problems pertaining to mathematical logic and foundations 01A60 History of mathematics in the 20th century 01A61 History of mathematics in the 21st century 03Axx Philosophical aspects of logic and foundations 01A65 Development of contemporary mathematics 01A67 Future perspectives in mathematics 03A05 Philosophical and critical aspects of logic and foundations {For philosophy of mathematics, see 01A70 Biographies, obituaries, personalia, bibliograalso 00A30} phies 01A72 Schools of mathematics 03A10 Logic in the philosophy of science 01A73 History of mathematics at specific universities 03A99 None of the above, but in this section 5 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 03Bxx General logic 03Cxx Model theory 03B05 Classical propositional logic 03C05 Equational classes, universal algebra in model theory [See also 08Axx, 08Bxx, 18C05] 03B10 Classical first-order logic 03C07 Basic properties of first-order languages and structures 03B16 Higher-order logic 03B20 Subsystems of classical logic (including intuition- 03C10 Quantifier elimination, model completeness and istic logic) related topics 03B22 Abstract deductive systems 03C13 Model theory of finite structures [See also 68Q15, 68Q19] 03B25 Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10] 03C15 Model theory of denumerable and separable structures 03B30 Foundations of classical theories (including reverse mathematics) [See also 03F35] 03C20 Ultraproducts and related constructions 03B35 Mechanization of proofs and logical operations 03C25 Model-theoretic forcing [See also 68V15] 03C30 Other model constructions 03B38 Type theory 03C35 Categoricity and completeness of theories 03B40 Combinatory logic and lambda calculus [See also 03C40 Interpolation, preservation, definability 68N18] 03B42 Logics of knowledge and belief (including belief 03C45 Classification theory, stability and related concepts in model theory [See also 03C48] change) 03C48 Abstract elementary classes and related topics [See also 03C45] 03B44 Temporal logic 03B45 Modal logic (including the logic of norms) {For 03C50 Models with special properties (saturated, rigid, knowledge and belief, see 03B42; for temporal logic, etc.) see 03B44; for provability logic, see also 03F45} 03C52 Properties of classes of models 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI 03C55 Set-theoretic model theory logics) {For proof-theoretic aspects, see 03F52} 03C57 Computable structure theory, computable model 03B48 Probability and inductive logic [See also 60A05] theory [See also 03D45] 03C60 Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness [See also 68T27, 03C62 Models of arithmetic and set theory [See also 68T37, 94D05] 03Hxx] 03B53 Paraconsistent logics 03C64 Model theory of ordered structures; o-minimality 03B55 Intermediate logics 03C65 Models of other mathematical theories 03B60 Other nonclassical logic 03C66 Continuous model theory, model theory of metric 03B62 Combined logics structures 03B65 Logic of natural languages [See also 68T50, 03C68 Other classical first-order model theory 91F20] 03C70 Logic on admissible sets 03B70 Logic in computer science [See also 68-XX] 03C75 Other infinitary logic 03B80 Other applications of logic 03C80 Logic with extra quantifiers and operators [See 03B99 None of the above, but in this section also 03B42, 03B44, 03B45, 03B48] 6 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 03C85 Second- and higher-order model theory 03D78 Computation over the reals, computable analysis {For constructive aspects, see 03F60} 03C90 Nonclassical models (Boolean-valued, sheaf, etc.) 03D80 Applications of computability and recursion theory 03C95 Abstract model theory 03C98 Applications of model theory [See also 03C60] 03D99 None of the above, but in this section 03C99 None of the above, but in this section 03Exx Set theory 03Dxx Computability and recursion the03E02 Partition relations ory 03E04 Ordered sets and their cofinalities; pcf theory 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection 03E05 Other combinatorial set theory with logical questions [See also 68Q45, 68Q70, 03E10 Ordinal and cardinal numbers 68R15] 03D10 Turing machines and related notions [See also 03E15 Descriptive set theory [See also 28A05, 54H05] 68Q04] 03E17 Cardinal characteristics of the continuum 03D15 Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17] 03E20 Other classical set theory (including functions, relations, and set algebra) 03D20 Recursive functions and relations, subrecursive hierarchies 03E25 Axiom of choice and related propositions 03D25 Recursively (computably) enumerable sets and 03E30 Axiomatics of classical set theory and its fragdegrees ments 03D28 Other Turing degree structures 03E35 Consistency and independence results 03D30 Other degrees and reducibilities in computability 03E40 Other aspects of forcing and Boolean-valued and recursion theory models 03D32 Algorithmic randomness and dimension [See also 03E45 Inner models, including constructibility, ordinal 68Q30] definability, and core models 03D35 Undecidability and degrees of sets of sentences 03E47 Other notions of set-theoretic definability 03D40 Word problems, etc. in computability and recursion theory [See also 06B25, 08A50, 20F10, 68R15] 03E50 Continuum hypothesis and Martin’s axiom [See also 03E57] 03D45 Theory of numerations, effectively presented structures [See also 03C57] {For intuitionistic and 03E55 Large cardinals similar approaches, see 03F55} 03E57 Generic absoluteness and forcing axioms [See also 03D50 Recursive equivalence types of sets and struc03E50] tures, isols 03E60 Determinacy principles 03D55 Hierarchies of computability and definability 03D60 Computability and recursion theory on ordinals, 03E65 Other set-theoretic hypotheses and axioms admissible sets, etc. 03E70 Nonclassical and second-order set theories 03D65 Higher-type and set recursion theory 03E72 Theory of fuzzy sets, etc. 03D70 Inductive definability 03E75 Applications of set theory 03D75 Abstract and axiomatic computability and recursion theory 03E99 None of the above, but in this section 7 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 03Fxx Proof theory and constructive 03G30 Categorical logic, topoi [See also 18B25, 18C05, 18C10] mathematics 03F03 Proof theory, general (including proof-theoretic 03G99 None of the above, but in this section semantics) 03F05 Cut-elimination and normal-form theorems 03Hxx Nonstandard models [See also 03C62] 03F07 Structure of proofs 03F10 Functionals in proof theory 03H05 Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 03F15 Recursive ordinals and ordinal notations 03F20 Complexity of proofs 03H10 Other applications of nonstandard models (economics, physics, etc.) 03F25 Relative consistency and interpretations 03F30 First-order arithmetic and fragments 03F35 Second- and higher-order arithmetic and frag- 03H15 Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05] ments [See also 03B30] 03F40 Gödel numberings and issues of incompleteness 03H99 None of the above, but in this section 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25] 05-XX Combinatorics {For finite 03F52 Proof-theoretic aspects of linear logic and other fields, see 11Txx} 03F50 Metamathematics of constructive systems substructural logics [See also 03B47] 05-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics 03F55 Intuitionistic mathematics 03F60 Constructive and recursive analysis [See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30] 05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics 03F65 Other constructive mathematics [See also 03D45] 03F99 None of the above, but in this section 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics 03Gxx Algebraic logic 03G05 Logical aspects of Boolean algebras [See also 05-03 History of combinatorics [Consider also classifica06Exx] tion numbers pertaining to Section 01] 03G10 Logical aspects of lattices and related structures 05-04 Software, source code, etc. for problems pertain[See also 06Bxx] ing to combinatorics 03G12 Quantum logic [See also 06C15, 81P10] 03G15 Cylindric and polyadic algebras; relation alge- 05-06 Proceedings, conferences, collections, etc. bras taining to combinatorics per- 03G20 Logical aspects of Lukasiewicz and Post algebras 05-08 Computational methods for problems pertaining [See also 06D25, 06D30] to combinatorics 03G25 Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35] 05-11 Research data for problems pertaining to combi03G27 Abstract algebraic logic natorics 8 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 05Axx Enumerative combinatorics {For 05Cxx Graph theory {For applications of enumeration in graph theory, see 05C30} graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15} 05A05 Permutations, words, matrices 05C05 Trees 05A10 Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx] 05C07 Vertex degrees [See also 05E30] 05A15 Exact enumeration problems, generating func- 05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.) tions [See also 33Cxx, 33Dxx] 05C10 Planar graphs; geometric and topological aspects of graph theory [See also 57K10, 57M15] 05A16 Asymptotic enumeration 05A17 Combinatorial aspects of partitions of integers 05C12 Distance in graphs [See also 11P81, 11P82, 11P83] 05C15 Coloring of graphs and hypergraphs 05A18 Partitions of sets 05A19 Combinatorial identities, bijective combinatorics 05C17 Perfect graphs 05C20 Directed graphs (digraphs), tournaments 05A20 Combinatorial inequalities 05C21 Flows in graphs 05A30 q-calculus and related topics [See also 33Dxx] 05C22 Signed and weighted graphs 05A40 Umbral calculus 05C25 Graphs and abstract algebra (groups, rings, 05A99 None of the above, but in this section fields, etc.) [See also 20F65] 05C30 Enumeration in graph theory 05Bxx Designs and configurations {For ap05C31 Graph polynomials plications of design theory, see 94C30} 05B05 Combinatorial aspects of block designs [See also 05C35 Extremal problems in graph theory [See also 90C35] 51E05, 62K10] 05C38 Paths and cycles [See also 90B10] 05B07 Triple systems 05B10 Combinatorial aspects of difference sets (number- 05C40 Connectivity theoretic, group-theoretic, etc.) [See also 11B13] 05C42 Density (toughness, etc.) 05B15 Orthogonal arrays, Latin squares, Room squares 05C45 Eulerian and Hamiltonian graphs 05B20 Combinatorial aspects of matrices (incidence, 05C48 Expander graphs Hadamard, etc.) 05C50 Graphs and linear algebra (matrices, eigenvalues, 05B25 Combinatorial aspects of finite geometries [See etc.) also 51D20, 51Exx] 05C51 Graph designs and isomorphic decomposition 05B30 Other designs, configurations [See also 51E30] [See also 05B30] 05B35 Combinatorial aspects of matroids and geometric 05C55 Generalized Ramsey theory [See also 05D10] lattices [See also 52B40, 90C27] 05C57 Games on graphs (graph-theoretic aspects) [See also 91A43, 91A46] 05B40 Combinatorial aspects of packing and covering [See also 11H31, 52C15, 52C17] 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms 05B45 Combinatorial aspects of tessellation and tiling (subgraph embedding, etc.) problems [See also 52C20, 52C22] 05C62 Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also 68R10} 05B50 Polyominoes 05B99 None of the above, but in this section 9 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 05Exx Algebraic combinatorics 05C63 Infinite graphs 05E05 Symmetric functions and generalizations 05C65 Hypergraphs 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05E10 Combinatorial aspects of representation theory [See also 20C30] 05E14 Combinatorial aspects of algebraic geometry [See also 14Nxx] 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, 05E16 Combinatorial aspects of groups and algebras etc.) [See also 22E45, 33C80] 05C72 Fractional graph theory, fuzzy graph theory 05E18 Group actions on combinatorial structures 05C75 Structural characterization of families of graphs 05E30 Association schemes, strongly regular graphs 05E40 Combinatorial aspects of commutative algebra 05C76 Graph operations (line graphs, products, etc.) 05E45 Combinatorial aspects of simplicial complexes 05C78 Graph labelling (graceful graphs, bandwidth, 05E99 None of the above, but in this section etc.) 05C80 Random graphs (graph-theoretic aspects) [See also 60B20] 06-XX Order, lattices, ordered algebraic structures [See also 18B35] 05C81 Random walks on graphs 06-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered struc05C82 Small world graphs, complex networks (graphtures theoretic aspects) [See also 90Bxx, 91D30] 05C83 Graph minors 06-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures 05C85 Graph algorithms (graph-theoretic aspects) [See 06-02 Research exposition (monographs, survey articles) also 68R10, 68W05] pertaining to ordered structures 05C90 Applications of graph theory [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 06-03 History of ordered structures [Consider also classification numbers pertaining to Section 01] 05C92 Chemical graph theory [See also 92E10] 06-04 Software, source code, etc. for problems pertaining to ordered structures 05C99 None of the above, but in this section 06-06 Proceedings, conferences, collections, etc. taining to ordered structures 05Dxx Extremal combinatorics 06-08 Computational methods for problems pertaining to ordered structures 05D05 Extremal set theory 06-11 Research data for problems pertaining to ordered structures 05D10 Ramsey theory [See also 05C55] 05D15 Transversal (matching) theory 06Axx Ordered sets 06A05 Total orders 05D40 Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Null- 06A06 Partial orders, general stellensatz, etc.) 06A07 Combinatorics of partially ordered sets 05D99 None of the above, but in this section 06A11 Algebraic aspects of posets 10 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. per- 06A12 Semilattices [See also 20M10] {For topological 06D22 Frames, locales {For topological questions, see semilattices, see 22A26} 54-XX} 06A15 Galois correspondences, closure operators (in re- 06D25 Post algebras (lattice-theoretic aspects) [See also lation to ordered sets) 03G20] 06A75 Generalizations of ordered sets 06D30 De Morgan algebras, Lukasiewicz algebras (lattice-theoretic aspects) [See also 03G20] 06A99 None of the above, but in this section 06D35 MV-algebras 06Bxx Lattices [See also 03G10] 06D50 Lattices and duality 06B05 Structure theory of lattices 06D72 Fuzzy lattices (soft algebras) and related topics 06B10 Lattice ideals, congruence relations 06D75 Other generalizations of distributive lattices 06B15 Representation theory of lattices 06D99 None of the above, but in this section 06B20 Varieties of lattices 06Exx Boolean algebras (Boolean rings) [See also 03G05] 06B23 Complete lattices, completions 06B25 Free lattices, projective lattices, word problems 06E05 Structure theory of Boolean algebras [See also 03D40, 08A50, 20F10] 06B30 Topological lattices [See also 06F30, 22A26, 06E10 Chain conditions, complete algebras 54F05, 54H12] 06E15 Stone spaces (Boolean spaces) and related structures 06B35 Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55] 06E20 Ring-theoretic properties of Boolean algebras [See also 16E50, 16G30] 06B75 Generalizations of lattices 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45] 06B99 None of the above, but in this section 06Cxx Modular lattices, complemented 06E30 Boolean functions [See also 94D10] lattices 06E75 Generalizations of Boolean algebras 06C05 Modular lattices, Desarguesian lattices 06E99 None of the above, but in this section 06C10 Semimodular lattices, geometric lattices 06C15 Complemented lattices, orthocomplemented lat- 06Fxx Ordered structures tices and posets [See also 03G12, 81P10] 06F05 Ordered semigroups and monoids [See also 20Mxx] 06C20 Complemented modular lattices, continuous geometries 06F07 Quantales 06C99 None of the above, but in this section 06F10 Noether lattices 06Dxx Distributive lattices 06F15 Ordered groups [See also 20F60] 06D05 Structure and representation theory of distribu- 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40] tive lattices 06F25 Ordered rings, algebras, modules {For ordered fields, see 12J15} [See also 13J25, 16W80] 06D10 Complete distributivity 06D15 Pseudocomplemented lattices 06D20 Heyting algebras (lattice-theoretic aspects) [See also 03G25] 06F30 Ordered topological structures (aspects of ordered structures) [See also 06B30, 22A26, 54F05, 54H12] 11 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 06F35 BCK-algebras, BCI-algebras (aspects of ordered 08A68 Heterogeneous algebras structures) [See also 03G25] 08A70 Applications of universal algebra in computer sci06F99 None of the above, but in this section ence 08A72 Fuzzy algebraic structures 08-XX General algebraic systems 08A99 None of the above, but in this section 08-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general algebraic 08Bxx Varieties [See also 03C05] systems 08B05 Equational logic, Mal’tsev conditions 08-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems 08B10 Congruence modularity, congruence distributivity 08-02 Research exposition (monographs, survey articles) 08B15 Lattices of varieties pertaining to general algebraic systems 08-03 History of general algebraic systems [Consider also 08B20 Free algebras classification numbers pertaining to Section 01] 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also 18A30] 08-04 Software, source code, etc. for problems pertaining to general algebraic systems 08B26 Subdirect products and subdirect irreducibility 08-06 Proceedings, conferences, collections, etc. per08B30 Injectives, projectives taining to general algebraic systems 08B99 None of the above, but in this section 08-08 Computational methods for problems pertaining to general algebraic systems 08Cxx Other classes of algebras 08-11 Research data for problems pertaining to general 08C05 Categories of algebras [See also 18C05] algebraic systems 08Axx Algebraic 03C05] structures [See also 08C10 Axiomatic model classes [See also 03Cxx, in particular 03C60] 08C15 Quasivarieties 08A02 Relational systems, laws of composition 08A05 Structure theory of algebraic structures 08C20 Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30] 08A30 Subalgebras, congruence relations 08C99 None of the above, but in this section 08A35 Automorphisms and endomorphisms of algebraic structures 11-XX Number theory 08A40 Operations and polynomials in algebraic struc- 11-00 General reference works (handbooks, dictionaries, tures, primal algebras bibliographies, etc.) pertaining to number theory 08A45 Equational compactness 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 08A50 Word problems (aspects of algebraic structures) [See also 03D40, 06B25, 20F10, 68R15] 11-02 Research exposition (monographs, survey articles) pertaining to number theory 08A55 Partial algebras 08A60 Unary algebras 08A62 Finitary algebras 08A65 Infinitary algebras 11-03 History of number theory [Consider also classification numbers pertaining to Section 01] 11-04 Software, source code, etc. for problems pertaining to number theory 12 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11-06 Proceedings, conferences, collections, etc. taining to number theory per- 11B73 Bell and Stirling numbers 11B75 Other combinatorial number theory 11-11 Research data for problems pertaining to number theory 11B83 Special sequences and polynomials 11Axx Elementary number theory {For 11B85 Automata sequences analogues in number fields, see 11R04} 11B99 None of the above, but in this section 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors 11Cxx Polynomials and matrices 11A07 Congruences; primitive roots; residue systems 11C08 Polynomials in number theory [See also 13F20] 11A15 Power residues, reciprocity 11A25 Arithmetic functions; related numbers; inversion formulas 11A41 Primes 11C20 Matrices, determinants in number theory [See also 15B36] 11C99 None of the above, but in this section 11A51 Factorization; primality 11Dxx Diophantine equations [See also 11A55 Continued fractions {For approximation results, 11Gxx, 14Gxx] see 11J70} [See also 11K50, 30B70, 40A15] 11D04 Linear Diophantine equations 11A63 Radix representation; digital problems {For metric results, see 11K16} 11D07 The Frobenius problem 11A67 Other number representations 11D09 Quadratic and bilinear Diophantine equations 11A99 None of the above, but in this section 11D25 Cubic and quartic Diophantine equations 11Bxx Sequences and sets 11D41 Higher degree equations; Fermat’s equation 11B05 Density, gaps, topology 11D45 Counting solutions of Diophantine equations 11B13 Additive bases, including sumsets [See also 05B10] 11D57 Multiplicative and norm form equations 11B25 Arithmetic progressions [See also 11N13] 11D59 Thue-Mahler equations 11B30 Arithmetic combinatorics; higher degree unifor11D61 Exponential Diophantine equations mity 11B34 Representation functions 11D68 Rational numbers as sums of fractions 11B37 Recurrences {For applications to special func11D72 Diophantine equations in many variables [See tions, see 33-XX} also 11P55] 11B39 Fibonacci and Lucas numbers and polynomials 11D75 Diophantine inequalities [See also 11J25] and generalizations 11B50 Sequences (mod m) 11D79 Congruences in many variables 11B57 Farey sequences; the sequences 1k , 2k , . . . 11D85 Representation problems [See also 11P55] 11B65 Binomial coefficients; factorials; q-identities [See 11D88 p-adic and power series fields also 05A10, 05A30] 11B68 Bernoulli and Euler numbers and polynomials 11D99 None of the above, but in this section 13 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11Exx Forms and linear algebraic groups 11F22 Relationship to Lie algebras and finite simple groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63} 11F23 Relations with algebraic geometry and topology 11E04 Quadratic forms over general fields 11F25 Hecke-Petersson operators, differential operators (one variable) 11E08 Quadratic forms over local rings and fields 11E10 Forms over real fields 11F27 Theta series; Weil representation; theta correspondences 11E12 Quadratic forms over global rings and fields 11F30 Fourier coefficients of automorphic forms 11E16 General binary quadratic forms 11F32 Modular correspondences, etc. 11E20 General ternary and quaternary quadratic forms; 11F33 Congruences for modular and p-adic modular forms [See also 14G20, 22E50] forms of more than two variables 11E25 Sums of squares and representations by other par- 11F37 Forms of half-integer weight; nonholomorphic modular forms ticular quadratic forms 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular 11E41 Class numbers of quadratic and Hermitian forms and automorphic forms; Hilbert modular surfaces [See also 14J20] 11E45 Analytic theory (Epstein zeta functions; relations 11F46 Siegel modular groups; Siegel and Hilbert-Siegel with automorphic forms and functions) modular and automorphic forms 11E57 Classical groups [See also 14Lxx, 20Gxx] 11F50 Jacobi forms 11E70 K-theory of quadratic and Hermitian forms 11F52 Modular forms associated to Drinfel’d modules 11E72 Galois cohomology of linear algebraic groups [See 11F55 Other groups and their modular and automorphic also 20G10] forms (several variables) 11E76 Forms of degree higher than two 11F60 Hecke-Petersson operators, differential operators 11E39 Bilinear and Hermitian forms (several variables) 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] 11F66 Langlands L-functions; one variable Dirichlet series and functional equations 11E88 Quadratic spaces; Clifford algebras [See also 15A63, 15A66] 11F67 Special values of automorphic L-series, periods of automorphic forms, cohomology, modular symbols 11E95 p-adic theory 11F68 Dirichlet series in several complex variables asso11E99 None of the above, but in this section ciated to automorphic forms; Weyl group multiple Dirichlet series 11Fxx Discontinuous groups and automor11F70 Representation-theoretic methods; automorphic phic forms [See also 11R39, 11S37, 14Gxx, representations over local and global fields 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45} 11F72 Spectral theory; trace formulas (e.g., that of Selberg) 11F03 Modular and automorphic functions 11F75 Cohomology of arithmetic groups 11F06 Structure of modular groups and generalizations; 11F77 Automorphic forms and their relations with perarithmetic groups [See also 20H05, 20H10, 22E40] fectoid spaces [See also 14G45] 11F11 Holomorphic modular forms of integral weight 11F80 Galois representations 11F12 Automorphic forms, one variable 11F85 p-adic theory, local fields [See also 14G20, 22E50] 11F20 Dedekind eta function, Dedekind sums 11F99 None of the above, but in this section 14 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11Gxx Arithmetic algebraic geometry 11H46 Products of linear forms (Diophantine geometry) [See also 11Dxx, 11H50 Minima of forms 14Gxx, 14Kxx] 11G05 Elliptic curves over global fields [See also 14H52] 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 11G07 Elliptic curves over local fields [See also 14G20, 11H56 Automorphism groups of lattices 14H52] 11H60 Mean value and transfer theorems 11G09 Drinfel’d modules; higher-dimensional motives, etc. [See also 14L05] 11H71 Relations with coding theory 11G10 Abelian varieties of dimension > 1 [See also 11H99 None of the above, but in this section 14Kxx] 11G15 Complex multiplication and moduli of abelian 11Jxx Diophantine approximation, tranvarieties [See also 14K22] scendental number theory [See also 11K60] 11G16 Elliptic and modular units [See also 11R27] 11J04 Homogeneous approximation to one number 11G18 Arithmetic aspects of modular and Shimura va- 11J06 Markov and Lagrange spectra and generalizations rieties [See also 14G35] 11J13 Simultaneous homogeneous approximation, linear forms 11G20 Curves over finite and local fields [See also 14H25] 11J17 Approximation by numbers from a fixed field 11G25 Varieties over finite and local fields [See also 11J20 Inhomogeneous linear forms 14G15, 14G20] 11G30 Curves of arbitrary genus or genus 6= 1 over 11J25 Diophantine inequalities [See also 11D75] global fields [See also 14H25] 11J54 Small fractional parts of polynomials and generalizations 11G32 Arithmetic aspects of dessins d’enfants, Belyı̆ theory 11G35 Varieties over global fields [See also 14G25] 11J61 Approximation in non-Archimedean valuations 11J68 Approximation to algebraic numbers 11G40 L-functions of varieties over global fields; Birch- 11J70 Continued fractions and generalizations [See also Swinnerton-Dyer conjecture [See also 14G10] 11A55, 11K50] 11G42 Arithmetic mirror symmetry [See also 14J33] 11J71 Distribution modulo one [See also 11K06] 11G45 Geometric class field theory [See also 11R37, 14C35, 19F05] 11J72 Irrationality; linear independence over a field 11G50 Heights [See also 14G40, 37P30] 11G55 Polylogarithms and relations with K-theory 11G99 None of the above, but in this section 11J81 Transcendence (general theory) 11J82 Measures of irrationality and of transcendence 11J83 Metric theory 11J85 Algebraic independence; Gel’fond’s method 11Hxx Geometry of numbers {For appli- 11J86 Linear forms in logarithms; Baker’s method cations in coding theory, see 94B75} 11J87 Schmidt Subspace Theorem and applications 11H06 Lattices and convex bodies (number-theoretic as11J89 Transcendence theory of elliptic and abelian funcpects) [See also 11P21, 52C05, 52C07] tions 11H16 Nonconvex bodies 11J91 Transcendence theory of other special functions 11H31 Lattice packing and covering (number-theoretic 11J93 Transcendence theory of Drinfel’d and t-modules aspects) [See also 05B40, 52C15, 52C17] 15 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11J95 Results involving abelian varieties 11J97 Number-theoretic analogues of methods Nevanlinna theory (work of Vojta et al.) 11L20 Sums over primes in 11L26 Sums over arbitrary intervals 11L40 Estimates on character sums 11J99 None of the above, but in this section 11L99 None of the above, but in this section 11Kxx Probabilistic theory: distribution 11Mxx Zeta and L-functions: analytic themodulo 1; metric theory of algorithms ory 11K06 General theory of distribution modulo 1 [See also 11M06 ζ(s) and L(s, χ) 11J71] 11M20 Real zeros of L(s, χ); results on L(1, χ) 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and also 11A63] other hypotheses 11K31 Special sequences 11M32 Multiple Dirichlet series and zeta functions and multizeta values 11K36 Well-distributed sequences and other variations 11M35 Hurwitz and Lerch zeta functions 11K38 Irregularities of distribution, discrepancy [See also 11Nxx] 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet se11K41 Continuous, p-adic and abstract analogues ries, Eisenstein series, etc. (explicit formulas) 11K45 Pseudo-random numbers; Monte Carlo methods 11M38 Zeta and L-functions in characteristic p [See also 65C05, 65C10] 11M41 Other Dirichlet series and zeta functions {For 11K50 Metric theory of continued fractions [See also local and global ground fields, see 11R42, 11R52, 11A55, 11J70] 11S40, 11S45; for algebro-geometric methods, see 14G10} [See also 11E45, 11F66, 11F70, 11F72] 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11M45 Tauberian theorems [See also 40E05] 11N99, 28Dxx] 11M50 Relations with random matrices 11K60 Diophantine approximation in probabilistic num11M55 Relations with noncommutative geometry ber theory [See also 11Jxx] 11K65 Arithmetic functions in probabilistic number 11M99 None of the above, but in this section theory [See also 11Nxx] 11Nxx Multiplicative number theory 11K70 Harmonic analysis and almost periodicity in probabilistic number theory 11K99 None of the above, but in this section 11N05 Distribution of primes 11N13 Primes in congruence classes 11Lxx Exponential sums and character 11N25 Distribution of integers with specified multiplicasums {For finite fields, see 11Txx} tive constraints 11L03 Trigonometric and exponential sums, general 11N30 Turán theory [See also 30Bxx] 11L05 Gauss and Kloosterman sums; generalizations 11N32 Primes represented by polynomials; other multiplicative structures of polynomial values 11L07 Estimates on exponential sums 11N35 Sieves 11L10 Jacobsthal and Brewer sums; other complete character sums 11N36 Applications of sieve methods 11L15 Weyl sums 11N37 Asymptotic results on arithmetic functions 16 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11N45 Asymptotic results on counting functions for al- 11R18 Cyclotomic extensions gebraic and topological structures 11R20 Other abelian and metabelian extensions 11N56 Rate of growth of arithmetic functions 11R21 Other number fields 11N60 Distribution functions associated with additive and positive multiplicative functions 11R23 Iwasawa theory 11N64 Other results on the distribution of values or the 11R27 Units and factorization characterization of arithmetic functions 11N69 Distribution of integers in special residue classes 11R29 Class numbers, class groups, discriminants 11N75 Applications of automorphic functions and forms 11R32 Galois theory to multiplicative problems [See also 11Fxx] 11R33 Integral representations related to algebraic 11N80 Generalized primes and integers numbers; Galois module structure of rings of integers [See also 20C10] 11N99 None of the above, but in this section 11R34 Galois cohomology [See also 12Gxx, 19A31] 11Pxx Additive number theory; partitions 11P05 Waring’s problem and variants 11P21 Lattice points in specified regions 11R37 Class field theory 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55] 11P32 Goldbach-type theorems; other additive ques11R42 Zeta functions and L-functions of number fields tions involving primes [See also 11M41, 19F27] 11P55 Applications of the Hardy-Littlewood method [See also 11D85] 11R44 Distribution of prime ideals [See also 11N05] 11P70 Inverse problems of additive number theory, in- 11R45 Density theorems cluding sumsets 11P81 Elementary theory of partitions [See also 05A17] 11R47 Other analytic theory [See also 11Nxx] 11P82 Analytic theory of partitions 11R52 Quaternion and other division algebras: arithmetic, zeta functions 11P83 Partitions; congruences and congruential restrictions 11R54 Other algebras and orders, and their zeta and L-functions [See also 11S45, 16Hxx, 16Kxx] 11P84 Partition identities; identities of RogersRamanujan type 11R56 Adèle rings and groups 11P99 None of the above, but in this section 11R58 Arithmetic theory of algebraic function fields [See also 14-XX] 11Rxx Algebraic number theory: global fields {For complex multiplication, see 11R59 Zeta functions and L-functions of function fields 11G15} 11R04 Algebraic numbers; rings of algebraic integers 11R60 Cyclotomic function Bernoulli objects, etc.) fields (class groups, 11R06 PV-numbers and generalizations; other special 11R65 Class groups and Picard groups of orders algebraic numbers; Mahler measure 11R70 K-theory of global fields [See also 19Fxx] 11R09 Polynomials (irreducibility, etc.) 11R11 Quadratic extensions 11R80 Totally real fields [See also 12J15] 11R16 Cubic and quartic extensions 11R99 None of the above, but in this section 17 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11Sxx Algebraic number theory: local and 11Uxx Connections of number theory and p-adic fields logic 11S05 Polynomials 11U05 Decidability (number-theoretic aspects) [See also 03B25] 11S15 Ramification and extension theory 11S20 Galois theory 11U07 Ultraproducts (number-theoretic aspects) [See also 03C20] 11S23 Integral representations 11U09 Model theory (number-theoretic aspects) [See also 03Cxx] 11S25 Galois cohomology [See also 12Gxx, 16H05] 11S31 Class field theory; p-adic formal groups [See also 14L05] 11U10 Nonstandard arithmetic (number-theoretic aspects) [See also 03H15] 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50] 11U99 None of the above, but in this section 11S40 Zeta functions and L-functions [See also 11M41, 19F27] 11S45 Algebras and orders, and their zeta functions [See 11Yxx Computational number theory {For software etc., see 11-04} also 11R52, 11R54, 16Hxx, 16Kxx] 11Y05 Factorization 11S70 K-theory of local fields [See also 19Fxx] 11S80 Other analytic theory (analogues of beta and 11Y11 Primality gamma functions, p-adic integration, etc.) 11S82 Non-Archimedean dynamical systems [See mainly 11Y16 Number-theoretic algorithms; complexity [See also 68Q25] 37Pxx] 11S85 Other nonanalytic theory 11Y35 Analytic computations 11S90 Prehomogeneous vector spaces 11Y40 Algebraic number theory computations 11S99 None of the above, but in this section 11Y50 Computer solution of Diophantine equations 11Txx Finite fields and commutative rings (number-theoretic aspects) 11Y55 Calculation of integer sequences 11T06 Polynomials over finite fields 11Y60 Evaluation of number-theoretic constants 11T22 Cyclotomy 11Y65 Continued fraction theoretic aspects) 11T23 Exponential sums calculations (number- 11T24 Other character sums and Gauss sums 11T30 Structure theory for finite fields and commutative rings (number-theoretic aspects) 11Y70 Values of arithmetic functions; tables 11Y99 None of the above, but in this section 11T55 Arithmetic theory of polynomial rings over finite fields 11Zxx Miscellaneous applications of number theory 11T60 Finite upper half-planes 11T71 Algebraic coding theory; cryptography (number11Z05 Miscellaneous applications of number theory theoretic aspects) 11T99 None of the above, but in this section 11Z99 None of the above, but in this section 18 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 12-XX Field theory and polynomi- 12Fxx Field extensions als 12F05 Algebraic field extensions 12-00 General reference works (handbooks, dictionaries, 12F10 Separable extensions, Galois theory bibliographies, etc.) pertaining to field theory 12F12 Inverse Galois theory 12-01 Introductory exposition (textbooks, tutorial pa- 12F15 Inseparable field extensions pers, etc.) pertaining to field theory 12F20 Transcendental field extensions 12-02 Research exposition (monographs, survey articles) 12F99 None of the above, but in this section pertaining to field theory 12-03 History of field theory [Consider also classification 12Gxx Homological methods (field theory) numbers pertaining to Section 01] 12G05 Galois cohomology [See also 14F22, 16Hxx, 16K50] 12-04 Software, source code, etc. for problems pertaining to field theory 12-06 Proceedings, conferences, collections, etc. taining to field theory 12G10 Cohomological dimension of fields per- 12G99 None of the above, but in this section 12Hxx Differential and difference algebra 12-08 Computational methods for problems pertaining to field theory 12H05 Differential algebra [See also 13Nxx] 12-11 Research data for problems pertaining to field the- 12H10 Difference algebra [See also 39Axx] ory 12H20 Abstract differential equations [See also 34Mxx] 12Dxx Real and complex fields 12H25 p-adic differential equations [See also 11S80, 14G20] 12D05 Polynomials in real and complex fields: factor12H99 None of the above, but in this section ization 12D10 Polynomials in real and complex fields: location 12Jxx Topological fields of zeros (algebraic theorems) {For the analytic the12J05 Normed fields ory, see 26C10, 30C15} 12J10 Valued fields 12D15 Fields related with sums of squares (formally real 12J12 Formally p-adic fields fields, Pythagorean fields, etc.) [See also 11Exx] 12D99 None of the above, but in this section 12J15 Ordered fields 12J17 Topological semifields 12Exx General field theory 12J20 General valuation theory for fields [See also 13A18] 12E05 Polynomials in general fields (irreducibility, etc.) 12J25 Non-Archimedean valued fields [See also 30G06, 12E10 Special polynomials in general fields 32P05, 46S10, 47S10] 12E12 Equations in general fields 12J27 Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10] 12E15 Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx] 12J99 None of the above, but in this section 12E20 Finite fields (field-theoretic aspects) 12Kxx Generalizations of fields 12E25 Hilbertian fields; Hilbert’s irreducibility theorem 12K05 Near-fields [See also 16Y30] 12E30 Field arithmetic 12K10 Semifields [See also 16Y60] 12E99 None of the above, but in this section 12K99 None of the above, but in this section 19 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 12Lxx Connections between field theory 13A70 General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal and logic graphs, etc.) [See also 05C25, 05E40] 12L05 Decidability and field theory [See also 03B25] 13A99 None of the above, but in this section 12L10 Ultraproducts and field theory [See also 03C20] 13Bxx Commutative ring extensions and related topics 12L12 Model theory of fields [See also 03C60] 12L15 Nonstandard arithmetic and field theory [See also 03H15] 13B02 Extension theory of commutative rings 12L99 None of the above, but in this section 13B05 Galois theory and commutative ring extensions 13B10 Morphisms of commutative rings 13-XX Commutative algebra 13B21 Integral dependence in commutative rings; going up, going down 13-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative al- 13B22 Integral closure of commutative rings and idegebra als [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 13-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra 13B25 Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] 13-02 Research exposition (monographs, survey articles) pertaining to commutative algebra 13B30 Rings of fractions and localization for commutative rings [See also 16S85] 13-03 History of commutative algebra [Consider also classification numbers pertaining to Section 01] 13B35 Completion of commutative rings [See also 13J10] 13-04 Software, source code, etc. for problems pertain- 13B40 Étale and flat extensions; Henselization; Artin ing to commutative algebra approximation [See also 13J15, 14B12, 14B25] 13-06 Proceedings, conferences, collections, etc. taining to commutative algebra per- 13B99 None of the above, but in this section 13-11 Research data for problems pertaining to commu- 13Cxx Theory of modules and ideals in tative algebra commutative rings 13Axx General commutative ring theory 13C05 Structure, classification theorems for modules and ideals in commutative rings 13A02 Graded rings [See also 16W50] 13C10 Projective and free modules and ideals in commutative rings [See also 19A13] 13A05 Divisibility and factorizations in commutative rings [See also 13F15] 13C11 Injective and flat modules and ideals in commutative rings 13A15 Ideals and multiplicative ideal theory in commutative rings 13C12 Torsion modules and ideals in commutative rings 13A18 Valuations and their generalizations for commu- 13C13 Other special types of modules and ideals in comtative rings [See also 12J20] mutative rings 13A30 Associated graded rings of ideals (Rees ring, form 13C14 Cohen-Macaulay modules [See also 13H10] ring), analytic spread and related topics 13C15 Dimension theory, depth, related commutative 13A35 Characteristic p methods (Frobenius endomorrings (catenary, etc.) phism) and reduction to characteristic p; tight closure [See also 13B22] 13C20 Class groups [See also 11R29] 13A50 Actions of groups on commutative rings; invari- 13C40 Linkage, complete intersections and determinanant theory [See also 14L24] tal ideals [See also 14M06, 14M10, 14M12] 20 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 13Fxx Arithmetic rings and other special commutative rings 13C70 Theory of modules and ideals in commutative 13C60 Module categories and commutative rings rings described by combinatorial properties [See 13F05 Dedekind, Prüfer, Krull and Mori rings and their also 05C25, 05E40] generalizations 13C99 None of the above, but in this section 13F07 Euclidean rings and generalizations 13Dxx Homological methods in commu- 13F10 Principal ideal rings tative ring theory {For noncommutative 13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See rings, see 16Exx; for general categories, also 13A05, 14M05] see 18Gxx} 13D02 Syzygies, resolutions, complexes and commuta- 13F20 Polynomial rings and ideals; rings of integertive rings valued polynomials [See also 11C08, 13B25] 13D03 (Co)homology of commutative rings and algebras 13F25 Formal power series rings [See also 13J05] (e.g., Hochschild, André-Quillen, cyclic, dihedral, 13F30 Valuation rings [See also 13A18] etc.) 13F35 Witt vectors and related rings 13D05 Homological dimension and commutative rings 13D07 Homological functors on modules of commutative 13F40 Excellent rings rings (Tor, Ext, etc.) 13F45 Seminormal rings 13D09 Derived categories and commutative rings 13F50 Rings with straightening laws, Hodge algebras 13D10 Deformations and infinitesimal methods in commutative ring theory [See also 14B10, 14B12, 13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes 14D15, 32Gxx] [See also 55U10] 13D15 Grothendieck groups, K-theory and commutative rings [See also 14C35, 18F30, 19Axx, 19D50] 13F60 Cluster algebras 13D22 Homological conjectures (intersection theorems) 13F65 Commutative rings defined by binomial ideals, in commutative ring theory toric rings, etc. [See also 14M25] 13D30 Torsion theory for commutative rings [See also 13F70 Other commutative rings defined by combinato13C12, 18E40] rial properties 13D40 Hilbert-Samuel and Hilbert-Kunz functions; 13F99 None of the above, but in this section Poincaré series 13D45 Local cohomology and commutative rings [See 13Gxx Integral domains also 14B15] 13G05 Integral domains 13D99 None of the above, but in this section 13G99 None of the above, but in this section 13Exx Chain conditions, finiteness condi13Hxx Local rings and semilocal rings tions in commutative ring theory 13H05 Regular local rings 13E05 Commutative Noetherian rings and modules 13E10 Commutative Artinian rings and modules, finite- 13H10 Special types (Cohen-Macaulay, Buchsbaum, etc.) [See also 14M05] dimensional algebras Gorenstein, 13E15 Commutative rings and modules of finite genera- 13H15 Multiplicity theory and related topics [See also 14C17] tion or presentation; number of generators 13E99 None of the above, but in this section 13H99 None of the above, but in this section 21 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 13Jxx Topological rings and modules [See 13P15 Solving polynomial systems; resultants also 16W60, 16W80] 13P20 Computational homological algebra [See also 13Dxx] 13J05 Power series rings [See also 13F25] 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 13J07 Analytical algebras and rings [See also 32B05] 13J10 Complete rings, completion [See also 13B35] 13P99 None of the above, but in this section 13J15 Henselian rings [See also 13B40] 13J20 Global topological rings 14-XX Algebraic geometry 13J25 Ordered rings [See also 06F25] 14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry 13J30 Real algebra [See also 12D15, 14Pxx] 13J99 None of the above, but in this section 14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry 13Lxx Applications of logic to commuta14-02 Research exposition (monographs, survey articles) tive algebra [See also 03Cxx, 03Hxx] pertaining to algebraic geometry 13L05 Applications of logic to commutative algebra [See 14-03 History of algebraic geometry [Consider also clasalso 03Cxx, 03Hxx] sification numbers pertaining to Section 01] 13L99 None of the above, but in this section 14-04 Software, source code, etc. for problems pertaining to algebraic geometry 13Mxx Finite commutative rings {For 14-06 Proceedings, conferences, collections, etc. pernumber-theoretic aspects, see 11Txx} taining to algebraic geometry 13M05 Structure of finite commutative rings 14-11 Research data for problems pertaining to algebraic geometry 13M10 Polynomials and finite commutative rings 13M99 None of the above, but in this section 14Axx Foundations of algebraic geometry 13Nxx Differential 12H05, 14F10] algebra [See also 14A05 Relevant commutative algebra [See also 13-XX] 14A10 Varieties and morphisms 13N05 Modules of differentials 14A15 Schemes and morphisms 13N10 Commutative rings of differential operators and 14A20 Generalizations (algebraic spaces, stacks) their modules [See also 16S32, 32C38] 14A21 Logarithmic algebraic geometry, log schemes 13N15 Derivations and commutative rings 14A22 Noncommutative algebraic geometry [See also 13N99 None of the above, but in this section 16S38] 13Pxx Computational aspects and appli- 14A23 Geometry over the field with one element cations of commutative rings [See also 14A25 Elementary questions in algebraic geometry 14Qxx, 68W30] {For software etc., see 1314A30 Fundamental constructions in algebraic geome04} 13P05 Polynomials, factorization in commutative rings [See also 12-08] try involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) {For categorical aspects, see 18Fxx, 18Gxx} 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 14A99 None of the above, but in this section 22 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 14Bxx Local theory in algebraic geometry 14Dxx Families, fibrations in algebraic geometry 14B05 Singularities in algebraic geometry [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 14B07 Deformations of singularities [See also 14D15, 14D06 Fibrations, degenerations in algebraic geometry 32S30] 14B10 Infinitesimal methods in algebraic geometry [See also 13D10] 14B12 Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10] 14D07 Variation of Hodge structures (algebro-geometric aspects) [See also 32G20] 14D10 Arithmetic ground fields (finite, local, global) and families or fibrations 14D15 Formal methods and deformations in algebraic geometry [See also 13D10, 14B07, 32Gxx] 14B15 Local cohomology and algebraic geometry [See also 13D45, 32C36] 14D20 Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14B20 Formal neighborhoods in algebraic geometry 14B25 Local structure of morphisms in algebraic geometry: étale, flat, etc. [See also 13B40] 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx] 14B99 None of the above, but in this section 14D22 Fine and coarse moduli spaces 14D23 Stacks and moduli problems 14Cxx Cycles and subschemes 14D24 Geometric Langlands program geometric aspects) [See also 22E57] 14C05 Parametrization (Chow and Hilbert schemes) (algebro- 14D99 None of the above, but in this section 14C15 (Equivariant) Chow groups and rings; motives 14C17 Intersection theory, characteristic classes, inter- 14Exx Birational geometry section multiplicities in algebraic geometry [See also 14E05 Rational and birational maps 13H15] 14E07 Birational automorphisms, Cremona group and generalizations 14C20 Divisors, linear systems, invertible sheaves 14C21 Pencils, nets, webs in algebraic geometry [See 14E08 Rationality questions in algebraic geometry [See also 14M20] also 53A60] 14E15 Global theory and resolution of singularities 14C22 Picard groups (algebro-geometric aspects) [See also 14B05, 32S20, 32S45] 14C25 Algebraic cycles 14E16 McKay correspondence 14C30 Transcendental methods, Hodge theory (algebrogeometric aspects) [See also 14D07, 32G20, 32J25, 14E18 Arcs and motivic integration 32S35], Hodge conjecture 14E20 Coverings in algebraic geometry [See also 14H30] 14E22 Ramification problems in algebraic geometry [See also 11S15] 14C34 Torelli problem [See also 32G20] 14C35 Applications of methods of algebraic K-theory in 14E25 Embeddings in algebraic geometry algebraic geometry [See also 19Exx] 14C40 Riemann-Roch theorems [See also 19E20, 19L10] 14E30 Minimal model program (Mori theory, extremal rays) 14C99 None of the above, but in this section 14E99 None of the above, but in this section 23 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 14Fxx (Co)homology theory in algebraic 14G17 Positive characteristic ground fields in algebraic geometry geometry [See also 13Dxx] 14G20 Local ground fields in algebraic geometry 14F06 Sheaves in algebraic geometry [See also 14F08, 14H60, 14J60, 18F20, 32Lxx, 46M20] 14G22 Rigid analytic geometry 14F08 Derived categories of sheaves, dg categories, and 14G25 Global ground fields in algebraic geometry related constructions in algebraic geometry [See also 14G27 Other nonalgebraically closed ground fields in al14A30, 14F06, 18Gxx] gebraic geometry 14F10 Differentials and other special sheaves; Dmodules; Bernstein-Sato ideals and polynomials 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois the[See also 13Nxx, 32C38] ory) 14F17 Vanishing theorems in algebraic geometry [See 14G35 Modular and Shimura varieties [See also 11F41, also 32L20] 11F46, 11G18] 14F18 Multiplier ideals 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30] 14F20 Étale and other Grothendieck topologies and (co)homologies 14G45 Perfectoid spaces and mixed characteristic 14F22 Brauer groups of schemes [See also 12G05, 16K50] 14G50 Applications to coding theory and cryptography of arithmetic geometry [See also 94A60, 94B27, 94B40] 14F25 Classical real and complex (co)homology in algebraic geometry 14G99 None of the above, but in this section 14F30 p-adic cohomology, crystalline cohomology 14F35 Homotopy theory and fundamental groups in al- 14Hxx Curves in algebraic geometry gebraic geometry [See also 14H30] 14H05 Algebraic functions and function fields in alge14F40 de Rham cohomology and algebraic geometry braic geometry [See also 11R58] [See also 14C30, 32C35, 32L10] 14H10 Families, moduli of curves (algebraic) 14F42 Motivic cohomology; motivic homotopy theory 14H15 Families, moduli of curves (analytic) [See also [See also 19E15] 30F10, 32G15] 14F43 Other algebro-geometric (co)homologies (e.g., 14H20 Singularities of curves, local rings [See also intersection, equivariant, Lawson, Deligne 13Hxx, 14B05] (co)homologies) 14H25 Arithmetic ground fields for curves [See also 14F45 Topological properties in algebraic geometry 11Dxx, 11G05, 14Gxx] 14F99 None of the above, but in this section 14H30 Coverings of curves, fundamental group [See also 14E20, 14F35] 14Gxx Arithmetic problems in algebraic 14H37 Automorphisms of curves geometry; Diophantine geometry [See also 14H40 Jacobians, Prym varieties [See also 32G20] 11Dxx, 11Gxx] 14H42 Theta functions and curves; Schottky problem [See also 14K25, 32G20] 14G05 Rational points 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 14H45 Special algebraic curves and curves of low genus [See also 11G40] 14H50 Plane and space curves 14G12 Hasse principle, weak and strong approximation, 14H51 Special divisors on curves (gonality, Brauer-Manin obstruction [See also 14F22] Noether theory) 14G15 Finite ground fields in algebraic geometry 14H52 Elliptic curves [See also 11G05, 11G07, 14Kxx] 24 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. Brill- 14H55 Riemann surfaces; Weierstrass points; gap se- 14J60 Vector bundles on surfaces and higherquences [See also 30Fxx] dimensional varieties, and their moduli [See also 14D20, 14F06, 14H60, 32Lxx] 14H57 Dessins d’enfants theory {For arithmetic aspects, see 11G32} 14J70 Hypersurfaces and algebraic geometry 14H60 Vector bundles on curves and their moduli [See 14J80 Topology of surfaces (Donaldson polynomials, also 14D20, 14F06, 14J60] Seiberg-Witten invariants) 14H70 Relationships between algebraic curves and inte- 14J81 Relationships with physics grable systems 14J99 None of the above, but in this section 14H81 Relationships between algebraic curves and physics 14Kxx Abelian varieties and schemes 14H99 None of the above, but in this section 14K02 Isogeny 14Jxx Surfaces and higher-dimensional va- 14K05 Algebraic theory of abelian varieties rieties {For analytic theory, see 32Jxx} 14K10 Algebraic moduli of abelian varieties, classification [See also 11G15] 14J10 Families, moduli, classification: algebraic theory 14J15 Moduli, classification: analytic theory; relations 14K12 Subvarieties of abelian varieties with modular forms [See also 32G13] 14K15 Arithmetic ground fields for abelian varieties [See 14J17 Singularities of surfaces or higher-dimensional vaalso 11Dxx, 11Fxx, 11G10, 14Gxx] rieties [See also 14B05, 14E15, 32S05, 32S25] 14K20 Analytic theory of abelian varieties; abelian in14J20 Arithmetic ground fields for surfaces or highertegrals and differentials dimensional varieties [See also 11Dxx, 11G25, 11G35, 14Gxx] 14K22 Complex multiplication and abelian varieties [See also 11G15] 14J25 Special surfaces {For Hilbert modular surfaces, see 14G35} 14K25 Theta functions and abelian varieties [See also 14H42] 14J26 Rational and ruled surfaces 14J27 Elliptic surfaces, elliptic or Calabi-Yau fibrations 14K30 Picard schemes, higher Jacobians [See also 14H40, 32G20] 14J28 K3 surfaces and Enriques surfaces 14K99 None of the above, but in this section 14J29 Surfaces of general type 14Lxx Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, 14J32 Calabi-Yau manifolds (algebro-geometric assee 17B45} pects) [See also 32Q25] 14J30 3-folds 14L05 Formal groups, p-divisible groups [See also 55N22] 14J33 Mirror symmetry (algebro-geometric aspects) [See also 11G42, 53D37] 14J35 4-folds 14L10 Group varieties 14J40 n-folds (n > 4) 14L15 Group schemes 14J42 Holomorphic symplectic varieties, hyper-Kähler 14L17 Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18C40] varieties 14L24 Geometric invariant theory [See also 13A50] 14J45 Fano varieties 14J50 Automorphisms of dimensional varieties surfaces and higher- 14L30 Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 25 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 14L35 Classical groups (algebro-geometric aspects) [See 14N25 Varieties of low degree also 20Gxx, 51N30] 14N30 Adjunction problems 14L40 Other algebraic groups (geometric aspects) 14N35 Gromov-Witten invariants, quantum coho14L99 None of the above, but in this section mology, Gopakumar-Vafa invariants, DonaldsonThomas invariants (algebro-geometric aspects) [See 14Mxx Special varieties also 53D45] 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 14N99 None of the above, but in this section 13F45, 13H10] 14M06 Linkage [See also 13C40] 14Pxx Real algebraic and real-analytic geometry 14M07 Low codimension problems in algebraic geome14P05 Real algebraic sets [See also 12D15, 13J30] try 14M10 Complete intersections [See also 13C40] 14P10 Semialgebraic sets and related spaces 14M12 Determinantal varieties [See also 13C40] 14P15 Real-analytic and semi-analytic sets [See also 32B20, 32C05] 14M15 Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14P20 Nash functions and manifolds [See also 32C07, 14M17 Homogeneous spaces and generalizations [See 58A07] also 32M10, 53C30, 57T15] 14P25 Topology of real algebraic varieties 14M20 Rational and unirational varieties [See also 14E08] 14P99 None of the above, but in this section 14M22 Rationally connected varieties 14M25 Toric varieties, Newton polyhedra, Okounkov 14Qxx Computational aspects in algebraic geometry {For software etc., see 14-04} bodies [See also 52B20] [See also 12-08, 13Pxx, 68W30] 14M27 Compactifications; symmetric and spherical varieties 14Q05 Computational aspects of algebraic curves [See also 14Hxx] 14M30 Supervarieties [See also 32C11, 58A50] 14M35 Character varieties 14Q10 Computational aspects of algebraic surfaces [See also 14Jxx] 14M99 None of the above, but in this section 14Q15 Computational aspects of higher-dimensional varieties [See also 14Jxx, 14Mxx] 14Nxx Projective and enumerative alge- braic geometry [See also 51-XX] 14Q20 Effectivity, complexity and computational aspects of algebraic geometry 14N05 Projective techniques in algebraic geometry [See also 51N35] 14Q25 Computational algebraic geometry over arith14N07 Secant varieties, tensor rank, varieties of sums of metic ground fields [See also 14Gxx, 14H25, 14Kxx] powers 14Q30 Computational real algebraic geometry [See also 14N10 Enumerative problems (combinatorial problems) 14Pxx] in algebraic geometry 14N15 Classical problems, Schubert calculus 14Q65 Geometric aspects of numerical algebraic geometry [See also 65H14] 14N20 Configurations and arrangements of linear subspaces 14Q99 None of the above, but in this section 26 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 14Rxx Affine geometry 15Axx Basic linear algebra 14R05 Classification of affine varieties 15A03 Vector spaces, linear dependence, rank, lineability 14R10 Affine spaces (automorphisms, embeddings, ex15A04 Linear transformations, semilinear transformaotic structures, cancellation problem) tions 14R15 Jacobian problem [See also 13F20] 15A06 Linear equations (linear algebraic aspects) 14R20 Group actions on affine varieties [See also 13A50, 14L30] 15A09 Theory of matrix inversion and generalized inverses 14R25 Affine fibrations [See also 14D06] 15A10 Applications of generalized inverses 14R99 None of the above, but in this section 15A12 Conditioning of matrices [See also 65F35] 15A15 Determinants, permanents, traces, other special matrix functions [See also 19B10, 19B14] 14Txx Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] 15A16 Matrix exponential and similar functions of matrices 14T10 Foundations of tropical geometry and relations with algebra {For algebraic aspects, see 15A80} 15A18 Eigenvalues, singular values, and eigenvectors 14T15 Combinatorial aspects of tropical varieties 15A20 Diagonalization, Jordan forms 14T20 Geometric aspects of tropical varieties 15A21 Canonical forms, reductions, classification 14T25 Arithmetic aspects of tropical varieties 15A22 Matrix pencils [See also 47A56] 14T90 Applications of tropical geometry 15A23 Factorization of matrices 14T99 None of the above, but in this section 15A24 Matrix equations and identities 15A27 Commutativity of matrices 15-XX Linear and multilinear alge- 15A29 Inverse problems in linear algebra bra; matrix theory 15A30 Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx] 15-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to linear algebra 15A39 Linear inequalities of matrices 15-01 Introductory exposition (textbooks, tutorial pa- 15A42 Inequalities involving eigenvalues and eigenvecpers, etc.) pertaining to linear algebra tors 15-02 Research exposition (monographs, survey articles) 15A45 Miscellaneous inequalities involving matrices pertaining to linear algebra 15A54 Matrices over function rings in one or more variables 15-03 History of linear algebra [Consider also classification numbers pertaining to Section 01] 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 15-04 Software, source code, etc. for problems pertain65F35, 65J05] ing to linear algebra 15-06 Proceedings, conferences, collections, etc. taining to linear algebra 15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx] per- 15A66 Clifford algebras, spinors 15-11 Research data for problems pertaining to linear algebra 15A67 Applications of Clifford algebras to physics, etc. 27 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 15A69 Multilinear algebra, tensor calculus 16-02 Research exposition (monographs, survey articles) pertaining to associative rings and algebras 15A72 Vector and tensor algebra, theory of invariants 16-03 History of associative rings and algebras [Consider [See also 13A50, 14L24] also classification numbers pertaining to Section 01] 15A75 Exterior algebra, Grassmann algebras 16-04 Software, source code, etc. for problems pertain15A78 Other algebras built from modules ing to associative rings and algebras 15A80 Max-plus and related algebras 15A83 Matrix completion problems 15A86 Linear preserver problems 16-06 Proceedings, conferences, collections, etc. taining to associative rings and algebras per- 16-11 Research data for problems pertaining to associative rings and algebras 15A99 None of the above, but in this section 16Bxx General and miscellaneous 15Bxx Special matrices 15B05 Toeplitz, Cauchy, and related matrices 15B10 Orthogonal matrices 16B50 Category-theoretic methods and results in associative algebras (except as in 16D90) [See also 18XX] 15B15 Fuzzy matrices 16B70 Applications of logic in associative algebras [See also 03Cxx] 15B30 Matrix Lie algebras 16B99 None of the above, but in this section 15B33 Matrices over special rings (quaternions, finite 16Dxx Modules, bimodules and ideals in fields, etc.) associative algebras 15B34 Boolean and Hadamard matrices 15B35 Sign pattern matrices 15B36 Matrices of integers [See also 11C20] 16D10 General module theory in associative algebras 16D20 Bimodules in associative algebras 16D25 Ideals in associative algebras 15B48 Positive matrices and their generalizations; cones 16D30 Infinite-dimensional simple rings (except as in of matrices 16Kxx) 15B51 Stochastic matrices 16D40 Free, projective, and flat modules and ideals in associative algebras [See also 19A13] 15B52 Random matrices (algebraic aspects) {For probabilistic aspects, see 60B20} 16D50 Injective modules, self-injective associative rings [See also 16L60] 15B57 Hermitian, skew-Hermitian, and related matrices 15B99 None of the above, but in this section 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras and classification for modules, bimod16-XX Associative rings and alge- 16D70ulesStructure and ideals (except as in 16Gxx), direct sum bras {For the commutative case, decomposition and cancellation in associative algebras) see 13-XX} 16D80 Other classes of modules and ideals in associative 16-00 General reference works (handbooks, dictionaries, algebras [See also 16G50] bibliographies, etc.) pertaining to associative rings and algebras 16D90 Module categories in associative algebras [See also 16Gxx, 16S90]; module theory in a category16-01 Introductory exposition (textbooks, tutorial patheoretic context; Morita equivalence and duality pers, etc.) pertaining to associative rings and algebras 16D99 None of the above, but in this section 28 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 16Exx Homological methods in associative 16Hxx Associative algebras and orders algebras {For commutative rings, see {For arithmetic aspects, see 11R52, 13Dxx; for general categories, see 18Gxx} 11R54, 11S45; for representation theory, see 16G30} 16E05 Syzygies, resolutions, complexes in associative algebras 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16E10 Homological dimension in associative algebras 16H10 Orders in separable algebras 16E20 Grothendieck groups, K-theory, etc. [See also 18F30, 19Axx, 19D50] 16H15 Commutative orders 16E30 Homological functors on modules (Tor, Ext, etc.) 16H20 Lattices over orders in associative algebras 16H99 None of the above, but in this section 16E35 Derived categories and associative algebras 16E40 (Co)homology of rings and associative algebras 16Kxx Division rings and semisimple (e.g., Hochschild, cyclic, dihedral, etc.) Artin rings [See also 12E15, 15A30] 16E45 Differential graded algebras and applications (as- 16K20 Finite-dimensional division rings {For crossed sociative algebraic aspects) products, see 16S35} 16E50 von Neumann regular rings and generalizations 16K40 Infinite-dimensional and general division rings (associative algebraic aspects) 16K50 Brauer groups (algebraic aspects) [See also 16E60 Semihereditary and hereditary rings, free ideal 12G05, 14F22] rings, Sylvester rings, etc. 16K99 None of the above, but in this section 16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen16Lxx Local rings and generalizations Macaulay rings, etc.) 16L30 Noncommutative local and semilocal rings, perfect rings 16E99 None of the above, but in this section 16Gxx Representation theory of associa- 16L60 Quasi-Frobenius rings [See also 16D50] tive rings and algebras 16L99 None of the above, but in this section 16G10 Representations of associative Artinian rings 16G20 Representations of quivers and partially ordered 16Nxx Radicals and radical properties of sets associative rings 16G30 Representations of orders, lattices, algebras over 16N20 Jacobson radical, quasimultiplication commutative rings [See also 16Hxx] 16N40 Nil and nilpotent radicals, sets, ideals, associative rings 16G50 Cohen-Macaulay modules in associative algebras 16G60 Representation type (finite, tame, wild, etc.) of 16N60 Prime and semiprime associative rings [See also 16D60, 16U10] associative algebras 16G70 Auslander-Reiten sequences (almost split se- 16N80 General radicals and associative rings {For radicals in module categories, see 16S90} quences) and Auslander-Reiten quivers 16G99 None of the above, but in this section 16N99 None of the above, but in this section 29 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 16Pxx Chain conditions, growth condi- 16S20 Centralizing and normalizing extensions tions, and other forms of finiteness for as- 16S30 Universal enveloping algebras of Lie algebras [See sociative rings and algebras mainly 17B35] 16P10 Finite rings and finite-dimensional associative al- 16S32 Rings of differential operators (associative algegebras {For semisimple, see 16K20; for commutabraic aspects) [See also 13N10, 32C38] tive, see 11Txx, 13Mxx} 16S34 Group rings [See also 20C05, 20C07], Laurent 16P20 Artinian rings and modules (associative rings and polynomial rings (associative algebraic aspects) algebras) 16S35 Twisted and skew group rings, crossed products 16P40 Noetherian rings and modules (associative rings 16S36 Ordinary and skew polynomial rings and semiand algebras) group rings [See also 20M25] 16P50 Localization and associative Noetherian rings 16S37 Quadratic and Koszul algebras [See also 16U20] 16P60 Chain conditions on annihilators and summands: 16S38 Rings arising from noncommutative algebraic geometry [See also 14A22] Goldie-type conditions [See also 16U20], Krull dimension (associative rings and algebras) 16S40 Smash products of general Hopf actions [See also 16T05] 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings 16S50 Endomorphism rings; matrix rings [See also 15and algebras) XX] 16P90 Growth rate, Gelfand-Kirillov dimension 16S60 Associative rings of functions, subdirect products, sheaves of rings 16P99 None of the above, but in this section 16S70 Extensions of associative rings by ideals 16Rxx Rings with polynomial identity 16S80 Deformations of associative rings [See also 13D10, 14D15] 16R10 T -ideals, identities, varieties of associative rings and algebras 16S85 Associative rings of fractions and localizations [See also 13B30] 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings 16S88 Leavitt path algebras 16R30 Trace rings and invariant theory (associative 16S90 Torsion theories; radicals on module categories rings and algebras) (associative algebraic aspects) [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} 16R40 Identities other than those of matrices over commutative rings 16S99 None of the above, but in this section 16R50 Other kinds of identities (generalized polynomial, 16Txx Hopf algebras, quantum groups and rational, involution) related topics 16R60 Functional identities (associative rings and alge16T05 Hopf algebras and their applications [See also bras) 16S40, 57T05] 16R99 None of the above, but in this section 16T10 Bialgebras 16Sxx Associative rings and algebras aris- 16T15 Coalgebras and comodules; corings ing under various constructions 16T20 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] 16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of in16T25 Yang-Baxter equations verses, etc.) 16T30 Connections of Hopf algebras with combinatorics 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) 16T99 None of the above, but in this section 30 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 16Yxx Generalizations {For nonassociative rings, see 17-XX} 16U10 Integral domains (associative rings and algebras) 16Uxx Conditions on elements 16Y20 Hyperrings 16U20 Ore rings, multiplicative sets, Ore localization 16Y30 Near-rings [See also 12K05] 16U30 Divisibility, noncommutative UFDs 16U40 Idempotent elements (associative rings and alge- 16Y60 Semirings [See also 12K10] bras) 16Y80 Γ and fuzzy structures 16U60 Units, groups of units (associative rings and al16Y99 None of the above, but in this section gebras) 16U70 Center, normalizer (invariant elements) (associa16Zxx Computational aspects of associative rings and algebras) tive rings {For software etc., see 16-04} 16U80 Generalizations of commutativity (associative 16Z05 Computational aspects of associative rings (genrings and algebras) eral theory) [See also 68W30] 16U90 Generalized inverses (associative rings and algebras) 16Z10 Gröbner-Shirshov bases 16U99 None of the above, but in this section 16Z99 None of the above, but in this section 16Wxx Associative rings and algebras with 17-XX Nonassociative rings and aladditional structure gebras 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 17-00 General reference works (handbooks, dictionaries, 46Kxx] bibliographies, etc.) pertaining to nonassociative rings and algebras 16W20 Automorphisms and endomorphisms 16W22 Actions of groups and semigroups; invariant the- 17-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and ory (associative rings and algebras) algebras 16W25 Derivations, actions of Lie algebras 17-02 Research exposition (monographs, survey articles) 16W50 Graded rings and modules (associative rings and pertaining to nonassociative rings and algebras algebras) 17-03 History of nonassociative rings and algebras [Con16W55 “Super” (or “skew”) structure [See also 17A70, sider also classification numbers pertaining to Sec17Bxx, 17C70] {For exterior algebras, see 15A75; tion 01] for Clifford algebras, see 11E88, 15A66} 16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras) [See also 13Jxx] 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 16W70 Filtered associative rings; filtrational and graded techniques 17-08 Computational methods for problems pertaining to nonassociative rings and algebras 16W80 Topological and ordered rings and modules [See also 06F25, 13Jxx] 17-11 Research data for problems pertaining to nonas16W99 None of the above, but in this section sociative rings and algebras 31 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 17Axx General nonassociative rings 17B22 Root systems 17A01 General theory of nonassociative rings and alge- 17B25 Exceptional (super)algebras bras 17B30 Solvable, nilpotent (super)algebras 17A05 Power-associative rings 17B35 Universal enveloping (super)algebras [See also 17A15 Noncommutative Jordan algebras 16S30] 17A20 Flexible algebras 17B37 Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 17A30 Nonassociative algebras satisfying other identi81R50, 82B23] ties 17B38 Yang-Baxter equations and Rota-Baxter opera17A32 Leibniz algebras tors 17A35 Nonassociative division algebras 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras 17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras) 17B45 Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 17A40 Ternary compositions 17B50 Modular Lie (super)algebras 17A42 Other n-ary compositions (n ≥ 3) 17A45 Quadratic algebras (but not quadratic Jordan al- 17B55 Homological methods in Lie (super)algebras gebras) 17B56 Cohomology of Lie (super)algebras 17A50 Free nonassociative algebras 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17A60 Structure theory for nonassociative algebras 17C40, 17C50] 17A61 Gröbner-Shirshov bases in nonassociative alge17B61 Hom-Lie and related algebras bras 17A65 Radical theory (nonassociative rings and alge- 17B62 Lie bialgebras; Lie coalgebras bras) 17B63 Poisson algebras 17A70 Superalgebras 17B65 Infinite-dimensional Lie (super)algebras [See also 22E65] 17A75 Composition algebras 17B66 Lie algebras of vector fields and related (super) algebras 17A80 Valued algebras 17A99 None of the above, but in this section 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17Bxx Lie algebras and Lie superalgebras 17B68 Virasoro and related algebras {For Lie groups, see 22Exx} 17B01 Identities, free Lie (super)algebras 17B69 Vertex operators; vertex operator algebras and related structures 17B05 Structure theory for Lie algebras and superalgebras 17B70 Graded Lie (super)algebras 17B08 Coadjoint orbits; nilpotent varieties 17B75 Color Lie (super)algebras 17B10 Representations of Lie algebras and Lie superal- 17B80 Applications of Lie algebras and superalgebras to gebras, algebraic theory (weights) integrable systems 17B15 Representations of Lie algebras and Lie superal- 17B81 Applications of Lie (super)algebras to physics, gebras, analytic theory etc. 17B20 Simple, semisimple, reductive (super)algebras 17B99 None of the above, but in this section 32 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 17Cxx Jordan algebras (algebras, triples 18-XX Category theory; homologiand pairs) cal algebra {For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} 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 18-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory 17C30 Associated groups, automorphisms of Jordan algebras 18-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory 17C36 Associated manifolds of Jordan algebras 18-02 Research exposition (monographs, survey articles) 17C37 Associated geometries of Jordan algebras pertaining to category theory 18-03 History of category theory [Consider also classification numbers pertaining to Section 01] 17C40 Exceptional Jordan structures 17C50 Jordan structures associated with other struc18-04 Software, source code, etc. for problems pertaintures [See also 16W10] ing to category theory 17C55 Finite-dimensional structures of Jordan algebras 18-06 Proceedings, conferences, collections, etc. pertaining to category theory 17C60 Division algebras and Jordan algebras 18-08 Computational methods for problems pertaining to category theory 17C65 Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 18-11 Research data for problems pertaining to category theory 17C70 Super structures 17C90 Applications of Jordan algebras to physics, etc. 18Axx General theory of categories and functors 17C99 None of the above, but in this section 18A05 Definitions and generalizations in theory of categories 17Dxx Other nonassociative rings and algebras 17D05 Alternative rings 18A10 Graphs, diagram schemes, precategories 18A15 Foundations, relations to logic and deductive systems [See also 03-XX] 17D10 Mal’tsev rings and algebras 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 17D15 Right alternative rings 17D20 (γ, δ)-rings, including (1, −1)-rings 18A22 Special properties of functors (faithful, full, etc.) 17D25 Lie-admissible algebras 18A23 Natural morphisms, dinatural morphisms 17D30 (non-Lie) Hom algebras and topics 18A25 Functor categories, comma categories 17D92 Genetic algebras 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 17D99 None of the above, but in this section 33 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 18A32 Factorization systems, substructures, quotient 18C40 Structured objects in a category (group objects, structures, congruences, amalgams etc.) 18A35 Categories admitting limits (complete cate- 18C50 Categorical semantics of formal languages [See also 68Q55, 68Q65] gories), functors preserving limits, completions 18A40 Adjoint functors (universal constructions, reflec- 18C99 None of the above, but in this section tive subcategories, Kan extensions, etc.) 18Dxx Categorical structures 18A50 Graded categories (general) {For dg categories, see 18G35} 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) 18A99 None of the above, but in this section 18D20 Enriched categories (over closed or monoidal categories) 18Bxx Special categories 18D25 Actions of a monoidal category, tensorial strength {For functional programming, see also 68N18} 18B05 Categories of sets, characterizations [See also 03XX] 18B10 Categories of spans/cospans, relations, or partial 18D30 Fibered categories maps 18D40 Internal categories and groupoids {For double 18B15 Embedding theorems, universal categories [See categories, see 18N10; for topological groupoids, see also 18E20] 22A22; for Lie groupoids, see 58H05} 18B20 Categories of machines, automata [See also 18D60 Profunctors (= correspondences, distributors, 03D05, 68Qxx] modules) 18B25 Topoi [See also 03G30, 18F10] 18D65 Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads) 18B35 Preorders, orders, domains and lattices (viewed as categories) [See also 06-XX] 18D70 Formal category theory 18B40 Groupoids, semigroupoids, semigroups, groups 18D99 None of the above, but in this section (viewed as categories) [See also 20Axx, 20L05, 20Mxx] 18Exx Categorical algebra 18B50 Extensive, distributive, and adhesive categories 18E05 Preadditive, additive categories 18B99 None of the above, but in this section 18E08 Regular categories, Barr-exact categories 18Cxx Categories and theories 18E10 Abelian categories, Grothendieck categories 18E13 Protomodular categories, semi-abelian categories, Mal’tsev categories [See also 08B05 and 18B10] 18C10 Theories (e.g., algebraic theories), structure, and semantics [See also 03G30] 18E20 Categorical embedding theorems [See also 18B15] 18C15 Monads (= standard construction, triple or 18E35 Localization of categories, calculus of fractions triad), algebras for monads, homology and derived {For homotopical aspects, see also 18N45, 55P60} functors for monads [See also 18Gxx] {For functional programming, see also 68N18} 18E40 Torsion theories, radicals [See also 13D30, 16S90] 18C05 Equational categories [See also 03C05, 08C05] 18C20 Eilenberg-Moore and Kleisli constructions for 18E45 Definable subcategories and connections with monads model theory [See also 13C60] 18C30 Sketches and generalizations 18E50 Categorical Galois theory 18C35 Accessible and locally presentable categories 18E99 None of the above, but in this section 34 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 18Fxx Categories in geometry and topol- 18G35 Chain complexes (category-theoretic aspects), dg categories [See also 14F08, 18G80, 55U15] ogy 18F05 Local categories and functors 18G40 Spectral sequences, hypercohomology [See also 55Txx] 18F10 Grothendieck topologies and Grothendieck topoi 18G45 2-groups, crossed modules, crossed complexes [See also 14F20, 18B25] 18F15 Abstract manifolds and fiber bundles (category- 18G50 Nonabelian homological theoretic aspects) theoretic aspects) [See also 55Rxx, 57Pxx] algebra (category- 18F20 Presheaves and sheaves, stacks, descent condi- 18G65 Stable module categories [See also 20C20] tions (category-theoretic aspects) [See also 14F06, 18G70 A∞ -categories, relations with homological mirror 14F08, 32C35, 32L10, 54B40, 55N30] symmetry [See also 14F08, 14J33, 53D37] 18F25 Algebraic K-theory and L-theory (categorytheoretic aspects) [See also 11Exx, 11R70, 11S70, 18G80 Derived categories, triangulated categories 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 18G85 Graph complexes and graph homology {For re57R65, 57R67] lations with deformation quantization, see 53D55} 18F30 Grothendieck groups (category-theoretic aspects) 18G90 Other (co)homology theories (category-theoretic [See also 13D15, 16E20, 19Axx] aspects) [See also 19D55, 46L80, 58J20, 58J22] 18F40 Synthetic differential geometry, tangent cate- 18G99 None of the above, but in this section gories, differential categories 18F50 Goodwillie calculus and functor calculus 18Mxx Monoidal categories and operads 18F60 Categories of topological spaces and continuous 18M05 Monoidal categories, symmetric monoidal categories [See also 19D23] mappings [See also 54-XX] 18F70 Frames and locales, pointfree topology, Stone du- 18M10 Traced monoidal categories, compact closed categories, star-autonomous categories ality [See also 06D22, 18B35] 18F75 Quantales [See also 06F07, 18B35] 18F99 None of the above, but in this section 18M15 Braided monoidal categories and ribbon categories {For applications to knot theory, see also 57Kxx; for applications to quantum groups, see also 16T20, 17B37, 81R50} 18Gxx Homological algebra in category 18M20 Fusion categories, modular tensor categories, theory, derived categories and functors modular functors {For applications to topological [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, quantum field theories, see also 57R56; for applica55Uxx, 57Txx] tions to conformal field theories, see also 81T40} 18G05 Projectives and injectives (category-theoretic as- 18M25 Tannakian categories {For applications to mopects) [See also 13C10, 13C11, 16D40, 16D50] tives, see also 14C15, 19E15} 18G10 Resolutions; derived functors (category-theoretic 18M30 String diagrams and graphical calculi aspects) [See also 13D02, 16E05, 18Gxx] 18M35 Categories of networks and processes, composi18G15 Ext and Tor, generalizations, Künneth formula tionality (category-theoretic aspects) [See also 55U25] 18M40 Dagger categories, categorical quantum mechan18G20 Homological dimension (category-theoretic asics [See also 81P68] pects) [See also 13D05, 16E10] 18M45 Categorical aspects of linear logic [See also 18G25 Relative homological algebra, projective classes 03B47] (category-theoretic aspects) 18M50 Bimonoidal, skew-monoidal, duoidal categories 18G31 Simplicial modules and Dold-Kan correspondence 18M60 Operads (general) 35 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 18M65 Non-symmetric operads, multicategories, generalized multicategories 19-XX K-theory [See also 16E20, 18F25] 18M70 Algebraic operads, cooperads, and Koszul dual19-00 General reference works (handbooks, dictionaries, ity bibliographies, etc.) pertaining to K-theory 18M75 Topological and simplicial operads [See also 19-01 Introductory exposition (textbooks, tutorial pa18N60] pers, etc.) pertaining to K-theory 18M80 Species, Hopf monoids, operads in combinatorics 19-02 Research exposition (monographs, survey articles) pertaining to K-theory 18M85 Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads 19-03 History of K-theory [Consider also classification numbers pertaining to Section 01] 18M90 Globular operads 19-04 Software, source code, etc. for problems pertain18M99 None of the above, but in this section ing to K-theory 18Nxx Higher categories and homotopical algebra per- 19-08 Computational methods for problems pertaining to K-theory 18N10 2-categories, bicategories, double categories 18N15 2-dimensional monad theory [See also 18C15] 18N20 Tricategories, weak n-categories, semi-strictification 19-06 Proceedings, conferences, collections, etc. taining to K-theory 19-11 Research data for problems pertaining to Ktheory coherence, 18N25 Categorification 18N30 Strict omega-categories, computads, polygraphs 19Axx Grothendieck groups and K0 [See also 13D15, 18F30] 19A13 Stability for projective modules [See also 13C10] 19A15 Efficient generation of modules 18N40 Homotopical algebra, Quillen model categories, derivators [See also 55U35] 19A22 Frobenius induction, Burnside and representation rings 18N45 Categories of fibrations, relations to K-theory, relations to type theory 19A31 K0 of group rings and orders 18N50 Simplicial sets, simplicial objects [See also 19A49 K0 of other rings 55U10] 19A99 None of the above, but in this section 18N55 Localizations (e.g., simplicial localization, Bousfield localization) [See also 18E35, 55P60] 19Bxx Whitehead groups and K1 18N60 (∞, 1)-categories (quasi-categories, Segal spaces, 19B10 Stable range conditions etc.); ∞-topoi, stable ∞-categories [See also 55U35, 55U40] 19B14 Stability for linear groups 18N65 (∞, n)-categories and (∞, ∞)-categories 19B28 K1 of group rings and orders [See also 57Q10] 18N70 ∞-operads and higher algebra [See also 18M75] 19B37 Congruence subgroup problems [See also 20H05] 18N99 None of the above, but in this section 19B99 None of the above, but in this section 36 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 19Cxx Steinberg groups and K2 19Gxx K-theory of forms [See also 11Exx] 19C09 Central extensions and Schur multipliers 19G05 Stability for quadratic modules 19C20 Symbols, presentations and stability of K2 19G12 Witt groups of rings [See also 11E81] 19C30 K2 and the Brauer group 19G24 L-theory of group rings [See also 11E81] 19C40 Excision for K2 19G38 Hermitian K-theory, relations with K-theory of rings 19C99 None of the above, but in this section 19G99 None of the above, but in this section 19Dxx Higher algebraic K-theory 19D06 Q- and plus-constructions 19Jxx Obstructions from topology 19D10 Algebraic K-theory of spaces 19J05 Finiteness and other obstructions in K0 19D23 Symmetric monoidal categories [See also 18M05] 19J10 Whitehead (and related) torsion 19J25 Surgery obstructions (K-theoretic aspects) [See also 57R67] 19D25 Karoubi-Villamayor-Gersten K-theory 19D35 Negative K-theory, NK and Nil 19J35 Obstructions to group actions (K-theoretic aspects) 19D45 Higher symbols, Milnor K-theory 19D50 Computations of higher K-theory of rings [See 19J99 None of the above, but in this section also 13D15, 16E20] 19D55 K-theory and homology; cyclic homology and co- 19Kxx K-theory and operator algebras homology [See also 18G90] [See mainly 46L80, and also 46M20] 19D99 None of the above, but in this section 19K14 K0 as an ordered group, traces 19Exx K-theory in geometry 19K33 Ext and K-homology [See also 55N22] 19E08 K-theory of schemes [See also 14C35] 19K35 Kasparov theory (KK-theory) [See also 58J22] 19E15 Algebraic cycles and motivic cohomology (Ktheoretic aspects) [See also 14C25, 14C35, 14F42] 19K56 Index theory [See also 58J20, 58J22] 19K99 None of the above, but in this section 19E20 Relations of K-theory with cohomology theories [See also 14Fxx] 19E99 None of the above, but in this section 19Lxx Topological K-theory [See also 55N15, 55R50, 55S25] 19L10 Riemann-Roch theorems, Chern characters 19Fxx K-theory in number theory [See 19L20 J-homomorphism, Adams operations [See also also 11R70, 11S70] 55Q50] 19F05 Generalized class field theory (K-theoretic as19L41 Connective K-theory, cobordism [See also 55N22] pects) [See also 11G45] 19F15 Symbols and arithmetic (K-theoretic aspects) 19L47 Equivariant K-theory [See also 55N91, 55P91, [See also 11R37] 55Q91, 55R91, 55S91] 19F27 Étale cohomology, higher regulators, zeta and 19L50 Twisted K-theory; differential K-theory L-functions (K-theoretic aspects) [See also 11G40, 19L64 Geometric applications of topological K-theory 11R42, 11S40, 14F20, 14G10] 19F99 None of the above, but in this section 19L99 None of the above, but in this section 37 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 19Mxx Miscellaneous applications of K- 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, theory 12F10, 20G40, 20H30, 51-XX] 19M05 Miscellaneous applications of K-theory 20B27 Infinite automorphism groups [See also 12F10] 19M99 None of the above, but in this section 20-XX Group theory and general- 20B30 Symmetric groups izations 20B35 Subgroups of symmetric groups 20-00 General reference works (handbooks, dictionaries, 20B99 None of the above, but in this section bibliographies, etc.) pertaining to group theory 20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory 20Cxx Representation theory of groups 20-02 Research exposition (monographs, survey articles) {For representation rings and Burnside rings, see also 19A22} pertaining to group theory 20-03 History of group theory [Consider also classifica- 20C05 Group rings of finite groups and their modules (group-theoretic aspects) [See also 16S34] tion numbers pertaining to Section 01] 20-04 Software, source code, etc. for problems pertain20C07 Group rings of infinite groups and their modules ing to group theory (group-theoretic aspects) [See also 16S34] 20-06 Proceedings, conferences, collections, etc. pertaining to group theory 20C08 Hecke algebras and their representations 20-08 Computational methods for problems pertaining 20C10 Integral representations of finite groups to group theory 20-11 Research data for problems pertaining to group 20C11 p-adic representations of finite groups theory 20C12 Integral representations of infinite groups 20Axx Foundations 20A05 Axiomatics and elementary properties of groups 20C15 Ordinary representations and characters 20A10 Metamathematical considerations in group the20C20 Modular representations and characters ory {For word problems, see 20F10} 20A15 Applications of logic to group theory 20C25 Projective representations and multipliers 20A99 None of the above, but in this section 20C30 Representations of finite symmetric groups 20Bxx Permutation groups 20C32 Representations of infinite symmetric groups 20B05 General theory for finite permutation groups 20B07 General theory for infinite permutation groups 20C33 Representations of finite groups of Lie type 20B10 Characterization groups 20C34 Representations of sporadic groups theorems for permutation 20B15 Primitive groups 20B20 Multiply transitive finite groups 20B22 Multiply transitive infinite groups 20C35 Applications of group representations to physics and other areas of science 20C99 None of the above, but in this section 38 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 20Dxx Abstract finite groups 20E32 Simple groups [See also 20D05] 20D05 Finite simple groups and their classification 20E34 General structure theorems for groups 20D06 Simple groups: alternating groups and groups of 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45] Lie type [See also 20Gxx] 20D08 Simple groups: sporadic groups 20E42 Groups with a BN -pair; buildings [See also 51E24] 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks [See 20E45 Conjugacy classes for groups also 20F17] 20E99 None of the above, but in this section 20D15 Finite nilpotent groups, p-groups 20D20 Sylow subgroups, Sylow properties, π-groups, πstructure 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 20Fxx Special aspects of infinite or finite groups 20F05 Generators, groups relations, and presentations of 20F06 Cancellation theory of groups; application of van Kampen diagrams [See also 57M05] 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 20D60 Arithmetic and combinatorial problems involv20F11 Groups of finite Morley rank [See also 03C45, ing abstract finite groups 03C60] 20D99 None of the above, but in this section 20F12 Commutator calculus 20Exx Structure and classification of infi- 20F14 Derived series, central series, and generalizations for groups nite or finite groups 20F16 Solvable groups, supersolvable groups [See also 20D10] 20E05 Free nonabelian groups 20E06 Free products of groups, free products with amal20F17 Formations of groups, Fitting classes [See also gamation, Higman-Neumann-Neumann extensions, 20D10] and generalizations 20F18 Nilpotent groups [See also 20D15] 20E07 Subgroup theorems; subgroup growth 20F19 Generalizations of solvable and nilpotent groups 20E08 Groups acting on trees [See also 20F65] 20F22 Other classes of groups defined by subgroup 20E10 Quasivarieties and varieties of groups chains 20E15 Chains and lattices of subgroups, subnormal sub- 20F24 FC-groups and their generalizations groups [See also 20F22] 20F28 Automorphism groups of groups [See also 20E36] 20E18 Limits, profinite groups 20F29 Representations of groups as automorphism groups of algebraic systems 20E22 Extensions, wreath products, and other compositions of groups [See also 20J05] 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) [See also 57M05, 57Sxx] 20E25 Local properties of groups 20F36 Braid groups; Artin groups 20E26 Residual properties and generalizations; residually finite groups 20F38 Other groups related to topology or analysis 20E28 Maximal subgroups 20F40 Associated Lie structures for groups 39 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 20F45 Engel conditions 20G44 Kac-Moody groups 20F50 Periodic groups; locally finite groups 20G45 Applications of linear algebraic groups to the sciences 20F55 Reflection and Coxeter groups (group-theoretic 20G99 None of the above, but in this section aspects) [See also 22E40, 51F15] 20F60 Ordered groups (group-theoretic aspects) [See 20Hxx Other groups of matrices [See also mainly 06F15] 15A30] 20F65 Geometric group theory [See also 05C25, 20E08, 57Mxx] 20H05 Unimodular groups, congruence subgroups (group-theoretic aspects) [See also 11F06, 19B37, 22E40, 51F20] 20F67 Hyperbolic groups and nonpositively curved 20H10 Fuchsian groups and their generalizations groups (group-theoretic aspects) [See also 11F06, 22E40, 20F69 Asymptotic properties of groups 30F35, 32Nxx] 20F70 Algebraic geometry over groups; equations over 20H15 Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, groups and 82D25] 20F99 None of the above, but in this section 20H20 Other matrix groups over fields 20Gxx Linear algebraic groups and related topics {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55} 20G05 Representation theory for linear algebraic groups 20H25 Other matrix groups over rings 20H30 Other matrix groups over finite fields 20H99 None of the above, but in this section 20Jxx Connections of group theory with homological algebra and category theory 20J05 Homological methods in group theory 20G07 Structure theory for linear algebraic groups 20J06 Cohomology of groups 20G10 Cohomology theory for linear algebraic groups 20J15 Category of groups 20G15 Linear algebraic groups over arbitrary fields 20J99 None of the above, but in this section 20G20 Linear algebraic groups over the reals, the com- 20Kxx Abelian groups plexes, the quaternions 20K01 Finite abelian groups {For sumsets, see 11B13, 20G25 Linear algebraic groups over local fields and their 11P70} integers 20K10 Torsion groups, primary groups and generalized 20G30 Linear algebraic groups over global fields and primary groups their integers 20K15 Torsion-free groups, finite rank 20G35 Linear algebraic groups over adèles and other 20K20 Torsion-free groups, infinite rank rings and schemes 20K21 Mixed groups 20G40 Linear algebraic groups over finite fields 20K25 Direct sums, direct products, etc. for abelian groups 20G41 Exceptional groups 20G42 Quantum groups (quantized function algebras) 20K27 Subgroups of abelian groups and their representations [See also 16T20, 17B37, 20K30 Automorphisms, homomorphisms, 81R50] phisms, etc. for abelian groups 20G43 Schur and q-Schur algebras 20K35 Extensions of abelian groups 40 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. endomor- 20K40 Homological and categorical methods for abelian 20M50 Connections of semigroups with homological algroups gebra and category theory 20K45 Topological methods for abelian groups [See also 20M75 Generalizations of semigroups 22A05, 22B05] 20M99 None of the above, but in this section 20K99 None of the above, but in this section 20Nxx Other generalizations of groups 20Lxx Groupoids (i.e. small categories 20N02 Sets with a single binary operation (groupoids) in which all morphisms are isomorphisms) {For groupoids in connection with category theory, {For sets with a single binary operation, see 20L05; for topological groupoids, see 22A22, 58H05} see 20N02; for topological groupoids, see 22A22, 58H05} 20N05 Loops, quasigroups [See also 05Bxx] 20L05 Groupoids (i.e. small categories in which all mor20N10 Ternary systems (heaps, semiheaps, heapoids, phisms are isomorphisms) {For sets with a sinetc.) gle binary operation, see 20N02; for topological groupoids, see 22A22, 58H05} 20N15 n-ary systems (n ≥ 3) 20L99 None of the above, but in this section 20N20 Hypergroups 20Mxx Semigroups 20N25 Fuzzy groups [See also 03E72] 20M05 Free semigroups, generators and relations, word 20N99 None of the above, but in this section problems [See also 03D40, 08A50, 20F10] 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 20Pxx Probabilistic methods in group theory [See also 60Bxx] 20P05 Probabilistic methods in group theory [See also 60Bxx] 20P99 None of the above, but in this section 22-XX Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX; for abstract harmonic analysis, see 43XX} 22-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to topological 20M20 Semigroups of transformations, relations, partigroups tions, etc. [See also 47D03, 47H20, 54H15] 22-01 Introductory exposition (textbooks, tutorial pa20M25 Semigroup rings, multiplicative semigroups of pers, etc.) pertaining to topological groups rings [See also 16S36, 16Y60] 22-02 Research exposition (monographs, survey articles) 20M30 Representation of semigroups; actions of semipertaining to topological groups groups on sets 22-03 History of topological groups [Consider also clas20M32 Algebraic monoids sification numbers pertaining to Section 01] 20M19 Orthodox semigroups 20M35 Semigroups in automata theory, linguistics, etc. 22-04 Software, source code, etc. for problems pertain[See also 03D05, 68Q70, 68T50] ing to topological groups 41 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 22-06 Proceedings, conferences, collections, etc. taining to topological groups per- 22D12 Other representations of locally compact groups 22D15 Group algebras of locally compact groups 22-08 Computational methods for problems pertaining 22D20 Representations of group algebras to topological groups 22D25 C ∗ -algebras and W ∗ -algebras in relation to group 22-11 Research data for problems pertaining to topologrepresentations [See also 46Lxx] ical groups 22D30 Induced representations for locally compact groups 22Axx Topological and differentiable algebraic systems {For topological rings and 22D35 Duality theorems for locally compact groups fields, see 12Jxx, 13Jxx, 16W80} 22D40 Ergodic theory on groups [See also 28Dxx] 22A05 Structure of general topological groups 22D45 Automorphism groups of locally compact groups 22A10 Analysis on general topological groups 22D50 Rigidity in locally compact groups 22A15 Structure of topological semigroups 22D55 Kazhdan’s property (T), the Haagerup property, and generalizations 22A20 Analysis on topological semigroups 22D99 None of the above, but in this section 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also 58H05] 22Exx Lie groups {For the topology of Lie groups and homogeneous spaces, see 22A25 Representations of general topological groups 57Sxx, 57Txx; for analysis thereon, see and semigroups 43A80, 43A85, 43A90} 22A26 Topological semilattices, lattices and applica22E05 Local Lie groups [See also 34-XX, 35-XX, 58H05] tions [See also 06B30, 06B35, 06F30] 22E10 General properties and structure of complex Lie 22A30 Other topological algebraic systems and their groups [See also 32M05] representations 22E15 General properties and structure of real Lie 22A99 None of the above, but in this section groups 22E20 General properties and structure of other Lie groups 22Bxx Locally compact abelian groups (LCA groups) 22E25 Nilpotent and solvable Lie groups 22B05 General properties and structure of LCA groups 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) 22B10 Structure of group algebras of LCA groups 22B99 None of the above, but in this section 22E30 Analysis on real and complex Lie groups [See also 33C80, 43-XX] 22Cxx Compact groups 22E35 Analysis on p-adic Lie groups 22C05 Compact groups 22E40 Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 22C99 None of the above, but in this section 22Dxx Locally compact groups and their algebras 22E41 Continuous cohomologyof Lie groups [See also 57R32, 57Txx, 58H10] 22E43 Structure and representation of the Lorentz group 22D05 General properties and structure of locally compact groups 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 22D10 Unitary representations of locally compact groups 42 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 22E46 Semisimple Lie groups and their representations 26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 26-02 Research exposition (monographs, survey articles) pertaining to real functions 17B10] 22E50 Representations of Lie and linear algebraic 26-03 History of real functions [Consider also classification numbers pertaining to Section 01] groups over local fields [See also 20G05] 26-04 Software, source code, etc. for problems pertain22E55 Representations of Lie and linear algebraic ing to real functions groups over global fields and adèle rings [See also 26-06 Proceedings, conferences, collections, etc. per20G05] taining to real functions 22E57 Geometric Langlands program: representation26-08 Computational methods for problems pertaining theoretic aspects [See also 14D24] to real functions 22E60 Lie algebras of Lie groups {For the algebraic the26-11 Research data for problems pertaining to real ory of Lie algebras, see 17Bxx} functions 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 26Axx Functions of one variable 58D05 58H05] 26A03 Foundations: limits and generalizations, elementary topology of the line 22E66 Analysis on and representations of infinitedimensional Lie groups 26A06 One-variable calculus 22E67 Loop groups and related constructions, group- 26A09 Elementary functions theoretic treatment [See also 58D05] 26A12 Rate of growth of functions, orders of infinity, 22E70 Applications of Lie groups to the sciences; exslowly varying functions [See also 26A48] plicit representations [See also 81R05, 81R10] 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for 22E99 None of the above, but in this section real functions in one variable {For properties determined by Fourier coefficients, see 42A16; for 22Fxx Noncompact transformation groups those determined by approximation properties, see 41A25, 41A27} 22F05 General theory of group and pseudogroup actions {For topological properties of spaces with an action, 26A16 Lipschitz (Hölder) classes see 57S20} 26A18 Iteration of real functions in one variable [See 22F10 Measurable group actions [See also 22D40, also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 28Dxx, 37Axx] 26A21 Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 22F30 Homogeneous spaces {For general actions on 54C50, 54H05] manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, 26A24 Differentiation (real functions of one variable): see especially 22E40} general theory, generalized derivatives, mean value theorems [See also 28A15] 22F50 Groups as automorphisms of other structures 22F99 None of the above, but in this section 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives 26-XX Real functions [See also 26A30 Singular functions, Cantor functions, functions with other special properties 54C30] 26A33 Fractional derivatives and integrals 26-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions 26A36 Antidifferentiation 43 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 26A39 Denjoy and Perron integrals, other special inte- 26Dxx Inequalities in real analysis {For grals maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for 26A42 Integrals of Riemann, Stieltjes and Lebesgue type probabilistic inequalities, see 60E15} [See also 28-XX] 26D05 Inequalities for trigonometric functions and polynomials 26A45 Functions of bounded variation, generalizations 26A46 Absolutely continuous real functions in one vari26D07 Inequalities involving other types of functions able 26A48 Monotonic functions, generalizations 26D10 Inequalities involving derivatives and differential and integral operators 26A51 Convexity of real functions in one variable, generalizations 26D15 Inequalities for sums, series and integrals 26A99 None of the above, but in this section 26D20 Other analytical inequalities 26Bxx Functions of several variables 26D99 None of the above, but in this section 26B05 Continuity and differentiation questions 26B10 Implicit function theorems, Jacobians, transfor- 26Exx Miscellaneous topics in real functions [See also 58Cxx] mations with several variables 26E05 Real-analytic functions [See also 32B05, 32C05] 26B12 Calculus of vector functions 26B15 Integration of real functions of several variables: 26E10 C ∞ -functions, quasi-analytic functions [See also 58C25] length, area, volume [See also 28A75, 51M25] 26B20 Integral formulas of real functions of several vari- 26E15 Calculus of functions on infinite-dimensional ables (Stokes, Gauss, Green, etc.) spaces [See also 46G05, 58Cxx] 26B25 Convexity of real functions of several variables, 26E20 Calculus of functions taking values in infinitegeneralizations dimensional spaces [See also 46E40, 46G10, 58Cxx] 26B30 Absolutely continuous real functions of several 26E25 Set-valued functions [See also 28B20, 49J53, variables, functions of bounded variation 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx} 26B35 Special properties of functions of several variables, Hölder conditions, etc. 26E30 Non-Archimedean analysis [See also 12J25] 26B40 Representation and superposition of functions 26E35 Nonstandard analysis [See also 03H05, 28E05, 26B99 None of the above, but in this section 54J05] 26Cxx Polynomials, rational functions in 26E40 Constructive real analysis [See also 03F60] real analysis 26E50 Fuzzy real analysis [See also 03E72, 28E10] 26C05 Real polynomials: analytic properties, etc. [See also 12Dxx, 12Exx] 26E60 Means [See also 47A64] 26C10 Real polynomials: location of zeros [See also 26E70 Real analysis on time scales or measure chains 12D10, 30C15, 65H05] {For dynamic equations on time scales or measure chains, see 34N05} 26C15 Real rational functions [See also 14Pxx] 26C99 None of the above, but in this section 26E99 None of the above, but in this section 44 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 28-XX Measure and integration 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] {For analysis on manifolds, see 58XX} 28A78 Hausdorff and packing measures 28-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and in- 28A80 Fractals [See also 37Fxx] tegration 28A99 None of the above, but in this section 28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration 28-02 Research exposition (monographs, survey articles) 28Bxx Set functions, measures and intepertaining to measure and integration grals with values in abstract spaces 28-03 History of measure and integration [Consider also 28B05 Vector-valued set functions, measures and inteclassification numbers pertaining to Section 01] grals [See also 46G10] 28-04 Software, source code, etc. for problems pertaining to measure and integration 28B10 Group- or semigroup-valued set functions, mea28-06 Proceedings, conferences, collections, etc. taining to measure and integration sures and integrals per- 28B15 Set functions, measures and integrals with values in ordered spaces 28-08 Computational methods for problems pertaining to measure and integration 28-11 Research data for problems pertaining to measure 28B20 Set-valued set functions and measures; integraand integration tion of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14] 28Axx Classical measure theory 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28A10 Real- or complex-valued set functions 28A12 Contents, measures, outer measures, capacities 28B99 None of the above, but in this section 28Cxx Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20] 28A15 Abstract differentiation theory, differentiation of 28C05 Integration theory via linear functionals (Radon set functions [See also 26A24] measures, Daniell integrals, etc.), representing set functions and measures 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of conver28C10 Set functions and measures on topological groups gence or semigroups, Haar measures, invariant measures 28A25 Integration with respect to measures and other [See also 22Axx, 43A05] set functions 28A33 Spaces of measures, convergence of measures [See 28C15 Set functions and measures on topological spaces (regularity of measures, etc.) also 46E27, 60Bxx] 28A35 Measures and integrals in product spaces 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 28A50 Integration and disintegration of measures 28A51 Lifting theory [See also 46G15] 28A60 Measures on Boolean rings, measure algebras 28C99 None of the above, but in this section [See also 54H10] 45 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 28Dxx Measure-theoretic ergodic theory 30-08 Computational methods for problems pertaining to functions of a complex variable [See also 65Exx] [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 60Fxx, 60G10] 30-11 Research data for problems pertaining to functions of a complex variable 28D05 Measure-preserving transformations {For measure-preserving transformations and dynami30Axx General properties of functions of cal systems, see 37A05} one complex variable 28D10 One-parameter continuous families of measurepreserving transformations {For dynamical systems 30A05 Monogenic and polygenic functions of one complex variable aspect, see 37A10} 28D15 General groups of measure-preserving trans- 30A10 Inequalities in the complex plane formations {For dynamical systems aspects, see 30A99 None of the above, but in this section 37A15} 30Bxx Series expansions of functions of one complex variable 28D20 Entropy and other invariants 28D99 None of the above, but in this section 30B10 Power series (including lacunary series) in one complex variable 28Exx Miscellaneous topics in measure 30B20 Random power series in one complex variable theory 30B30 Boundary behavior of power series in one complex variable; over-convergence 28E05 Nonstandard measure theory [See also 03H05, 26E35] 28E10 Fuzzy measure theory [See also 03E72, 26E50, 94D05] 30B40 Analytic continuation of functions of one complex variable 30B50 Dirichlet series, exponential series and other series in one complex variable [See also 11M41, 42XX] 28E15 Other connections with logic and set theory 28E99 None of the above, but in this section 30B60 Completeness problems, closure of a system of functions of one complex variable 30-XX Functions of a complex vari30B70 Continued fractions; complex-analytic aspects able [See also 11A55, 40A15] 30-00 General reference works (handbooks, dictionaries, 30B99 None of the above, but in this section bibliographies, etc.) pertaining to functions of a complex variable 30Cxx Geometric function theory 30-01 Introductory exposition (textbooks, tutorial pa- 30C10 Polynomials and rational functions of one compers, etc.) pertaining to functions of a complex plex variable variable 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable 30-02 Research exposition (monographs, survey articles) (e.g., zeros of functions with bounded Dirichlet inpertaining to functions of a complex variable tegral) {For algebraic theory, see 12D10; for real 30-03 History of functions of a complex variable [Conmethods, see 26C10} sider also classification numbers pertaining to Sec30C20 Conformal mappings of special domains tion 01] 30-04 Software, source code, etc. for problems pertain- 30C25 Covering theorems in conformal mapping theory ing to functions of a complex variable 30C30 Schwarz-Christoffel-type mappings [See also 65E10] 30-06 Proceedings, conferences, collections, etc. pertaining to functions of a complex variable 30C35 General theory of conformal mappings 46 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 30C40 Kernel functions in one complex variable and ap- 30D60 Quasi-analytic and other classes of functions of plications one complex variable 30C45 Special classes of univalent and multivalent func- 30D99 None of the above, but in this section tions of one complex variable (starlike, convex, bounded rotation, etc.) 30Exx Miscellaneous topics of analysis in 30C50 Coefficient problems for univalent and multiva- the complex plane lent functions of one complex variable 30E05 Moment problems and interpolation problems in 30C55 General theory of univalent and multivalent functhe complex plane tions of one complex variable 30C62 Quasiconformal mappings in the complex plane 30E10 Approximation in the complex plane 30C65 Quasiconformal mappings in Rn , other generalizations 30E15 Asymptotic representations in the complex plane 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane [See also 45Exx] 30C75 Extremal problems for conformal and quasicon- 30E25 Boundary value problems in the complex plane formal mappings, other methods [See also 45Exx] 30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordi- 30E99 None of the above, but in this section nation 30C85 Capacity and harmonic measure in the complex 30Fxx Riemann surfaces plane [See also 31A15] 30F10 Compact Riemann surfaces and uniformization [See also 14H15, 32G15] 30C99 None of the above, but in this section 30F15 Harmonic functions on Riemann surfaces 30Dxx Entire and meromorphic functions of one complex variable, and related topics 30F20 Classification theory of Riemann surfaces 30D05 Functional equations in the complex plane, iter- 30F25 Ideal boundary theory for Riemann surfaces ation and composition of analytic functions of one complex variable [See also 34Mxx, 37Fxx, 39-XX] 30F30 Differentials on Riemann surfaces 30D10 Representations of entire functions of one com30F35 Fuchsian groups and automorphic functions (asplex variable by series and integrals pects of compact Riemann surfaces and uniformization) [See also 11Fxx, 20H10, 22E40, 32Gxx, 30D15 Special classes of entire functions of one complex 32Nxx] variable and growth estimates 30D20 Entire functions of one complex variable, general 30F40 Kleinian groups (aspects of compact Riemann theory surfaces and uniformization) [See also 20H10] 30D30 Meromorphic functions of one complex variable, 30F45 Conformal metrics (hyperbolic, Poincaré, disgeneral theory tance functions) 30D35 Value distribution of meromorphic functions of 30F50 Klein surfaces one complex variable, Nevanlinna theory 30F60 Teichmüller theory for Riemann surfaces [See also 32G15] 30D40 Cluster sets, prime ends, boundary behavior 30D45 Normal functions of one complex variable, normal families 30F99 None of the above, but in this section 47 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 30Gxx Generalized function theory 30Kxx Universal holomorphic functions of 30G06 Non-Archimedean function theory [See also one complex variable 12J25]; nonstandard function theory [See also 30K05 Universal Taylor series in one complex variable 03H05] 30G12 Finely holomorphic functions and topological 30K10 Universal Dirichlet series in one complex variable function theory 30K15 Universal functions of one complex variable 30G20 Generalizations of Bers and Vekua type (pseudoanalytic, p-analytic, etc.) 30K20 Compositional universality 30G25 Discrete analytic functions 30K99 None of the above, but in this section 30G30 Other generalizations of analytic functions (including abstract-valued functions) 30Lxx Analysis on metric spaces 30G35 Functions of hypercomplex variables and gener30L05 Geometric embeddings of metric spaces alized variables 30G99 None of the above, but in this section 30L10 Quasiconformal mappings in metric spaces 30Hxx Spaces and algebras of analytic 30L15 Inequalities in metric spaces functions of one complex variable 30H05 Spaces of bounded analytic functions of one complex variable 30L99 None of the above, but in this section 31-XX Potential theory {For probabilistic potential theory, see 30H15 Nevanlinna spaces and Smirnov spaces 30H20 Bergman spaces and Fock spaces [See also 46E30, 60J45} 30H10 Hardy spaces [See also 42B30, 46E30] 46E35] 30H25 Besov spaces and Qp -spaces 30H30 Bloch spaces 30H35 BMO-spaces 30H40 Zygmund spaces 30H45 de Branges-Rovnyak spaces 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 30H50 Algebras of analytic functions of one complex 31-03 History of potential theory [Consider also classification numbers pertaining to Section 01] variable 30H80 Corona theorems 30H99 None of the above, but in this section 31-04 Software, source code, etc. for problems pertaining to potential theory 30Jxx Function theory on the disc 31-06 Proceedings, conferences, collections, etc. taining to potential theory per- 30J05 Inner functions of one complex variable 30J10 Blaschke products 30J15 Singular inner functions of one complex variable 30J99 None of the above, but in this section 31-08 Computational methods for problems pertaining to potential theory [See also 65Exx] 31-11 Research data for problems pertaining to potential theory 48 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 31Axx Two-dimensional potential theory 31C12 Potential theory on Riemannian manifolds and other spaces [See also 53C20] {For Hodge theory, 31A05 Harmonic, subharmonic, superharmonic funcsee 58A14} tions in two dimensions 31C15 Potentials and capacities on other spaces 31A10 Integral representations, integral operators, integral equations methods in two dimensions 31C20 Discrete potential theory 31A15 Potentials and capacity, harmonic measure, ex- 31C25 Dirichlet forms tremal length and related notions in two dimensions 31C35 Martin boundary theory [See also 60J50] [See also 30C85] 31A20 Boundary behavior (theorems of Fatou type, 31C40 Fine potential theory; fine properties of sets and functions etc.) of harmonic functions in two dimensions 31A25 Boundary value and inverse problems for har- 31C45 Other generalizations (nonlinear potential theory, etc.) monic functions in two dimensions 31A30 Biharmonic, polyharmonic functions and equa- 31C99 None of the above, but in this section tions, Poisson’s equation in two dimensions 31Dxx Axiomatic potential theory 31A35 Connections of harmonic functions with differential equations in two dimensions 31D05 Axiomatic potential theory 31A99 None of the above, but in this section 31D99 None of the above, but in this section 31Bxx Higher-dimensional potential the- 31Exx Potential theory on fractals and ory metric spaces 31B05 Harmonic, subharmonic, superharmonic func- 31E05 Potential theory on fractals and metric spaces tions in higher dimensions 31E99 None of the above, but in this section 31B10 Integral representations, integral operators, integral equations methods in higher dimensions 32-XX Several complex variables and analytic spaces {For infinitedimensional holomorphy, see also 31B20 Boundary value and inverse problems for har46G20, 58B12} monic functions in higher dimensions 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 31B25 Boundary behavior of harmonic functions in 32-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex higher dimensions variables and analytic spaces 31B30 Biharmonic and polyharmonic equations and 32-01 Introductory exposition (textbooks, tutorial pafunctions in higher dimensions pers, etc.) pertaining to several complex variables 31B35 Connections of harmonic functions with differenand analytic spaces tial equations in higher dimensions 32-02 Research exposition (monographs, survey articles) 31B99 None of the above, but in this section pertaining to several complex variables and analytic spaces 31Cxx Generalizations of potential theory 31C05 Harmonic, subharmonic, superharmonic functions on other spaces 32-03 History of several complex variables and analytic spaces [Consider also classification numbers pertaining to Section 01] 31C10 Pluriharmonic and plurisubharmonic functions 32-04 Software, source code, etc. for problems pertain[See also 32U05] ing to several complex variables and analytic spaces 49 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 32-06 Proceedings, conferences, collections, etc. per- 32A35 H p -spaces, Nevanlinna spaces of functions in sevtaining to several complex variables and analytic eral complex variables [See also 32M15, 42B30, spaces 43A85, 46J15] 32-08 Computational methods for problems pertaining 32A36 Bergman spaces of functions in several complex to several complex variables and analytic spaces variables [See also 65Exx] 32A37 Other spaces of holomorphic functions of several 32-11 Research data for problems pertaining to several complex variables (e.g., bounded mean oscillation complex variables and analytic spaces (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 32Axx Holomorphic functions of several 32A38 Algebras of holomorphic functions of several complex variables complex variables [See also 46J10, 46J15] 32A05 Power series, series of functions of several complex variables 32A40 Boundary behavior of holomorphic functions of several complex variables 32A08 Polynomials and rational functions of several complex variables 32A45 Hyperfunctions [See also 46F15] 32A10 Holomorphic functions of several complex vari32A50 Harmonic analysis of several complex variables ables [See mainly 43-XX] 32A12 Multifunctions of several complex variables 32A55 Singular integrals of functions in several complex 32A15 Entire functions of several complex variables variables 32A17 Special families of functions of several complex 32A60 Zero sets of holomorphic functions of several variables complex variables 32A18 Bloch functions, normal functions of several com32A65 Banach algebra techniques applied to functions plex variables of several complex variables [See also 46Jxx] 32A19 Normal families of holomorphic functions, mappings of several complex variables, and related top- 32A70 Functional analysis techniques applied to functions of several complex variables [See also 46Exx] ics (taut manifolds etc.) 32A20 Meromorphic functions of several complex vari- 32A99 None of the above, but in this section ables 32A22 Nevanlinna theory; growth estimates; other in- 32Bxx Local analytic geometry [See also equalities of several complex variables {For geomet- 13-XX, 14-XX] ric theory, see 32H25, 32H30} 32B05 Analytic algebras and generalizations, prepara32A25 Integral representations; canonical kernels tion theorems (Szegő, Bergman, etc.) 32B10 Germs of analytic sets, local parametrization 32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) 32B15 Analytic subsets of affine space 32A27 Residues for several complex variables [See also 32B20 Semi-analytic sets, subanalytic sets, and general32C30] izations [See also 14P15] 32A30 Other generalizations of function theory of one complex variable (should also be assigned at least 32B25 Triangulation and topological properties of semione classification number from Section 30) {For analytic andsubanalytic sets, and related questions functions of several hypercomplex variables, see 30G35} 32B99 None of the above, but in this section 50 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 32Exx Holomorphic convexity 32Cxx Analytic spaces 32C05 Real-analytic manifolds, real-analytic spaces [See 32E05 Holomorphically convex complex spaces, reduction theory also 14Pxx, 58A07] 32C07 Real-analytic sets, complex Nash functions [See 32E10 Stein spaces, Stein manifolds also 14P15, 14P20] 32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables 32C09 Embedding of real-analytic manifolds 32E30 Holomorphic, polynomial and rational approxi32C11 Complex supergeometry [See also 14A22, 14M30, mation, and interpolation in several complex vari58A50] ables; Runge pairs 32C15 Complex spaces 32E35 Global boundary behavior of holomorphic functions of several complex variables 32C18 Topology of analytic spaces 32E40 The Levi problem 32C20 Normal analytic spaces 32E99 None of the above, but in this section 32C22 Embedding of analytic spaces 32Fxx Geometric convexity in several complex variables 32C25 Analytic subsets and submanifolds 32C30 Integration on analytic sets and spaces, currents 32F10 q-convexity, q-concavity [See also 32A25, 32A27] 32F17 Other notions of convexity in relation to several 32C35 Analytic sheaves and cohomology groups [See complex variables also 14Fxx, 18F20, 55N30] 32F18 Finite-type conditions for the boundary of a do32C36 Local cohomology of analytic spaces main 32F27 Topological consequences of geometric convexity 32C37 Duality theorems for analytic spaces 32C38 Sheaves of differential operators and their mod- 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.) ules, D-modules [See also 14F10, 16S32, 35A27, 58J15] 32F45 Invariant metrics and pseudodistances in several complex variables 32C55 The Levi problem in complex spaces; generalizations 32F99 None of the above, but in this section 32C81 Applications of analytic spaces to physics and 32Gxx Deformations of analytic structures other areas of science 32G05 Deformations of complex structures [See also 32C99 None of the above, but in this section 13D10, 16S80, 58H10, 58H15] 32G07 Deformations of special (e.g., CR) structures 32Dxx Analytic continuation 32G08 Deformations of fiber bundles 32D05 Domains of holomorphy 32G10 Deformations of submanifolds and subspaces 32D10 Envelopes of holomorphy 32D15 Continuation of analytic objects in several complex variables 32G13 Complex-analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 32D20 Removable singularities in several complex vari- 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) [See ables also 14H15, 30Fxx] 32D26 Riemann domains 32G20 Period matrices, variation of Hodge structure; 32D99 None of the above, but in this section degenerations [See also 14D05, 14D07, 14K30] 51 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 32G34 Moduli and deformations for ordinary differential 32J81 Applications of compact analytic spaces to the equations (e.g., Knizhnik-Zamolodchikov equation) sciences [See also 34Mxx] 32J99 None of the above, but in this section 32G81 Applications of deformations of analytic structures to the sciences 32Kxx Generalizations of analytic spaces 32G99 None of the above, but in this section 32K05 Banach analytic manifolds and spaces [See also 46G20, 58Bxx] 32Hxx Holomorphic mappings and corre32K07 Formal and graded complex spaces [See also spondences 58C50] 32H02 Holomorphic mappings, (holomorphic) embed32K12 Holomorphic maps with infinite-dimensional ardings and related questions in several complex variguments or values [See also 46G20] ables 32K15 Differentiable functions on analytic spaces, dif32H04 Meromorphic mappings in several complex variferentiable spaces [See also 58C25] ables 32K99 None of the above, but in this section 32H12 Boundary uniqueness of mappings in several complex variables 32Lxx Holomorphic fiber spaces [See also 32H25 Picard-type theorems and generalizations for 55Rxx] several complex variables {For function-theoretic 32L05 Holomorphic bundles and generalizations properties, see 32A22} 32H30 Value distribution theory in higher dimensions 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F06, {For function-theoretic properties, see 32A22} 14H60, 14J60, 18F20, 55N30] 32H35 Proper holomorphic mappings, finiteness theo32L15 Bundle convexity [See also 32F10] rems 32H40 Boundary regularity of mappings in several com- 32L20 Vanishing theorems plex variables 32L25 Twistor theory, double fibrations (complexanalytic aspects) [See also 53C28] 32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several 32L81 Applications of holomorphic fiber spaces to the complex variables sciences 32H99 None of the above, but in this section 32L99 None of the above, but in this section 32Jxx Compact analytic spaces {For Rie- 32Mxx Complex spaces with a group of aumann surfaces, see 14Hxx, 30Fxx; for al- tomorphisms gebraic theory, see 14Jxx} 32M05 Complex Lie groups, group actions on complex spaces [See also 22E10] 32J05 Compactification of analytic spaces 32J10 Algebraic dependence theorems 32M10 Homogeneous complex manifolds [See also 14M17, 57T15] 32J15 Compact complex surfaces 32M12 Almost homogeneous manifolds and spaces [See also 14M17] 32J17 Compact complex 3-folds 32J18 Compact complex n-folds 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects) [See also 14C30] 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) [See also 22E10, 22E40, 53C35, 57T15] 32J27 Compact Kähler manifolds: generalizations, clas- 32M17 Automorphism groups of Cn and affine manisification folds 52 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 32M18 Automorphism groups of other complex spaces 32Q56 Oka principle and Oka manifolds 32M25 Complex vector fields, holomorphic foliations, Cactions 32Q57 Classification theorems for complex manifolds 32Q60 Almost complex manifolds 32M99 None of the above, but in this section 32Q65 Pseudoholomorphic curves 32Nxx Automorphic functions [See also 32Q99 None of the above, but in this section 11Fxx, 20H10, 22E40, 30F35] 32N05 General theory of automorphic functions of sev- 32Sxx eral complex variables Complex singularities [See also 58Kxx] 32N10 Automorphic forms in several complex variables 32N15 Automorphic functions in symmetric domains 32N99 None of the above, but in this section 32S05 Local complex singularities [See also 14J17] 32S10 Invariants of analytic local rings 32S15 Equisingularity (topological and analytic) [See also 14E15] 32Pxx Non-Archimedean analysis (should also be assigned at least one other classifi- 32S20 Global theory of complex singularities; cohomological properties [See also 14E15] cation number from Section 32 describing the type of problem) 32S22 Relations with arrangements of hyperplanes [See also 52C35] 32P05 Non-Archimedean analysis (should also be assigned at least one other classification number from 32S25 Complex surface and hypersurface singularities Section 32 describing the type of problem) [See also 14J17] 32P99 None of the above, but in this section 32S30 Deformations of complex singularities; vanishing cycles [See also 14B07] 32Qxx Complex manifolds 32Q02 Special domains (Reinhardt, Hartogs, circular, 32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects) [See also 14C30, 14D07] tube, etc.) in Cn and complex manifolds 32Q05 Negative curvature complex manifolds 32S40 Monodromy; relations with differential equations and D-modules (complex-analytic aspects) 32Q10 Positive curvature complex manifolds 32Q15 Kähler manifolds 32S45 Modifications; resolution of singularities (complex-analytic aspects) [See also 14E15] 32Q20 Kähler-Einstein manifolds [See also 53Cxx] 32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invari32Q25 Calabi-Yau theory (complex-analytic aspects) ants [See also 14J32] 32Q26 Notions of stability for complex manifolds 32S55 Milnor fibration; relations with knot theory [See also 57K10, 57K45] 32Q28 Stein manifolds 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) [See also 58Kxx] 32Q35 Complex manifolds as subdomains of Euclidean space 32S65 Singularities of holomorphic vector fields and foliations 32Q40 Embedding theorems for complex manifolds 32Q30 Uniformization of complex manifolds 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 32S70 Other operations on complex singularities 32Q55 Topological aspects of complex manifolds 32S99 None of the above, but in this section 53 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 32Txx Pseudoconvex domains 32Wxx Differential operators in several variables 32T05 Domains of holomorphy 32W05 ∂ and ∂-Neumann operators 32T15 Strongly pseudoconvex domains 32W10 ∂ b and ∂ b -Neumann operators 32T20 Worm domains 32W20 Complex Monge-Ampère operators 32T25 Finite-type domains 32T27 Geometric and analytic invariants on weakly 32W25 Pseudodifferential operators in several complex variables pseudoconvex boundaries 32T35 Exhaustion functions 32W30 Heat kernels in several complex variables 32T40 Peak functions 32W50 Other partial differential equations of complex analysis in several variables 32T99 None of the above, but in this section 32W99 None of the above, but in this section 32Uxx Pluripotential theory 32U05 Plurisubharmonic functions and generalizations [See also 31C10] 32U10 Plurisubharmonic exhaustion functions 32U15 General pluripotential theory 32U20 Capacity theory and generalizations 32U25 Lelong numbers 32U30 Removable sets in pluripotential theory 33-XX Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11XX; for representation theory, see 22Exx} 32U35 Plurisubharmonic extremal functions, pluricom33-00 General reference works (handbooks, dictionaries, plex Green functions bibliographies, etc.) pertaining to special functions 32U40 Currents 33-01 Introductory exposition (textbooks, tutorial pa32U99 None of the above, but in this section pers, etc.) pertaining to special functions 32Vxx CR manifolds 33-02 Research exposition (monographs, survey articles) pertaining to special functions 32V05 CR structures, CR operators, and generaliza33-03 History of special functions [Consider also classitions fication numbers pertaining to Section 01] 32V10 CR functions 33-04 Software, source code, etc. for problems pertain32V15 CR manifolds as boundaries of domains ing to special functions 32V20 Analysis on CR manifolds 33-06 Proceedings, conferences, collections, etc. taining to special functions per- 32V25 Extension of functions and other analytic objects from CR manifolds 33-11 Research data for problems pertaining to special functions 32V30 Embeddings of CR manifolds 32V35 Finite-type conditions on CR manifolds 33Bxx Elementary classical functions 32V40 Real submanifolds in complex manifolds 33B10 Exponential and trigonometric functions 32V99 None of the above, but in this section 33B15 Gamma, beta and polygamma functions 54 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 33B20 Incomplete beta and gamma functions (error 33Dxx Basic hypergeometric functions functions, probability integral, Fresnel integrals) 33D05 q-gamma functions, q-beta functions and integrals 33B30 Higher logarithm functions 33B99 None of the above, but in this section 33D15 Basic hypergeometric functions in one variable, r φs 33Cxx Hypergeometric functions 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33C05 Classical hypergeometric functions, 2 F1 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 33C10 Bessel and Airy functions, cylinder functions, 0 F1 33C15 Confluent hypergeometric functions, Whittaker 33D52 Basic orthogonal polynomials and functions assofunctions, 1 F1 ciated with root systems (Macdonald polynomials, etc.) 33C20 Generalized hypergeometric series, p Fq 33D60 Basic hypergeometric integrals and functions de33C45 Orthogonal polynomials and functions of hyperfined by them geometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) {For general orthogonal polynomials 33D65 Bibasic functions and multiple bases and functions, see also 42C05} 33D67 Basic hypergeometric functions associated with root systems 33C47 Other special orthogonal polynomials and functions 33D70 Other basic hypergeometric functions and integrals in several variables 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in 33D80 Connections of basic hypergeometric functions one variable with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics 33C52 Orthogonal polynomials and functions associated 33D90 Applications of basic hypergeometric functions with root systems 33D99 None of the above, but in this section 33C55 Spherical harmonics 33C60 Hypergeometric integrals and functions defined 33Exx Other special functions by them (E, G, H and I functions) 33E05 Elliptic functions and integrals 33C65 Appell, Horn and Lauricella functions 33E10 Lamé, Mathieu, and spheroidal wave functions 33C67 Hypergeometric functions associated with root 33E12 Mittag-Leffler functions and generalizations systems 33E15 Other wave functions 33C70 Other hypergeometric functions and integrals in 33E17 Painlevé-type functions several variables 33E20 Other functions defined by series and integrals 33C75 Elliptic integrals as hypergeometric functions 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 33E30 Other functions coming from differential, difference and integral equations 33C90 Applications of hypergeometric functions 33E50 Special functions in characteristic p (gamma functions, etc.) 33C99 None of the above, but in this section 33E99 None of the above, but in this section 55 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 33Fxx Computational aspects of special 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solufunctions {For software etc., see 33-04} tions to ordinary differential equations 33F05 Numerical approximation and evaluation of spe34A25 Analytical theory of ordinary differential equacial functions [See also 65D20] tions: series, transformations, transforms, opera33F10 Symbolic computation of special functions tional calculus, etc. [See also 44-XX] (Gosper and Zeilberger algorithms, etc.) [See also 34A26 Geometric methods in ordinary differential equa68W30] tions 33F99 None of the above, but in this section 34A30 Linear ordinary differential equations and systems, general 34-XX Ordinary differential equa- 34A33 Ordinary lattice differential equations tions 34A34 Nonlinear ordinary differential equations and systems, general theory 34-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differ- 34A35 Ordinary differential equations of infinite order ential equations 34A36 Discontinuous ordinary differential equations 34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equa- 34A37 Ordinary differential equations with impulses tions 34A38 Hybrid systems of ordinary differential equations 34-02 Research exposition (monographs, survey articles) 34A40 Differential inequalities involving functions of a pertaining to ordinary differential equations single real variable [See also 26D20] 34-03 History of ordinary differential equations [Con- 34A45 Theoretical approximation of solutions to ordisider also classification numbers pertaining to Secnary differential equations {For numerical analysis, tion 01] see 65Lxx} 34-04 Software, source code, etc. for problems pertain- 34A55 Inverse problems involving ordinary differential equations ing to ordinary differential equations 34-06 Proceedings, conferences, collections, etc. taining to ordinary differential equations per- 34A60 Ordinary differential inclusions [See also 49J21, 49K21] 34-11 Research data for problems pertaining to ordinary 34A99 None of the above, but in this section differential equations 34Bxx Boundary value problems for ordi34Axx General theory for ordinary differ- nary differential equations {For ordinary differential operators, see 34Lxx} ential equations 34B05 Linear boundary value problems for ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations 34B07 Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter 34A06 Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) 34B08 Parameter dependent boundary value problems for ordinary differential equations 34A07 Fuzzy ordinary differential equations 34A08 Fractional ordinary differential equations and 34B09 Boundary eigenvalue problems for ordinary diffractional differential inclusions ferential equations 34A09 Implicit ordinary differential differential-algebraic equations equations, 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 56 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 34B15 Nonlinear boundary value problems for ordinary 34C15 Nonlinear oscillations and coupled oscillators for differential equations ordinary differential equations 34B16 Singular nonlinear boundary value problems for 34C20 Transformation and reduction of ordinary differordinary differential equations ential equations and systems, normal forms 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34C23 Bifurcation theory for ordinary differential equa34B20 Weyl theory and its generalizations for ordinary tions [See also 37Gxx] differential equations 34B24 Sturm-Liouville theory [See also 34Lxx] 34B27 Green’s functions for ordinary differential equations 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34C25 Periodic solutions to ordinary differential equations 34C26 Relaxation oscillations for ordinary differential equations 34B37 Boundary value problems with impulses for ordi34C27 Almost and pseudo-almost periodic solutions to nary differential equations ordinary differential equations 34B40 Boundary value problems on infinite intervals for ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations [See also 37Dxx] 34B45 Boundary value problems on graphs and networks for ordinary differential equations 34B60 Applications of boundary value problems involv- 34C29 Averaging method for ordinary differential equations ing ordinary differential equations 34B99 None of the above, but in this section 34Cxx Qualitative theory for ordinary differential equations [See also 37-XX] 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 34C40 Ordinary differential equations and systems on manifolds 34C07 Theory of limit cycles of polynomial and ana- 34C41 Equivalence and asymptotic equivalence of ordilytic vector fields (existence, uniqueness, bounds, nary differential equations Hilbert’s 16th problem and ramifications) for ordinary differential equations 34C45 Invariant manifolds for ordinary differential 34C08 Ordinary differential equations and connections equations with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 34C46 Multifrequency systems of ordinary differential 34C10 Oscillation theory, zeros, disconjugacy and comequations parison theory for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary 34C55 Hysteresis for ordinary differential equations differential equations 34C12 Monotone systems involving ordinary differential 34C60 Qualitative investigation and simulation of ordiequations nary differential equation models 34C14 Symmetries, invariants of ordinary differential equations [See also 37C79] 34C99 None of the above, but in this section 57 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 34Dxx Stability theory for ordinary differ- 34Fxx Ordinary differential equations and ential equations [See also 37C75, 93Dxx] systems with randomness [See also 34K50, 34D05 Asymptotic properties of solutions to ordinary 60H10, 93E03] differential equations 34F05 Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03] 34D06 Synchronization of solutions to ordinary differential equations 34D08 Characteristic and Lyapunov exponents of ordi- 34F10 Bifurcation of solutions to ordinary differential equations involving randomness nary differential equations 34D09 Dichotomy, trichotomy of solutions to ordinary 34F15 Resonance phenomena for ordinary differential differential equations equations involving randomness 34D10 Perturbations of ordinary differential equations 34D15 Singular perturbations of ordinary differential 34F99 None of the above, but in this section equations 34D20 Stability of solutions to ordinary differential equations 34Gxx Differential equations in abstract 34D23 Global stability of solutions to ordinary differen- spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] tial equations 34D30 Structural stability and analogous concepts of so- 34G10 Linear differential equations in abstract spaces lutions to ordinary differential equations [See also [See also 47D06, 47D09] 37C20] 34D35 Stability of manifolds of solutions to ordinary dif- 34G20 Nonlinear differential equations in abstract ferential equations spaces [See also 47Hxx, 47Jxx] 34D45 Attractors of solutions to ordinary differential equations [See also 37C70, 37D45] 34G25 Evolution inclusions 34D99 None of the above, but in this section 34G99 None of the above, but in this section 34Exx Asymptotic theory for ordinary differential equations 34E05 Asymptotic expansions of solutions to ordinary 34Hxx Control problems including ordinary differential equations [See also 49J15, differential equations 49K15, 93C15] 34E10 Perturbations, asymptotics of solutions to ordinary differential equations 34H05 Control problems involving ordinary differential equations [See also 49J15, 49K15, 93C15] 34E13 Multiple scale methods for ordinary differential equations 34E15 Singular perturbations, general theory for ordi- 34H10 Chaos control for problems involving ordinary differential equations nary differential equations 34E17 Canard solutions to ordinary differential equa34H15 Stabilization of solutions to ordinary differential tions equations 34E18 Methods of nonstandard analysis for ordinary differential equations 34H20 Bifurcation control of ordinary differential equa34E20 Singular perturbations, turning point theory, tions WKB methods for ordinary differential equations 34E99 None of the above, but in this section 34H99 None of the above, but in this section 58 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 34Kxx Functional-differential equations 34K26 Singular perturbations of functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34K27 Perturbations of functional-differential equations 34K04 Symmetries, invariants of functional-differential equations [See also 37C79] 34K29 Inverse problems for functional-differential equations 34K05 General theory of functional-differential equations 34K30 Functional-differential equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 34K06 Linear functional-differential equations 34K07 Theoretical approximation of functional-differential equations solutions to 34K31 Lattice functional-differential equations 34K08 Spectral theory of functional-differential opera- 34K32 Implicit functional-differential equations tors 34K33 Averaging for functional-differential equations 34K09 Functional-differential inclusions 34K10 Boundary value problems differential equations for functional- 34K34 Hybrid systems of functional-differential equations 34K11 Oscillation theory of functional-differential equa34K35 Control problems for functional-differential equations tions [See also 49J21, 49K21, 93C23] 34K12 Growth, boundedness, comparison of solutions to 34K36 Fuzzy functional-differential equations functional-differential equations [See also 37C35] 34K13 Periodic solutions to functional-differential equa- 34K37 Functional-differential equations with fractional tions [See also 37C27] derivatives 34K14 Almost and pseudo-almost periodic solutions to 34K38 Functional-differential inequalities functional-differential equations 34K16 Heteroclinic and homoclinic orbits of functional- 34K39 Discontinuous functional-differential equations differential equations [See also 37C29] 34K17 Transformation and reduction of functional- 34K40 Neutral functional-differential equations differential equations and systems, normal forms 34K41 Functional-differential equations in the complex 34K18 Bifurcation theory of functional-differential domain equations [See also 37Gxx] 34K19 Invariant manifolds of functional-differential 34K42 Functional-differential equations on time scales or measure chains equations 34K20 Stability theory of functional-differential equa- 34K43 Functional-differential equations with statetions [See also 37C75] dependent arguments 34K21 Stationary solutions of functional-differential 34K45 Functional-differential equations with impulses equations 34K23 Complex (chaotic) behavior of solutions to 34K50 Stochastic functional-differential equations [See functional-differential equations [See also 37D45] also 34Fxx, 60Hxx] 34K24 Synchronization of functional-differential equa34K60 Qualitative investigation and simulation of modtions els involving functional-differential equations 34K25 Asymptotic theory of functional-differential equations 34K99 None of the above, but in this section 59 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 34Lxx Ordinary differential operators [See 34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the also 47E05] complex domain, normal forms 34L05 General spectral theory of ordinary differential 34M40 Stokes phenomena and connection problems (linoperators ear and nonlinear) for ordinary differential equa34L10 Eigenfunctions, eigenfunction expansions, comtions in the complex domain pleteness of eigenfunctions of ordinary differential 34M45 Ordinary differential equations on complex manoperators ifolds 34L15 Eigenvalues, estimation of eigenvalues, upper and 34M46 Spectral theory for ordinary differential operalower bounds of ordinary differential operators tors in the complex domain 34L16 Numerical approximation of eigenvalues and of 34M50 Inverse problems (Riemann-Hilbert, inverse difother parts of the spectrum of ordinary differential ferential Galois, etc.) for ordinary differential equaoperators tions in the complex domain 34L20 Asymptotic distribution of eigenvalues, asymp- 34M55 Painlevé and other special ordinary differential totic theory of eigenfunctions for ordinary differenequations in the complex domain; classification, hitial operators erarchies 34L25 Scattering theory, inverse scattering involving or- 34M56 Isomonodromic deformations for ordinary differdinary differential operators ential equations in the complex domain 34L30 Nonlinear ordinary differential operators 34M60 Singular perturbation problems for ordinary differential equations in the complex domain (complex 34L40 Particular ordinary differential operators (Dirac, WKB, turning points, steepest descent) [See also one-dimensional Schrödinger, etc.) 34E20] 34L99 None of the above, but in this section 34M65 Topological structure of trajectories of ordinary differential equations in the complex domain 34Mxx Ordinary differential equations in 34M99 None of the above, but in this section the complex domain [See also 30Dxx, 32G34] 34Nxx Dynamic equations on time scales 34M03 Linear ordinary differential equations and sys- or measure chains {For real analysis on tems in the complex domain time scales, see 26E70} 34M04 Nonlinear ordinary differential equations and 34N05 Dynamic equations on time scales or measure chains {For real analysis on time scales or measure systems in the complex domain chains, see 26E70} 34M05 Entire and meromorphic solutions to ordinary 34N99 None of the above, but in this section differential equations in the complex domain 34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain 35-XX Partial differential equations 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differ- 35-00 General reference works (handbooks, dictionaries, ential bibliographies, etc.) pertaining to partial differenequations in the complex domain tial equations 34M25 Formal solutions and transform techniques for 35-01 Introductory exposition (textbooks, tutorial paordinary differential equations in the complex dopers, etc.) pertaining to partial differential equamain tions 34M30 Asymptotics and summation methods for ordi- 35-02 Research exposition (monographs, survey articles) nary differential equations in the complex domain pertaining to partial differential equations 60 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 35-03 History of partial differential equations [Consider 35Bxx Qualitative properties of solutions also classification numbers pertaining to Section 01] to partial differential equations 35-04 Software, source code, etc. for problems pertain- 35B05 Oscillation, zeros of solutions, mean value theoing to partial differential equations rems, etc. in context of PDEs 35-06 Proceedings, conferences, collections, etc. taining to partial differential equations per- 35B06 Symmetries, invariants, etc. in context of PDEs 35B07 Axially symmetric solutions to PDEs 35-11 Research data for problems pertaining to partial 35B08 Entire solutions to PDEs differential equations 35B09 Positive solutions to PDEs 35Axx General topics in partial differential 35B10 Periodic solutions to PDEs equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35B15 Almost and pseudo-almost periodic solutions to PDEs 35B20 Perturbations in context of PDEs 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35B25 Singular perturbations in context of PDEs 35A08 Fundamental solutions to PDEs 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure [See also 74Q05, 74Q10, 76M50, 78M40, 80M40] 35A09 Classical solutions to PDEs 35A10 Cauchy-Kovalevskaya theorems 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs [See also 37Cxx] 35A15 Variational methods applied to PDEs 35A16 Topological and monotonicity methods applied 35B32 Bifurcations in context of PDEs [See also 34C23, to PDEs 34F10, 34H20, 37F46, 37Gxx, 37H20, 35J20, 37L10, 35A17 Parametrices in context of PDEs 37M20, 47J15, 58E05, 58E07, 58J55, 74G60, 74H60] 35A18 Wave front sets in context of PDEs 35B33 Critical exponents in context of PDEs 35A20 Analyticity in context of PDEs 35B34 Resonance in context of PDEs [See also 34F15, 70J40, 70K28, 70K30, 81U24] 35A21 Singularity in context of PDEs 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35B35 Stability in context of PDEs [See also 34Dxx, 37B25, 37C20, 37C75, 37F15, 37J25, 37K45, 37L15, 49K40, 58K25, 93Dxx] 35A23 Inequalities applied to PDEs involving deriva35B36 Pattern formations in context of PDEs [See also tives, differential and integral operators, or integrals 92C15] 35A24 Methods of ordinary differential equations ap35B38 Critical points of functionals in context of PDEs plied to PDEs (e.g., energy functionals) [See also 57R70, 58K05, 58E05] 35A25 Other special methods applied to PDEs 35A27 Microlocal methods and methods of sheaf theory 35B40 Asymptotic behavior of solutions to PDEs and homological algebra applied to PDEs [See also 35B41 Attractors [See also 34D45, 37B35, 37C70, 32C38, 58J15] 37D45, 37G35, 37L30, 37M22] 35A30 Geometric theory, characteristics, transforma- 35B42 Inertial manifolds [See also 37L25] tions in context of PDEs [See also 58J70, 58J72] 35B44 Blow-up in context of PDEs 35A35 Theoretical approximation in context of PDEs {For numerical analysis, see 65Mxx, 65Nxx} 35B45 A priori estimates in context of PDEs 35A99 None of the above, but in this section 35B50 Maximum principles in context of PDEs 61 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 35Fxx General first-order partial differen35B53 Liouville theorems and Phragmén-Lindelöf theo- tial equations and systems of first-order partial differential equations rems in context of PDEs 35B51 Comparison principles in context of PDEs 35B60 Continuation and prolongation of solutions to 35F05 Linear first-order PDEs PDEs [See also 58A15, 58A17, 58Hxx] 35F10 Initial value problems for linear first-order PDEs 35B65 Smoothness and regularity of solutions to PDEs 35B99 None of the above, but in this section 35F15 Boundary value problems for linear first-order PDEs 35Cxx Representations of solutions to par35F16 Initial-boundary value problems for linear firsttial differential equations order PDEs 35C05 Solutions to PDEs in closed form 35C06 Self-similar solutions to PDEs 35F20 Nonlinear first-order PDEs 35C07 Traveling wave solutions 35F21 Hamilton-Jacobi equations {For calculus of variations and optimal control, see 49Lxx; for mechanics of particles and systems, see 70H20} 35C08 Soliton solutions [See also 37K40] 35C09 Trigonometric solutions to PDEs 35F25 Initial value problems for nonlinear first-order PDEs 35C10 Series solutions to PDEs 35C11 Polynomial solutions to PDEs 35F30 Boundary value problems for nonlinear first-order PDEs 35C15 Integral representations of solutions to PDEs 35C20 Asymptotic expansions of solutions to PDEs 35F31 Initial-boundary value problems for nonlinear first-order PDEs 35C99 None of the above, but in this section 35Dxx Generalized solutions to partial dif35F35 Systems of linear first-order PDEs ferential equations 35D30 Weak solutions to PDEs 35F40 Initial value problems for systems of linear firstorder PDEs 35D35 Strong solutions to PDEs 35D40 Viscosity solutions to PDEs 35F45 Boundary value problems for systems of linear first-order PDEs 35D99 None of the above, but in this section 35F46 Initial-boundary value problems for systems of 35Exx Partial differential equations and linear first-order PDEs systems of partial differential equations with constant coefficients [See also 35N05] 35F50 Systems of nonlinear first-order PDEs 35E05 Fundamental solutions to PDEs and systems of 35F55 Initial value problems for systems of nonlinear PDEs with constant coefficients first-order PDEs 35E10 Convexity properties of solutions to PDEs and systems of PDEs with constant coefficients 35F60 Boundary value problems for systems of nonlin35E15 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 None of the above, but in this section 35F61 Initial-boundary value problems for systems of nonlinear first-order PDEs 35F99 None of the above, but in this section 62 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. ear first-order PDEs 35Gxx General higher-order partial dif- 35Jxx Elliptic equations and elliptic sysferential equations and systems of higher- tems {For global analysis, analysis on manorder partial differential equations ifolds, see 58J10, 58J20} 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation [See also 31Axx, 35G10 Initial value problems for linear higher-order 31Bxx] PDEs 35J08 Green’s functions for elliptic equations 35G15 Boundary value problems for linear higher-order 35J10 Schrödinger operator, Schrödinger equation {For PDEs ordinary differential equations, see 34L40; for operator theory, see 47D08; for quantum theory, see 35G16 Initial-boundary value problems for linear 81Q05; for statistical mechanics, see 82B44} higher-order PDEs 35G05 Linear higher-order PDEs 35J15 Second-order elliptic equations 35G20 Nonlinear higher-order PDEs 35G25 Initial value problems for nonlinear higher-order PDEs 35G30 Boundary value problems for nonlinear higherorder PDEs 35J20 Variational methods for second-order elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35J30 Higher-order elliptic equations [See also 31A30, 31B30] 35G31 Initial-boundary value problems for nonlinear higher-order PDEs 35J35 Variational methods for higher-order elliptic equations 35G35 Systems of linear higher-order PDEs 35G40 Initial value problems for systems of linear higher-order PDEs 35J40 Boundary value problems for higher-order elliptic equations 35J46 First-order elliptic systems 35G45 Boundary value problems for systems of linear 35J47 Second-order elliptic systems higher-order PDEs 35J48 Higher-order elliptic systems 35G46 Initial-boundary value problems for systems of 35J50 Variational methods for elliptic systems linear higher-order PDEs 35G50 Systems of nonlinear higher-order PDEs 35J56 Boundary value problems for first-order elliptic systems 35G55 Initial value problems for systems of nonlinear 35J57 Boundary value problems for second-order elliptic higher-order PDEs systems 35G60 Boundary value problems for systems of nonlin- 35J58 Boundary value problems for higher-order elliptic ear higher-order PDEs systems 35G61 Initial-boundary value problems for systems of 35J60 Nonlinear elliptic equations nonlinear higher-order PDEs 35J61 Semilinear elliptic equations 35G99 None of the above, but in this section 35J62 Quasilinear elliptic equations 35Hxx Close-to-elliptic equations 35J65 Nonlinear boundary value problems for linear elliptic equations 35H10 Hypoelliptic equations 35H20 Subelliptic equations 35J66 Nonlinear boundary value problems for nonlinear elliptic equations 35H30 Quasielliptic equations 35J67 Boundary values of solutions to elliptic equations and elliptic systems 35H99 None of the above, but in this section 35J70 Degenerate elliptic equations 63 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 35J75 Singular elliptic equations 35K46 Initial value problems for higher-order parabolic systems 35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic op- 35K51 Initial-boundary value problems for second-order erators [See also 35R35, 49J40] parabolic systems 35J87 Unilateral problems for nonlinear elliptic equa- 35K52 Initial-boundary value problems for higher-order tions and variational inequalities with nonlinear elparabolic systems liptic operators [See also 35R35, 49J40] 35K55 Nonlinear parabolic equations 35J88 Unilateral problems for elliptic systems and systems of variational inequalities with elliptic opera- 35K57 Reaction-diffusion equations {For diffusion protors [See also 35R35, 49J40] cesses and reaction effects, see 47D07, 58J65, 60J60, 60J70, 74N25, 76R50, 76V05, 80A23, 82B24, 35J91 Semilinear elliptic equations with Laplacian, bi82C24, 92E20} Laplacian or poly-Laplacian 35J92 Quasilinear elliptic equations with p-Laplacian 35K58 Semilinear parabolic equations 35J93 Quasilinear elliptic equations with mean curva- 35K59 Quasilinear parabolic equations ture operator 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35J94 Elliptic equations with infinity-Laplacian 35J96 Monge-Ampère equations {For complex Monge- 35K61 Nonlinear initial, boundary and initial-boundary Ampère operators, see 32W20; for parabolic Mongevalue problems for nonlinear parabolic equations Ampère equations, see 35K96} 35K65 Degenerate parabolic equations 35J99 None of the above, but in this section 35K67 Singular parabolic equations 35Kxx Parabolic equations and parabolic 35K70 Ultraparabolic equations, pseudoparabolic equasystems {For global analysis, analysis on tions, etc. manifolds, see 58J35} 35K05 Heat equation 35K08 Heat kernel 35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators [See also 35R35, 49J40] 35K86 Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear 35K15 Initial value problems for second-order parabolic parabolic operators [See also 35R35, 49J40] equations 35K87 Unilateral problems for parabolic systems and 35K20 Initial-boundary value problems for second-order systems of variational inequalities with parabolic parabolic equations operators [See also 35R35, 49J40] 35K10 Second-order parabolic equations 35K25 Higher-order parabolic equations 35K90 Abstract parabolic equations 35K30 Initial value problems for higher-order parabolic 35K91 Semilinear parabolic equations with Laplacian, equations bi-Laplacian or poly-Laplacian 35K35 Initial-boundary value problems for higher-order 35K92 Quasilinear parabolic equations with p-Laplacian parabolic equations 35K93 Quasilinear parabolic equations with mean curvature operator 35K40 Second-order parabolic systems 35K41 Higher-order parabolic systems 35K96 Parabolic Monge-Ampère equations 35K45 Initial value problems for second-order parabolic systems 35K99 None of the above, but in this section 64 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 35Lxx Hyperbolic equations and hyper- 35L71 Second-order semilinear hyperbolic equations bolic systems {For global analysis, see 35L72 Second-order quasilinear hyperbolic equations 58J45} 35L02 First-order hyperbolic equations 35L75 Higher-order nonlinear hyperbolic equations 35L76 Higher-order semilinear hyperbolic equations 35L03 Initial value problems for first-order hyperbolic equations 35L77 Higher-order quasilinear hyperbolic equations 35L04 Initial-boundary value problems for first-order 35L80 Degenerate hyperbolic equations hyperbolic equations 35L81 Singular hyperbolic equations 35L05 Wave equation 35L82 Pseudohyperbolic equations 35L10 Second-order hyperbolic equations 35L85 Unilateral problems for linear hyperbolic equa35L15 Initial value problems for second-order hyperbolic tions and variational inequalities with linear hyperequations bolic operators [See also 35R35, 49J40] 35L20 Initial-boundary value problems for second-order 35L86 Unilateral problems for nonlinear hyperbolic hyperbolic equations equations and variational inequalities with nonlinear hyperbolic operators [See also 35R35, 49J40] 35L25 Higher-order hyperbolic equations 35L87 Unilateral problems for hyperbolic systems and 35L30 Initial value problems for higher-order hyperbolic systems of variational inequalities with hyperbolic equations operators [See also 35R35, 49J40] 35L35 Initial-boundary value problems for higher-order 35L90 Abstract hyperbolic equations hyperbolic equations 35L99 None of the above, but in this section 35L40 First-order hyperbolic systems 35L45 Initial value problems for first-order hyperbolic 35Mxx Partial differential equations of systems mixed type and mixed-type systems of 35L50 Initial-boundary value problems for first-order partial differential equations hyperbolic systems 35M10 PDEs of mixed type 35L51 Second-order hyperbolic systems 35M11 Initial value problems for PDEs of mixed type 35L52 Initial value problems for second-order hyperbolic 35M12 Boundary value problems for PDEs of mixed systems type 35L53 Initial-boundary value problems for second-order 35M13 Initial-boundary value problems for PDEs of hyperbolic systems mixed type 35L55 Higher-order hyperbolic systems 35M30 Mixed-type systems of PDEs 35L56 Initial value problems for higher-order hyperbolic 35M31 Initial value problems for mixed-type systems of systems PDEs 35L57 Initial-boundary value problems for higher-order 35M32 Boundary value problems for mixed-type syshyperbolic systems tems of PDEs 35L60 First-order nonlinear hyperbolic equations 35L65 Hyperbolic conservation laws 35M33 Initial-boundary value problems for mixed-type systems of PDEs 35L67 Shocks and singularities for hyperbolic equations 35M85 Unilateral problems for linear PDEs of mixed type and variational inequalities with partial dif[See also 58Kxx, 74J40, 76L05] ferential operators of mixed type [See also 35R35, 35L70 Second-order nonlinear hyperbolic equations 49J40] 65 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 35M86 Unilateral problems for nonlinear PDEs of mixed 35Qxx Partial differential equations of type and variational inequalities with nonlinear par- mathematical physics and other areas of tial differential operators of mixed type [See also application [See also 35J05, 35J10, 35K05, 35R35, 49J40] 35L05] 35M87 Unilateral problems for mixed-type systems of 35Q05 Euler-Poisson-Darboux equations PDEs and systems of variational inequalities with partial differential operators of mixed type [See also 35Q07 Fuchsian PDEs 35R35, 49J40] 35Q15 Riemann-Hilbert problems in context of PDEs [See also 30E25, 31A25, 31B20] 35M99 None of the above, but in this section 35Q20 Boltzmann equations {For fluid mechanics, see 35Nxx Overdetermined problems for par76P05; for statistical mechanics, see 82B40, 82C40, 82D05} tial differential equations and systems of partial differential equations {For global 35Q30 Navier-Stokes equations {For fluid mechanics, analysis, see 58Hxx, 58J10, 58J15} see 76D05, 76D07, 76N10} 35N05 Overdetermined systems of PDEs with constant 35Q31 Euler equations {For fluid mechanics, see 76D05, coefficients 76D07, 76N10} 35N10 Overdetermined systems of PDEs with variable 35Q35 PDEs in connection with fluid mechanics coefficients 35Q40 PDEs in connection with quantum mechanics 35N15 ∂-Neumann problems and formal complexes in 35Q41 Time-dependent Schrödinger equations and context of PDEs [See also 32W05, 32W10, 58J10] Dirac equations {For quantum theory, see 81Q05; 35N20 Overdetermined initial value problems for PDEs for relativity and gravitational theory, see 83A05, and systems of PDEs 83C10} 35N25 Overdetermined boundary value problems for 35Q49 Transport equations {For calculus of variations PDEs and systems of PDEs and optimal control, see 49Q22; for fluid mechanics, see 76F25; for statistical mechanics, see 82C70, 35N30 Overdetermined initial-boundary value problems 82D75; for operations research, see 90B06; for for PDEs and systems of PDEs mathematical programming, see 90C08} 35N99 None of the above, but in this section 35Q51 Soliton equations {For dynamical systems and ergodic theory, see 37K40} 35Pxx Spectral theory and eigenvalue 35Q53 KdV equations (Korteweg-de Vries equations) problems for partial differential equations {For dynamical systems and ergodic theory, see {For operator theory, see 47Axx, 47Bxx, 37K10} 47F05} 35Q55 NLS equations (nonlinear Schrödinger equations) {For dynamical systems and ergodic theory, see 37K10} 35P05 General topics in linear spectral theory for PDEs 35P10 Completeness of eigenfunctions and eigenfunc35Q56 Ginzburg-Landau equations {For optics and election expansions in context of PDEs tromagnetic theory, see 78A25} 35P15 Estimates of eigenvalues in context of PDEs 35Q60 PDEs in connection with optics and electromag35P20 Asymptotic distributions of eigenvalues in connetic theory text of PDEs 35Q61 Maxwell equations {For optics and electromag35P25 Scattering theory for PDEs [See also 47A40] netic theory, see 78A25; for relativity and gravitational theory, see 83C22} 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35Q62 PDEs in connection with statistics 35P99 None of the above, but in this section 35Q68 PDEs in connection with computer science 66 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 35Q70 PDEs in connection with mechanics of particles 35Rxx Miscellaneous topics in partial difand systems of particles ferential equations {For equations on man- ifolds, see 32Wxx, 58Jxx; for manifolds of 35Q74 PDEs in connection with mechanics of desolutions, see 58Bxx; for stochastic PDEs, formable solids see 60H15} 35Q75 PDEs in connection with relativity and gravita- 35R01 PDEs on manifolds [See also 32Wxx, 53Cxx, tional theory 58Jxx] 35Q76 Einstein equations {For several complex vari- 35R02 PDEs on graphs and networks (ramified or polygonal spaces) ables and analytic spaces, see 32Q40; for differential geometry, see 53C07; for relativity and gravitational 35R03 PDEs on Heisenberg groups, Lie groups, Carnot theory, see 83C05, 83C25, 83D05} groups, etc. 35Q79 PDEs in connection with classical thermodynam- 35R05 PDEs with low regular coefficients and/or low ics and heat transfer regular data 35Q81 PDEs in connection with semiconductor devices 35R06 PDEs with measure {For statistical mechanics, see 82D37} 35R07 PDEs on time scales 35Q82 PDEs in connection with statistical mechanics 35R09 Integral partial differential equations [See also 45Kxx] 35Q83 Vlasov equations {For statistical mechanics, see 35R10 Functional partial differential equations 82C70, 82D75} 35R11 Fractional partial differential equations 35Q84 Fokker-Planck equations {For fluid mechanics, see 76X05, 76W05; for statistical mechanics, see 35R12 Impulsive partial differential equations 82C31} 35R13 Fuzzy partial differential equations 35Q85 PDEs in connection with astronomy and astro35R15 PDEs on infinite-dimensional (e.g., function) physics spaces (= PDEs in infinitely many variables) [See also 46Gxx, 58D25] 35Q86 PDEs in connection with geophysics 35R20 Operator partial differential equations (= PDEs 35Q89 PDEs in connection with mean field game theory on finite-dimensional spaces for abstract space val{For calculus of variations and optimal control, see ued functions) [See also 34Gxx, 47A50, 47D03, 49N80; for game theory, see 91A16} 47D06, 47D09, 47H20, 47Jxx] 35Q90 PDEs in connection with mathematical program- 35R25 Ill-posed problems for PDEs ming 35R30 Inverse problems for PDEs 35Q91 PDEs in connection with game theory, eco- 35R35 Free boundary problems for PDEs nomics, social and behavioral sciences 35R37 Moving boundary problems for PDEs 35Q92 PDEs in connection with biology, chemistry and 35R45 Partial differential inequalities and systems of other natural sciences partial differential inequalities 35Q93 PDEs in connection with control and optimiza- 35R50 PDEs of infinite order tion 35R60 PDEs with randomness, stochastic partial differential equations [See also 60H15] 35Q94 PDEs in connection with information and communication 35R70 PDEs with multivalued right-hand sides 35Q99 None of the above, but in this section 35R99 None of the above, but in this section 67 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 35Sxx Pseudodifferential operators and 37-11 Research data for problems pertaining to dynamical systems and ergodic theory other generalizations of partial differential operators {For operator theory, see 47G30, 58J40} 37Axx Ergodic theory [See also 28Dxx] 35S05 Pseudodifferential operators as generalizations of partial differential operators [See also 32W25, 37A05 Dynamical aspects of measure-preserving transformations 47G30, 47L80, 58J40] 35S10 Initial value problems for PDEs with pseudodif37A10 Dynamical systems involving one-parameter conferential operators tinuous families of measure-preserving transformations 35S15 Boundary value problems for PDEs with pseudodifferential operators 37A15 General groups of measure-preserving transfor35S16 Initial-boundary value problems for PDEs with mations and dynamical systems [See mainly 22Fxx] pseudodifferential operators 35S30 Fourier integral operators applied to PDEs [See 37A17 Homogeneous flows [See also 22Fxx] also 43A32, 58J40] 35S35 Topological aspects for pseudodifferential opera- 37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations tors in context of PDEs: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15] 37A25 Ergodicity, mixing, rates of mixing 35S50 Paradifferential operators as generalizations of 37A30 Ergodic theorems, spectral theory, Markov oppartial differential operators in context of PDEs erators {For operator ergodic theory, see mainly 35S99 None of the above, but in this section 47A35} Entropy and other invariants, isomorphism, clas37-XX Dynamical systems and er- 37A35sification in ergodic theory godic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 37A40 Nonsingular (and infinite-measure preserving) transformations 46Lxx, 58Jxx, 70-XX] 37-00 General reference works (handbooks, dictionaries, 37A44 Relations between ergodic theory and number theory [See also 11Kxx] bibliographies, etc.) pertaining to dynamical systems and ergodic theory 37A46 Relations between ergodic theory and harmonic 37-01 Introductory exposition (textbooks, tutorial paanalysis pers, etc.) pertaining to dynamical systems and ergodic theory 37A50 Dynamical systems and their relations with prob37-02 Research exposition (monographs, survey articles) ability theory and stochastic processes [See also pertaining to dynamical systems and ergodic theory 60Fxx, 60G10] 37-03 History of dynamical systems and ergodic theory ∗ [Consider also classification numbers pertaining to 37A55 Dynamical systems and the theory of C algebras [See mainly 46L55] Section 01] 37-04 Software, source code, etc. for problems pertain- 37A60 Dynamical aspects of statistical mechanics [See ing to dynamical systems and ergodic theory also 82Cxx] 37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory 37A99 None of the above, but in this section 68 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 37Bxx Topological dynamics 37B02 Dynamics in general topological spaces 37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 37B05 Dynamical systems involving transformations 37C35 Orbit growth in dynamical systems and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems [See also 37Dxx] 37B10 Symbolic dynamics 37C45 Dimension theory of smooth dynamical systems 37B15 Dynamical aspects of cellular automata {For computational aspects, see 68Q80} 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics 37B20 Notions of recurrence and recurrent behavior in dynamical systems 37C55 Periodic and quasi-periodic flows and diffeomorphisms 37B25 Stability of topological dynamical systems 37B30 Index theory for dynamical systems, Morse- 37C60 Nonautonomous smooth dynamical systems [See also 37B55] Conley indices 37B35 Gradient-like and recurrent behavior; isolated 37C65 Monotone flows as dynamical systems (locally maximal) invariant sets; attractors, re- 37C70 Attractors and repellers of smooth dynamical pellers for topological dynamical systems systems and their topological structure 37B40 Topological entropy 37C75 Stability theory for smooth dynamical systems 37B45 Continua theory in dynamics 37B51 Multidimensional shifts of finite type 37C79 Symmetries and invariants of dynamical systems [See also 34C14, 34K04] 37B52 Tiling dynamics 37C81 Equivariant dynamical systems 37B55 Topological dynamics of nonautonomous systems 37C83 Dynamical systems with singularities (billiards, etc.) 37B65 Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dy- 37C85 Dynamics induced by group actions other than Z and R, and C [See mainly 22Fxx, and also 32M25, namical systems 57R30, 57Sxx] 37B99 None of the above, but in this section 37C86 Foliations generated by dynamical systems 37Cxx Smooth dynamical systems: gen- 37C99 None of the above, but in this section eral theory [See also 34Cxx, 34Dxx] 37C05 Dynamical systems involving smooth mappings 37Dxx Dynamical systems with hyperbolic behavior and diffeomorphisms 37C10 Dynamics induced by flows and semiflows 37D05 Dynamical systems with hyperbolic orbits and sets 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 37D10 Invariant manifold theory for dynamical systems 37C20 Generic properties, structural stability of dynam- 37D15 Morse-Smale systems ical systems 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37C27 Periodic orbits of vector fields and flows 37C29 Homoclinic and heteroclinic orbits for dynamical 37D30 Partially hyperbolic systems and dominated splittings systems 69 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 37D35 Thermodynamic formalism, variational princi- 37F25 Renormalization of holomorphic dynamical sysples, equilibrium states for dynamical systems tems 37D40 Dynamical systems of geometric origin and hy- 37F31 Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics perbolicity (geodesic and horocycle flows, etc.) 37D45 Strange attractors, chaotic dynamics of systems 37F32 Fuchsian and Kleinian groups as dynamical systems with hyperbolic behavior 37F34 Teichmüller theory; moduli spaces of holomorphic dynamical systems 37D99 None of the above, but in this section 37Exx Low-dimensional dynamical sys- 37F35 Conformal densities and Hausdorff dimension for holomorphic dynamical systems tems 37F40 Geometric limits in holomorphic dynamics 37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth) 37F44 Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps 37E10 Dynamical systems involving maps of the circle 37F46 Bifurcations; parameter spaces in holomorphic 37E15 Combinatorial dynamics (types of periodic ordynamics; the Mandelbrot and Multibrot sets bits) 37F50 Small divisors, rotation domains and lineariza37E20 Universality and renormalization of dynamical tion in holomorphic dynamics systems [See also 37F25] 37F75 Dynamical aspects of holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx] 37E25 Dynamical systems involving maps of trees and graphs 37F80 Higher-dimensional holomorphic and meromorphic dynamics 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37F99 None of the above, but in this section 37E35 Flows on surfaces 37Gxx Local and nonlocal bifurcation theory for dynamical systems [See also 34C23, 34K18] 37E40 Dynamical aspects of twist maps 37E45 Rotation numbers and vectors 37G05 Normal forms for dynamical systems 37E99 None of the above, but in this section 37G10 Bifurcations of singular points in dynamical systems 37Fxx Dynamical systems over complex numbers [See also 30D05, 32H50] 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 37F05 Dynamical systems involving relations and correspondences in one complex variable 37G20 Hyperbolic singular points with homoclinic trajectories in dynamical systems 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and 37G25 Bifurcations connected with nontransversal intersection in dynamical systems Julia sets [See also 32A10, 32A20, 32H02, 32H04] 37F12 Critical orbits for holomorphic dynamical sys- 37G30 Infinite nonwandering sets arising in bifurcations of dynamical systems tems 37G35 Dynamical aspects of attractors and their bifur37F15 Expanding holomorphic maps; hyperbolicity; cations structural stability of holomorphic dynamical systems 37G40 Dynamical aspects of symmetries, equivariant bifurcation theory 37F20 Combinatorics and topology in relation with holomorphic dynamical systems 37G99 None of the above, but in this section 70 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 37Hxx Random dynamical systems [See 37J39 Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and also 15B52, 34D08, 34F05, 47B80, 70L05, differential geometry (symplectic geometry, Poisson 82C05, 93Exx] geometry, etc.) [See also 53D20] 37H05 General theory of random and stochastic dynam37J40 Perturbations of finite-dimensional Hamiltonian ical systems systems, normal forms, small divisors, KAM the37H10 Generation, random and stochastic difference ory, Arnol’d diffusion and differential equations [See also 34F05, 34K50, 37J46 Periodic, homoclinic and heteroclinic orbits of 60H10, 60H15] finite-dimensional Hamiltonian systems 37H12 Random iteration 37J51 Action-minimizing orbits and measures for finite37H15 Random dynamical systems aspects of multidimensional Hamiltonian and Lagrangian systems; plicative ergodic theory, Lyapunov exponents [See variational principles; degree-theoretic methods also 34D08, 37Axx, 37Cxx, 37Dxx] 37J55 Contact systems [See also 53D10] 37H20 Bifurcation theory for random and stochastic dy37J60 Nonholonomic dynamical systems [See also namical systems [See also 37Gxx] 70F25] 37H30 Stability theory for random and stochastic dynamical systems 37J65 Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) 37H99 None of the above, but in this section 37J70 Completely integrable discrete dynamical systems 37Jxx Dynamical aspects of finite- 37J99 None of the above, but in this section dimensional Hamiltonian and Lagrangian systems [See also 53Dxx, 70Fxx, 70Hxx] 37Kxx Dynamical system aspects of 37J06 General theory of finite-dimensional Hamilto- infinite-dimensional Hamiltonian and Lanian and Lagrangian systems, Hamiltonian and La- grangian systems [See also 35Axx, 35Qxx] grangian structures, symmetries, invariants 37K06 General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws 37J11 Symplectic and canonical mappings 37J12 Fixed points and periodic points of finitedimensional Hamiltonian and Lagrangian systems 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration 37J20 Bifurcation problems for finite-dimensional methods, integrability tests, integrable hierarchies Hamiltonian and Lagrangian systems (KdV, KP, Toda, etc.) 37J25 Stability problems for finite-dimensional Hamil37K15 Inverse spectral and scattering methods for tonian and Lagrangian systems infinite-dimensional Hamiltonian and Lagrangian systems 37J30 Obstructions to integrability for finitedimensional Hamiltonian and Lagrangian systems 37K20 Relations of infinite-dimensional Hamiltonian (nonintegrability criteria) and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions 37J35 Completely integrable finite-dimensional Hamil[See also 14H70] tonian systems, integration methods, integrability tests 37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, 37J37 Relations of finite-dimensional Hamiltonian and geometry and differential geometry Lagrangian systems with Lie algebras and other algebraic structures 37K30 Relations of infinite-dimensional Hamiltonian 37J38 Relations of finite-dimensional Hamiltonian and and Lagrangian dynamical systems with infiniteLagrangian systems with algebraic geometry, comdimensional Lie algebras and other algebraic strucplex analysis, special functions tures 71 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 37K35 Lie-Bäcklund and other transformations for 37L50 Noncompact semigroups; dispersive equations; infinite-dimensional Hamiltonian and Lagrangian perturbations of infinite-dimensional dissipative dysystems namical systems 37K40 Soliton theory, asymptotic behavior of solutions 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] of infinite-dimensional Hamiltonian systems 37K45 Stability problems for infinite-dimensional 37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems [See also 37K60] Hamiltonian and Lagrangian systems 37L65 Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems 37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 37K55 Perturbations, KAM for infinite-dimensional 37L99 None of the above, but in this section Hamiltonian and Lagrangian systems 37K58 Variational principles and methods for infinite- 37Mxx Approximation methods and nudimensional Hamiltonian and Lagrangian systems merical treatment of dynamical systems {For numerical analysis, see also 65Pxx; 37K60 Lattice dynamics; integrable lattice equations for software etc., see 37-04} [See also 37L60] 37M05 Simulation of dynamical systems 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics 37M10 Time series analysis of dynamical systems 37K99 None of the above, but in this section 37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems 37Lxx Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx] 37M20 Computational methods for bifurcation prob- lems in dynamical systems 37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution 37M21 Computational methods for invariant manifolds of dynamical systems equations 37L10 Normal forms, center manifold theory, bifurca- 37M22 Computational methods for attractors of dynamical systems tion theory for infinite-dimensional dissipative dynamical systems 37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of 37L15 Stability problems for infinite-dimensional dissiLyapunov exponents, entropy, etc.) pative dynamical systems 37M99 None of the above, but in this section 37L20 Symmetries of infinite-dimensional dissipative dynamical systems 37Nxx Applications of dynamical systems 37L25 Inertial manifolds and other invariant attracting 37N05 Dynamical systems in classical and celestial mesets of infinite-dimensional dissipative dynamical chanics [See mainly 70Fxx, 70Hxx, 70Kxx] systems 37N10 Dynamical systems in fluid mechanics, oceanog37L30 Infinite-dimensional dissipative dynamical raphy and meteorology [See mainly 76-XX, espesystems–attractors and their dimensions, Lyapunov cially 76D05, 76F20, 86A05, 86A10] exponents 37N15 Dynamical systems in solid mechanics [See 37L40 Invariant measures for infinite-dimensional dissimainly 74Hxx] pative dynamical systems 37N20 Dynamical systems in other branches of physics 37L45 Hyperbolicity; Lyapunov functions for infinite(quantum mechanics, general relativity, laser dimensional dissipative dynamical systems physics) 72 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 37N25 Dynamical systems in biology [See also 92-XX] 39-03 History of difference and functional equations [Consider also classification numbers pertaining to 37N30 Dynamical systems in numerical analysis [See Section 01] also 65-XX] 39-04 Software, source code, etc. for problems pertain37N35 Dynamical systems in control [See also 93-XX] ing to difference and functional equations 37N40 Dynamical systems in optimization and eco- 39-06 Proceedings, conferences, collections, etc. pernomics [See also 90-XX, 91-XX] taining to difference and functional equations 37N99 None of the above, but in this section 39-08 Computational methods for problems pertaining to difference and functional equations 37Pxx Arithmetic and non-Archimedean 39-11 Research data for problems pertaining to differdynamical systems [See also 11S82, 37A44] ence and functional equations 37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 39Axx Difference equations {For dynamic 37P10 Arithmetic and non-Archimedean dynamical sys- equations on time scales, see 34N05; for dynamical systems, see 37-XX} tems involving analytic and meromorphic maps 37P15 Dynamical systems over global ground fields 39A05 General theory of difference equations 37P20 Dynamical systems over non-Archimedean local 39A06 Linear difference equations ground fields 39A10 Additive difference equations 37P25 Dynamical systems over finite ground fields 39A12 Discrete version of topics in analysis 37P30 Height functions; Green functions; invariant mea- 39A13 Difference equations, scaling (q-differences) [See sures in arithmetic and non-Archimedean dynamialso 33Dxx] cal systems [See also 11G50, 14G40] 39A14 Partial difference equations 37P35 Arithmetic properties of periodic points 39A20 Multiplicative and other generalized difference 37P40 Non-Archimedean Fatou and Julia sets equations, e.g., of Lyness type 37P45 Families and moduli spaces in arithmetic and 39A21 Oscillation theory for difference equations non-Archimedean dynamical systems 39A22 Growth, boundedness, comparison of solutions to 37P50 Dynamical systems on Berkovich spaces difference equations 37P55 Arithmetic dynamics on general algebraic vari- 39A23 Periodic solutions of difference equations eties 39A24 Almost periodic solutions of difference equations 37P99 None of the above, but in this section 39A26 Fuzzy difference equations 39-XX Difference and functional 39A27 Boundary value problems for difference equations 39A28 Bifurcation theory for difference equations equations 39-00 General reference works (handbooks, dictionaries, 39A30 Stability theory for difference equations bibliographies, etc.) pertaining to difference and 39A33 Chaotic behavior of solutions of difference equafunctional equations tions 39-01 Introductory exposition (textbooks, tutorial pa- 39A36 Integrable difference and lattice equations; intepers, etc.) pertaining to difference and functional grability tests equations 39A45 Difference equations in the complex domain 39-02 Research exposition (monographs, survey articles) pertaining to difference and functional equations 39A50 Stochastic difference equations 73 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 39A60 Applications of difference equations 39A70 Difference operators [See also 47B39] 39A99 None of the above, but in this section 40-04 Software, source code, etc. for problems pertaining to sequences, series, summability 40-06 Proceedings, conferences, collections, etc. taining to sequences, series, summability per- 39Bxx Functional equations and inequali- 40-08 Computational methods for problems pertaining to sequences, series, summability ties [See also 30D05] 39B05 General theory of functional equations and in- 40-11 Research data for problems pertaining to seequalities quences, series, summability 39B12 Iteration theory, iterative and composite equa40Axx Convergence and divergence of intions [See also 26A18, 30D05, 37-XX] finite limiting processes 39B22 Functional equations for real functions [See also 40A05 Convergence and divergence of series and se26A51, 26B25] quences 39B32 Functional equations for complex functions [See also 30D05] 40A10 Convergence and divergence of integrals 39B42 Matrix and operator functional equations [See 40A15 Convergence and divergence of continued fracalso 47Jxx] tions [See also 30B70] 39B52 Functional equations for functions with more 40A20 Convergence and divergence of infinite products general domains and/or ranges 39B55 Orthogonal additivity and other conditional 40A25 Approximation to limiting values (summation of series, etc.) {For the Euler-Maclaurin summation functional equations formula, see 65B15} 39B62 Functional inequalities, including subadditivity, 40A30 Convergence and divergence of series and seconvexity, etc. [See also 26A51, 26B25, 26Dxx] quences of functions 39B72 Systems of functional equations and inequalities 40A35 Ideal and statistical convergence [See also 40G15] 39B82 Stability, separation, extension, and related topics for functional equations [See also 46A22] 40A99 None of the above, but in this section 39B99 None of the above, but in this section 40Bxx Multiple sequences and series 40-XX Sequences, series, summa- 40B05 Multiple sequences and series (should also be assigned at least one other classification number in bility this section) 40-00 General reference works (handbooks, dictionaries, 40B99 None of the above, but in this section bibliographies, etc.) pertaining to sequences, series, summability 40Cxx General summability methods 40-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summa- 40C05 Matrix methods for summability bility 40C10 Integral methods for summability 40-02 Research exposition (monographs, survey articles) 40C15 Function-theoretic methods (including power sepertaining to sequences, series, summability ries methods and semicontinuous methods) for 40-03 History of sequences, series, summability [Consummability sider also classification numbers pertaining to Section 01] 40C99 None of the above, but in this section 74 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 40Jxx Summability in abstract structures (should also be assigned at least one other classification number from Section 40) [See also 43A55, 46A35, 46B15] 40Dxx Direct theorems on summability 40D05 General theorems on summability 40D09 Structure of summability fields 40D10 Tauberian constants and oscillation limits in 40J05 Summability in abstract structures (should also summability theory be assigned at least one other classification number from Section 40) [See also 43A55, 46A35, 46B15] 40D15 Convergence factors and summability factors 40D20 Summability and bounded fields of methods 40J99 None of the above, but in this section 40D25 Inclusion and equivalence theorems in summability theory 40D99 None of the above, but in this section 41-XX Approximations and expansions {For approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approximation, see 65Dxx} 40Exx Inversion theorems 40E05 Tauberian theorems, general 40E10 Growth estimates 40E15 Lacunary inversion theorems 40E20 Tauberian constants 40E99 None of the above, but in this section 41-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to approximations 40Fxx Absolute and strong summability and expansions (should also be assigned at least one other classification number in Section 40) 40F05 Absolute and strong summability (should also be assigned at least one other classification number in Section 40) 40F99 None of the above, but in this section 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 40Gxx Special methods of summability 41-03 History of approximations and expansions [Consider also classification numbers pertaining to Section 01] 40G05 Cesàro, Euler, Nörlund and Hausdorff methods 40G10 Abel, Borel and power series methods 40G15 Summability methods using statistical convergence [See also 40A35] 41-04 Software, source code, etc. for problems pertaining to approximations and expansions 40G99 None of the above, but in this section 40Hxx Functional analytic methods in 41-06 Proceedings, conferences, collections, etc. pertaining to approximations and expansions summability 40H05 Functional analytic methods in summability 41-11 Research data for problems pertaining to approximations and expansions 40H99 None of the above, but in this section 75 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 41Axx Approximations and expansions {For approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approximation, see 65Dxx} 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A80 Remainders in approximation formulas 41A81 Weighted approximation 41A99 None of the above, but in this section 41A05 Interpolation in approximation theory [See also 42A15, 65D05] 42-XX Harmonic analysis on Eu41A10 Approximation by polynomials {For approxima- clidean spaces tion by trigonometric polynomials, see 42A10} 42-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to harmonic analysis on Euclidean spaces 41A15 Spline approximation 41A17 Inequalities in approximation (Bernstein, Jack42-01 Introductory exposition (textbooks, tutorial pason, Nikol’skiı̆-type inequalities) pers, etc.) pertaining to harmonic analysis on Eu41A20 Approximation by rational functions clidean spaces 41A21 Padé approximation 42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces 41A25 Rate of convergence, degree of approximation 42-03 History of harmonic analysis on Euclidean spaces [Consider also classification numbers pertaining to Section 01] 41A27 Inverse theorems in approximation theory 41A28 Simultaneous approximation 42-04 Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces 41A29 Approximation with constraints 41A30 Approximation by other special function classes 42-06 Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces 41A35 Approximation by operators (in particular, by integral operators) 42-08 Computational methods for problems pertaining to harmonic analysis on Euclidean spaces 41A36 Approximation by positive operators 42-11 Research data for problems pertaining to harmonic analysis on Euclidean spaces 41A40 Saturation in approximation theory 41A44 Best constants in approximation theory 42Axx Harmonic analysis in one variable 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 42A05 Trigonometric polynomials, tremal problems inequalities, ex- 42A10 Trigonometric approximation 42A15 Trigonometric interpolation 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30} 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) 42A20 Convergence and absolute convergence of Fourier and trigonometric series 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 42A24 Summability and absolute summability of Fourier and trigonometric series 41A63 Multidimensional problems (should also be assigned at least one other classification number from 42A32 Trigonometric series of special types (positive coSection 41) efficients, monotonic coefficients, etc.) 41A55 Approximate quadratures 76 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 42A38 Fourier and Fourier-Stieltjes transforms and 42Cxx Nontrigonometric harmonic analyother transforms of Fourier type sis 42A45 Multipliers in one variable harmonic analysis 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis [See 42A50 Conjugate functions, conjugate series, singular also 33C45, 33C50, 33D45] integrals 42A55 Lacunary series of trigonometric and other func- 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) tions; Riesz products 42A61 Probabilistic methods for one variable harmonic 42C15 General harmonic expansions, frames analysis 42A63 Uniqueness of trigonometric expansions, unique- 42C20 Other transformations of harmonic type ness of Fourier expansions, Riemann theory, local42C25 Uniqueness and localization for orthogonal series ization 42A65 Completeness of sets of functions in one variable 42C30 Completeness of sets of functions in nontrigonoharmonic analysis metric harmonic analysis 42A70 Trigonometric moment problems in one variable 42C40 Nontrigonometric harmonic analysis involving harmonic analysis wavelets and other special systems 42A75 Classical almost periodic functions, mean peri42C99 None of the above, but in this section odic functions [See also 43A60] 42A82 Positive definite functions in one variable harmonic analysis 43-XX Abstract harmonic analysis 42A85 Convolution, factorization for one variable har- {For other analysis on topological monic analysis and Lie groups, see 22Exx} 42A99 None of the above, but in this section 43-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to abstract harmonic analysis 42Bxx Harmonic analysis in several variables {For automorphic theory, see mainly 11F30} 43-01 Introductory exposition (textbooks, tutorial pa42B05 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 (CalderónZygmund, etc.) pers, 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 [Consider also classification numbers pertaining to Section 01] 43-04 Software, source code, etc. for problems pertaining to abstract harmonic analysis 43-06 Proceedings, conferences, collections, etc. taining to abstract harmonic analysis 42B25 Maximal functions, Littlewood-Paley theory per- 42B30 H p -spaces 43-08 Computational methods for problems pertaining to abstract harmonic analysis 42B35 Function spaces arising in harmonic analysis 42B37 Harmonic analysis and PDEs [See also 35-XX] 43-11 Research data for problems pertaining to abstract harmonic analysis 42B99 None of the above, but in this section 77 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 43Axx Abstract harmonic analysis {For 43A80 Analysis on other specific Lie groups [See also 22Exx] other analysis on topological and Lie groups, see 22Exx} 43A85 Harmonic analysis on homogeneous spaces 43A05 Measures on groups and semigroups, etc. 43A07 Means on groups, semigroups, etc.; amenable 43A90 Harmonic analysis and spherical functions [See groups also 22E45, 22E46, 33C55] 43A10 Measure algebras on groups, semigroups, etc. 43A15 Lp -spaces and other function spaces on groups, 43A95 Categorical methods for abstract harmonic analysis [See also 46Mxx] semigroups, etc. 43A17 Analysis on ordered groups, H p -theory 43A99 None of the above, but in this section 43A20 L1 -algebras on groups, semigroups, etc. 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 44-XX Integral transforms, op43A25 Fourier and Fourier-Stieltjes transforms on lo- erational calculus {For fractional cally compact and other abelian groups derivatives and integrals, see 43A30 Fourier and Fourier-Stieltjes transforms on non26A33; for Fourier transforms, see abelian groups and on semigroups, etc. 42A38, 42B10; for integral trans43A32 Other transforms and operators of Fourier type forms in distribution spaces, see 43A35 Positive definite functions on groups, semigroups, 46F12; for numerical methods, see etc. 65R10} 43A40 Character groups and dual objects 43A45 Spectral synthesis on groups, semigroups, etc. 44-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral trans43A46 Special sets (thin sets, Kronecker sets, Helson forms sets, Ditkin sets, Sidon sets, etc.) 43A50 Convergence of Fourier series and of inverse 44-01 Introductory exposition (textbooks, tutorial patransforms pers, etc.) pertaining to integral transforms 43A55 Summability methods on groups, semigroups, etc. [See also 40J05] 44-02 Research exposition (monographs, survey articles) pertaining to integral transforms 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic 44-03 History of integral transforms [Consider also clasfunctions sification numbers pertaining to Section 01] 43A62 Harmonic analysis on hypergroups 43A65 Representations of groups, semigroups, etc. (as- 44-04 Software, source code, etc. for problems pertaining to integral transforms pects of abstract harmonic analysis) [See also 22A10, 22A20, 22Dxx, 22E45] 43A70 Analysis on specific locally compact and other 44-06 Proceedings, conferences, collections, etc. taining to integral transforms abelian groups [See also 11R56, 22B05] 43A75 Harmonic analysis on specific compact groups 43A77 Harmonic analysis on general compact groups 44-11 Research data for problems pertaining to integral transforms 78 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. per- 44Axx Integral transforms, operational calculus {For fractional derivatives and integrals, see 26A33; for Fourier transforms, see 42A38, 42B10; for integral transforms in distribution spaces, see 46F12; for numerical methods, see 65R10} 45Axx Linear integral equations 45A05 Linear integral equations 45A99 None of the above, but in this section 45Bxx Fredholm integral equations 45B05 Fredholm integral equations 44A05 General integral transforms [See also 42A38] 45B99 None of the above, but in this section 44A10 Laplace transform 45Cxx Eigenvalue problems for integral equations [See also 34Lxx, 35Pxx, 45P05, 44A15 Special integral transforms (Legendre, Hilbert, 47A75] 44A12 Radon transform [See also 92C55] etc.) 44A20 Integral transforms of special functions 45C05 Eigenvalue problems for integral equations [See also 34Lxx, 35Pxx, 45P05, 47A75] 44A30 Multiple integral transforms 45C99 None of the above, but in this section 44A35 Convolution as an integral transform 45Dxx Volterra integral equations [See 44A40 Calculus of Mikusiński and other operational cal- also 34A12] culi 45D05 Volterra integral equations [See also 34A12] 44A45 Classical operational calculus 45D99 None of the above, but in this section 44A55 Discrete operational calculus 45Exx Singular integral equations [See also 44A60 Moment problems {For trigonometric moment 30E20, 30E25, 44A15, 44A35] problems, see 42A70} 45E05 Integral equations with kernels of Cauchy type [See also 35J15] 44A99 None of the above, but in this section 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35] 45-XX Integral equations 45-00 General reference works (handbooks, dictionaries, 45E99 None of the above, but in this section bibliographies, etc.) pertaining to integral equations 45Fxx Systems of linear integral equations 45-01 Introductory exposition (textbooks, tutorial pa- 45F05 Systems of nonsingular linear integral equations pers, etc.) pertaining to integral equations 45F10 Dual, triple, etc., integral and series equations 45-02 Research exposition (monographs, survey articles) 45F15 Systems of singular linear integral equations pertaining to integral equations 45F99 None of the above, but in this section 45-03 History of integral equations [Consider also classification numbers pertaining to Section 01] 45Gxx Nonlinear integral equations [See 45-04 Software, source code, etc. for problems pertain- also 47H30, 47Jxx] ing to integral equations 45G05 Singular nonlinear integral equations 45-06 Proceedings, conferences, collections, etc. per45G10 Other nonlinear integral equations taining to integral equations 45G15 Systems of nonlinear integral equations 45-11 Research data for problems pertaining to integral equations 45G99 None of the above, but in this section 79 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 45Hxx Integral equations with miscella- 45Pxx Integral operators [See also 47B38, neous special kernels [See also 44A15] 47G10] 45H05 Integral equations with miscellaneous special ker- 45P05 Integral operators [See also 47B38, 47G10] nels [See also 44A15] 45P99 None of the above, but in this section 45H99 None of the above, but in this section 45Jxx Integro-ordinary differential equa- 45Qxx Inverse problems for integral equations tions [See also 34K05, 34K30, 47G20] 45J05 Integro-ordinary differential equations [See also 45Q05 Inverse problems for integral equations 34K05, 34K30, 47G20] 45Q99 None of the above, but in this section 45J99 None of the above, but in this section 45Kxx Integro-partial differential equa- 45Rxx Random integral equations [See tions [See also 34K30, 35R09, 35R10, also 60H20] 47G20] 45R05 Random integral equations [See also 60H20] 45K05 Integro-partial differential equations [See also 45R99 None of the above, but in this section 34K30, 35R09, 35R10, 47G20] 45K99 None of the above, but in this section 46-XX Functional analysis {For 45Lxx Theoretical approximation of solu- manifolds modeled on topological tions to integral equations {For numerical linear spaces, see 57Nxx, 58Bxx} analysis, see 65Rxx} 45L05 Theoretical approximation of solutions to integral 46-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analequations {For numerical analysis, see 65Rxx} ysis 45L99 None of the above, but in this section 46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis 45Mxx Qualitative behavior of solutions to integral equations 46-02 Research exposition (monographs, survey articles) pertaining to functional analysis 45M05 Asymptotics of solutions to integral equations 45M10 Stability theory for integral equations 46-03 History of functional analysis [Consider also classification numbers pertaining to Section 01] 45M15 Periodic solutions of integral equations 46-04 Software, source code, etc. for problems pertaining to functional analysis 45M20 Positive solutions of integral equations 45M99 None of the above, but in this section 46-06 Proceedings, conferences, collections, etc. taining to functional analysis per- 45Nxx Abstract integral equations, integral equations in abstract spaces 46-08 Computational methods for problems pertaining to functional analysis 45N05 Abstract integral equations, integral equations in abstract spaces 46-11 Research data for problems pertaining to functional analysis 45N99 None of the above, but in this section 80 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 46Axx Topological linear spaces and re- 46A63 Topological invariants ((DN), (Ω), etc.) for locally convex spaces lated structures {For function spaces, see 46Exx} 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 46A03 General theory of locally convex spaces 46A04 Locally convex Fréchet spaces and (DF)-spaces 46A80 Modular spaces 46A08 Barrelled spaces, bornological spaces 46A99 None of the above, but in this section 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, 46Bxx Normed linear spaces and BaMontel spaces, etc.) nach spaces; Banach lattices {For function 46A13 Spaces defined by inductive or projective limits spaces, see 46Exx} (LB, LF, etc.) [See also 46M40] 46B03 Isomorphic theory (including renorming) of Banach spaces 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach 46B04 Isometric theory of Banach spaces spaces, etc.) 46B06 Asymptotic theory of Banach spaces [See also 46A17 Bornologies and related structures; Mackey con52A23] vergence, etc. 46B07 Local theory of Banach spaces 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking 46B08 Ultraproduct techniques in Banach space theory [See also 46M07] values in an ordered structure more general than R, etc.) 46B09 Probabilistic methods in Banach space theory [See also 60Bxx] 46A20 Duality theory for topological vector spaces 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10] 46B10 Duality and reflexivity in normed linear and Banach spaces [See also 46A25] 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces [See also 46A35, 42C15] 46A30 Open mapping and closed graph theorems; completeness (including B-, Br -completeness) 46B20 Geometry and structure of normed linear spaces 46A25 Reflexivity and semi-reflexivity [See also 46B10] 46A32 Spaces of linear operators; topological ten- 46B22 Radon-Nikodým, Kreı̆n-Milman and related sor products; approximation properties [See also properties [See also 46G10] 46B28, 46M05, 47L05, 47L20] 46B25 Classical Banach spaces in the general theory 46A35 Summability and bases in topological vector 46B26 Nonseparable Banach spaces spaces [See also 46B15] 46A40 Ordered topological linear spaces, vector lattices 46B28 Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, [See also 06F20, 46B40, 46B42] 47L20] 46A45 Sequence spaces (including Köthe sequence 46B40 Ordered normed spaces [See also 46A40, 46B42] spaces) [See also 46B45] 46B42 Banach lattices [See also 46A40, 46B40] 46A50 Compactness in topological linear spaces; angelic spaces, etc. 46B45 Banach sequence spaces [See also 46A45] 46A55 Convex sets in topological linear spaces; Choquet 46B50 Compactness in Banach (or normed) spaces theory [See also 52A07] 46B70 Interpolation between normed linear spaces [See 46A61 Graded Fréchet spaces and tame operators also 46M35] 81 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 46B80 Nonlinear classification of Banach spaces; nonlin- 46E30 Spaces of measurable functions (Lp -spaces, Orear quotients licz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer 46E35 Sobolev spaces and other spaces of “smooth” science [See also 05C12, 68Rxx] functions, embedding theorems, trace theorems 46B87 Lineability in functional analysis [See also 15A03] 46E36 Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces 46B99 None of the above, but in this section 46Cxx Inner product spaces and their generalizations, Hilbert spaces {For function 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables spaces, see 46Exx} 46C05 Hilbert and pre-Hilbert spaces: geometry and 46E40 Spaces of vector- and operator-valued functions topology (including spaces with semidefinite inner product) 46E50 Spaces of differentiable or holomorphic func46C07 Hilbert subspaces (= operator ranges); completions on infinite-dimensional spaces [See also 46G20, mentation (Aronszajn, de Branges, etc.) [See also 46G25, 47H60] 46B70, 46M35] 46E99 None of the above, but in this section 46C15 Characterizations of Hilbert spaces 46C20 Spaces with indefinite inner product (Kreı̆n spaces, Pontryagin spaces, etc.) [See also 47B50] 46Fxx Distributions, generalized func- 46C50 Generalizations of inner products (semi-inner tions, distribution spaces [See also 46T30] products, partial inner products, etc.) 46F05 Topological linear spaces of test functions, dis46C99 None of the above, but in this section tributions and ultradistributions [See also 46E10, 46E35] 46Exx Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For 46F10 Operations with distributions and generalized function algebras, see 46J10} functions 46E05 Lattices of continuous, differentiable or analytic 46F12 Integral transforms in distribution spaces [See functions also 42-XX, 44-XX] 46E10 Topological linear spaces of continuous, differentiable or analytic functions 46F15 Hyperfunctions, analytic functionals [See also 46E15 Banach spaces of continuous, differentiable or an32A25, 32A45, 32C35, 58J15] alytic functions 46E20 Hilbert spaces of continuous, differentiable or an- 46F20 Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, alytic functions 32A40] 46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de 46F25 Distributions on infinite-dimensional spaces [See Branges-Rovnyak and other structured spaces) [See also 58C35] also 47B32] 46E25 Rings and algebras of continuous, differentiable 46F30 Generalized functions for nonlinear analysis or analytic functions {For Banach function alge(Rosinger, Colombeau, nonstandard, etc.) bras, see 46J10, 46J15} 46E27 Spaces of measures [See also 28A33, 46Gxx] 46F99 None of the above, but in this section 82 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 46Gxx Measures, integration, derivative, holomorphy (all involving infinitedimensional spaces) [See also 28-XX, 46Txx] 46Jxx Commutative Banach algebras and commutative topological algebras [See also 46E25] 46J05 General theory of commutative topological algebras 46G05 Derivatives of functions in infinite-dimensional spaces [See also 46T20, 58C20, 58C25] 46J10 Banach algebras of continuous functions, function algebras [See also 46E25] 46G10 Vector-valued measures and integration [See also 28Bxx, 46B22] 46J15 Banach algebras of differentiable or analytic functions, H p -spaces [See also 30H10, 32A35, 32A37, 46G12 Measures and integration on abstract linear 32A38, 42B30] spaces [See also 28C20, 46T12] 46J20 Ideals, maximal ideals, boundaries 46G15 Functional analytic lifting theory [See also 46J25 Representations of commutative topological alge28A51] bras 46G20 Infinite-dimensional holomorphy [See also 32- 46J30 Subalgebras of commutative topological algebras XX, 46E50, 46T25, 58B12, 58C10] 46J40 Structure and classification of commutative topological algebras 46G25 (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60] 46J45 Radical Banach algebras 46G99 None of the above, but in this section 46J99 None of the above, but in this section 46Hxx Topological algebras, normed rings 46Kxx Topological (rings and) algebras and algebras, Banach algebras {For group with an involution [See also 16W10] algebras, convolution algebras and mea- 46K05 General theory of topological algebras with involution sure algebras, see 43A10, 43A20} 46K10 Representations of topological algebras with involution 46H05 General theory of topological algebras 46H10 Ideals and subalgebras 46K15 Hilbert algebras 46H15 Representations of topological algebras 46K50 Nonselfadjoint (sub)algebras in algebras with involution 46H20 Structure, classification of topological algebras 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46K70 Nonassociative topological algebras with an involution [See also 46H70, 46L70] 46K99 None of the above, but in this section 46H30 Functional calculus in topological algebras [See also 47A60] 46Lxx Selfadjoint operator algebras (C ∗ - algebras, von Neumann (W ∗ -) algebras, 46H35 Topological algebras of operators [See mainly etc.) [See also 22D25, 47Lxx] 47Lxx] 46L05 General theory of C ∗ -algebras 46H40 Automatic continuity 46L06 Tensor products of C ∗ -algebras 46H70 Nonassociative topological algebras [See also 46L07 Operator spaces and completely bounded maps 46K70, 46L70] [See also 47L25] 46H99 None of the above, but in this section 46L08 C ∗ -modules 83 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 46L09 Free products of C ∗ -algebras 46Mxx Methods of category theory in functional analysis [See also 18-XX] 46L10 General theory of von Neumann algebras 46M05 Tensor products in functional analysis [See also 46A32, 46B28, 47A80] 46L30 States of selfadjoint operator algebras 46M07 Ultraproducts in functional analysis [See also 46B08, 46S20] 46L35 Classifications of C ∗ -algebras 46L36 Classification of factors 46M10 Projective and injective objects in functional analysis [See also 46A22] 46L37 Subfactors and their classification 46M15 Categories, functors in functional analysis {For K-theory, Ext, etc., see 19K33, 46L80, 46M18, 46M20} 46L40 Automorphisms of selfadjoint operator algebras 46L45 Decomposition theory for C ∗ -algebras 46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 46L51 Noncommutative measure and integration 46L52 Noncommutative function spaces 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) [See also 14F06, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx] 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 46L55 Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 37A55] 46L57 Derivations, dissipations and positive semigroups in C ∗ -algebras 46M35 Abstract interpolation of topological vector spaces [See also 46B70] 46M40 Inductive and projective limits in functional analysis [See also 46A13] 46M99 None of the above, but in this section 46L60 Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 46Nxx Miscellaneous applications of func82B10, 82C10] tional analysis [See also 47Nxx] 46L65 Quantizations, deformations for selfadjoint oper- 46N10 Applications of functional analysis in optimizaator algebras tion, convex analysis, mathematical programming, economics 46L67 Quantum groups (operator algebraic aspects) 46N20 Applications of functional analysis to differential 46L70 Nonassociative selfadjoint operator algebras [See and integral equations also 46H70, 46K70] 46N30 Applications of functional analysis in probability theory and statistics 46L80 K-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 46N40 Applications of functional analysis in numerical 58J22] analysis [See also 65Jxx] 46L85 Noncommutative topology [See also 58B32, 46N50 Applications of functional analysis in quantum 58B34, 58J22] physics 46L87 Noncommutative differential geometry [See also 46N55 Applications of functional analysis in statistical 58B32, 58B34, 58J22] physics 46L89 Other “noncommutative” mathematics based on 46N60 Applications of functional analysis in biology and C ∗ -algebra theory [See also 58B32, 58B34, 58J22] other sciences 46L99 None of the above, but in this section 46N99 None of the above, but in this section 84 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 46Sxx Other (nonclassical) types of func- 47-04 Software, source code, etc. for problems pertaining to operator theory tional analysis [See also 47Sxx] 46S05 Quaternionic functional analysis 47-06 Proceedings, conferences, collections, etc. taining to operator theory per- 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional 47-08 Computational methods for problems pertaining to operator theory analysis [See also 12J25, 32P05] 46S20 Nonstandard functional analysis [See also 03H05] 47-11 Research data for problems pertaining to operator theory 46S30 Constructive functional analysis [See also 03F60] 46S40 Fuzzy functional analysis [See also 03E72] 47Axx General theory of linear operators 46S50 Functional analysis in probabilistic metric linear 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) spaces 46S60 Functional analysis on superspaces (supermani- 47A06 Linear relations (multivalued linear operators) folds) or graded spaces [See also 58A50, 58C50] 47A07 Forms (bilinear, sesquilinear, multilinear) 46S99 None of the above, but in this section 47A08 Operator matrices [See also 47A13] 47A10 Spectrum, resolvent 46Txx Nonlinear functional analysis [See 47A11 Local spectral properties of linear operators also 47Hxx, 47Jxx, 58Cxx, 58Dxx] 46T05 Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx] 46T10 Manifolds of mappings 47A12 Numerical range, numerical radius 47A13 Several-variable operator theory (spectral, Fredholm, etc.) 46T12 Measure (Gaussian, cylindrical, etc.) and inte- 47A15 Invariant subspaces of linear operators [See also 47A46] grals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX] 47A16 Cyclic vectors, hypercyclic and chaotic operators 46T20 Continuous and differentiable maps in nonlinear 47A20 Dilations, extensions, compressions of linear opfunctional analysis [See also 46G05] erators 46T25 Holomorphic maps in nonlinear functional anal47A25 Spectral sets of linear operators ysis [See also 46G20] 47A30 Norms (inequalities, more than one norm, etc.) 46T30 Distributions and generalized functions on nonof linear operators linear spaces [See also 46Fxx] 47A35 Ergodic theory of linear operators [See also 46T99 None of the above, but in this section 28Dxx, 37Axx] 47-XX Operator theory 47A40 Scattering theory of linear operators [See also 34L25, 35P25, 37K15, 58J50, 81Uxx] 47-00 General reference works (handbooks, dictionaries, 47A45 Canonical models for contractions and nonselfadbibliographies, etc.) pertaining to operator theory joint linear operators 47-01 Introductory exposition (textbooks, tutorial pa- 47A46 Chains (nests) of projections or of invariant subpers, etc.) pertaining to operator theory spaces, integrals along chains, etc. 47-02 Research exposition (monographs, survey articles) 47A48 Operator colligations (= nodes), vessels, linear pertaining to operator theory systems, characteristic functions, realizations, etc. 47-03 History of operator theory [Consider also classifi- 47A50 Equations and inequalities involving linear opercation numbers pertaining to Section 01] ators, with vector unknowns 85 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 47A52 Linear operators and ill-posed problems, regu- 47B07 Linear operators defined by compactness properlarization [See also 35R25, 47J06, 65F22, 65J20, ties 65L08, 65M30, 65R30] 47B10 Linear operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann 47A53 (Semi-) Fredholm operators; index theories [See classes, etc.) [See also 47L20] also 58B15, 58J20] 47A55 Perturbation theory of linear operators [See also 47B12 Sectorial operators 47H14, 58J37, 70H09, 81Q15] 47B13 Cowen-Douglas operators 47A56 Functions whose values are linear operators 47B15 Hermitian and normal operators (spectral mea(operator- and matrix-valued functions, etc., insures, functional calculus, etc.) cluding analytic and meromorphic ones) 47B20 Subnormal operators, hyponormal operators, etc. 47A57 Linear operator methods in interpolation, moment and extension problems [See also 30E05, 47B25 Linear symmetric and selfadjoint operators (unbounded) 42A70, 42A82, 44A60] 47B28 Nonselfadjoint operators [See also 47A45, 81Q12] 47A58 Linear operator approximation theory 47B32 Linear operators in reproducing-kernel Hilbert 47A60 Functional calculus for linear operators spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22] 47A62 Equations involving linear operators, with operator unknowns 47A63 Linear operator inequalities 47B33 Linear composition operators 47B34 Kernel operators 47A64 Operator means involving linear operators, 47B35 Toeplitz operators, Hankel operators, Wienershorted linear operators, etc. Hopf operators {For other integral operators, see also 45P05, 47G10} [See also 32A25, 32M15] 47A65 Structure theory of linear operators 47B36 Jacobi (tridiagonal) operators (matrices) and 47A66 Quasitriangular and nonquasitriangular, quasidigeneralizations agonal and nonquasidiagonal linear operators 47B37 Linear operators on special spaces (weighted 47A67 Representation theory of linear operators shifts, operators on sequence spaces, etc.) 47A68 Factorization theory (including Wiener-Hopf and 47B38 Linear operators on function spaces (general) spectral factorizations) of linear operators 47B39 Linear difference operators [See also 39A70] 47A70 (Generalized) eigenfunction expansions of linear 47B40 Spectral operators, decomposable operators, operators; rigged Hilbert spaces well-bounded operators, etc. 47A75 Eigenvalue problems for linear operators [See also 47B44 Linear accretive operators, dissipative operators, 47J10, 49R05] etc. 47A80 Tensor products of linear operators [See also 47B47 Commutators, derivations, elementary operators, 46M05] etc. 47A99 None of the above, but in this section 47B48 Linear operators on Banach algebras 47Bxx Special classes of linear operators 47B49 Transformers, preservers (linear operators on spaces of linear operators) 47B01 Operators on Banach spaces 47B50 Linear operators on spaces with an indefinite metric [See also 46C20] 47B02 Operators on Hilbert spaces (general) 47B60 Linear operators on ordered spaces 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers, Kolmogorov 47B65 Positive linear operators and order-bounded opnumbers, entropy numbers, etc. of operators erators 86 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 47B80 Random linear operators [See also 47H40, 60H25] 47Fxx Partial differential operators [See also 35Pxx, 58Jxx] 47B90 Operator theory and harmonic analysis [See also 42-XX, 43-XX, 44-XX] 47F05 General theory of partial differential operators (should also be assigned at least one other classifica47B91 Operators on complex function spaces tion number in Section 47) [See also 35Pxx, 58Jxx] 47B92 Operators on real function spaces 47F10 Elliptic operators and their generalizations {For elliptic complexes, see 58J10} 47B93 Operators arising in mathematical physics 47F99 None of the above, but in this section 47B99 None of the above, but in this section 47Gxx Integral, integro-differential, and 47Cxx Individual linear operators as elepseudodifferential operators [See also ments of algebraic systems 58Jxx] 47C05 Linear operators in algebras 47G10 Integral operators [See also 45P05] ∗ 47C10 Linear operators in -algebras 47G20 Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx] 47C15 Linear operators in C - or von Neumann algebras ∗ 47G30 Pseudodifferential operators [See also 35Sxx, 58Jxx] 47C99 None of the above, but in this section 47Dxx Groups and semigroups of linear 47G40 Potential operators [See also 31-XX] operators, their generalizations and appli47G99 None of the above, but in this section cations 47D03 Groups and semigroups of linear operators [See 47Hxx Nonlinear operators and their also 20M20] {For nonlinear operators, see 47H20} properties {For global and geometric 47D06 One-parameter semigroups and linear evolution aspects, 58Cxx} equations [See also 34G10, 34K30] see 49J53, 58-XX, especially 47D07 Markov semigroups and applications to diffusion 47H04 Set-valued operators [See also 28B20, 54C60, 58C06] processes {For Markov processes, see 60Jxx} 47D08 Schrödinger and Feynman-Kac semigroups 47H05 Monotone operators and generalizations 47D09 Operator sine and cosine functions and higher- 47H06 Nonlinear accretive operators, dissipative operators, etc. order Cauchy problems [See also 34G10] 47D60 C-semigroups, regularized semigroups 47D62 Integrated semigroups 47D99 None of the above, but in this section 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. 47Exx Ordinary differential operators [See 47H09 Contraction-type mappings, nonexpansive mapalso 34Bxx, 34Lxx] pings, A-proper mappings, etc. 47E05 General theory of ordinary differential operators 47H10 Fixed-point theorems [See also 37C25, 54H25, (should also be assigned at least one other classifica55M20, 58C30] tion number in Section 47) [See also 34Bxx, 34Lxx] 47H11 Degree theory for nonlinear operators [See also 47E07 Functional-differential and differential-difference 55M25, 58C30] operators [See also 34K08] 47H14 Perturbations of nonlinear operators [See also 47E99 None of the above, but in this section 47A55, 58J37, 70H09, 70K60, 81Q15] 87 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 47H20 Semigroups of nonlinear operators [See also 47Lxx Linear spaces and algebras of oper37L05, 47J35, 54H15, 58D07] ators [See also 46Lxx] 47H25 Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35] 47L05 Linear spaces of operators [See also 46A32, 46B28] 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı̆, Uryson, etc.) [See also 47L07 Convex sets and cones of operators [See also 46A55] 45Gxx, 45P05] 47H40 Random nonlinear operators [See also 47B80, 60H25] 47L10 Algebras of operators on Banach spaces and other topological linear spaces 47H60 Multilinear and polynomial operators [See also 47L15 Operator algebras with symbol structure 46G25] 47H99 None of the above, but in this section 47L20 Operator ideals [See also 47B10] 47Jxx Equations and inequalities involving 47L22 Ideals of polynomials and of multilinear mappings in operator theory nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX} 47L25 Operator spaces (= matricially normed spaces) [See also 46L07] 47J05 Equations involving nonlinear operators (general) [See also 47H10, 47J25] 47J06 Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30] 47L30 Abstract operator algebras on Hilbert spaces 47L35 Nest algebras, CSL algebras 47J07 Abstract inverse mapping and implicit function theorems involving nonlinear operators [See also 47L40 Limit algebras, subalgebras of C ∗ -algebras 46T20, 58C15] 47J10 Nonlinear spectral theory, nonlinear eigenvalue 47L45 Dual algebras; weakly closed singly generated operator algebras problems [See also 49R05] 47J15 Abstract bifurcation theory involving nonlinear 47L50 Dual spaces of operator algebras operators [See also 34C23, 37Gxx, 58E07, 58E09] 47J20 Variational and other types of inequalities involv- 47L55 Representations of (nonselfadjoint) operator algebras ing nonlinear operators (general) [See also 49J40] 47J22 Variational and other types of inclusions [See also 47L60 Algebras of unbounded operators; partial alge34A60, 49J21, 49K21] bras of operators 47J25 Iterative procedures involving nonlinear operators 47L65 Crossed product algebras (analytic crossed prod[See also 47J26, 65J15] ucts) 47J26 Fixed-point iterations [See also 47J25] 47L70 Nonassociative nonselfadjoint operator algebras 47J30 Variational methods involving nonlinear operators [See also 58Exx] 47L75 Other nonselfadjoint operator algebras 47J35 Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47L80 Algebras of specific types of operators (Toeplitz, 47H20, 58D25] integral, pseudodifferential, etc.) 47J40 Equations with nonlinear hysteresis operators 47L90 Applications of operator algebras to the sciences [See also 34C55, 74N30] 47J99 None of the above, but in this section 47L99 None of the above, but in this section 88 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 47Nxx Miscellaneous applications of oper- 49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal conator theory [See also 46Nxx] trol 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, eco- 49-03 History of calculus of variations and optimal control [Consider also classification numbers pertaining nomics to Section 01] 47N20 Applications of operator theory to differential 49-04 Software, source code, etc. for problems pertainand integral equations ing to calculus of variations and optimal control 47N30 Applications of operator theory in probability 49-06 Proceedings, conferences, collections, etc. pertheory and statistics taining to calculus of variations and optimal control 47N40 Applications of operator theory in numerical 49-11 Research data for problems pertaining to calculus analysis [See also 65Jxx] of variations and optimal control 47N50 Applications of operator theory in the physical sciences 49Jxx Existence theories in calculus of 47N60 Applications of operator theory in chemistry and variations and optimal control life sciences 47N70 Applications of operator theory in systems, signals, circuits, and control theory 47N99 None of the above, but in this section 47Sxx Other (nonclassical) types of operator theory [See also 46Sxx] 47S05 Quaternionic operator theory 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 47S10 Operator theory over fields other than R, C or 49J21 Existence theories for optimal control problems involving relations other than differential equations the quaternions; non-Archimedean operator theory 47S20 Nonstandard operator theory [See also 03H05] 47S30 Constructive operator theory [See also 03F60] 49J27 Existence theories for problems in abstract spaces [See also 90C48, 93C25] 49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 47S50 Operator theory in probabilistic metric linear spaces [See also 54E70] 49J35 Existence of solutions for minimax problems 47S40 Fuzzy operator theory [See also 03E72] 47S99 None of the above, but in this section 49J40 Variational inequalities [See also 47J20] 49J45 Methods involving semicontinuity and convergence; relaxation 49-XX Calculus of variations and optimal control; optimization [See 49J50 Fréchet and Gateaux differentiability in optimization [See also 46G05, 58C20] also 34H05, 34K35, 65Kxx, 90Cxx, 49J52 Nonsmooth analysis [See also 46G05, 58C50, 93-XX] 90C56] 49-00 General reference works (handbooks, dictionaries, 49J53 Set-valued and variational analysis [See also bibliographies, etc.) pertaining to calculus of vari28B20, 47H04, 54C60, 58C06] ations and optimal control 49J55 Existence of optimal solutions to problems involv49-01 Introductory exposition (textbooks, tutorial paing randomness [See also 93E20] pers, etc.) pertaining to calculus of variations and optimal control 49J99 None of the above, but in this section 89 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 49Kxx Optimality conditions 49M27 Decomposition methods 49K05 Optimality conditions for free problems in one 49M29 Numerical methods involving duality independent variable 49M37 Numerical methods based on nonlinear program49K10 Optimality conditions for free problems in two or ming [See also 65Kxx, 90C30] more independent variables 49M41 PDE constrained optimization (numerical as49K15 Optimality conditions for problems involving orpects) dinary differential equations 49M99 None of the above, but in this section 49K20 Optimality conditions for problems involving partial differential equations 49Nxx Miscellaneous topics in calculus of 49K21 Optimality conditions for problems involving re- variations and optimal control lations other than differential equations 49N05 Linear optimal control problems [See also 93C05] 49K27 Optimality conditions for problems in abstract 49N10 Linear-quadratic optimal control problems spaces [See also 90C48, 93C25] 49N15 Duality theory (optimization) [See also 90C46] 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang 49N20 Periodic optimal control problems controls, etc.) 49N25 Impulsive optimal control problems 49K35 Optimality conditions for minimax problems 49N30 Problems with incomplete information (opti49K40 Sensitivity, stability, well-posedness [See also mization) [See also 93C41] 90C31] 49N35 Optimal feedback synthesis [See also 93B52] 49K45 Optimality conditions for problems involving 49N45 Inverse problems in optimal control randomness [See also 93E20] 49N60 Regularity of solutions in optimal control 49K99 None of the above, but in this section 49N70 Differential games and control [See also 91A23] 49Lxx Hamilton-Jacobi theories [See also 49N75 Pursuit and evasion games [See also 91A24] 70H20, 35F21] 49L12 Hamilton-Jacobi equations in optimal control and 49N80 Mean field games and control [See also 91A16] differential games 49N90 Applications of optimal control and differential games [See also 90C90, 91A80, 93C95] 49L20 Dynamic programming in optimal control and differential games 49N99 None of the above, but in this section 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 49Qxx Manifolds and measure-geometric topics [See also 58Exx] 49L99 None of the above, but in this section 49Q05 Minimal surfaces and optimization [See also 53A10, 58E12] 49Mxx Numerical methods in optimal con- trol [See also 65Kxx, 90-08, 90Cxx] 49Q10 Optimization of shapes other than minimal surfaces [See also 90C90] 49M05 Numerical methods based on necessary conditions 49Q12 Sensitivity analysis for optimization problems on manifolds 49M15 Newton-type methods [See also 90C53] 49Q15 Geometric measure and integration theory, integral and normal currents in optimization [See also 28A75, 32C30, 58A25, 58C35] 49M20 Numerical methods of relaxation type 49M25 Discrete approximations in optimal control 90 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 49Q20 Variational problems in a geometric measure- 51Axx Linear incidence geometry theoretic setting 51A05 General theory of linear incidence geometry and projective geometries 49Q22 Optimal transportation [See also 90B06] 49Q99 None of the above, but in this section 51A10 Homomorphism, automorphism and dualities in linear incidence geometry 49Rxx Variational methods for eigenvalues of operators (should also be assigned 51A15 Linear incidence geometric structures with parallelism at least one other classification number in Section 49) [See also 47A75] 51A20 Configuration theorems in linear incidence geometry 49R05 Variational methods for eigenvalues of operators (should also be assigned at least one other classifi51A25 Algebraization in linear incidence geometry [See cation number in Section 49) [See also 47A75] also 12Kxx, 20N05] 49R99 None of the above, but in this section 51A30 Desarguesian and Pappian geometries 49Sxx Variational principles of physics (should also be assigned at least one other 51A35 Non-Desarguesian affine and projective planes classification number in Section 49) 51A40 Translation planes and spreads in linear incidence geometry 49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49) 51A45 Incidence structures embeddable into projective geometries 49S99 None of the above, but in this section 51A50 Polar geometry, symplectic spaces, orthogonal spaces 51-XX Geometry {For algebraic geometry, see 14-XX; for differential 51A99 None of the above, but in this section geometry, see 53-XX} 51Bxx Nonlinear incidence geometry 51-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry 51B05 General theory of nonlinear incidence geometry 51-01 Introductory exposition (textbooks, tutorial pa51B10 Möbius geometries pers, etc.) pertaining to geometry 51-02 Research exposition (monographs, survey articles) 51B15 Laguerre geometries pertaining to geometry 51B20 Minkowski geometries in nonlinear incidence ge51-03 History of geometry [Consider also classification ometry numbers pertaining to Section 01] 51B25 Lie geometries in nonlinear incidence geometry 51-04 Software, source code, etc. for problems pertaining to geometry 51B99 None of the above, but in this section 51-06 Proceedings, conferences, collections, etc. taining to geometry per- 51Cxx Ring geometry (Hjelmslev, Barbil51-08 Computational methods for problems pertaining ian, etc.) to geometry 51C05 Ring geometry (Hjelmslev, Barbilian, etc.) 51-11 Research data for problems pertaining to geometry 51C99 None of the above, but in this section 91 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 51Dxx Geometric closure systems 51Fxx Metric geometry 51D05 Abstract (Maeda) geometries 51F05 Absolute planes in metric geometry 51D10 Abstract geometries with exchange axiom 51F10 Absolute spaces in metric geometry 51D15 Abstract geometries with parallelism 51F15 Reflection groups, reflection geometries [See also 20H10, 20H15] {For Coxeter groups, see 20F55} 51D20 Combinatorial geometries and geometric closure 51F20 Congruence and orthogonality in metric geomesystems [See also 05B25, 05B35] try [See also 20H05] 51D25 Lattices of subspaces and geometric closure sys51F25 Orthogonal and unitary groups in metric geometems [See also 05B35] try [See also 20H05] 51D30 Continuous geometries, geometric closure sys- 51F30 Lipschitz and coarse geometry of metric spaces tems and related topics [See also 06Cxx] [See also 53C23] 51D99 None of the above, but in this section 51F99 None of the above, but in this section 51Exx Finite geometry and special inci- 51Gxx Ordered geometries (ordered incidence structures dence structures, etc.) 51E05 General block designs in finite geometry [See also 51G05 Ordered geometries (ordered incidence struc05B05] tures, etc.) 51E10 Steiner systems in finite geometry [See also 51G99 None of the above, but in this section 05B05] 51Hxx Topological geometry 51E12 Generalized quadrangles and generalized polygons in finite geometry 51H05 General theory of topological geometry 51E14 Finite partial geometries (general), nets, partial 51H10 Topological linear incidence structures spreads 51H15 Topological nonlinear incidence structures 51E15 Finite affine and projective planes (geometric as51H20 Topological geometries on manifolds [See also 57pects) XX] 51E20 Combinatorial structures in finite projective 51H25 Geometries with differentiable structure [See also spaces [See also 05Bxx] 53Cxx, especially 53C70] 51E21 Blocking sets, ovals, k-arcs 51H30 Geometries with algebraic manifold structure [See also 14-XX] 51E22 Linear codes and caps in Galois spaces [See also 94B05] 51H99 None of the above, but in this section 51E23 Spreads and packing problems in finite geometry 51E24 Buildings and the geometry of diagrams 51Jxx Incidence groups 51J05 General theory of incidence groups 51E25 Other finite nonlinear geometries 51J10 Projective incidence groups 51E26 Other finite linear geometries 51J15 Kinematic spaces 51E30 Other finite incidence structures (geometric as- 51J20 Representation by near-fields and near-algebras pects) [See also 05B30] [See also 12K05, 16Y30] 51E99 None of the above, but in this section 51J99 None of the above, but in this section 92 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 51Kxx Distance geometry 51Nxx Analytic and descriptive geometry 51K05 General theory of distance geometry 51N05 Descriptive geometry [See also 65D17, 68U07] 51K10 Synthetic differential geometry 51N10 Affine analytic geometry 51N15 Projective analytic geometry 51K99 None of the above, but in this section 51N20 Euclidean analytic geometry 51Lxx Geometric order structures [See 51N25 Analytic geometry with other transformation groups also 53C75] 51N30 Geometry of classical groups [See also 14L35, 20Gxx] 51L05 Geometry of orders of nondifferentiable curves 51L10 Directly differentiable curves in geometric order 51N35 Questions of classical algebraic geometry [See structures also 14Nxx] 51L15 n-vertex theorems via direct methods 51N99 None of the above, but in this section 51L20 Geometry of orders of surfaces 51Pxx Classical or axiomatic geometry and physics (should also be assigned at least one other classification number from Sections 70–86) 51L99 None of the above, but in this section 51Mxx Real and complex geometry 51P05 Classical or axiomatic geometry and physics (should also be assigned at least one other classification number from Sections 70–86) 51M04 Elementary problems in Euclidean geometries 51M05 Euclidean geometries (general) and generaliza51P99 None of the above, but in this section tions 51M09 Elementary problems in hyperbolic and elliptic geometries 52-XX Convex and discrete geometry 51M10 Hyperbolic and elliptic geometries (general) and generalizations 52-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to convex and dis51M15 Geometric constructions in real or complex gecrete geometry ometry 52-01 Introductory exposition (textbooks, tutorial pa51M16 Inequalities and extremum problems in real pers, etc.) pertaining to convex and discrete geomor complex geometry {For convex problems, see etry 52A40} 52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also 51F15] 52-03 History of convex and discrete geometry [Consider also classification numbers pertaining to Section 01] 51M25 Length, area and volume in real or complex ge52-04 Software, source code, etc. for problems pertainometry [See also 26B15] ing to convex and discrete geometry 51M30 Line geometries and their generalizations [See 52-06 Proceedings, conferences, collections, etc. peralso 53A25] taining to convex and discrete geometry 51M35 Synthetic treatment of fundamental manifolds in 52-08 Computational methods for problems pertaining projective geometries (Grassmannians, Veronesians to convex and discrete geometry and their generalizations) [See also 14M15] 52-11 Research data for problems pertaining to convex and discrete geometry 51M99 None of the above, but in this section 93 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 52Axx General convexity 52Bxx Polytopes and polyhedra 52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) [See also 05Cxx] 52A05 Convex sets without dimension restrictions (aspects of convex geometry) 52B10 Three-dimensional polytopes 52A01 Axiomatic and generalized convexity 52A07 Convex sets in topological vector spaces (aspects 52B11 n-dimensional polytopes of convex geometry) [See also 46A55] 52B12 Special polytopes (linear programming, centrally symmetric, etc.) 52A10 Convex sets in 2 dimensions (including convex curves) [See also 53A04] 52B15 Symmetry properties of polytopes 52A15 Convex sets in 3 dimensions (including convex 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic surfaces) [See also 53A05, 53C45] geometry) [See also 06A11, 13F20, 13F55, 13Hxx, 52C05, 52C07] 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 52B22 Shellability for polytopes and polyhedra 52A21 Convexity and finite-dimensional Banach spaces 52B35 Gale and other diagrams (including special norms, zonoids, etc.) (aspects of 52B40 Matroids in convex geometry (realizations in the convex geometry) [See also 46Bxx] context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx] 52A22 Random convex sets and integral geometry (aspects of convex geometry) [See also 53C65, 60D05] 52B45 Dissections and valuations (Hilbert’s third problem, etc.) 52A23 Asymptotic theory of convex bodies [See also 52B55 Computational aspects related to convexity {For 46B06] computational methods, see 52-08; for computational geometry and algorithms, see 68Q25, 68U05; 52A27 Approximation by convex sets for numerical algorithms, see 65Yxx} [See also 68Uxx] 52A30 Variants of convex sets (star-shaped, (m, n)convex, etc.) 52B60 Isoperimetric problems for polytopes 52A35 Helly-type theorems and geometric transversal 52B70 Polyhedral manifolds theory 52B99 None of the above, but in this section 52A37 Other problems of combinatorial convexity 52Cxx Discrete geometry 52A38 Length, area, volume and convex sets (aspects of convex geometry) [See also 26B15, 28A75, 49Q20] 52C05 Lattices and convex bodies in 2 dimensions (aspects of discrete geometry) [See also 11H06, 11H31, 11P21] 52A39 Mixed volumes and related topics in convex geometry 52C07 Lattices and convex bodies in n dimensions (aspects of discrete geometry) [See also 11H06, 11H31, 52A40 Inequalities and extremum problems involving 11P21] convexity in convex geometry 52C10 Erdős problems and related topics of discrete geometry [See also 11Hxx] 52A41 Convex functions and convex programs in convex geometry [See also 26B25, 90C25] 52C15 Packing and covering in 2 dimensions (aspects of discrete geometry) [See also 05B40, 11H31] 52A55 Spherical and hyperbolic convexity 52C17 Packing and covering in n dimensions (aspects of 52A99 None of the above, but in this section discrete geometry) [See also 05B40, 11H31] 94 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 52C20 Tilings in 2 dimensions (aspects of discrete ge- 53Axx Classical differential geometry ometry) [See also 05B45, 51M20] 53A04 Curves in Euclidean and related spaces 52C22 Tilings in n dimensions (aspects of discrete ge53A05 Surfaces in Euclidean and related spaces ometry) [See also 05B45, 51M20] 53A07 Higher-dimensional and -codimensional surfaces 52C23 Quasicrystals and aperiodic tilings in discrete gein Euclidean and related n-spaces ometry 53A10 Minimal surfaces in differential geometry, sur52C25 Rigidity and flexibility of structures (aspects of faces with prescribed mean curvature [See also discrete geometry) [See also 70B15] 49Q05, 49Q10, 53C42] 52C26 Circle packings and discrete conformal geometry 53A15 Affine differential geometry 52C30 Planar arrangements of lines and pseudolines (as- 53A17 Differential geometric aspects in kinematics pects of discrete geometry) 53A20 Projective differential geometry 52C35 Arrangements of points, flats, hyperplanes (as53A25 Differential line geometry pects of discrete geometry) [See also 14N20, 32S22] 53A31 Differential geometry of submanifolds of Möbius 52C40 Oriented matroids in discrete geometry space 52C45 Combinatorial complexity of geometric struc- 53A35 Non-Euclidean differential geometry tures [See also 68U05] 53A40 Other special differential geometries 52C99 None of the above, but in this section 53A45 Differential geometric aspects in vector and tensor analysis 53-XX Differential geometry {For 53A55 Differential invariants (local theory), geometric differential topology, see 57Rxx; for objects foundational questions of differen- 53A60 Differential geometry of webs [See also 14C21, 20N05] tiable manifolds, see 58Axx} 53-00 General reference works (handbooks, dictionaries, 53A70 Discrete differential geometry bibliographies, etc.) pertaining to differential ge- 53A99 None of the above, but in this section ometry 53-01 Introductory exposition (textbooks, tutorial pa- 53Bxx Local differential geometry pers, etc.) pertaining to differential geometry 53B05 Linear and affine connections 53-02 Research exposition (monographs, survey articles) 53B10 Projective connections pertaining to differential geometry 53B12 Differential geometric aspects of statistical man53-03 History of differential geometry [Consider also ifolds and information geometry classification numbers pertaining to Section 01] 53B15 Other connections 53-04 Software, source code, etc. for problems pertain53B20 Local Riemannian geometry ing to differential geometry 53-06 Proceedings, conferences, collections, etc. taining to differential geometry per- 53B21 Methods of local Riemannian geometry 53B25 Local submanifolds [See also 53C40] 53-08 Computational methods for problems pertaining 53B30 Local differential geometry of Lorentz metrics, to differential geometry indefinite metrics 53-11 Research data for problems pertaining to differen- 53B35 Local differential geometry of Hermitian and tial geometry Kählerian structures [See also 32Qxx] 95 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 53B40 Local differential geometry of Finsler spaces and 53C30 Differential geometry of homogeneous manifolds generalizations (areal metrics) [See also 14M15, 14M17, 32M10, 57T15] 53B50 Applications of local differential geometry to the sciences 53C35 Differential geometry of symmetric spaces [See also 32M15, 57T15] 53B99 None of the above, but in this section 53Cxx Global differential geometry [See 53C38 Calibrations and calibrated geometries also 51H25, 58-XX] {For related bundle theory, see 55Rxx, 57Rxx} 53C40 Global submanifolds [See also 53B25] 53C05 Connections, general theory 53C07 Special connections and metrics on vector 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, bundles (Hermite-Einstein, Yang-Mills) [See also 49Q10, 53A10, 57R40, 57R42] 32Q20] 53C08 Differential geometric aspects of gerbes and dif53C43 Differential geometric aspects of harmonic maps ferential characters [See also 58E20] 53C10 G-structures 53C12 Foliations (differential geometric aspects) [See 53C45 Global surface theory (convex surfaces à la A. D. also 57R30, 57R32] Aleksandrov) 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C17 Sub-Riemannian geometry 53C18 Conformal structures on manifolds 53C20 Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C55 Global differential geometry of Hermitian and Kählerian manifolds [See also 32Qxx] 53C21 Methods of global Riemannian geometry, includ- 53C56 Other complex differential geometry [See also 32Qxx] ing PDE methods; curvature restrictions [See also 58J60] 53C22 Geodesics in global differential geometry [See also 53C60 Global differential geometry of Finsler spaces and 58E10] generalizations (areal metrics) [See also 58B20] 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric 53C65 Integral geometry [See also 52A22, 60D05]; difspaces ferential forms, currents, etc. [See mainly 58Axx] 53C24 Rigidity results 53C25 Special Riemannian Sasakian, etc.) manifolds (Einstein, 53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry 53C27 Spin and Spinc geometry 53C28 Twistor methods in differential geometry [See also 32L25] 53C29 Issues of holonomy in differential geometry 53C70 Direct methods (G-spaces of Busemann, etc.) 53C75 Geometric orders, order geometry [See also 51Lxx] 53C80 Applications of global differential geometry to the sciences 53C99 None of the above, but in this section 96 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 53Dxx Symplectic geometry, contact ge- 53Zxx Applications of differential geometry to sciences and engineering ometry [See also 37Jxx, 70Gxx, 70Hxx] 53D05 Symplectic manifolds, general 53Z05 Applications of differential geometry to physics 53D10 Contact manifolds, general 53Z10 Applications of differential geometry to biology 53D12 Lagrangian submanifolds; Maslov index 53D15 Almost contact and almost symplectic manifolds 53D17 Poisson manifolds; Poisson groupoids and algebroids 53D18 Generalized geometries (à la Hitchin) 53D20 Momentum maps; symplectic reduction 53D22 Canonical transformations in symplectic and contact geometry 53Z15 Applications of differential geometry to chemistry 53Z30 Applications of differential geometry to engineering 53Z50 Applications of differential geometry to data and computer science 53D25 Geodesic flows in symplectic geometry and con- 53Z99 None of the above, but in this section tact geometry 53D30 Symplectic structures of moduli spaces 54-XX General topology {For the topology of manifolds of all dimen53D37 Symplectic aspects of mirror symmetry, homo- sions, see 57Nxx} 53D35 Global theory of symplectic and contact manifolds [See also 57Rxx] logical mirror symmetry, and Fukaya category [See also 14J33] 54-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general topology 53D40 Symplectic aspects of Floer homology and cohomology 54-01 Introductory exposition (textbooks, tutorial pa53D42 Symplectic field theory; contact homology pers, etc.) pertaining to general topology 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 54-02 Research exposition (monographs, survey articles) pertaining to general topology 53D50 Geometric quantization 53D55 Deformation quantization, star products 54-03 History of general topology [Consider also classification numbers pertaining to Section 01] 53D99 None of the above, but in this section 53Exx Geometric evolution equations 54-04 Software, source code, etc. for problems pertaining to general topology 53E10 Flows related to mean curvature 53E20 Ricci flows 54-06 Proceedings, conferences, collections, etc. taining to general topology 53E30 Flows related to complex manifolds (e.g., KählerRicci flows, Chern-Ricci flows) 54-08 Computational methods for problems pertaining to general topology 53E40 Higher-order geometric flows 53E50 Flows related to symplectic and contact structures 53E99 None of the above, but in this section 54-11 Research data for problems pertaining to general topology 97 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. per- 54Axx Generalities in topology 54C20 Extension of maps 54A05 Topological spaces and generalizations (closure 54C25 Embedding spaces, etc.) 54C30 Real-valued functions in general topology [See 54A10 Several topologies on one set (change of topology, also 26-XX] comparison of topologies, lattices of topologies) 54C35 Function spaces in general topology [See also 46Exx, 58D15] 54A15 Syntopogeneous structures 54A20 Convergence in general topology (sequences, fil- 54C40 Algebraic properties of function spaces in general topology [See also 46J10] ters, limits, convergence spaces, nets, etc.) 54A25 Cardinality properties (cardinal functions and in- 54C45 C- and C ∗ -embedding equalities, discrete subsets) [See also 03Exx] {For 54C50 Topology of special sets defined by functions [See ultrafilters, see 54D80} also 26A21] 54A35 Consistency and independence results in general 54C55 Absolute neighborhood extensor, absolute extentopology [See also 03E35] sor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15] 54A40 Fuzzy topology [See also 03E72] 54C56 Shape theory in general topology [See also 55P55, 57N25] 54A99 None of the above, but in this section 54Bxx Basic constructions in general 54C60 Set-valued maps in general topology [See also 26E25, 28B20, 47H04, 58C06] topology 54B05 Subspaces in general topology 54C65 Selections in general topology [See also 28B20] 54B10 Product spaces in general topology 54C70 Entropy in general topology 54B15 Quotient spaces, topology decompositions in general 54C99 None of the above, but in this section 54Dxx Fairly general properties of topo- 54B17 Adjunction spaces and similar constructions in logical spaces general topology 54D05 Connected and locally connected spaces (general 54B20 Hyperspaces in general topology aspects) 54B30 Categorical methods in general topology [See also 54D10 Lower separation axioms (T0 –T3 , etc.) 18F60] 54D15 Higher separation axioms (completely regular, 54B35 Spectra in general topology normal, perfectly or collectionwise normal, etc.) 54B40 Presheaves and sheaves in general topology [See 54D20 Noncompact covering properties (paracompact, also 18F20] Lindelöf, etc.) 54B99 None of the above, but in this section 54D25 “P -minimal” and “P -closed” spaces 54Cxx Maps and general types of topolog- 54D30 Compactness ical spaces defined by maps 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54C05 Continuous maps 54D40 Remainders in general topology 54C08 Weak and generalized continuity 54D45 Local compactness, σ-compactness 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54D50 k-spaces 54C15 Retraction 54D55 Sequential spaces 98 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 54D60 Realcompactness and realcompactification 54D65 Separability of topological spaces 54D70 Base properties of topological spaces 54F50 Topological spaces of dimension ≤ 1; curves, dendrites [See also 26A03] 54F55 Unicoherence, multicoherence 54F65 Topological characterizations of particular spaces 54D80 Special constructions of topological spaces 54F99 None of the above, but in this section (spaces of ultrafilters, etc.) 54D99 None of the above, but in this section 54Gxx Peculiar topological spaces 54Exx Topological spaces with richer 54G05 Extremally disconnected spaces, F -spaces, etc. structures 54G10 P -spaces 54E05 Proximity structures and generalizations 54G12 Scattered spaces 54E15 Uniform structures and generalizations 54G15 Pathological topological spaces 54E17 Nearness spaces 54G20 Counterexamples in general topology 54E18 p-spaces, M -spaces, σ-spaces, etc. 54G99 None of the above, but in this section 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 None of the above, but in this section 54Hxx Connections of general topology with other structures, applications 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 54H10 Topological representations of algebraic systems [See also 22-XX] 54H11 Topological groups (topological aspects) [See also 22A05] 54H12 Topological lattices, etc. (topological aspects) [See also 06B30, 06F30] 54H13 Topological fields, rings, etc. (topological aspects) [See also 12Jxx] {For algebraic aspects, see 13Jxx, 16W80} 54Fxx Special properties of topological 54H15 Transformation groups and semigroups (topological aspects) [See also 20M20, 22-XX, 57Sxx] spaces 54H25 Fixed-point and coincidence theorems (topologi54F05 Linearly ordered topological spaces, generalized cal aspects) [See also 47H10, 55M20] ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 54H30 Applications of general topology to computer science (e.g., digital topology, image processing) [See 54F15 Continua and generalizations also 68U03] 54F16 Hyperspaces of continua 54H99 None of the above, but in this section 54F17 Inverse limits of set-valued functions 54Jxx Nonstandard topology [See also 54F35 Higher-dimensional local connectedness [See also 03H05] 55Mxx, 55Nxx] 54J05 Nonstandard topology [See also 03H05] 54F45 Dimension theory in general topology [See also 55M10] 54J99 None of the above, but in this section 99 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 55-XX Algebraic topology 55N15 Topological K-theory [See also 19Lxx] {For algebraic K-theory, see 18F25, 19-XX} 55-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic topol- 55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology ogy 55-01 Introductory exposition (textbooks, tutorial pa- 55N22 Bordism and cobordism theories and formal group laws in algebraic topology [See also 14L05, pers, etc.) pertaining to algebraic topology 19L41, 57R75, 57R77, 57R85, 57R90] 55-02 Research exposition (monographs, survey articles) 55N25 Homology with local coefficients, equivariant copertaining to algebraic topology homology 55-03 History of algebraic topology [Consider also clas55N30 Sheaf cohomology in algebraic topology [See also sification numbers pertaining to Section 01] 18F20, 32C35, 32L10] 55-04 Software, source code, etc. for problems pertain55N31 Persistent homology and applications, topologiing to algebraic topology cal data analysis [See also 62R40, 68T09] 55-06 Proceedings, conferences, collections, etc. per55N32 Orbifold cohomology taining to algebraic topology 55N33 Intersection homology and cohomology in alge55-08 Computational methods for problems pertaining braic topology to algebraic topology 55N34 Elliptic cohomology 55-11 Research data for problems pertaining to algebraic topology 55N35 Other homology theories in algebraic topology 55N40 Axioms for homology theory and uniqueness the- 55Mxx Classical topics in algebraic topolorems in algebraic topology ogy {For the topology of Euclidean spaces 55N45 Products and intersections in homology and coand manifolds, see 57Nxx} homology 55M05 Duality in algebraic topology 55M10 Dimension theory in algebraic topology [See also 54F45] 55N91 Equivariant homology and cohomology in algebraic topology [See also 19L47] 55N99 None of the above, but in this section 55M15 Absolute neighborhood retracts [See also 54C55] 55M20 Fixed points and coincidences in algebraic topol- 55Pxx Homotopy theory {For simple homotopy type, see 57Q10} ogy [See also 54H25] 55M25 Degree, winding number 55P05 Homotopy extension properties, cofibrations in algebraic topology 55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological 55P10 Homotopy equivalences in algebraic topology robotics (topological aspects) 55P15 Classification of homotopy type 55M35 Finite groups of transformations in algebraic 55P20 Eilenberg-Mac Lane spaces topology (including Smith theory) [See also 57S17] 55P25 Spanier-Whitehead duality 55M99 None of the above, but in this section 55P30 Eckmann-Hilton duality 55Nxx Homology and cohomology theories 55P35 Loop spaces in algebraic topology [See also 57Txx] 55P40 Suspensions 55N05 Čech types 55N07 Steenrod-Sitnikov homologies 55N10 Singular homology and cohomology theory 55P42 Stable homotopy theory, spectra 55P43 Spectra with additional structure (E∞ , A∞ , ring spectra, etc.) 100 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 55P45 H-spaces and duals 55P47 Infinite loop spaces 55Rxx Fiber spaces and bundles in algebraic topology [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25] 55P48 Loop space machines and operads in algebraic 55R05 Fiber spaces in algebraic topology topology [See also 18Mxx] 55P50 String topology 55R10 Fiber bundles in algebraic topology 55P55 Shape theory [See also 54C56, 55Q07] 55R12 Transfer for fiber spaces and bundles in algebraic topology 55P57 Proper homotopy theory 55P60 Localization and completion in homotopy theory 55R15 Classification of fiber spaces or bundles in algebraic topology 55P62 Rational homotopy theory 55P65 Homotopy functors in algebraic topology 55R20 Spectral sequences and homology of fiber spaces in algebraic topology [See also 55Txx] 55P91 Equivariant homotopy theory in algebraic topology [See also 19L47] 55R25 Sphere bundles and vector bundles in algebraic topology 55P92 Relations between equivariant and nonequivariant homotopy theory in algebraic topology 55R35 Classifying spaces of groups and H-spaces in algebraic topology 55P99 None of the above, but in this section 55Qxx Homotopy groups 55R37 Maps between classifying spaces in algebraic topology 55Q05 Homotopy groups, general; sets of homotopy 55R40 Homology of classifying spaces and characterisclasses tic classes in algebraic topology [See also 57Txx, 55Q07 Shape groups 57R20] 55Q10 Stable homotopy groups 55Q15 Whitehead products and generalizations 55R45 Homology and homotopy of BO and BU; Bott periodicity 55Q20 Homotopy groups of wedges, joins, and simple 55R50 Stable classes of vector space bundles in algebraic spaces topology and relations to K-theory [See also 19Lxx] {For algebraic K-theory, see 18F25, 19-XX} 55Q25 Hopf invariants 55Q35 Operations in homotopy groups 55R55 Fiberings with singularities in algebraic topology 55Q40 Homotopy groups of spheres 55R60 Microbundles and block bundles in algebraic topology [See also 57N55, 57Q50] 55Q45 Stable homotopy of spheres 55Q50 J-morphism [See also 19L20] 55Q51 vn -periodicity 55R65 Generalizations of fiber spaces and bundles in algebraic topology 55Q52 Homotopy groups of special spaces 55R70 Fibrewise topology 55Q55 Cohomotopy groups 55R80 Discriminantal varieties and configuration spaces in algebraic topology 55Q70 Homotopy groups of special types [See also 55N05, 55N07] 55R91 Equivariant fiber spaces and bundles in algebraic topology [See also 19L47] 55Q91 Equivariant homotopy groups [See also 19L47] 55Q99 None of the above, but in this section 55R99 None of the above, but in this section 101 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 55Sxx Operations and obstructions in al- 55Uxx Applied homological algebra and gebraic topology category theory in algebraic topology [See also 18Gxx] 55S05 Primary cohomology operations in algebraic topology 55U05 Abstract complexes in algebraic topology 55U10 Simplicial sets and complexes in algebraic topology 55S10 Steenrod algebra 55S12 Dyer-Lashof operations 55U15 Chain complexes in algebraic topology 55S15 Symmetric products and cyclic products in alge55U20 Universal coefficient theorems, Bockstein operabraic topology tor 55S20 Secondary and higher cohomology operations in 55U25 Homology of a product, Künneth formula algebraic topology 55U30 Duality in applied homological algebra and cat55S25 K-theory operations and generalized cohomology egory theory (aspects of algebraic topology) operations in algebraic topology [See also 19D55, 19Lxx] 55U35 Abstract and axiomatic homotopy theory in algebraic topology 55S30 Massey products 55U40 Topological categories, foundations of homotopy 55S35 Obstruction theory in algebraic topology theory 55S36 Extension and compression of mappings in alge- 55U99 None of the above, but in this section braic topology 57-XX Manifolds and cell com55S40 Sectioning fiber spaces and bundles in algebraic plexes {For complex manifolds, see topology 32Qxx} 55S37 Classification of mappings in algebraic topology 55S45 Postnikov systems, k-invariants 57-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and 55S91 Equivariant operations and obstructions in algecell complexes braic topology [See also 19L47] 57-01 Introductory exposition (textbooks, tutorial pa55S99 None of the above, but in this section pers, etc.) pertaining to manifolds and cell complexes 55Txx Spectral sequences in algebraic 57-02 Research exposition (monographs, survey articles) topology [See also 18G40, 55R20] pertaining to manifolds and cell complexes 55T05 General theory of spectral sequences in algebraic 57-03 History of manifolds and cell complexes [Consider topology also classification numbers pertaining to Section 01] 55T10 Serre spectral sequences 57-04 Software, source code, etc. for problems pertaining to manifolds and cell complexes 55T15 Adams spectral sequences 55T20 Eilenberg-Moore spectral sequences [See also 57T35] 55T25 Generalized cohomology and spectral sequences in algebraic topology 55T99 None of the above, but in this section 57-06 Proceedings, conferences, collections, etc. taining 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 102 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. per- 57Kxx Low-dimensional topology in spe- 57M30 Wild embeddings cific dimensions 57M50 General geometric structures on low-dimensional manifolds 57K10 Knot theory 57K12 Generalized knots (virtual knots, welded knots, 57M60 Group actions on manifolds and cell complexes quandles, etc.) in low dimensions 57K14 Knot polynomials 57M99 None of the above, but in this section 57K16 Finite-type and quantum invariants, topological 57Nxx Topological manifolds quantum field theories (TQFT) 57K18 Homology theories in knot theory (Khovanov, 57N16 Geometric structures on manifolds of high or arbitrary dimension [See also 57M50] Heegaard-Floer, etc.) 57K20 2-dimensional topology (including mapping class 57N17 Topology of topological vector spaces groups of surfaces, Teichmüller theory, curve com57N20 Topology of infinite-dimensional manifolds [See plexes, etc.) also 58Bxx] 57K30 General topology of 3-manifolds 57N25 Shapes (aspects of topological manifolds) [See also 54C56, 55P55, 55Q07] 57K31 Invariants of 3-manifolds (also skein modules; character varieties) 57N30 Engulfing in topological manifolds 57K32 Hyperbolic 3-manifolds 57N35 Embeddings and immersions in topological manifolds 57K33 Contact structures in 3 dimensions [See also 57R17] 57N37 Isotopy and pseudo-isotopy 57K35 Other geometric structures on 3-manifolds 57N40 Neighborhoods of submanifolds 57K40 General topology of 4-manifolds 57N45 Flatness and tameness of topological manifolds 57K41 Invariants of 4-manifolds (e.g., Donaldson and 57N50 S n−1 ⊂ E n , Schoenflies problem Seiberg-Witten invariants) 57K43 Symplectic structures in 4 dimensions [See also 57N55 Microbundles and block bundles [See also 55R60, 57Q50] 57R17] 57N60 Cellularity in topological manifolds 57K45 Higher-dimensional knots and links 57K50 Low-dimensional manifolds of specific dimension 57N65 Algebraic topology of manifolds 5 or higher 57N70 Cobordism and concordance in topological manifolds 57K99 None of the above, but in this section 57Mxx General low-dimensional topology 57N75 General position and transversality 57N80 Stratifications in topological manifolds 57M05 Fundamental group, presentations, free differential calculus 57N99 None of the above, but in this section 57M07 Topological methods in group theory 57M10 Covering spaces and low-dimensional topology 57Pxx Generalized manifolds [See also 18F15] 57M12 Low-dimensional topology of special (e.g., 57P05 Local properties of generalized manifolds branched) coverings 57P10 Poincaré duality spaces 57M15 Relations of low-dimensional topology with graph theory [See also 05Cxx] 57P99 None of the above, but in this section 103 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 57Qxx PL-topology 57R20 Characteristic classes and numbers in differential topology 57Q05 General topology of complexes 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28] 57R22 Topology of vector bundles and fiber bundles [See also 55Rxx] 57R25 Vector fields, frame fields in differential topology 57Q12 Wall finiteness obstruction for CW-complexes 57R27 Controllability of vector fields on C ∞ and realanalytic manifolds [See also 49Qxx, 37C10, 93B05] 57Q15 Triangulating manifolds 57R30 Foliations in differential topology; geometric theory [See also 53C12] 57Q20 Cobordism in PL-topology 57Q25 Comparison of PL-structures: Hauptvermutung classification, 57Q30 Engulfing 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10] 57R35 Differentiable mappings in differential topology 57Q35 Embeddings and immersions in PL-topology 57R40 Embeddings in differential topology 57Q37 Isotopy in PL-topology 57R42 Immersions in differential topology 57Q40 Regular neighborhoods in PL-topology 57R45 Singularities of differentiable mappings in differential topology 57Q50 Microbundles and block bundles [See also 55R60, 57N55] 57Q55 Approximations in PL-topology 57Q60 Cobordism and concordance in PL-topology 57Q65 General position and transversality 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) 57Q70 Discrete Morse theory and related ideas in manifold topology 57R57 Applications of global analysis to structures on manifolds [See also 57K41, 58-XX] 57Q91 Equivariant PL-topology 57R58 Floer homology 57Q99 None of the above, but in this section 57R60 Homotopy spheres, Poincaré conjecture 57Rxx Differential topology {For foun- 57R65 Surgery and handlebodies dational questions of differentiable mani- 57R67 Surgery obstructions, Wall groups [See also folds, see 58Axx; for infinite-dimensional 19J25] manifolds, see 58Bxx} 57R70 Critical points and critical submanifolds in differential topology 57R05 Triangulating 57R10 Smoothing in differential topology 57R75 O- and SO-cobordism 57R12 Smooth approximations in differential topology 57R77 Complex cobordism (U- and SU-cobordism) [See also 55N22] 57R15 Specialized structures on manifolds (spin mani57R80 h- and s-cobordism folds, framed manifolds, etc.) 57R85 Equivariant cobordism 57R17 Symplectic and contact topology in high or arbi57R90 Other types of cobordism [See also 55N22] trary dimension [See also 57K33, 57K43] 57R18 Topology and geometry of orbifolds 57R91 Equivariant algebraic topology of manifolds 57R95 Realizing cycles by submanifolds 57R19 Algebraic topology on manifolds and differential topology 57R99 None of the above, but in this section 104 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 57Sxx Topological transformation groups 57Z20 Relations of manifolds and cell complexes with engineering [See also 20F34, 22-XX, 37-XX, 54H15, 58D05] 57Z25 Relations of manifolds and cell complexes with 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms computer and data science 57Z99 None of the above, but in this section 57S10 Compact groups of homeomorphisms 58-XX Global analysis, analysis on 57S15 Compact Lie groups of differentiable transforma- manifolds [See also 32Cxx, 32Fxx, tions 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, 57S17 Finite transformation groups see 49Q15} 57S20 Noncompact Lie groups of transformations 57S12 Toric topology 58-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis 57S25 Groups acting on specific manifolds 57S30 Discontinuous groups of transformations 58-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis 57S99 None of the above, but in this section 57Txx Homology and homotopy of topological groups and related structures 57T05 Hopf algebras (aspects of homology and homotopy of topological groups) [See also 16T05] 58-02 Research exposition (monographs, survey articles) pertaining to global analysis 58-03 History of global analysis [Consider also classification numbers pertaining to Section 01] 58-04 Software, source code, etc. for problems pertaining to global analysis 57T10 Homology and cohomology of Lie groups 57T15 Homology and cohomology of homogeneous 58-06 Proceedings, conferences, collections, etc. spaces of Lie groups taining to global analysis per- 57T20 Homotopy groups of topological groups and ho- 58-08 Computational methods for problems pertaining mogeneous spaces to global analysis 57T25 Homology and cohomology of H-spaces 57T30 Bar and cobar constructions [See also 18N40, 55Uxx] 58-11 Research data for problems pertaining to global analysis 58Axx General theory of differentiable 57T35 Applications of Eilenberg-Moore spectral se- manifolds [See also 32Cxx] quences [See also 55R20, 55T20] 58A03 Topos-theoretic approach to differentiable mani57T99 None of the above, but in this section folds 58A05 Differentiable manifolds, foundations 57Zxx Relations of manifolds and cell com58A07 Real-analytic and Nash manifolds [See also plexes with science and engineering 14P20, 32C07] 57Z05 Relations of manifolds and cell complexes with physics 58A10 Differential forms in global analysis 57Z10 Relations of manifolds and cell complexes with 58A12 de Rham theory in global analysis [See also biology 14Fxx] 57Z15 Relations of manifolds and cell complexes with 58A14 Hodge theory in global analysis [See also 14C30, chemistry 14Fxx, 32J25, 32S35] 105 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 58A15 Exterior differential systems (Cartan theory) 58C15 Implicit function theorems; global Newton methods on manifolds 58A17 Pfaffian systems 58A20 Jets in global analysis 58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds [See also 26Exx, 46G05] 58A25 Currents in global analysis [See also 32C30, 53C65] 58C25 Differentiable maps on manifolds 58A30 Vector distributions (subbundles of the tangent 58C30 Fixed-point theorems on manifolds [See also bundles) 47H10] 58A32 Natural bundles 58C35 Integration on manifolds; measures on manifolds [See also 28Cxx] 58A35 Stratified sets [See also 32S60] 58C40 Spectral theory; eigenvalue problems on manifolds [See also 47J10, 58E07] 58A40 Differential spaces 58A50 Supermanifolds and graded manifolds [See also 14A22, 32C11] 58C50 Analysis on supermanifolds or graded manifolds 58A99 None of the above, but in this section 58C99 None of the above, but in this section 58Bxx Infinite-dimensional manifolds 58Dxx Spaces and manifolds of mappings 58B05 Homotopy and topological questions for infinite- (including nonlinear versions of 46Exx) dimensional manifolds [See also 46Txx, 53Cxx] 58B10 Differentiability questions dimensional manifolds for infinite- 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05] 58B12 Questions of holomorphy and infinite58D07 Groups and semigroups of nonlinear operators dimensional manifolds [See also 32-XX, 46G20] [See also 17B65, 47H20] 58B15 Fredholm structures on infinite-dimensional manifolds [See also 47A53] 58D10 Spaces of embeddings and immersions 58B20 Riemannian, Finsler and other geometric struc- 58D15 Manifolds of mappings [See also 46T10, 54C35] tures on infinite-dimensional manifolds [See also 53C20, 53C60] 58D17 Manifolds of metrics (especially Riemannian) 58B25 Group structures and generalizations on infinite58D19 Group actions and symmetry properties dimensional manifolds [See also 22E65, 58D05] 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12] 58B32 Geometry of quantum groups 58B34 Noncommutative geometry (à la Connes) 58D25 Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx] 58B99 None of the above, but in this section 58Cxx Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx] 58D27 Moduli problems for differential geometric structures 58C05 Real-valued functions on manifolds 58D29 Moduli problems for topological structures 58C06 Set-valued and function-space-valued mappings on manifolds [See also 47H04, 54C60] 58D30 Applications of manifolds of mappings to the sciences 58C07 Continuity properties of mappings on manifolds 58C10 Holomorphic maps on manifolds [See also 32-XX] 58D99 None of the above, but in this section 106 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 58Exx Variational problems in infinite- 58H15 Deformations of general structures on manifolds [See also 32Gxx, 58J10] dimensional spaces 58E05 Abstract critical point theory (Morse theory, 58H99 None of the above, but in this section Lyusternik-Shnirel’man theory, etc.) in infinitedimensional spaces 58Jxx Partial differential equations on 58E07 Variational problems in abstract bifurcation the- manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] ory in infinite-dimensional spaces 58E09 Group-invariant bifurcation theory in infinite- 58J05 Elliptic equations on manifolds, general theory [See also 35-XX] dimensional spaces 58E10 Variational problems in applications to the the- 58J10 Differential complexes [See also 35Nxx]; elliptic complexes ory of geodesics (problems in one independent variable) 58J15 Relations of PDEs on manifolds with hyperfunctions 58E11 Critical metrics 58E12 Variational problems concerning minimal sur- 58J20 Index theory and related fixed-point theorems on manifolds [See also 19K56, 46L80] faces (problems in two independent variables) [See also 49Q05] 58J22 Exotic index theories on manifolds [See also 19K56, 46L05, 46L10, 46L80, 46M20] 58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals 58J26 Elliptic genera [See also 81T13], etc. 58J28 Eta-invariants, Chern-Simons invariants 58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc. [See also 58J30 Spectral flows 90C29, 91Bxx] 58J32 Boundary value problems on manifolds 58E20 Harmonic maps, etc. [See also 53C43] 58J35 Heat and other parabolic equation methods for PDEs on manifolds 58E25 Applications of variational problems to control theory [See also 49-XX, 93-XX] 58J37 Perturbations of PDEs on manifolds; asymptotics 58E30 Variational principles in infinite-dimensional 58J40 Pseudodifferential and Fourier integral operators spaces on manifolds [See also 35Sxx] 58E35 Variational inequalities (global problems) in 58J42 Noncommutative global analysis, noncommutainfinite-dimensional spaces tive residues 58E40 Variational aspects of group actions in infinite58J45 Hyperbolic equations on manifolds [See also dimensional spaces 35Lxx] 58E50 Applications of variational problems in infinite- 58J47 Propagation of singularities; initial value probdimensional spaces to the sciences lems on manifolds 58E99 None of the above, but in this section 58J50 Spectral problems; spectral geometry; scattering theory on manifolds [See also 35Pxx] 58Hxx Pseudogroups, differentiable groupoids and general structures on man- 58J51 Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity ifolds 58H05 Pseudogroups and differentiable groupoids [See also 22A22, 22E65] 58J52 Determinants and determinant bundles, analytic torsion 58J53 Isospectrality 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) 58J55 Bifurcation theory for PDEs on manifolds [See [See also 57R32] also 35B32] 107 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 60-XX Probability theory and stochastic processes {For additional 58J65 Diffusion processes and stochastic analysis on applications, see 05Cxx, 11Kxx, 34manifolds [See also 35R60, 60H10, 60J60] XX, 35-XX, 62-XX, 90-XX, 76-XX, 58J70 Invariance and symmetry properties for PDEs on 81-XX, 82-XX, 91-XX, 92-XX, 93manifolds [See also 35A30] XX, 94-XX} 58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) 58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds [See 60-00 General reference works (handbooks, dictionaries, also 35A22] bibliographies, etc.) pertaining to probability theory 58J90 Applications of PDEs on manifolds 60-01 Introductory exposition (textbooks, tutorial pa58J99 None of the above, but in this section pers, etc.) pertaining to probability theory 58Kxx Theory of singularities and catas- 60-02 Research exposition (monographs, survey articles) pertaining to probability theory trophe theory [See also 32Sxx, 37-XX] 58K05 Critical points of functions and mappings on 60-03 History of probability theory [Consider also classification numbers pertaining to Section 01] manifolds 60-04 Software, source code, etc. for problems pertaining to probability theory 58K10 Monodromy on manifolds 58K15 Topological properties of mappings on manifolds 60-06 Proceedings, conferences, collections, etc. pertaining to probability theory 58K20 Algebraic and analytic properties of mappings on manifolds 60-08 Computational methods for problems pertaining to probability theory 58K25 Stability theory for manifolds 60-11 Research data for problems pertaining to probability theory 58K30 Global theory of singularities 58K35 Catastrophe theory 58K40 Classification; finite determinacy of map germs 60Axx Foundations of probability theory 58K45 Singularities of vector fields, topological aspects 60A05 Axioms; other general questions in probability 58K50 Normal forms on manifolds 60A10 Probabilistic measure theory {For ergodic theory, see 28Dxx, 60Fxx} 58K55 Asymptotic behavior of solutions to equations on 60A86 Fuzzy probability manifolds 58K60 Deformation of singularities 60A99 None of the above, but in this section 58K65 Topological invariants on manifolds 58K70 Symmetries, equivariance on manifolds 60Bxx Probability theory on algebraic and topological structures 58K99 None of the above, but in this section 60B05 Probability measures on topological spaces 60B10 Convergence of probability measures 58Zxx Applications of global analysis to 60B11 Probability theory on linear topological spaces the sciences [See also 28C20] 58Z05 Applications of global analysis to the sciences 58Z99 None of the above, but in this section 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 108 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 60B15 Probability measures on groups or semigroups, 60Gxx Stochastic processes Fourier transforms, factorization 60G05 Foundations of stochastic processes 60B20 Random matrices (probabilistic aspects) {For algebraic aspects, see 15B52} 60G07 General theory of stochastic processes 60B99 None of the above, but in this section 60G10 Stationary stochastic processes 60G09 Exchangeability for stochastic processes 60G12 General second-order stochastic processes 60Cxx Combinatorial probability 60G15 Gaussian processes 60C05 Combinatorial probability 60G17 Sample path properties 60C99 None of the above, but in this section 60G18 Self-similar stochastic processes 60G20 Generalized stochastic processes 60Dxx Geometric probability and stochas- 60G22 Fractional processes, including fractional Browtic geometry [See also 52A22, 53C65] nian motion 60D05 Geometric probability and stochastic geometry 60G25 Prediction theory (aspects of stochastic processes) [See also 62M20] [See also 52A22, 53C65] 60G30 Continuity and singularity of induced measures 60D99 None of the above, but in this section [See 60G35 Signal detection and filtering (aspects of stochastic processes) [See also 62M20, 93E10, 93E11, also 94Axx] 60E05 Probability distributions: general theory 60G40 Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60Exx Distribution 62Exx, 62Hxx] theory 60G42 Martingales with discrete parameter 60E07 Infinitely divisible distributions; stable distributions 60G44 Martingales with continuous parameter 60E10 Characteristic functions; other transforms 60G46 Martingales and classical analysis 60G48 Generalizations of martingales 60E15 Inequalities; stochastic orderings 60E99 None of the above, but in this section 60G50 Sums of independent random variables; random walks 60G51 Processes with independent increments; Lévy processes 60Fxx Limit theorems in probability the60G52 Stable stochastic processes ory [See also 28Dxx, 60B12] 60F05 Central limit and other weak theorems 60G53 Feller processes 60F10 Large deviations 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 60F15 Strong limit theorems 60G57 Random measures 60F17 Functional limit theorems; invariance principles 60F20 Zero-one laws 60G60 Random fields 60G65 Nonlinear processes (e.g., G-Brownian motion, G-Lévy processes) 60F25 Lp -limit theorems 60G70 Extreme value theory; extremal stochastic processes 60F99 None of the above, but in this section 60G99 None of the above, but in this section 109 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 60Hxx Stochastic analysis [See also 58J65] 60J45 Probabilistic potential theory [See also 31Cxx, 31D05] 60H05 Stochastic integrals 60J46 Dirichlet form methods in Markov processes 60H07 Stochastic calculus of variations and the Malli60J50 Boundary theory for Markov processes avin calculus 60H10 Stochastic ordinary differential equations (as- 60J55 Local time and additive functionals pects of stochastic analysis) [See also 34F05] 60J57 Multiplicative functionals and Markov processes 60H15 Stochastic partial differential equations (aspects 60J60 Diffusion processes [See also 58J65] of stochastic analysis) [See also 35R60] 60J65 Brownian motion [See also 58J65] 60H17 Singular stochastic partial differential equations 60J67 Stochastic (Schramm-)Loewner evolution (SLE) 60H20 Stochastic integral equations 60J68 Superprocesses 60H25 Random operators and equations (aspects of 60J70 Applications of Brownian motions and diffusion stochastic analysis) [See also 47B80] theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60H30 Applications of stochastic analysis (to PDEs, etc.) 60J74 Jump processes on discrete state spaces 60H35 Computational methods for stochastic equations 60J76 Jump processes on general state spaces (aspects of stochastic analysis) [See also 65C30] 60J80 Branching processes (Galton-Watson, birth-and60H40 White noise theory death, etc.) 60H50 Regularization by noise 60J85 Applications of branching processes [See also 92Dxx] 60H99 None of the above, but in this section 60J90 Coalescent processes 60Jxx Markov processes 60J05 Discrete-time Markov processes on general state spaces 60J95 Applications of coalescent processes [See also 92Dxx] 60J99 None of the above, but in this section 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60Kxx Special processes 60J20 Applications of Markov chains and discrete-time 60K05 Renewal theory Markov processes on general state spaces (social 60K10 Applications of renewal theory (reliability, demobility, learning theory, industrial processes, etc.) mand theory, etc.) [See also 90B30, 91D10, 91E40] 60K15 Markov renewal processes, semi-Markov pro60J22 Computational methods in Markov chains [See cesses also 65C40] 60K20 Applications of Markov renewal processes (relia60J25 Continuous-time Markov processes on general bility, queueing networks, etc.) [See also 90Bxx] state spaces 60K25 Queueing theory (aspects of probability theory) 60J27 Continuous-time Markov processes on discrete [See also 68M20, 90B22] state spaces 60K30 Applications of queueing theory (congestion, al60J28 Applications of continuous-time Markov prolocation, storage, traffic, etc.) [See also 90Bxx] cesses on discrete state spaces 60K35 Interacting random processes; statistical me60J35 Transition functions, generators and resolvents chanics type models; percolation theory [See also [See also 47D03, 47D07] 82B43, 82C43] 60J40 Right processes 60K37 Processes in random environments 110 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 60K40 Other physical applications of random processes 62Bxx Sufficiency and information 60K50 Anomalous diffusion models (subdiffusion, su- 62B05 Sufficient statistics and fields perdiffusion, continuous-time random walks, etc.) [See also 60G22, 60G55, 60J74, 60J76] {For applica- 62B10 Statistical aspects of information-theoretic topics tions to physics and the sciences, see 76-XX, 82Cxx, [See also 94A17] 92-XX} 62B11 Information geometry (statistical aspects) {For 60K99 None of the above, but in this section differential geometric aspects, see 53B12} 60Lxx Rough analysis 62B15 Theory of statistical experiments 60L10 Signatures and data streams 62B86 Statistical aspects of fuzziness, sufficiency, and information 60L20 Rough paths 60L30 Regularity structures 62B99 None of the above, but in this section 60L40 Paracontrolled distributions and alternative approaches 60L50 Rough partial differential equations 60L70 Algebraic structures and computation 60L90 Applications of rough analysis 62Cxx Statistical decision theory [See also 90B50, 91B06] {For game theory, see 91A35] 62C05 General considerations in statistical decision theory 60L99 None of the above, but in this section 62C07 Complete class results in statistical decision theory 62-XX Statistics 62-00 General reference works (handbooks, dictionaries, 62C10 Bayesian problems; characterization of Bayes procedures bibliographies, etc.) pertaining to statistics 62-01 Introductory exposition (textbooks, tutorial pa- 62C12 Empirical decision procedures; empirical Bayes pers, etc.) pertaining to statistics procedures 62-02 Research exposition (monographs, survey articles) 62C15 Admissibility in statistical decision theory pertaining to statistics 62-03 History of statistics [Consider also classification 62C20 Minimax procedures in statistical decision theory numbers pertaining to Section 01] 62-04 Software, source code, etc. for problems pertain- 62C25 Compound decision problems in statistical decision theory ing to statistics 62-06 Proceedings, conferences, collections, etc. taining to statistics per- 62C86 Statistical decision theory and fuzziness 62-08 Computational methods for problems pertaining to statistics 62C99 None of the above, but in this section 62-11 Research data for problems pertaining to statistics 62Dxx Statistical sampling theory and re- lated topics 62Axx Foundational topics in statistics 62D05 Sampling theory, sample surveys 62A01 Foundations and philosophical topics in statistics 62D10 Missing data 62A09 Graphical methods 62A86 Fuzzy analysis in statistics 62A99 None of the above, but in this section 62D20 Causal inference from observational studies 62D99 None of the above, but in this section 111 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 62Exx Statistical distribution theory [See 62G30 Order statistics; empirical distribution functions also 60Exx] 62G32 Statistics of extreme values; tail inference 62E10 Characterization and structure theory of statisti62G35 Nonparametric robustness cal distributions 62G86 Nonparametric inference and fuzziness 62E15 Exact distribution theory in statistics 62E17 Approximations (nonasymptotic) to statistical distributions 62G99 None of the above, but in this section 62E20 Asymptotic distribution theory in statistics 62Hxx Multivariate analysis [See also 60Exx] 62E86 Fuzziness in connection with statistical distribu- 62H05 Characterization and structure theory for multitions variate probability distributions; copulas 62E99 None of the above, but in this section 62H10 Multivariate distribution of statistics 62Fxx Parametric inference 62H11 Directional data; spatial statistics 62F03 Parametric hypothesis testing 62H12 Estimation in multivariate analysis 62F05 Asymptotic properties of parametric tests 62H15 Hypothesis testing in multivariate analysis 62F07 Statistical ranking and selection procedures 62H17 Contingency tables 62F10 Point estimation 62H20 Measures of association (correlation, canonical correlation, etc.) 62F12 Asymptotic properties of parametric estimators 62H22 Probabilistic graphical models 62F15 Bayesian inference 62F25 Parametric tolerance and confidence regions 62H25 Factor analysis and principal components; correspondence analysis 62F30 Parametric inference under constraints 62H30 Classification and discrimination; cluster analysis (statistical aspects) [See also 68T10, 91C20]; 62F35 Robustness and adaptive procedures (parametric mixture models inference) 62F40 Bootstrap, jackknife and other resampling meth- 62H35 Image analysis in multivariate analysis ods 62H86 Multivariate analysis and fuzziness 62F86 Parametric inference and fuzziness 62H99 None of the above, but in this section 62F99 None of the above, but in this section 62Jxx Linear inference, regression 62Gxx Nonparametric inference 62J02 General nonlinear regression 62G05 Nonparametric estimation 62J05 Linear regression; mixed models 62G07 Density estimation 62J07 Ridge regression; shrinkage estimators (Lasso) 62G08 Nonparametric regression and quantile regres- 62J10 Analysis of variance and covariance (ANOVA) sion 62J12 Generalized linear models (logistic models) 62G09 Nonparametric statistical resampling methods 62J15 Paired and multiple comparisons; multiple testing 62G10 Nonparametric hypothesis testing 62J20 Diagnostics, and linear inference and regression 62G15 Nonparametric tolerance and confidence regions 62J86 Fuzziness, and linear inference and regression 62G20 Asymptotic properties of nonparametric inference 62J99 None of the above, but in this section 112 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 62Kxx Design of statistical experiments 62Nxx Survival analysis and censored data [See also 05Bxx] 62N01 Censored data models 62K05 Optimal statistical designs 62N02 Estimation in survival analysis and censored data 62K10 Statistical block designs 62N03 Testing in survival analysis and censored data 62K15 Factorial statistical designs 62N05 Reliability and life testing [See also 90B25] 62K20 Response surface designs 62N86 Fuzziness, and survival analysis and censored data 62K25 Robust parameter designs 62N99 None of the above, but in this section 62K86 Fuzziness and design of statistical experiments 62K99 None of the above, but in this section 62Pxx Applications of statistics [See also 90-XX, 91-XX, 92-XX] 62Lxx Sequential statistical methods 62P05 Applications of statistics to actuarial sciences and financial mathematics 62L05 Sequential statistical design 62L10 Sequential statistical analysis 62P10 Applications of statistics to biology and medical sciences; meta analysis 62L12 Sequential estimation 62L15 Optimal stopping in statistics [See also 60G40, 91A60] 62P12 Applications of statistics to environmental and related topics 62P15 Applications of statistics to psychology 62L20 Stochastic approximation 62L86 Fuzziness and sequential statistical methods 62P20 Applications of statistics to economics [See also 91Bxx] 62L99 None of the above, but in this section 62P25 Applications of statistics to social sciences 62Mxx Inference from stochastic processes 62P30 Applications of statistics in engineering and industry; control charts 62M02 Markov processes: hypothesis testing 62P35 Applications of statistics to physics 62M05 Markov processes: estimation; hidden Markov 62P99 None of the above, but in this section models 62M07 Non-Markovian processes: hypothesis testing 62Qxx Statistical tables 62M09 Non-Markovian processes: estimation 62Q05 Statistical tables 62M10 Time series, auto-correlation, regression, etc. in 62Q99 None of the above, but in this section statistics (GARCH) [See also 91B84] 62M15 Inference from stochastic processes and spectral 62Rxx Statistics on algebraic and topological structures analysis 62M20 Inference from stochastic processes and predic- 62R01 Algebraic statistics tion [See also 60G25]; filtering [See also 60G35, 62R07 Statistical aspects of big data and data sci93E10, 93E11] ence {For computer science aspects, see 68T09; for information-theoretic aspects, see 94A16} 62M30 Inference from spatial processes 62M40 Random fields; image analysis 62R10 Functional data analysis 62M45 Neural nets and related approaches to inference 62R20 Statistics on metric spaces from stochastic processes 62R30 Statistics on manifolds 62M86 Inference from stochastic processes and fuzziness 62R40 Topological data analysis [See also 55N31] 62M99 None of the above, but in this section 62R99 None of the above, but in this section 113 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 65-XX Numerical analysis 65Dxx Numerical approximation and computational geometry (primarily algo65-00 General reference works (handbooks, dictionaries, rithms) {For theoretical aspects, see 41bibliographies, etc.) pertaining to numerical analyXX, 68Uxx} sis 65-01 Introductory exposition (textbooks, tutorial pa- 65D05 Numerical interpolation pers, etc.) pertaining to numerical analysis 65-02 Research exposition (monographs, survey articles) 65D07 Numerical computation using splines pertaining to numerical analysis 65-03 History of numerical analysis [Consider also classification numbers pertaining to Section 01] 65D10 Numerical smoothing, curve fitting 65D12 Numerical radial basis function approximation 65-04 Software, source code, etc. for problems pertaining to numerical analysis 65D15 Algorithms for approximation of functions 65-06 Proceedings, conferences, collections, etc. pertaining to numerical analysis 65D17 Computer-aided design (modeling of curves and surfaces) [See also 68U07] 65-11 Research data for problems pertaining to numerical analysis 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry [See also 65Axx Tables in numerical analysis 51N05, 68U05] 65A05 Tables in numerical analysis 65D19 Computational issues in computer and robotic 65A99 None of the above, but in this section vision 65Bxx Acceleration of convergence in nu65D20 Computation of special functions and constants, merical analysis construction of tables [See also 33F05] 65B05 Extrapolation to the limit, deferred corrections 65B10 Numerical summation of series 65D25 Numerical differentiation 65B15 Euler-Maclaurin formula in numerical analysis 65D30 Numerical integration 65B99 None of the above, but in this section 65D32 Numerical quadrature and cubature formulas 65Cxx Probabilistic methods, stochastic 65D40 High-dimensional functions; sparse grids differential equations 65C05 Monte Carlo methods [See also 82M31] 65D99 None of the above, but in this section 65C10 Random number generation in numerical analysis [See also 11K45] 65C20 Probabilistic models, generic numerical methods 65Exx Numerical methods in in probability and statistics [See also 60-08, 62-08] analysis (potential theory, etc.) complex 65C30 Numerical solutions to stochastic differential and 65E05 General theory of numerical methods in complex integral equations {For theoretical aspects, see analysis (potential theory, etc.) [See also 30-08, 3160H35} [See also 65M75, 65N75] 08, 32-08] 65C35 Stochastic particle methods [See also 82M60] 65C40 Numerical analysis or methods applied to Markov chains [See also 60J22] 65C99 None of the above, but in this section 65E10 Numerical methods in conformal mappings [See also 30C30] 65E99 None of the above, but in this section 114 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 65Fxx Numerical linear algebra 65Hxx Nonlinear algebraic or transcendental equations 65F05 Direct numerical methods for linear systems and 65H04 Numerical computation of roots of polynomial matrix inversion equations 65F08 Preconditioners for iterative methods 65H05 Numerical computation of solutions to single equations 65F10 Iterative numerical methods for linear systems 65H10 Numerical computation of solutions to systems [See also 65N22] of equations 65F15 Numerical computation of eigenvalues and eigen- 65H14 Numerical algebraic geometry vectors of matrices 65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems [See also 47Hxx, 47Jxx, 65F18 Numerical solutions to inverse eigenvalue prob58C40, 58E07, 90C30] lems 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations [See also 58C30, 90C30] 65F22 Ill-posedness and regularization problems in nu- 65H99 None of the above, but in this section merical linear algebra 65Jxx Numerical analysis in abstract spaces 65F25 Orthogonalization in numerical linear algebra 65F35 Numerical computation of matrix norms, conditioning, scaling [See also 15A12, 15A60] 65J05 General theory of numerical analysis in abstract spaces 65F40 Numerical computation of determinants 65J08 Numerical solutions to abstract evolution equations 65F45 Numerical methods for matrix equations 65J10 Numerical solutions to equations with linear operators (do not use 65Fxx) 65F50 Computational methods for sparse matrices 65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx) 65F55 Numerical methods for low-rank matrix approxi- 65J20 Numerical solutions of ill-posed problems in abmation; matrix compression stract spaces; regularization 65F60 Numerical computation of matrix exponential 65J22 Numerical solution to inverse problems in abstract spaces and similar matrix functions 65J99 None of the above, but in this section 65F99 None of the above, but in this section 65Kxx Numerical methods for mathemat65Gxx Error analysis and interval analysis ical programming, optimization and variational techniques 65G20 Algorithms with automatic result verification 65G30 Interval and finite arithmetic 65K05 Numerical mathematical programming methods [See also 90Cxx] 65G40 General methods in interval analysis 65K10 Numerical optimization and variational techniques [See also 49Mxx, 93-08] 65G50 Roundoff error 65K15 Numerical methods for variational inequalities and related problems 65G99 None of the above, but in this section 65K99 None of the above, but in this section 115 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 65Lxx Numerical methods for ordinary 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems differential equations involving PDEs 65L03 Numerical methods for functional-differential equations 65M15 Error bounds for initial value and initialboundary value problems involving PDEs 65L04 Numerical methods for stiff equations 65M20 Method of lines for initial value and initial65L05 Numerical methods for initial value problems boundary value problems involving PDEs 65L06 Multistep, Runge-Kutta and extrapolation meth65M22 Numerical solution of discretized equations for ods for ordinary differential equations initial value and initial-boundary value problems involving PDEs [See also 65Fxx, 65Hxx] 65L07 Numerical investigation of stability of solutions 65L08 Numerical solution of ill-posed problems involv- 65M25 Numerical aspects of the method of charactering ordinary differential equations istics for initial value and initial-boundary value problems involving PDEs 65L09 Numerical solution of inverse problems involving ordinary differential equations 65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems in65L10 Numerical solution of boundary value problems volving PDEs involving ordinary differential equations 65M32 Numerical methods for inverse problems for ini65L11 Numerical solution of singularly perturbed probtial value and initial-boundary value problems inlems involving ordinary differential equations volving PDEs 65L12 Finite difference and finite volume methods for 65M38 Boundary element methods for initial value and ordinary differential equations initial-boundary value problems involving PDEs 65L15 Numerical solution of eigenvalue problems involv65M50 Mesh generation, refinement, and adaptive ing ordinary differential equations methods for the numerical solution of initial 65L20 Stability and convergence of numerical methods value and initial-boundary value problems involvfor ordinary differential equations ing PDEs 65L50 Mesh generation, refinement, and adaptive meth- 65M55 Multigrid methods; domain decomposition for ods for ordinary differential equations initial value and initial-boundary value problems involving PDEs 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value 65L70 Error bounds for numerical methods for ordinary problems involving PDEs differential equations differential-algebraic 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 65L99 None of the above, but in this section 65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems in65Mxx Numerical methods for partial difvolving PDEs 65L80 Numerical equations methods for ferential equations, initial value and timedependent initial-boundary value prob- 65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value lems problems involving PDEs 65M06 Finite difference methods for initial value and 65M85 Fictitious domain methods for initial value and initial-boundary value problems involving PDEs initial-boundary value problems involving PDEs 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65M99 None of the above, but in this section 116 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 65Nxx Numerical methods for partial dif- 65Pxx Numerical problems in dynamical ferential equations, boundary value prob- systems [See also 37Mxx] lems 65N06 Finite difference methods for boundary value problems involving PDEs 65N08 Finite volume methods for boundary value problems involving PDEs 65P10 Numerical methods for Hamiltonian systems including symplectic integrators 65P20 Numerical chaos 65P30 Numerical bifurcation problems 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65P40 Numerical nonlinear stabilities in dynamical systems 65N15 Error bounds for boundary value problems involving PDEs 65P99 None of the above, but in this section 65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs 65Qxx Numerical methods for difference 65N21 Numerical methods for inverse problems for and functional equations, recurrence relaboundary value problems involving PDEs tions 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs [See also 65Q10 Numerical methods for difference equations 65Fxx, 65Hxx] 65Q20 Numerical methods for functional equations 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65Q30 Numerical aspects of recurrence relations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving 65Q99 None of the above, but in this section PDEs 65N35 Spectral, collocation and related methods for 65Rxx Numerical methods for integral boundary value problems involving PDEs equations, integral transforms 65N38 Boundary element methods for boundary value 65R10 Numerical methods for integral transforms problems involving PDEs 65N40 Method of lines for boundary value problems in- 65R15 Numerical methods for eigenvalue problems in integral equations volving PDEs 65N45 Method of contraction of the boundary for 65R20 Numerical methods for integral equations boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive meth- 65R30 Numerical methods for ill-posed problems for integral equations ods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for 65R32 Numerical methods for inverse problems for inboundary value problems involving PDEs tegral equations 65N75 Probabilistic methods, particle methods, etc. for 65R99 None of the above, but in this section boundary value problems involving PDEs 65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving 65Sxx Graphical methods in numerical PDEs analysis 65N85 Fictitious domain methods for boundary value 65S05 Graphical methods in numerical analysis problems involving PDEs 65N99 None of the above, but in this section 65S99 None of the above, but in this section 117 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 65Txx Numerical methods in Fourier anal- 68-06 Proceedings, conferences, collections, etc. pertaining to computer science ysis 65T40 Numerical methods for trigonometric approxima- 68-11 Research data for problems pertaining to comtion and interpolation puter science 65T50 Numerical methods for discrete and fast Fourier 68Mxx Computer system organization transforms 65T60 Numerical methods for wavelets 68M01 General theory of computer systems 65T99 None of the above, but in this section 68M07 Mathematical problems of computer architecture [See also 68W35] 65Yxx Computer aspects of numerical al- 68M10 Network design and communication in computer gorithms systems [See also 68R10, 90B18] 65Y04 Numerical algorithms for computer arithmetic, 68M11 Internet topics [See also 68U35] etc. [See also 68M07] 68M12 Network protocols 65Y05 Parallel numerical computation 65Y10 Numerical algorithms for specific classes of archi- 68M14 Distributed systems tectures 68M15 Reliability, testing and fault tolerance of networks and computer systems 65Y15 Packaged methods for numerical algorithms 65Y20 Complexity and performance of numerical algo- 68M18 Wireless sensor networks as related to computer science [See also 90B18, 90B80] rithms [See also 68Q25] 65Y99 None of the above, but in this section 65Zxx Applications to the sciences 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems [See also 60K20, 60K25, 90B22, 90B35, 90B36] 65Z05 Applications to the sciences 68M25 Computer security 65Z99 None of the above, but in this section 68M99 None of the above, but in this section 68-XX Computer science {For pa- 68Nxx Theory of software pers containing software, source 68N01 General topics in the theory of software code, etc. in a specific mathemati- 68N15 Theory of programming languages cal area, see the classification num- 68N17 Logic programming ber -04 in that area} 68N18 Functional programming and lambda calculus 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to computer science [See also 03B40] 68N19 Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) 68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science 68N20 Theory of compilers and interpreters 68-02 Research exposition (monographs, survey articles) 68N25 Theory of operating systems pertaining to computer science 68-03 History of computer science [Consider also classi- 68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, fication numbers pertaining to Section 01] etc.) 68-04 Software, source code, etc. for problems pertaining to computer science 68N99 None of the above, but in this section 118 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 68Pxx Theory of data 68Q27 Parameterized complexity, tractability and kernelization 68P01 General topics in the theory of data 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32] 68P05 Data structures 68P10 Searching and sorting 68Q32 Computational learning theory [See also 68T05] 68P15 Database theory 68Q42 Grammars and rewriting systems 68P20 Information storage and retrieval of data 68P25 Data encryption (aspects in computer science) [See also 81P94, 94A60] 68Q45 Formal languages and automata [See also 03D05, 68Q70, 94A45] 68Q55 Semantics in the theory of computing [See also 03B70, 06B35, 18C50] 68P27 Privacy of data 68P30 Coding and information theory (compaction, compression, models of communication, encoding 68Q60 Specification and verification (program logics, model checking, etc.) [See also 03B70] schemes, etc.) (aspects in computer science) [See also 94Axx, 94Bxx] 68Q65 Abstract data types; algebraic specification [See also 18C50] 68P99 None of the above, but in this section 68Q70 Algebraic theory of languages and automata [See also 18B20, 20M35] 68Qxx Theory of computing 68Q01 General topics in the theory of computing 68Q04 Classical models of computation (Turing machines, etc.) [See also 03D10] 68Q06 Networks and circuits as models of computation; circuit complexity [See also 94C11] 68Q80 Cellular automata (computational aspects) {For cellular automata as dynamical systems, see 37B15} 68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) 68Q07 Biologically inspired models of computation 68Q87 Probability in computer science (algorithm anal(DNA computing, membrane computing, etc.) ysis, random structures, phase transitions, etc.) [See also 68W20, 68W40] 68Q09 Other nonclassical models of computation {For quantum computing, see mainly 68Q12, 81P68} 68Q99 None of the above, but in this section 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85] 68Rxx Discrete mathematics in relation to 68Q11 Communication complexity, information com- computer science plexity 68R01 General topics of discrete mathematics in relation to computer science 68Q12 Quantum algorithms and complexity in the theory of computing [See also 68Q09, 81P68] 68R05 Combinatorics in computer science 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68R07 Computational aspects of satisfiability [See also 68T20] 68Q19] 68Q17 Computational difficulty of problems (lower 68R10 Graph theory (including graph drawing) in computer science [See also 05Cxx, 90B10, 90C35] bounds, completeness, difficulty of approximation, etc.) [See also 68Q15] 68R12 Metric embeddings as related to computational 68Q19 Descriptive complexity and finite models [See problems and algorithms also 03C13] 68R15 Combinatorics on words 68Q25 Analysis of algorithms and problem complexity [See also 68W40] 68R99 None of the above, but in this section 119 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 68Txx Artificial intelligence 68U35 Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.) [See also 68M11] 68T01 General topics in artificial intelligence 68T05 Learning and adaptive systems in artificial intel68U99 None of the above, but in this section ligence [See also 68Q32] 68T07 Artificial neural networks and deep learning 68Vxx Computer science support for 68T09 Computational aspects of data analysis and big mathematical research and practice data [See also 62R07] {For homological aspects, see 68V05 Computer assisted proofs of proofs-by55N31} exhaustion type {For rigorous numerics, see 65Gxx; for proofs employing automated or interactive the68T10 Pattern recognition, speech recognition {For orem provers, see 68V15} cluster analysis, see 62H30} 68T20 Problem solving in the context of artificial intel- 68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.) [See ligence (heuristics, search strategies, etc.) also 03B35] 68T27 Logic in artificial intelligence 68V20 Formalization of mathematics in connection with 68T30 Knowledge representation theorem provers [See also 03B35, 68V15] 68T35 Theory of languages and software systems 68V25 Presentation and content markup for mathemat(knowledge-based systems, expert systems, etc.) for ics artificial intelligence 68V30 Mathematical knowledge management 68T37 Reasoning under uncertainty in the context of artificial intelligence 68V35 Digital mathematics libraries and repositories 68T40 Artificial intelligence for robotics [See also 93C85] 68V99 None of the above, but in this section 68T42 Agent technology and artificial intelligence 68Wxx Algorithms in computer science {For numerical algorithms, see 65-XX; 68T50 Natural language processing [See also 03B65, for combinatorics and graph theory, see 91F20] 05C85, 68Rxx} 68T45 Machine vision and scene understanding 68T99 None of the above, but in this section 68W01 General topics in the theory of algorithms 68Uxx Computing methodologies and ap- 68W05 Nonnumerical algorithms plications 68W10 Parallel algorithms in computer science 68U01 General topics in computing methodologies 68W15 Distributed algorithms 68U03 Computational aspects of digital topology {For 68W20 Randomized algorithms topological aspects, see 54H30; for homological aspects, see 55-XX} 68W25 Approximation algorithms 68U05 Computer graphics; computational geometry 68W27 Online algorithms; streaming algorithms (digital and algorithmic aspects) {For methods of 68W30 Symbolic computation and algebraic computanumerical mathematics, see 65D18} tion [See also 11Yxx, 12-08, 13Pxx, 14Qxx, 16Z05, 68U07 Computer science aspects of computer-aided de17-08, 33F10] sign {For methods of numerical mathematics, see 68W32 Algorithms on strings 65D17} 68U10 Computing methodologies for image processing 68W35 Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.) [See also 68M07] 68U15 Computing methodologies for text processing; mathematical typography 68W40 Analysis of algorithms [See also 68Q25] 120 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 68W50 Evolutionary algorithms, genetic algorithms 70Bxx Kinematics [See also 53A17] (computational aspects) [See also 68T05, 68T20, 70B05 Kinematics of a particle 90C59] 70B10 Kinematics of a rigid body 68W99 None of the above, but in this section 70B15 Kinematics of mechanisms and robots [See also 68T40, 70Q05, 93C85] 70-XX Mechanics of particles and 70B99 None of the above, but in this section systems {For relativistic mechanics, see 83A05, 83C10; for statisti- 70Cxx Statics 70C20 Statics cal mechanics, see 82-XX} 70C99 None of the above, but in this section 70-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of par- 70Exx Dynamics of a rigid body and of ticles and systems multibody systems 70-01 Introductory exposition (textbooks, tutorial pa- 70E05 Motion of the gyroscope pers, etc.) pertaining to mechanics of particles and 70E15 Free motion of a rigid body [See also 70M20] systems 70E17 Motion of a rigid body with a fixed point 70-02 Research exposition (monographs, survey articles) 70E18 Motion of a rigid body in contact with a solid pertaining to mechanics of particles and systems surface [See also 70F25] 70-03 History of mechanics of particles and systems 70E20 Perturbation methods for rigid body dynamics [Consider also classification numbers pertaining to Section 01] 70E40 Integrable cases of motion in rigid body dynamics 70-04 Software, source code, etc. for problems pertain- 70E45 Higher-dimensional generalizations in rigid body dynamics ing to mechanics of particles and systems 70E50 Stability problems in rigid body dynamics 70-05 Experimental work for problems pertaining to me70E55 Dynamics of multibody systems chanics of particles and systems 70-06 Proceedings, conferences, collections, etc. pertaining to mechanics of particles and systems 70E60 Robot dynamics and control of rigid bodies [See also 68T40, 70Q05, 93C85] 70E99 None of the above, but in this section 70-08 Computational methods for problems pertaining to mechanics of particles and systems 70Fxx Dynamics of a system of particles, including celestial mechanics 70-10 Mathematical modeling or simulation for problems pertaining to mechanics of particles and sys- 70F05 Two-body problems tems 70F07 Three-body problems 70-11 Research data for problems pertaining to mechan- 70F10 n-body problems ics of particles and systems 70F15 Celestial mechanics 70Axx Axiomatics, foundations 70A05 Axiomatics, foundations 70A99 None of the above, but in this section 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 121 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 70F25 Nonholonomic systems related to the dynamics 70H09 Perturbation theories for problems in Hamiltoof a system of particles nian and Lagrangian mechanics 70F35 Collision of rigid or pseudo-rigid bodies 70H11 Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics 70F40 Problems involving a system of particles with friction 70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics 70F45 The dynamics of infinite particle systems 70F99 None of the above, but in this section 70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics 70Gxx General models, approaches, and 70H15 Canonical and symplectic transformations for methods [See also 37-XX] problems in Hamiltonian and Lagrangian mechanics 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in 70H20 Hamilton-Jacobi equations in mechanics mechanics 70G40 Topological and differential topological methods 70H25 Hamilton’s principle for problems in mechanics 70H30 Other variational principles in mechanics 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, 70H33 Symmetries and conservation laws, reverse symnonholonomic, etc.) for problems in mechanics [See metries, invariant manifolds and their bifurcations, also 53Cxx, 53Dxx, 58Axx] reduction for problems in Hamiltonian and Lagrangian mechanics 70G55 Algebraic geometry methods for problems in mechanics 70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian 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 70H45 Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx] 70H50 Higher-order theories for problems in Hamiltonian and Lagrangian mechanics 70H99 None of the above, but in this section 70G99 None of the above, but in this section 70Jxx Linear vibration theory 70Hxx Hamiltonian and Lagrangian me- 70J10 Modal analysis in linear vibration theory chanics [See also 37Jxx] 70H03 Lagrange’s equations 70H05 Hamilton’s equations 70J25 Stability for problems in linear vibration theory 70J30 Free motions in linear vibration theory 70H06 Completely integrable systems and methods of 70J35 Forced motions in linear vibration theory integration for problems in Hamiltonian and Lagrangian mechanics 70J40 Parametric resonances in linear vibration theory 70H07 Nonintegrable systems for problems in Hamilto70J50 Systems arising from the discretization of strucnian and Lagrangian mechanics tural vibration problems 70H08 Nearly integrable Hamiltonian systems, KAM theory 70J99 None of the above, but in this section 122 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 70Kxx Nonlinear dynamics in mechanics 70Mxx Orbital mechanics [See also 34Cxx, 37-XX] 70M20 Orbital mechanics 70K05 Phase plane analysis, limit cycles for nonlinear 70M99 None of the above, but in this section problems in mechanics 70Pxx Variable mass, rockets 70K20 Stability for nonlinear problems in mechanics 70K25 Free motions for nonlinear problems in mechan- 70P05 Variable mass, rockets ics 70P99 None of the above, but in this section 70K28 Parametric resonances for nonlinear problems in mechanics 70Qxx Control of mechanical systems [See also 60Gxx, 60Jxx] 70K30 Nonlinear resonances for nonlinear problems in mechanics 70Q05 Control of mechanical systems 70K40 Forced motions for nonlinear problems in me- 70Q99 None of the above, but in this section chanics 70Sxx Classical field theories [See also 70K42 Equilibria and periodic trajectories for nonlinear 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] problems in mechanics 70S05 Lagrangian formalism and Hamiltonian formal70K43 Quasi-periodic motions and invariant tori for ism in mechanics of particles and systems nonlinear problems in mechanics 70S10 Symmetries and conservation laws in mechanics 70K44 Homoclinic and heteroclinic trajectories for nonof particles and systems linear problems in mechanics 70S15 Yang-Mills and other gauge theories in mechanics 70K45 Normal forms for nonlinear problems in mechanof particles and systems ics 70S20 More general nonquantum field theories in me70K50 Bifurcations and instability for nonlinear probchanics of particles and systems lems in mechanics 70S99 None of the above, but in this section 70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics [See also 37D45] 70K60 General perturbation schemes for nonlinear problems in mechanics 74-XX Mechanics of deformable solids 70K65 Averaging of perturbations for nonlinear prob- 74-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of delems in mechanics formable solids 70K70 Systems with slow and fast motions for nonlinear 74-01 Introductory exposition (textbooks, tutorial paproblems in mechanics pers, etc.) pertaining to mechanics of deformable solids 70K75 Nonlinear modes 70K99 None of the above, but in this section 74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 70Lxx Random and stochastic aspects of 74-03 History of mechanics of deformable solids [Consider also classification numbers pertaining to Secthe mechanics of particles and systems tion 01] 70L05 Random vibrations in mechanics of particles and 74-04 Software, source code, etc. for problems pertainsystems [See also 74H50] ing to mechanics of deformable solids 70L10 Stochastic geometric mechanics 74-05 Experimental work for problems pertaining to me70L99 None of the above, but in this section chanics of deformable solids 123 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 74-06 Proceedings, conferences, collections, etc. taining to mechanics of deformable solids per- 74Cxx Plastic materials, materials of stress-rate and internal-variable type 74-10 Mathematical modeling or simulation for prob- 74C05 Small-strain, rate-independent theories of plaslems pertaining to mechanics of deformable solids ticity (including rigid-plastic and elasto-plastic materials) 74-11 Research data for problems pertaining to mechanics of deformable solids 74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) 74Axx Generalities, axiomatics, founda74C15 Large-strain, rate-independent theories of plastions of continuum mechanics of solids ticity (including nonlinear plasticity) 74A05 Kinematics of deformation 74A10 Stress 74C20 Large-strain, rate-dependent theories of plasticity 74A15 Thermodynamics in solid mechanics 74C99 None of the above, but in this section 74A20 Theory of constitutive functions in solid mechanics 74Dxx Materials of strain-rate type and 74A25 Molecular, statistical, and kinetic theories in history type, other materials with memory (including elastic materials with vissolid mechanics 74A30 Nonsimple materials 74A35 Polar materials 74A40 Random materials and composite materials 74A45 Theories of fracture and damage cous damping, various viscoelastic materials) 74D05 Linear constitutive equations for materials with memory 74D10 Nonlinear constitutive equations for materials with memory 74A50 Structured surfaces and interfaces, coexistent 74D99 None of the above, but in this section phases 74A55 Theories of friction (tribology) 74A60 Micromechanical theories 74Exx Material properties given special treatment 74A65 Reactive materials 74E05 Inhomogeneity in solid mechanics 74A70 Peridynamics 74E10 Anisotropy in solid mechanics 74A99 None of the above, but in this section 74E15 Crystalline structure 74Bxx Elastic materials 74E20 Granularity 74B05 Classical linear elasticity 74E25 Texture in solid mechanics 74B10 Linear elasticity with initial stresses 74E30 Composite and mixture properties 74B15 Equations linearized about a deformed state 74E35 Random structure in solid mechanics (small deformations superposed on large) 74B20 Nonlinear elasticity 74E40 Chemical structure in solid mechanics 74B99 None of the above, but in this section 74E99 None of the above, but in this section 124 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 74Fxx Coupling of solid mechanics with 74Hxx Dynamical problems in solid meother effects chanics 74H05 Explicit solutions of dynamical problems in solid mechanics 74F05 Thermal effects in solid mechanics 74F10 Fluid-solid interactions (including aero- and 74H10 Analytic approximation of solutions (perturbahydro-elasticity, porosity, etc.) tion methods, asymptotic methods, series, etc.) of 74F15 Electromagnetic effects in solid mechanics dynamical problems in solid mechanics 74F20 Mixture effects in solid mechanics 74H15 Numerical approximation of solutions of dynamical problems in solid mechanics 74F25 Chemical and reactive effects in solid mechanics 74H20 Existence of solutions of dynamical problems in solid mechanics 74F99 None of the above, but in this section 74Gxx Equilibrium (steady-state) prob- 74H25 Uniqueness of solutions of dynamical problems in solid mechanics lems in solid mechanics 74G05 Explicit solutions of equilibrium problems in 74H30 Regularity of solutions of dynamical problems in solid mechanics solid mechanics 74G10 Analytic approximation of solutions (perturba- 74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics tion methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics 74H40 Long-time behavior of solutions for dynamical problems in solid mechanics 74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics 74G22 Existence of solutions of equilibrium problems in solid mechanics 74H50 Random vibrations in dynamical problems in solid mechanics 74G30 Uniqueness of solutions of equilibrium problems in solid mechanics 74H55 Stability of dynamical problems in solid mechanics 74G35 Multiplicity of solutions of equilibrium problems in solid mechanics 74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics 74G40 Regularity of solutions of equilibrium problems in solid mechanics 74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics 74G45 Bounds for solutions of equilibrium problems in solid mechanics 74H75 Inverse problems in dynamical solid mechanics 74G50 Saint-Venant’s principle 74H80 Energy minimization in dynamical problems in solid mechanics 74G55 Qualitative behavior of solutions of equilibrium 74H99 None of the above, but in this section problems in solid mechanics 74G60 Bifurcation and buckling 74Jxx Waves in solid mechanics 74G65 Energy minimization in equilibrium problems in 74J05 Linear waves in solid mechanics solid mechanics 74J10 Bulk waves in solid mechanics 74G70 Stress concentrations, singularities in solid mechanics 74J15 Surface waves in solid mechanics 74G75 Inverse problems in equilibrium solid mechanics 74J20 Wave scattering in solid mechanics 74G99 None of the above, but in this section 74J25 Inverse problems for waves in solid mechanics 125 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] 74J30 Nonlinear waves in solid mechanics 74J35 Solitary waves in solid mechanics 74N05 Crystals in solids 74J40 Shocks and related discontinuities in solid me- 74N10 Displacive transformations in solids chanics 74N15 Analysis of microstructure in solids 74J99 None of the above, but in this section 74N20 Dynamics of phase boundaries in solids 74N25 Transformations involving diffusion in solids 74Kxx Thin bodies, structures 74N30 Problems involving hysteresis in solids 74K05 Strings 74N99 None of the above, but in this section 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74K15 Membranes 74Pxx Optimization problems in solid mechanics [See also 49Qxx] 74K20 Plates 74P05 Compliance or weight optimization in solid mechanics 74K25 Shells 74P10 Optimization of other properties in solid mechanics 74K30 Junctions 74K35 Thin films 74P15 Topological methods for optimization problems in solid mechanics 74K99 None of the above, but in this section 74P20 Geometrical methods for optimization problems in solid mechanics 74Lxx Special subfields of solid mechanics 74P99 None of the above, but in this section 74L05 Geophysical solid mechanics [See also 86-XX] 74Qxx Homogenization, determination of effective properties in solid mechanics 74L10 Soil and rock mechanics 74Q05 Homogenization in equilibrium problems of solid mechanics 74L15 Biomechanical solid mechanics [See also 92C10] 74Q10 Homogenization and oscillations in dynamical problems of solid mechanics 74L99 None of the above, but in this section 74Mxx Special kinds of problems in solid mechanics 74Q15 Effective constitutive equations in solid mechanics 74Q20 Bounds on effective properties in solid mechanics 74M05 Control, switches and devices (“smart materi74Q99 None of the above, but in this section als”) in solid mechanics [See also 93Cxx] 74M10 Friction in solid mechanics 74M15 Contact in solid mechanics 74Rxx Fracture and damage 74R05 Brittle damage 74R10 Brittle fracture 74M20 Impact in solid mechanics 74R15 High-velocity fracture 74M25 Micromechanics of solids 74R20 Anelastic fracture and damage 74M99 None of the above, but in this section 74R99 None of the above, but in this section 126 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 74Sxx Numerical and other methods in 76-10 Mathematical modeling or simulation for problems pertaining to fluid mechanics solid mechanics [See also 65-XX, 74G15, 74H15] 76-11 Research data for problems pertaining to fluid mechanics 74S05 Finite element methods applied to problems in solid mechanics 74S10 Finite volume methods applied to problems in 76Axx Foundations, constitutive equations, rheology, hydrodynamical models of solid mechanics non-fluid phenomena 74S15 Boundary element methods applied to problems 76A02 Foundations of fluid mechanics in solid mechanics 74S20 Finite difference methods applied to problems in 76A05 Non-Newtonian fluids solid mechanics 76A10 Viscoelastic fluids 74S22 Isogeometric methods applied to problems in 76A15 Liquid crystals [See also 82D30] solid mechanics 74S25 Spectral and related methods applied to problems 76A20 Thin fluid films in solid mechanics 76A25 Superfluids (classical aspects) 74S40 Applications of fractional calculus in solid me76A30 Traffic and pedestrian flow models chanics 74S50 Applications of graph theory in solid mechanics 76A99 None of the above, but in this section 74S60 Stochastic and other probabilistic methods ap76Bxx Incompressible inviscid fluids plied to problems in solid mechanics 74S70 Complex-variable methods applied to problems in 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids [See also 35Q35] solid mechanics 74S99 None of the above, but in this section 76B07 Free-surface potential flows for incompressible inviscid fluids 76-XX Fluid mechanics {For gen- 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theeral continuum mechanics, see ory, sloshing 74Axx, or other parts of 74-XX} 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to fluid mechanics 76B20 Ship waves 76-01 Introductory exposition (textbooks, tutorial pa76B25 Solitary waves for incompressible inviscid fluids pers, etc.) pertaining to fluid mechanics [See also 35C11] 76-02 Research exposition (monographs, survey articles) 76B45 Capillarity (surface tension) for incompressible pertaining to fluid mechanics inviscid fluids [See also 76D45] 76-03 History of fluid mechanics [Consider also classifi76B47 Vortex flows for incompressible inviscid fluids cation numbers pertaining to Section 01] 76-04 Software, source code, etc. for problems pertain- 76B55 Internal waves for incompressible inviscid fluids ing to fluid mechanics 76B70 Stratification effects in inviscid fluids 76-05 Experimental work for problems pertaining to 76B75 Flow control and optimization for incompressible fluid mechanics inviscid fluids [See also 49Q10, 93C20, 93C95] 76-06 Proceedings, conferences, collections, etc. pertaining to fluid mechanics 76B99 None of the above, but in this section 127 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 76Dxx Incompressible viscous fluids 76Fxx Turbulence [See also 37-XX, 60Gxx, 76D03 Existence, uniqueness, and regularity theory for 60Jxx] incompressible viscous fluids [See also 35Q30] 76F02 Fundamentals of turbulence 76D05 Navier-Stokes equations for incompressible vis76F05 Isotropic turbulence; homogeneous turbulence cous fluids [See also 35Q30] 76D06 Statistical solutions of Navier-Stokes and related 76F06 Transition to turbulence equations [See also 60H30, 76M35] 76F10 Shear flows and turbulence 76D07 Stokes and related (Oseen, etc.) flows 76F20 Dynamical systems approach to turbulence [See 76D08 Lubrication theory also 37-XX] 76D09 Viscous-inviscid interaction 76F25 Turbulent transport, mixing 76D10 Boundary-layer theory, separation and reattach76F30 Renormalization and other field-theoretical ment, higher-order effects methods for turbulence [See also 81T99] 76D17 Viscous vortex flows 76F35 Convective turbulence [See also 76E15, 76Rxx] 76D25 Wakes and jets 76D27 Other free boundary flows; Hele-Shaw flows 76F40 Turbulent boundary layers 76D33 Waves for incompressible viscous fluids 76F45 Stratification effects in turbulence 76D45 Capillarity (surface tension) for incompressible 76F50 Compressibility effects in turbulence viscous fluids [See also 76B45] 76F55 Statistical turbulence modeling [See also 76M35] 76D50 Stratification effects in viscous fluids 76D55 Flow control and optimization for incompressible 76F60 k-ε modeling in turbulence viscous fluids [See also 49Q10, 93C20, 93C95] 76F65 Direct numerical and large eddy simulation of turbulence 76D99 None of the above, but in this section 76Exx Hydrodynamic stability 76F70 Control of turbulent flows 76E05 Parallel shear flows in hydrodynamic stability 76F80 Turbulent combustion; reactive turbulence 76E06 Convection in hydrodynamic stability 76F99 None of the above, but in this section 76E07 Rotation in hydrodynamic stability 76Gxx General aerodynamics and sub- 76E09 Stability and instability of nonparallel flows in sonic flows hydrodynamic stability 76E15 Absolute and convective instability and stability 76G25 General aerodynamics and subsonic flows in hydrodynamic stability 76G99 None of the above, but in this section 76E17 Interfacial stability and instability in hydrodynamic stability 76Hxx Transonic flows 76E19 Compressibility effects in hydrodynamic stability 76H05 Transonic flows 76E20 Stability and instability of geophysical and astro76H99 None of the above, but in this section physical flows 76E25 Stability and instability of magnetohydrody76Jxx Supersonic flows namic and electrohydrodynamic flows 76E30 Nonlinear effects in hydrodynamic stability 76J20 Supersonic flows 76E99 None of the above, but in this section 76J99 None of the above, but in this section 128 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 76Kxx Hypersonic flows 76K05 Hypersonic flows 76K99 None of the above, but in this section 76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics 76M99 None of the above, but in this section 76Nxx Compressible fluids and gas dy76Lxx Shock waves and blast waves in fluid namics, general mechanics [See also 35L67] 76N06 Compressible Navier-Stokes equations 76L05 Shock waves and blast waves in fluid mechanics 76N10 Existence, uniqueness, and regularity theory for [See also 35L67] compressible fluids and gas dynamics [See also 76L99 None of the above, but in this section 35L60, 35L65, 35Q30] 76N15 Gas dynamics, general 76Mxx Basic methods in fluid mechanics 76N17 Viscous-inviscid interaction for compressible flu[See also 65-XX] ids and gas dynamics 76M10 Finite element methods applied to problems in 76N20 Boundary-layer theory for compressible fluids fluid mechanics and gas dynamics 76M12 Finite volume methods applied to problems in 76N25 Flow control and optimization for compressible fluid mechanics fluids and gas dynamics 76M15 Boundary element methods applied to problems 76N30 Waves in compressible fluids in fluid mechanics 76N99 None of the above, but in this section 76M20 Finite difference methods applied to problems in fluid mechanics 76Pxx Rarefied gas flows, Boltzmann equation in fluid mechanics [See also 76M22 Spectral methods applied to problems in fluid 82B40, 82C40, 82D05] 76M21 Inverse problems in fluid mechanics mechanics 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics [See also 82B40, 82C40, 82D05] 76M23 Vortex methods applied to problems in fluid mechanics 76P99 None of the above, but in this section 76M27 Visualization algorithms applied to problems in 76Qxx Hydro- and aero-acoustics fluid mechanics 76Q05 Hydro- and aero-acoustics 76M28 Particle methods and lattice-gas methods 76Q99 None of the above, but in this section 76M30 Variational methods applied to problems in fluid mechanics 76Rxx Diffusion and convection 76M35 Stochastic analysis applied to problems in fluid 76R05 Forced convection mechanics 76R10 Free convection 76M40 Complex variables methods applied to problems 76R50 Diffusion [See also 60J60] in fluid mechanics 76M45 Asymptotic methods, singular perturbations ap- 76R99 None of the above, but in this section plied to problems in fluid mechanics 76Sxx Flows in porous media; filtration; 76M50 Homogenization applied to problems in fluid meseepage chanics 76S05 Flows in porous media; filtration; seepage 76M55 Dimensional analysis and similarity applied to problems in fluid mechanics 76S99 None of the above, but in this section 129 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 76Txx Multiphase and multicomponent 76Zxx Biological fluid mechanics [See also flows 74F10, 74L15, 92Cxx] 76T06 Liquid-liquid two component flows 76Z05 Physiological flows [See also 92C35] 76T10 Liquid-gas two-phase flows, bubbly flows 76T15 Dusty-gas two-phase flows 76Z10 Biopropulsion in water and in air 76T17 Two gas multicomponent flows 76Z99 None of the above, but in this section 76T20 Suspensions 76T25 Granular flows [See also 74C99, 74E20] 76T30 Three or more component flows 78-XX Optics, electromagnetic theory {For quantum optics, see 81V80} 76T99 None of the above, but in this section 76Uxx Rotating fluids 76U05 General theory of rotating fluids 78-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to optics and electromagnetic theory 76U60 Geophysical flows [See also 86A05, 86A10] 76U65 Rossby waves [See also 86A05, 86A10] 76U99 None of the above, but in this section 76Vxx Reaction effects in flows [See also 80A32] 76V05 Reaction effects in flows [See also 80A32] 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 76V99 None of the above, but in this section 76Wxx Magnetohydrodynamics and elec- 78-03 History of optics and electromagnetic theory [Consider also classification numbers pertaining to Sectrohydrodynamics tion 01] 76W05 Magnetohydrodynamics and electrohydrodynamics 78-04 Software, source code, etc. for problems pertaining to optics and electromagnetic theory 76W99 None of the above, but in this section 76Xxx Ionized gas flow in electromagnetic 78-05 Experimental work for problems pertaining to opfields; plasmic flow [See also 82D10] tics and electromagnetic theory 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 78-06 Proceedings, conferences, collections, etc. taining to optics and electromagnetic theory 76X99 None of the above, but in this section per- 76Yxx Quantum hydrodynamics and rela78-10 Mathematical modeling or simulation for probtivistic hydrodynamics [See also 82D50, lems pertaining to optics and electromagnetic the83C55, 85A30] ory 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 76Y99 None of the above, but in this section 78-11 Research data for problems pertaining to optics and electromagnetic theory 130 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 78Axx General 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic 78A02 Foundations in optics and electromagnetic thetheory ory 78M12 Finite volume methods, finite integration tech78A05 Geometric optics niques applied to problems in optics and electromagnetic theory 78A10 Physical optics 78M15 Boundary element methods applied to problems 78A15 Electron optics in optics and electromagnetic theory 78A20 Space charge waves 78M16 Multipole methods applied to problems in optics and electromagnetic theory 78A25 Electromagnetic theory, general 78M20 Finite difference methods applied to problems in optics and electromagnetic theory 78A30 Electro- and magnetostatics 78M22 Spectral, collocation and related methods applied to problems in optics and electromagnetic theory 78A35 Motion of charged particles 78A37 Ion traps 78A40 Waves and radiation in optics and electromag- 78M30 Variational methods applied to problems in optics and electromagnetic theory netic theory 78A45 Diffraction, scattering {For WKB methods see 78M31 Monte Carlo methods applied to problems in optics and electromagnetic theory 34E20} 78M32 Neural and heuristic methods applied to prob78A46 Inverse problems (including inverse scattering) in lems in optics and electromagnetic theory optics and electromagnetic theory 78M34 Model reduction in optics and electromagnetic 78A48 Composite media; random media in optics and theory electromagnetic theory 78M35 Asymptotic analysis in optics and electromag78A50 Antennas, waveguides in optics and electromagnetic theory netic theory 78M40 Homogenization in optics and electromagnetic theory 78A55 Technical applications of optics and electromagnetic theory 78M50 Optimization problems in optics and electromagnetic theory 78A57 Electrochemistry 78A60 Lasers, masers, optical bistability, nonlinear optics [See also 81V80] 78M99 None of the above, but in this section 80-XX Classical thermodynamics, heat transfer {For thermodynamics 78A97 Mathematically heuristic optics and electromag- of solids, see 74A15} 78A70 Biological applications of optics and electromagnetic theory [See also 91D30, 92C30] netic theory (must also be assigned at least one 80-00 General reference works (handbooks, dictionaries, other classification number in Section 78) bibliographies, etc.) pertaining to classical thermodynamics 78A99 None of the above, but in this section 80-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics 78Mxx Basic methods for problems in optics and electromagnetic theory [See also 80-02 Research exposition (monographs, survey articles) 65-XX] pertaining to classical thermodynamics 78M05 Method of moments applied to problems in op- 80-03 History of classical thermodynamics [Consider tics and electromagnetic theory also classification numbers pertaining to Section 01] 131 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 80-04 Software, source code, etc. for problems pertain- 80M20 Finite difference methods applied to problems in ing to classical thermodynamics thermodynamics and heat transfer 80-05 Experimental work for problems pertaining to 80M22 Spectral, collocation and related (meshless) classical thermodynamics methods applied to problems in thermodynamics and heat transfer 80-06 Proceedings, conferences, collections, etc. pertaining to classical thermodynamics 80M30 Variational methods applied to problems in thermodynamics and heat transfer 80-10 Mathematical modeling or simulation for problems pertaining to classical thermodynamics 80M31 Monte Carlo methods applied to problems in thermodynamics and heat transfer 80-11 Research data for problems pertaining to classical thermodynamics 80M35 Asymptotic analysis for problems in thermodynamics and heat transfer 80Axx Thermodynamics and heat transfer 80A05 Foundations of thermodynamics and heat transfer 80M40 Homogenization for problems in thermodynamics and heat transfer 80M50 Optimization problems in thermodynamics and heat transfer 80A10 Classical and relativistic thermodynamics 80A17 Thermodynamics of continua [See also 74A15] 80M60 Stochastic analysis in thermodynamics and heat transfer 80A19 Diffusive and convective heat and mass transfer, heat flow 80M99 None of the above, but in this section 80A21 Radiative heat transfer 80A22 Stefan problems, phase changes, etc. [See also 74Nxx] 80A23 Inverse problems in thermodynamics and heat transfer 80A25 Combustion 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 80A30 Chemical kinetics in thermodynamics and heat 81-02 Research exposition (monographs, survey articles) transfer [See also 76V05, 92C45, 92E20] pertaining to quantum theory 80A32 Chemically reacting flows [See also 92C45, 81-03 History of quantum theory [Consider also classifi92E20] cation numbers pertaining to Section 01] 80A50 Chemistry (general) in thermodynamics and heat 81-04 Software, source code, etc. for problems pertaintransfer [See mainly 92Exx] ing to quantum theory 80A99 None of the above, but in this section 81-05 Experimental work for problems pertaining to quantum theory 80Mxx Basic methods in thermodynamics 81-06 Proceedings, conferences, collections, etc. perand heat transfer [See also 65-XX] taining to quantum theory 80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat 81-08 Computational methods for problems pertaining to quantum theory transfer 80M12 Finite volume methods applied to problems in 81-10 Mathematical modeling or simulation for problems pertaining to quantum theory thermodynamics and heat transfer 80M15 Boundary element methods applied to problems 81-11 Research data for problems pertaining to quantum in thermodynamics and heat transfer theory 132 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 81Pxx Foundations, quantum information 81Qxx General mathematical topics and and its processing, quantum axioms, and methods in quantum theory philosophy 81P05 General and philosophical questions in quantum theory 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) [See 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis also 03G12, 06C15] 81P13 Contextuality in quantum theory 81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators 81P15 Quantum measurement theory, state operations, state preparations 81P16 Quantum state spaces, operational and proba- 81Q15 Perturbation theories for operators and differential equations in quantum theory bilistic concepts 81P17 Quantum entropies 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum 81P18 Quantum state tomography, quantum state distheory crimination 81P20 Stochastic mechanics (including stochastic elec- 81Q30 Feynman integrals and graphs; applications of altrodynamics) gebraic topology and algebraic geometry [See also 14D05, 32S40] 81P40 Quantum coherence, entanglement, quantum correlations 81Q35 Quantum mechanics on special spaces: mani81P42 Entanglement measures, concurrencies, separafolds, fractals, graphs, lattices [See also 81R20] bility criteria 81P43 Quantum discord 81Q37 Quantum dots, waveguides, ratchets, etc. [See also 82D20, 82D77] 81P45 Quantum information, communication, networks (quantum-theoretic aspects) [See also 94A15, 81Q40 Bethe-Salpeter and other integral equations aris94A17] ing in quantum theory 81P47 Quantum channels, fidelity [See also 94A40] 81P48 LOCC, teleportation, dense coding, remote state 81Q50 Quantum chaos [See also 37Dxx] operations, distillation 81P50 Quantum state estimation, approximate cloning 81Q60 Supersymmetry and quantum mechanics 81P55 Special bases (entangled, mutual unbiased, etc.) 81Q65 Alternative quantum mechanics (including hidden variables, etc.) 81P65 Quantum gates 81P68 Quantum computation [See also 68Q09] {For al81Q70 Differential geometric methods, including holongorithmic aspects, see 68Q12} omy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory 81P70 Quantum coding (general) 81P73 Computational stability and error-correcting codes for quantum computation and communica- 81Q80 Special quantum systems, such as solvable systems tion processing 81P94 Quantum cryptography (quantum-theoretic as- 81Q93 Quantum control pects) [See also 94A60] 81P99 None of the above, but in this section 81Q99 None of the above, but in this section 133 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 81Rxx Groups and algebras in quantum 81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechantheory ics 81R05 Finite-dimensional groups and algebras motivated by physics and their representations [See also 81S40 Path integrals in quantum mechanics [See also 58D30, 81Q30, 81T18] 20C35, 22E70] 81R10 Infinite-dimensional groups and algebras moti- 81S99 None of the above, but in this section vated by physics, including Virasoro, Kac-Moody, W -algebras and other current algebras and their 81Txx Quantum field theory; related clasrepresentations [See also 17B65, 17B67, 22E65, sical field theories [See also 70Sxx] 22E67, 22E70] 81T05 Axiomatic quantum field theory; operator alge81R12 Groups and algebras in quantum theory and rebras lations with integrable systems [See also 17Bxx, 81T08 Constructive quantum field theory 37J35] 81R15 Operator algebra methods applied to problems 81T10 Model quantum field theories in quantum theory [See also 46Lxx, 81T05] 81T11 Higher spin theories 81R20 Covariant wave equations in quantum theory, rel- 81T12 Effective quantum field theories ativistic quantum mechanics [See also 81Q35] 81T13 Yang-Mills and other gauge theories in quantum 81R25 Spinor and twistor methods applied to problems field theory [See also 53C07, 58E15] in quantum theory [See also 32L25] 81T15 Perturbative methods of renormalization applied to problems in quantum field theory 81R30 Coherent states [See also 22E45]; squeezed states in quantum theory [See also 81V80] 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory 81R40 Symmetry breaking in quantum theory 81R50 Quantum groups and related algebraic methods 81T17 Renormalization group methods applied to problems in quantum field theory applied to problems in quantum theory [See also 16T20, 17B37] 81T18 Feynman diagrams 81R60 Noncommutative geometry in quantum theory 81R99 None of the above, but in this section 81T20 Quantum field theory on curved space or spacetime backgrounds 81T25 Quantum field theory on lattices 81Sxx General quantum mechanics and 81T27 Continuum limits in quantum field theory problems of quantization 81T28 Thermal quantum field theory [See also 82B30] 81S05 Commutation relations and statistics as related 81T30 String and superstring theories; other extended to quantum mechanics (general) objects (e.g., branes) in quantum field theory [See 81S07 Uncertainty relations, also entropic also 83E30] 81S08 Canonical quantization 81T32 Matrix models and tensor models for quantum field theory 81S10 Geometry and quantization, symplectic methods 81T33 Dimensional compactification in quantum field [See also 53D50] theory 81S20 Stochastic quantization 81T35 Correspondence, duality, holography (AdS/CFT, 81S22 Open systems, reduced dynamics, master equagauge/gravity, etc.) [See also 83E05] tions, decoherence [See also 82C31] 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81S25 Quantum stochastic calculus 134 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 81T45 Topological field theories in quantum mechanics 81V19 Other fundamental interactions in quantum the[See also 57R56, 58Dxx] ory 81T50 Anomalies in quantum field theory 81V22 Unified quantum theories 81T55 Casimir effect in quantum field theory 81V25 Other elementary particle theory in quantum theory 81T60 Supersymmetric field theories in quantum me- 81V27 Anyons chanics 81V35 Nuclear physics 81T70 Quantization in field theory; cohomological 81V45 Atomic physics methods [See also 58D29] 81V55 Molecular physics [See also 92E10] 81T75 Noncommutative geometry methods in quantum 81V60 Mono-, di- and multipole moments (EM and field theory [See also 46L85, 46L87, 58B34] other), gyromagnetic relations 81T99 None of the above, but in this section 81V65 Quantum dots as quasi particles [See also 82D20] 81Uxx Quantum scattering theory [See 81V70 Many-body theory; quantum Hall effect also 34A55, 34L25, 34L40, 35P25, 47A40] 81V72 Particle exchange symmetries in quantum theory (general) 81U05 2-body potential quantum scattering theory {For WKB methods, see also 34E20} 81V73 Bosonic systems in quantum theory 81V74 Fermionic systems in quantum theory 81U10 n-body potential quantum scattering theory 81U15 Exactly and quasi-solvable systems arising in 81V80 Quantum optics quantum theory 81V99 None of the above, but in this section 81U20 S-matrix theory, etc. in quantum theory 82-XX Statistical mechanics, structure of matter 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 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 81U40 Inverse scattering problems in quantum theory 81U90 Particle decays in scattering 81U99 None of the above, but in this section 82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics 82-03 History of statistical mechanics [Consider also classification numbers pertaining to Section 01] 81Vxx Applications of quantum theory to 82-04 Software, source code, etc. for problems pertaining to statistical mechanics specific physical systems 81V05 Strong interaction, including quantum chromo- 82-05 Experimental work for problems pertaining to statistical mechanics dynamics 82-06 Proceedings, conferences, collections, etc. per81V10 Electromagnetic interaction; quantum electrodytaining to statistical mechanics namics 82-10 Mathematical modeling or simulation for prob81V15 Weak interaction in quantum theory lems pertaining to statistical mechanics 81V17 Gravitational interaction in quantum theory [See 82-11 Research data for problems pertaining to statistialso 83Cxx, 83Exx] cal mechanics 135 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 82Bxx Equilibrium statistical mechanics 82B03 Foundations of equilibrium statistical mechanics 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) 82C03 Foundations of time-dependent statistical mechanics 82B05 Classical equilibrium statistical mechanics (general) 82C05 Classical dynamic and nonequilibrium statistical mechanics (general) 82B10 Quantum equilibrium statistical mechanics (general) 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general) 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical 82C20 Dynamic lattice systems (kinetic Ising, etc.) and mechanics systems on graphs in time-dependent statistical mechanics 82B21 Continuum models (systems of particles, etc.) 82C21 Dynamic continuum models (systems of partiarising in equilibrium statistical mechanics cles, etc.) in time-dependent statistical mechanics 82B23 Exactly solvable models; Bethe ansatz 82C22 Interacting particle systems in time-dependent statistical mechanics [See also 60K35] 82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics 82C23 Exactly solvable dynamic models in timedependent statistical mechanics [See also 37K60] 82B26 Phase transitions (general) in equilibrium statis82C24 Interface problems; diffusion-limited aggregation tical mechanics in time-dependent statistical mechanics 82B27 Critical phenomena in equilibrium statistical me82C26 Dynamic and nonequilibrium phase transitions chanics (general) in statistical mechanics 82B28 Renormalization group methods in equilibrium 82C27 Dynamic critical phenomena in statistical mestatistical mechanics [See also 81T17] chanics 82C28 Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics [See also 81T17] 82B31 Stochastic methods applied to problems in equilibrium statistical mechanics 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent sta82B35 Irreversible thermodynamics, including Onsagertistical mechanics [See also 60H10] Machlup theory [See also 92E20] 82B30 Statistical thermodynamics [See also 80-XX] 82B40 Kinetic theory of gases in equilibrium statistical mechanics 82C32 Neural nets applied to problems in timedependent statistical mechanics [See also 68T05, 91E40, 92B20] 82B41 Random walks, random surfaces, lattice animals, 82C35 Irreversible thermodynamics, including OnsagerMachlup theory etc. in equilibrium statistical mechanics [See also 60G50, 82C41] 82C40 Kinetic theory of gases in time-dependent statistical mechanics 82B43 Percolation [See also 60K35] 82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics 82B99 None of the above, but in this section 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics [See also 60G50] 82C43 Time-dependent percolation in statistical mechanics [See also 60K35] 136 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 82C44 Dynamics of disordered systems (random Ising 82Mxx Basic methods in statistical mesystems, etc.) in time-dependent statistical me- chanics [See also 65-XX] chanics 82M10 Finite element, Galerkin and related methods applied to problems in statistical mechanics 82C70 Transport processes in time-dependent statistical mechanics 82M12 Finite volume methods applied to problems in statistical mechanics 82C99 None of the above, but in this section 82M15 Boundary element methods applied to problems in statistical mechanics 82Dxx Applications of statistical mechan82M20 Finite difference methods applied to problems in ics to specific types of physical systems statistical mechanics 82D03 Statistical mechanical studies in condensed mat82M22 Spectral, collocation and related (meshless) ter (general) methods applied to problems in statistical mechanics 82D05 Statistical mechanical studies of gases 82M30 Variational methods applied to problems in statistical mechanics 82D10 Statistical mechanical studies of plasmas 82M31 Monte Carlo methods applied to problems in statistical mechanics [See also 65C05] 82D15 Statistical mechanical studies of liquids 82D20 Statistical mechanical studies of solids 82M36 Computational density functional analysis in statistical mechanics 82D25 Statistical mechanical studies of crystals {For crystallographic group theory, see 20H15} 82M37 Computational molecular dynamics in statistical mechanics 82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and 82M60 Stochastic analysis in statistical mechanics [See also 65C35] spin glasses) 82M99 None of the above, but in this section 82D35 Statistical mechanical studies of metals 82D37 Statistical mechanical studies of semiconductors 83-XX Relativity and gravitational 82D40 Statistical mechanical studies of magnetic mate- theory rials 83-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to relativity and gravitational theory 82D45 Statistical mechanical studies of ferroelectrics 82D50 Statistical mechanical studies of superfluids 83-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational 82D55 Statistical mechanical studies of superconductors theory 82D60 Statistical mechanical studies of polymers 83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory 82D75 Nuclear reactor theory; neutron transport 83-03 History of relativity and gravitational theory [Consider also classification numbers pertaining to 82D77 Quantum waveguides, quantum wires [See also Section 01] 78A50] 82D80 Statistical mechanical studies of nanostructures and nanoparticles 82D99 None of the above, but in this section 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 137 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 83-06 Proceedings, conferences, collections, etc. per- 83C40 Gravitational energy and conservation laws; taining to relativity and gravitational theory groups of motions 83-08 Computational methods for problems pertaining 83C45 Quantization of the gravitational field to relativity and gravitational theory 83C47 Methods of quantum field theory in general relativity and gravitational theory [See also 81T20] 83-10 Mathematical modeling or simulation for problems pertaining to relativity and gravitational the- 83C50 Electromagnetic fields in general relativity and ory gravitational theory 83-11 Research data for problems pertaining to relativ- 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) ity and gravitational theory 83C56 Dark matter and dark energy 83Axx Special relativity 83C57 Black holes 83A05 Special relativity 83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism 83A99 None of the above, but in this section 83Bxx Observational and experimental 83C65 Methods of noncommutative geometry in general relativity [See also 58B34] questions in relativity and gravitational theory 83C75 Space-time singularities, cosmic censorship, etc. 83B05 Observational and experimental questions in rel- 83C80 Analogues of general relativity in lower dimenativity and gravitational theory sions 83C99 None of the above, but in this section 83B99 None of the above, but in this section 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmet83C05 Einstein’s equations (general structure, canonical ric field theories 83Cxx General relativity formalism, Cauchy problems) 83C10 Equations of motion in general relativity and gravitational theory 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83D99 None of the above, but in this section 83C15 Exact solutions to problems in general relativity and gravitational theory 83Exx Unified, higher-dimensional and su83C20 Classes of solutions; algebraically special solu- per field theories tions, metrics with symmetries for problems in gen- 83E05 Geometrodynamics and the holographic principle eral relativity and gravitational theory [See also 81T35] 83C22 Einstein-Maxwell equations 83E15 Kaluza-Klein and other higher-dimensional theories 83C25 Approximation procedures, weak fields in general 83E30 String and superstring theories in gravitational relativity and gravitational theory theory [See also 81T30] 83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational the- 83E50 Supergravity ory 83E99 None of the above, but in this section 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.) in general relativity and grav- 83Fxx Cosmology itational theory 83F05 Cosmology 83C35 Gravitational waves 83F99 None of the above, but in this section 138 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 85-XX Astronomy and astro- 86-XX Geophysics [See also 76U05, physics {For celestial mechanics, 76V05] see 70F15} 86-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geophysics 85-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to astronomy and 86-01 Introductory exposition (textbooks, tutorial paastrophysics pers, etc.) pertaining to geophysics 85-01 Introductory exposition (textbooks, tutorial pa- 86-02 Research exposition (monographs, survey articles) pers, etc.) pertaining to astronomy and astropertaining to geophysics physics 86-03 History of geophysics [Consider also classification 85-02 Research exposition (monographs, survey articles) numbers pertaining to Section 01] pertaining to astronomy and astrophysics 86-04 Software, source code, etc. for problems pertain85-03 History of astronomy and astrophysics [Consider ing to geophysics also classification numbers pertaining to Section 01] 86-05 Experimental work for problems pertaining to 85-04 Software, source code, etc. for problems pertaingeophysics ing to astronomy and astrophysics 86-06 Proceedings, conferences, collections, etc. per85-05 Experimental work for problems pertaining to astaining to geophysics tronomy and astrophysics 86-08 Computational methods for problems pertaining to geophysics 85-06 Proceedings, conferences, collections, etc. pertaining to astronomy and astrophysics 86-10 Mathematical modeling or simulation for problems pertaining to geophysics 85-08 Computational methods for problems pertaining to astronomy and astrophysics 86-11 Research data for problems pertaining to geophysics 85-10 Mathematical modeling or simulation for problems pertaining to astronomy and astrophysics 86Axx Geophysics [See also 76U05, 76V05] 85-11 Research data for problems pertaining to astronomy and astrophysics 86A04 General questions in geophysics 85Axx Astronomy and astrophysics {For celestial mechanics, see 70F15} 85A04 General questions in astronomy and astrophysics 86A05 Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05] 86A08 Climate science and climate modeling 86A10 Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05] 85A05 Galactic and stellar dynamics 85A15 Galactic and stellar structure 86A15 Seismology (including tsunami modeling), earthquakes 85A20 Planetary atmospheres 85A25 Radiative transfer in astronomy and astrophysics 86A20 Potentials, prospecting 86A22 Inverse problems in geophysics [See also 35R30] 85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics [See also 76Y05] 86A25 Geo-electricity and geomagnetism [See also 76W05, 78A25] 85A35 Statistical astronomy 86A30 Geodesy, mapping problems 85A40 Cosmology {For relativistic cosmology, see 83F05} 86A32 Geostatistics 85A99 None of the above, but in this section 86A40 Glaciology 139 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 86A60 Geological problems 86A70 Vulcanology; magma and lava flow 86A99 None of the above, but in this section 90B15 Stochastic network models in operations research {For network control, see 93B70} 90B18 Communication networks in operations research [See also 68M10, 68M12, 68M18, 94A05] {For networks as computational models, see 68Q06} 90-XX Operations research, math- 90B20 Traffic problems in operations research 90B22 Queues and service in operations research [See ematical programming also 60K25, 68M20] 90-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operations re- 90B25 Reliability, availability, maintenance, inspection in operations research [See also 60K10, 62N05] search and mathematical programming 90B30 Production models 90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and 90B35 Deterministic scheduling theory in operations research [See also 68M20] mathematical programming 90-02 Research exposition (monographs, survey articles) 90B36 Stochastic scheduling theory in operations research [See also 68M20] pertaining to operations research and mathematical programming 90B40 Search theory 90-03 History of operations research and mathematical 90B50 Management decision making, including multiple programming [Consider also classification numbers objectives [See also 90C29, 90C31, 91A35, 91B06] pertaining to Section 01] 90B60 Marketing, advertising [See also 91B60] 90-04 Software, source code, etc. for problems pertain90B70 Theory of organizations, manpower planning in ing to operations research and mathematical prooperations research [See also 91D35] gramming 90B80 Discrete location and assignment [See also 90-05 Experimental work for problems pertaining to op90C10] erations research and mathematical programming 90B85 Continuous location 90-06 Proceedings, conferences, collections, etc. pertaining to operations research and mathematical 90B90 Case-oriented studies in operations research programming 90B99 None of the above, but in this section 90-08 Computational methods for problems pertaining to operations research and mathematical program- 90Cxx Mathematical programming [See ming also 49Mxx, 65Kxx] 90-10 Mathematical modeling or simulation for prob- 90C05 Linear programming lems pertaining to operations research and math90C06 Large-scale problems in mathematical programematical programming ming 90-11 Research data for problems pertaining to opera- 90C08 Special problems of linear programming (transtions research and mathematical programming portation, multi-index, data envelopment analysis, etc.) 90Bxx Operations research and manage- 90C09 Boolean programming ment science 90C10 Integer programming 90B05 Inventory, storage, reservoirs 90C11 Mixed integer programming 90B06 Transportation, logistics and supply chain man90C15 Stochastic programming agement 90C17 Robustness in mathematical programming 90B10 Deterministic network models in operations research {For network control, see 93B70} 90C20 Quadratic programming 140 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 90C22 Semidefinite programming 90C23 Polynomial optimization 90C24 Tropical optimization (e.g., max-plus optimiza- 90C90 Applications of mathematical programming tion) 90C25 Convex programming 90C99 None of the above, but in this section 90C26 Nonconvex programming, global optimization 90C27 Combinatorial optimization 91-XX Game theory, economics, finance, and other social and behavioral sciences 90C29 Multi-objective and goal programming 90C30 Nonlinear programming 90C31 Sensitivity, stability, parametric optimization 91-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to game theory, eco90C33 Complementarity and equilibrium problems and nomics, and finance variational inequalities (finite dimensions) (aspects of mathematical programming) 91-01 Introductory exposition (textbooks, tutorial pa90C34 Semi-infinite programming pers, etc.) pertaining to game theory, economics, and finance 90C35 Programming involving graphs or networks [See 90C32 Fractional programming also 90C27] 91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance 90C39 Dynamic programming [See also 49L20] 90C40 Markov and semi-Markov decision processes 90C46 Optimality conditions and duality in mathemat- 91-03 History of game theory, economics, and finance ical programming [See also 49N15] [Consider also classification numbers pertaining to Section 01] 90C47 Minimax problems in mathematical programming [See also 49K35] 91-04 Software, source code, etc. for problems pertain90C48 Programming in abstract spaces ing to game theory, economics, and finance 90C49 Extreme-point and pivoting methods 91-05 Experimental work for problems pertaining to game theory, economics, and finance 90C51 Interior-point methods 90C52 Methods of reduced gradient type 90C53 Methods of quasi-Newton type 91-06 Proceedings, conferences, collections, etc. pertaining to game theory, economics, and finance 90C55 Methods of successive quadratic programming type 90C56 Derivative-free methods and methods using gen- 91-08 Computational methods for problems pertaining to game theory, economics, and finance eralized derivatives [See also 49J52] 90C57 Polyhedral combinatorics, branch-and-cut branch-and-bound, 91-10 Mathematical modeling or simulation for problems pertaining to game theory, economics, and finance 90C59 Approximation methods and heuristics in mathematical programming 90C60 Abstract computational complexity for mathe- 91-11 Research data for problems pertaining to game theory, economics, and finance matical programming problems [See also 68Q25] 141 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 91Axx Game theory 91A68 Algorithmic game theory and complexity [See also 68Qxx, 68Wxx] 91A05 2-person games 91A70 Spaces of games 91A06 n-person games, n > 2 91A80 Applications of game theory 91A07 Games with infinitely many players 91A81 Quantum games 91A10 Noncooperative games 91A86 Game theory and fuzziness 91A11 Equilibrium refinements 91A90 Experimental studies 91A12 Cooperative games 91A99 None of the above, but in this section 91A14 Potential and congestion games 91Bxx Mathematical economics econometrics, see 62P20} 91A15 Stochastic games, stochastic differential games {For 91A16 Mean field games (aspects of game theory) [See 91B02 Fundamental topics (basic mathematics, also 35Q89, 49N80] methodology; applicable to economics in general) 91A18 Games in extensive form 91B03 Mechanism design theory 91A20 Multistage and repeated games 91B05 Risk models (general) {For actuarial and financial risk, see 91Gxx} 91A22 Evolutionary games 91A23 Differential games (aspects of game theory) [See 91B06 Decision theory [See also 62Cxx, 90B50, 91A35] also 49N70] 91B08 Individual preferences 91A24 Positional games (pursuit and evasion, etc.) [See 91B10 Group preferences also 49N75] 91B12 Voting theory 91A25 Dynamic games 91B14 Social choice 91A26 Rationality and learning in game theory 91B15 Welfare economics 91A27 Games with incomplete information, Bayesian 91B16 Utility theory [See also 91A30] games 91A28 Signaling and communication in game theory 91B18 Public goods 91A30 Utility theory for games [See also 91B16] 91B24 Microeconomic theory (price theory and economic markets) 91A35 Decision theory for games [See also 62Cxx, 91B26 Auctions, bargaining, bidding and selling, and 90B50, 91B06] other market models 91A40 Other game-theoretic models 91B32 Resource and cost allocation (including fair division, apportionment, etc.) 91A43 Games involving graphs {For games on graphs, see 05C57} 91B38 Production theory, theory of the firm 91A44 Games involving topology, set theory, or logic 91B39 Labor markets 91A46 Combinatorial games 91B41 Contract theory (moral hazard, adverse selection) 91A50 Discrete-time games 91B42 Consumer behavior, demand theory 91A55 Games of timing 91B43 Principal-agent models 91A60 Probabilistic games; gambling [See also 60G40] 91A65 Hierarchical games) games (including Stackelberg 91B44 Economics of information 91B50 General equilibrium theory 142 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 91Dxx Mathematical sociology (including anthropology) 91B51 Dynamic stochastic general equilibrium theory 91B52 Special types of economic equilibria 91D10 Models of societies, social and urban evolution 91B54 Special types of economic markets (including 91D15 Social learning Cournot, Bertrand) 91D20 Mathematical geography and demography 91B55 Economic dynamics 91D25 Spatial models in sociology [See also 91B72] 91B60 Trade models 91D30 Social networks; opinion dynamics 91B62 Economic growth models 91B64 Macroeconomic theory (monetary models, models of taxation) 91D35 Manpower systems in sociology [See also 90B70, 91B39] 91D99 None of the above, but in this section 91B66 Multisectoral models in economics 91B68 Matching models 91B69 Heterogeneous agent models 91B70 Stochastic models in economics 91B72 Spatial models in economics [See also 91D25] 91Exx Mathematical psychology {For psychometrics, see 62P15} 91E10 Cognitive psychology 91E30 Psychophysics and psychophysiology; perception 91E40 Memory and learning in psychology [See also 68T05] 91B74 Economic models of real-world systems (e.g., electricity markets, etc.) 91E45 Measurement and performance in psychology 91B76 Environmental economics (natural resource mod- 91E99 None of the above, but in this section els, harvesting, pollution, etc.) 91B80 Applications of statistical and quantum mechan- 91Fxx Other social and behavioral sciences (mathematical treatment) ics to economics (econophysics) 91F10 History, political science 91B82 Statistical methods; economic indices and measures [See also 62P20] 91F20 Linguistics [See also 03B65, 68T50] 91B84 Economic time series analysis {For statistical 91F99 None of the above, but in this section theory of time series, see 62M10} 91B86 Mathematical economics and fuzziness 91B99 None of the above, but in this section 91Gxx Actuarial science and mathematical finance {For statistics, see 62P05} 91G05 Actuarial mathematics 91Cxx Social and behavioral sciences: gen- 91G10 Portfolio theory eral topics {For statistics, see 62P25} 91G15 Financial markets 91C05 Measurement theory in the social and behavioral 91G20 Derivative securities (option pricing, hedging, sciences etc.) 91C15 One- and multidimensional scaling in the social 91G30 Interest rates, asset pricing, etc. and behavioral sciences models) (stochastic 91C20 Clustering in the social and behavioral sciences 91G40 Credit risk [See also 62H30] 91G45 Financial networks (including contagion, sys91C99 None of the above, but in this section temic risk, regulation) 143 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 92Cxx Physiological, cellular and medical 91G60 Numerical methods (including Monte Carlo topics 91G50 Corporate finance (dividends, real options, etc.) methods) 92C05 Biophysics 91G70 Statistical methods; risk measures [See also 92C10 Biomechanics [See also 74L15] 62P05, 62P20] 92C15 Developmental biology, pattern formation 91G80 Financial applications of other theories [See also 35Q91, 37N40, 49N90, 60J70, 60K10, 60H30, 92C17 Cell movement (chemotaxis, etc.) 93E20] 92C20 Neural biology 91G99 None of the above, but in this section 92C30 Physiology (general) 92C32 Pathology, pathophysiology 92-XX Biology and other natural 92C35 Physiological flow [See also 76Z05] sciences 92C37 Cell biology 92-00 General reference works (handbooks, dictionaries, 92C40 Biochemistry, molecular biology bibliographies, etc.) pertaining to biology 92C42 Systems biology, networks 92-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30] 92-02 Research exposition (monographs, survey articles) pertaining to biology 92C47 Biosensors (not for medical applications) 92-03 History of biology [Consider also classification 92C50 Medical applications (general) numbers pertaining to Section 01] 92C55 Biomedical imaging and signal processing [See 92-04 Software, source code, etc. for problems pertainalso 44A12, 65R10, 94A08, 94A12] ing to biology 92C60 Medical epidemiology {For theoretical aspects, 92-05 Experimental work for problems pertaining to bisee 92D30} ology 92C70 Microbiology 92-06 Proceedings, conferences, collections, etc. per92C75 Biotechnology taining to biology 92-08 Computational methods for problems pertaining 92C80 Plant biology to biology 92C99 None of the above, but in this section 92-10 Mathematical modeling or simulation for problems pertaining to biology 92Dxx Genetics and population dynamics 92-11 Research data for problems pertaining to biology 92D10 Genetics and epigenetics {For genetic algebras, see 17D92} 92Bxx Mathematical biology in general 92D15 Problems related to evolution 92B05 General biology and biomathematics 92D20 Protein sequences, DNA sequences 92B10 Taxonomy, cladistics, statistics in mathematical 92D25 Population dynamics (general) biology 92D30 Epidemiology {For medical applications, see 92B15 General biostatistics [See also 62P10] 92C60} 92B20 Neural networks for/in biological studies, artifi- 92D40 Ecology cial life and related topics [See also 68T05, 82C32, 92D45 Pest management 94Cxx] 92B25 Biological rhythms and synchronization 92D50 Animal behavior 92B99 None of the above, but in this section 92D99 None of the above, but in this section 144 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 92Exx Chemistry {For biochemistry, see 93Axx General systems theory 92C40} 93A05 Axiomatic systems theory 92E10 Molecular structure (graph-theoretic methods, 93A10 General systems methods of differential topology, etc.) 93A13 Hierarchical systems 92E20 Classical flows, reactions, etc. in chemistry [See 93A14 Decentralized systems also 80A30, 80A32] 93A15 Large-scale systems 92E99 None of the above, but in this section 93A16 Multi-agent systems 92Fxx Other natural sciences (mathemat- 93A99 None of the above, but in this section ical treatment) 93Bxx Controllability, observability, and 92F05 Other natural sciences (mathematical treatment) system structure 93B03 Attainable sets, reachability 92F99 None of the above, but in this section 93B05 Controllability 93-XX Systems theory; control 93B07 Observability {For optimal control, see 49-XX} 93B10 Canonical structure 93B11 System structure simplification 93-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to systems and con- 93B12 Variable structure systems trol theory 93B15 Realizations from input-output data 93-01 Introductory exposition (textbooks, tutorial pa- 93B17 Transformations pers, etc.) pertaining to systems and control theory 93B18 Linearizations 93-02 Research exposition (monographs, survey articles) 93B20 Minimal systems representations pertaining to systems and control theory 93B24 Topological methods 93-03 History of systems and control theory [Consider also classification numbers pertaining to Section 01] 93B25 Algebraic methods 93B27 Geometric methods 93-04 Software, source code, etc. for problems pertaining to systems and control theory 93B28 Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70] 93-05 Experimental work for problems pertaining to sys93B30 System identification tems and control theory 93-06 Proceedings, conferences, collections, etc. taining to systems and control theory per- 93B35 Sensitivity (robustness) 93B36 H ∞ -control 93B45 Model predictive control 93-08 Computational methods for problems pertaining to systems and control theory 93B47 Iterative learning control 93-10 Mathematical modeling or simulation for prob- 93B50 Synthesis problems lems pertaining to systems and control theory 93B51 Design techniques (robust design, computeraided design, etc.) 93-11 Research data for problems pertaining to systems and control theory 93B52 Feedback control 145 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 93B53 Observers 93B55 Pole and zero placement problems 93C83 Control/observation systems involving computers (process control, etc.) 93B60 Eigenvalue problems 93C85 Automated systems (robots, etc.) in control theory [See also 68T40, 70B15, 70Q05] 93B70 Networked control 93C95 Application models in control theory 93B99 None of the above, but in this section 93C99 None of the above, but in this section 93Cxx Model systems in control theory 93Dxx Stability of control systems 93C05 Linear systems in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp , lp , etc.) in control theory 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordi- 93D09 Robust stability nary differential equations [See also 34H05] 93D10 Popov-type stability of feedback systems 93C20 Control/observation systems governed by partial 93D15 Stabilization of systems by feedback differential equations 93D20 Asymptotic stability in control theory 93C23 Control/observation systems governed by functional-differential equations [See also 34K35] 93D21 Adaptive or robust stabilization 93C25 Control/observation systems in abstract spaces 93D23 Exponential stability 93C27 Impulsive control/observation systems 93D25 Input-output approaches in control theory 93C28 Positive control/observation systems 93D30 Lyapunov and storage functions 93C29 Boolean control/observation systems 93D40 Finite-time stability 93C30 Control/observation systems governed by func- 93D50 Consensus tional relations other than differential equations 93D99 None of the above, but in this section (such as hybrid and switching systems) 93C35 Multivariable systems, multidimensional control 93Exx Stochastic systems and control systems 93E03 Stochastic systems in control theory (general) 93C40 Adaptive control/observation systems 93E10 Estimation and detection in stochastic control 93C41 Control/observation systems with incomplete intheory [See also 60G35] formation 93E11 Filtering in stochastic control theory [See also 93C42 Fuzzy control/observation systems 60G35] 93C43 Delay control/observation systems 93E12 Identification in stochastic control theory 93C55 Discrete-time control/observation systems 93E14 Data smoothing in stochastic control theory 93C57 Sampled-data control/observation systems 93E15 Stochastic stability in control theory 93C62 Digital control/observation systems 93E20 Optimal stochastic control [See also 49J55, 49K45] 93C65 Discrete event control/observation systems 93C70 Time-scale analysis and singular perturbations in 93E24 Least squares and related methods for stochastic control systems control/observation systems 93C73 Perturbations in control/observation systems 93E35 Stochastic learning and adaptive control 93C80 Frequency-response methods in control theory 93E99 None of the above, but in this section 146 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 94-XX Information and communi- 94A16 Informational aspects of data analysis and big data [See also 62R07, 68T09] {For homological ascation theory, circuits pects, see 55N31} 94-00 General reference works (handbooks, dictionaries, 94A17 Measures of information, entropy bibliographies, etc.) pertaining to information and 94A20 Sampling theory in information and communicacommunication theory tion theory 94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communi- 94A24 Coding theorems (Shannon theory) cation theory 94A29 Source coding [See also 68P30] 94-02 Research exposition (monographs, survey articles) 94A34 Rate-distortion theory in information and compertaining to information and communication themunication theory ory 94A40 Channel models (including quantum) in informa94-03 History of information and communication theory tion and communication theory [See also 81P47] [Consider also classification numbers pertaining to Section 01] 94A45 Prefix, length-variable, comma-free codes [See also 20M35, 68Q45] 94-04 Software, source code, etc. for problems pertaining to information and communication theory 94A50 Theory of questionnaires 94-05 Experimental work for problems pertaining to in- 94A55 Shift register sequences and sequences over finite formation and communication theory alphabets in information and communication theory 94-06 Proceedings, conferences, collections, etc. pertaining to information and communication theory 94A60 Cryptography [See also 11T71, 14G50, 68P25, 81P94] 94-08 Computational methods for problems pertaining to information and communication theory 94A62 Authentication, digital signatures and secret sharing [See also 81P94] 94-10 Mathematical modeling or simulation for problems pertaining to information and communication 94A99 None of the above, but in this section theory 94-11 Research data for problems pertaining to informa- 94Bxx Theory of error-correcting codes and error-detecting codes tion and communication theory 94Axx Communication, information 94B05 Linear codes, general 94B10 Convolutional codes 94A05 Communication theory [See also 60G35, 90B18] 94B12 Combined modulation schemes (including trellis 94A08 Image processing (compression, reconstruction, codes) in coding theory etc.) in information and communication theory [See 94B15 Cyclic codes also 68U10] 94A11 Application of orthogonal and other special func- 94B20 Burst-correcting codes tions 94B25 Combinatorial codes 94A12 Signal theory (characterization, reconstruction, 94B27 Geometric methods (including applications of alfiltering, etc.) gebraic geometry) applied to coding theory [See also 11T71, 14G50] 94A13 Detection theory in information and communication theory 94B30 Majority codes 94A14 Modulation and demodulation in information 94B35 Decoding and communication theory 94B40 Arithmetic codes [See also 11T71, 14G50] 94A15 Information theory (general) [See also 62B10, 81P45] 94B50 Synchronization error-correcting codes 147 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 94B60 Other types of codes 97-06 Proceedings, conferences, collections, etc. taining to mathematics education 94B65 Bounds on codes per- 97-11 Research data for problems pertaining to mathematics education 94B70 Error probability in coding theory 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding 97Axx History and society (aspects of mathematics education) theory [See also 11H31, 11H71] 97A30 History in mathematics education {For mathematics history, see 01-XX; for biographies, see 01A70; for history of mathematics education, see 94Cxx Circuits, networks [See also 68Q06] 97-03} 94C05 Analytic circuit theory 97A40 Mathematics education and society {For sociol94B99 None of the above, but in this section ogy (and profession) of mathematics, see 01A80} 94C11 Switching theory, applications of Boolean algebras to circuits and networks 97A99 None of the above, but in this section 94C12 Fault detection; testing in circuits and networks 97Bxx Educational policy and systems 94C15 Applications of graph theory to circuits and net97B10 Mathematics educational research and planning works [See also 05Cxx, 68R10] 97B20 Educational policy for general education 94C30 Applications of design theory to circuits and networks [See also 05Bxx] 97B30 Educational policy for vocational education 94C60 Circuits in qualitative investigation and simula- 97B40 Educational policy for higher education tion of models 97B50 Mathematics teacher education 94C99 None of the above, but in this section 97B60 Educational policy for adult and further education 94Dxx Miscellaneous topics in information 97B70 Syllabuses, educational standards and communication theory 97B99 None of the above, but in this section 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory) [See also 97Cxx Psychology of mathematics educa03B52, 03E72, 28E10] tion, research in mathematics education 94D10 Boolean functions [See also 06E30] {For connec97C10 Comprehensive works on psychology of mathetions with circuits and networks, see 94C11} matics education 94D99 None of the above, but in this section 97C20 Affective behavior and mathematics education 97-XX Mathematics education 97C30 Cognitive processes, learning theories (aspects of mathematics education) 97-00 General reference works (handbooks, dictionaries, 97C40 Intelligence and aptitudes (aspects of mathematics education) bibliographies, etc.) pertaining to mathematics education 97C50 Language and verbal communities (aspects of mathematics education) 97-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education 97C60 Sociological aspects of learning (aspects of mathematics education) 97-02 Research exposition (monographs, survey articles) pertaining to mathematics education 97C70 Teaching-learning processes in mathematics education 97-03 History of mathematics education [Consider also classification numbers pertaining to Section 01] 97C99 None of the above, but in this section 148 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 97Dxx Education and instruction in math- 97F60 Number theory (educational aspects) ematics 97D10 Comprehensive works and comparative studies on education and instruction in mathematics 97D20 Philosophical and (maths didactics) theoretical 97F70 Measures and units (educational aspects) 97F80 Ratio and proportion, percentages (educational aspects) contributions 97F90 Real life mathematics, practical arithmetic (educational aspects) 97D30 Objectives and goals of mathematics teaching 97D40 Mathematics teaching methods and classroom 97F99 None of the above, but in this section techniques 97D50 Teaching mathematical problem solving and heuristic strategies 97Gxx Geometry education 97D60 Student assessment, achievement control and 97G10 Comprehensive works on geometry education rating (aspects of mathematics education) 97D70 Learning difficulties and student errors (aspects 97G20 Informal geometry (educational aspects) of mathematics education) 97G30 Area and volume (educational aspects) 97D80 Mathematics teaching units and draft lessons 97D99 None of the above, but in this section 97G40 Plane and solid geometry (educational aspects) 97Exx Education of foundations of mathe- 97G50 Transformation geometry (educational aspects) matics 97E10 Comprehensive works on education of foundations of mathematics 97G60 Plane and spherical trigonometry (educational aspects) 97E20 Philosophy and mathematics (educational as- 97G70 Analytic geometry, vector algebra (educational aspects) pects) 97E30 Logic (educational aspects) 97G80 Descriptive geometry (educational aspects) 97E40 Language of mathematics (educational aspects) 97G99 None of the above, but in this section 97E50 Reasoning and proving in the mathematics classroom 97Hxx Algebra education 97E60 Sets, relations, set theory (educational aspects) 97H10 Comprehensive works on algebra education 97E99 None of the above, but in this section 97H20 Elementary algebra (educational aspects) 97Fxx Education of arithmetic and number theory 97H30 Equations and inequalities (educational aspects) 97F10 Comprehensive works on education of arithmetic and number theory 97H40 Groups, rings, fields (educational aspects) 97F20 Pre-numerical stage, concept of numbers 97H50 Ordered algebraic structures (educational aspects) 97F30 Natural numbers (educational aspects) 97F40 Integers, rational numbers (educational aspects) 97H60 Linear algebra (educational aspects) 97F50 Real numbers, complex numbers (educational aspects) 97H99 None of the above, but in this section 149 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 97Ixx Analysis education 97M60 Biology, chemistry, medicine (aspects of mathematics education) 97I10 Comprehensive works on analysis education 97M70 Behavioral and social sciences (aspects of mathematics education) 97I20 Mappings and functions (educational aspects) 97I30 Sequences and series (educational aspects) 97M80 Arts, music, language, architecture (aspects of mathematics education) 97I40 Differential calculus (educational aspects) 97I50 Integral calculus (educational aspects) 97M99 None of the above, but in this section 97I60 Functions of several variables (educational aspects) 97I70 Functional equations (educational aspects) 97I80 Complex analysis (educational aspects) 97Nxx Education of numerical mathematics 97N10 Comprehensive works education of numerical mathematics 97I99 None of the above, but in this section 97Kxx Education of combinatorics, graph theory, probability theory, and statistics 97N20 Rounding, estimation, theory of errors (educational aspects) 97N30 Numerical algebra (educational aspects) 97K10 Comprehensive works on combinatorics, graph theory, and probability (educational aspects) 97N40 Numerical analysis (educational aspects) 97K20 Combinatorics (educational aspects) 97K30 Graph theory (educational aspects) 97K40 Descriptive statistics (educational aspects) 97K50 Probability theory (educational aspects) 97N50 Interpolation and approximation (educational aspects) 97N60 Mathematical programming (educational aspects) 97K60 Distributions and stochastic processes (educa- 97N70 Discrete mathematics (educational aspects) tional aspects) 97N80 Mathematical software, computer programs (ed97K70 Foundations and methodology of statistics (eduucational aspects) cational aspects) 97N99 None of the above, but in this section 97K80 Applied statistics (educational aspects) 97K99 None of the above, but in this section 97Pxx Computer science (educational aspects) 97Mxx Education of mathematical model97P10 Comprehensive works on computer science (eduing and applications of mathematics cational aspects) 97M10 Modeling and interdisciplinarity (aspects of mathematics education) 97P20 Theoretical computer science (educational aspects) 97M20 Mathematics in vocational training and career education 97P30 Systems, databases (educational aspects) 97M30 Financial and insurance mathematics (aspects of 97P40 Programming languages (educational aspects) mathematics education) 97M40 Operations research, economics (aspects of 97P50 Programming techniques (educational aspects) mathematics education) 97P80 Artificial intelligence (educational aspects) 97M50 Physics, astronomy, technology, engineering (aspects of mathematics education) 97P99 None of the above, but in this section 150 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 97Uxx Educational material and media 97U50 Computer-assisted instruction, e-learning (aspects of mathematics education) 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) 97U60 Manipulative materials (aspects of mathematics education) 97U70 Technological tools, calculators (aspects of mathematics education) 97U30 Teachers’ manuals and planning aids (aspects of 97U80 Audiovisual media (aspects of mathematics edumathematics education) cation) 97U40 Problem books, competitions, examinations (aspects of mathematics education) 97U99 None of the above, but in this section 151 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license.