0001 Textbooks (general mathematics) 0002 Research monographs (general mathematics) 0099 General mathematics 00XX General mathematics 00A05 General mathematics 00A06 Mathematics for nonmathematicians 00A07 Problem books 00A08 Mathematical recreation 00A15 Bibliographies 00A20 Dictionaries and other general reference works 00A22 Formularies 00A30 Philosophy of mathematics 00A35 Methodology of mathematics, didactics 00A69 General applied mathematics 00A71 Theory of mathematical modeling 00A72 General methods of simulation 00A73 Dimensional analysis 00A79 Physics 00A99 Miscellaneous topics in general mathematics 00Axx Topics in general mathematics 00B05 Collections of abstracts of lectures 00B10 Collections of articles of general interest 00B15 Collections of articles of miscellaneous specific interest 00B20 Proceedings of conferences of general interest 00B25 Proceedings of conferences of miscellaneous specific interest 00B30 Festschriften 00B50 Volumes of selected translations 00B55 Miscellaneous volumes of translations 00B60 Collections of reprinted articles 00Bxx Conference proceedings and collections of papers 0100 Reference works (history) 0101 Textbooks (history) 0102 Research monographs (history) 0106 Proceedings of conferences, etc. (history) 0199 History of mathematics and biography 01XX History and biography 01A05 General histories, source books 01A07 Ethnomathematics 01A10 Paleolithic or Neolithic mathematics, etc. 01A12 Native American mathematics 01A13 Native African mathematics 01A15 PreGreek mathematics of Europe 01A16 Egyptian mathematics 01A17 Babylonian mathematics 01A20 Greek or Roman mathematics 01A25 Chinese mathematics 01A27 Japanese mathematics 01A29 Southeast Asian mathematics 01A30 Mathematics of Islam (Medieval) 01A32 Indian mathematics 01A35 Mathematics in the medieval 01A40 Mathematics in the 15th and 16th centuries, Renaissance 01A45 Mathematics in the 17th century 01A50 Mathematics in the 18th century 01A55 Mathematics in the 19th century 01A60 Mathematics in the 20th century 01A65 Development of contemporary mathematics 01A67 Future prospectives in mathematics 01A70 Biographies, obituaries, personalia, bibliographies 01A72 Schools of mathematics 01A73 History of mathematics at universities 01A74 History of mathematics at institutions and academies (nonuniversity) 01A75 Collected or selected works 01A80 Sociology (and profession) of mathematics 01A99 Miscellaneous topics in history of mathematics 0300 Reference works (mathematical logic) 0301 Textbooks (mathematical logic) 0302 Research monographs (mathematical logic) 0303 Historical (mathematical logic) 0304 Machine computation, programs (mathematical logic) 0306 Proceedings of conferences (mathematical logic) 0399 Mathematical logic and foundations 03XX Mathematical logic 03A05 Philosophical and critical 03B05 Classical propositional logic 03B10 Firstorder logic 03B15 Higherorder logic 03B20 Subsystems of classical logic 03B22 Abstract deductive systems 03B25 Decidability of theories and sets of sentences 03B30 Foundations of classical theories 03B35 Mechanical theorem proving 03B40 Combinatory logic 03B45 Modal logic, etc. 03B46 Relevance logic, etc. 03B48 Probability logic, etc. 03B50 Manyvalued logic 03B52 Fuzzy logic 03B53 Paraconsistent logic 03B55 Intermediate logics 03B60 Other nonclassical logic 03B65 Logic of natural languages 03B70 Logic of programming 03B80 Appl. of logic 03B99 General logic 03Bxx General logic 03C05 Universal algebra (model theory) 03C07 Basic properties of firstorder languages and structures 03C10 Quantifier elimination and related topics 03C13 Finite models 03C15 Countable models 03C20 Ultraproducts and related constructions 03C25 Modeltheoretic forcing 03C30 Other model constructions 03C35 Categoricity, etc. 03C40 Interpolation, etc. (model theory) 03C45 Stability (model theory) 03C50 Models with special properties 03C52 Properties of classes of models 03C55 Settheoretic model theory 03C57 Recursiontheoretic model theory 03C60 Modeltheoretic algebra 03C62 Models of arithmetic and set theory 03C65 Models of other mathematical theories 03C68 Other classical firstorder model theory 03C70 Logic on admissible sets 03C75 Other infinitary logic 03C80 Logic with extra quantifiers and operators 03C85 Higherorder model theory 03C90 Nonclassical models 03C95 Abstract model theory 03C99 Model theory (logic) 03Cxx Model theory (logic) 03D03 Rewriting systems 03D05 Automata theory in connection with logical questions 03D10 Turing machines and related notions 03D15 Complexity of computation 03D20 Recursive functions 03D25 Recursively enumerable sets 03D30 Degrees, other than r.e. 03D35 Undecidability 03D40 Word problems, etc. (logic) 03D45 Effectively presented structures, etc. 03D50 Recursive equivalence types 03D55 Hierarchies 03D60 Recursion theory on ordinals, admissible sets, etc. 03D65 Other generalized recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic recursion theory 03D80 Appl. of recursion theory 03D99 Recursion theory 03Dxx Recursion theory 03E05 Combinatorial set theory (logic) 03E10 Ordinal and cardinal arithmetic 03E15 Descriptive set theory (logic) 03E20 Other classical set theory (logic) 03E25 Axiom of choice and related propositions (logic) 03E30 Axiomatics of classical set theory and its fragments 03E35 Consistency and independence results (set theory) 03E40 Other aspects of forcing (set theory) 03E45 Constructibility, ordinal definability, and related notions 03E47 Other notions of settheoretic definability 03E50 Continuum hypothesis and generalizations (logic) 03E55 Large cardinals 03E60 Axiom of determinacy, etc. 03E65 Other hypotheses and axioms (set theory) 03E70 Nonclassical set theories 03E72 Fuzzy sets (logic) 03E75 Appl. of set theory 03E99 Set theory (logic) 03Exx Set theory (logic) 03F03 General aspects of proof theory 03F05 Cutelimination, etc. 03F07 Structure of proofs 03F10 Functionals in proof theory 03F15 Recursive ordinals and ordinal notations 03F20 Complexity of proofs 03F25 Relative consistency and interpretations 03F30 Firstorder arithmetic and fragments 03F35 Higherorder arithmetic and fragments 03F40 Goedel numberings in proof theory 03F50 Metamathematics of constructive systems 03F55 Intuitionistic mathematics 03F60 Constructive and recursive analysis 03F65 Other constructive mathematics 03F99 Metamathematics, etc. 03Fxx Metamathematics, etc. 03G05 Boolean algebras in algebraic logic 03G10 Lattices and related structures (algebraic logic) 03G12 Quantum logic 03G15 Cylindric and polyadic algebras, etc. 03G20 Post and Lukasiewicz algebras (algebraic logic) 03G25 Other algebras related to logic 03G30 Categorical logic 03G99 Algebraic logic 03Gxx Algebraic logic 03H05 Nonstandard models in mathematics 03H10 Appl. of nonstandard models to other sciences 03H15 Nonstandard models of arithmetic 03H99 Nonstandard models 03Hxx Nonstandard models 0400 Reference works (set theory) 0401 Textbooks (set theory) 0402 Research monographs (set theory) 0403 Historical (set theory) 0404 Machine computation, programs (set theory) 0406 Proceedings of conferences (set theory) 0499 Set theory 04XX Set theory 04A03 Set algebra 04A05 Relations, functions 04A10 Ordinal and cardinal numbers; generalizations 04A15 Descriptive set theory 04A20 Combinatorial set theory 04A25 Axiom of choice and equivalent propositions 04A30 Continuum hypothesis and generalizations 04A72 Fuzzy sets 04A99 Miscellaneous topics in set theory 0501 Textbooks (combinatorics) 0502 Research monographs (combinatorics) 0503 Historical (combinatorics) 0504 Machine computation, programs (combinatorics) 0506 Proceedings of conferences (combinatorics) 0599 Combinatorics 05XX Combinatorics 05A05 Combinatorial choice problems 05A10 Combinatorial functions 05A15 Combinatorial enumeration problems 05A16 Asymptotic enumeration 05A17 Partitions of integres (combinatorics) 05A18 Partitions of sets 05A19 Combinatorial identities 05A20 Combinatorial inequalities 05A30 qcalculus and related topics 05A40 Umbral calculus 05A99 Classical combinatorial problems 05Axx Classical combinatorial problems 05B05 Block designs (combinatorics) 05B07 Triple systems 05B10 Difference sets 05B15 Orthogonal arrays, etc. 05B20 (0,1)matrices (combinatorics) 05B25 Finite geometries (combinatorics) 05B30 Other designs, configurations 05B35 Matroids (combinatorics) 05B40 Packing and covering (combinatorics) 05B45 Tessellation and tiling problems 05B50 Polyominoes 05B99 Designs and configurations 05Bxx Designs and configurations 05C05 Trees 05C10 Topological graph theory 05C12 Distance in graphs 05C15 Chromatic theory of graphs and maps 05C20 Directed graphs (digraphs) 05C25 Graphs and groups 05C30 Enumeration of graphs and maps 05C35 Extremal problems (graph theory) 05C38 Paths and cycles 05C40 Connectivity 05C45 Eulerian and Hamiltonian graphs 05C50 Graphs and matrices 05C55 Generalized Ramsey theory 05C60 Isomorphism problems (graph theory) 05C65 Hypergraphs 05C70 Factorization, etc. 05C75 Structural characterization of types of graphs 05C78 Graph labelling 05C80 Random graphs 05C85 Graph algorithms 05C90 Appl. of graph theory 05C99 Graph theory 05Cxx Graph theory 05D05 Extremal set theory 05D10 Ramsey theory 05D15 Transversal (matching) theory 05D99 Extremal combinatorics 05Dxx Extremal combinatorics 05E05 Symmetric functions 05E10 Tableaux, etc. 05E15 Combinatorial problems concerning the classical groups 05E20 Group actions on designs, etc. 05E25 Group actions on posets, etc. 05E30 Association schemes, etc. 05E35 Orthogonal polynomials (combinatorics) 05E99 Algebraic combinatorics 05Exx Algebraic combinatorics 0600 Reference works (ordered structures) 0601 Textbooks (ordered structures) 0602 Research monographs (ordered structures) 0603 Historical (ordered structures) 0604 Machine computation, programs (ordered structures) 0606 Proceedings of conferences (ordered structures) 0699 Order, lattices, ordered algebraic structures 06XX Ordered structures 06A05 Total order 06A06 Partial order 06A07 Combinatorics of partially ordered sets 06A08 Shellable posets, etc. 06A09 Cohomology of posets 06A12 Semilattices 06A15 Galois correspondences (ordered structures) 06A23 Completions of lattices 06A99 Ordered sets 06Axx Ordered sets 06B05 Structure theory of lattices 06B10 Ideals, etc. (lattices) 06B15 Representation theory of lattices 06B20 Varieties of lattices 06B25 Free lattices, etc. 06B30 Topological lattices 06B35 Continuous lattices 06B99 Lattices 06Bxx Lattices 06C05 Modular lattices 06C10 Geometric lattices 06C15 Complemented lattices 06C20 Complemented modular lattices, etc. 06C99 Lattices (modular and complemented) 06Cxx Lattices (modular and complemented) 06D05 Structure and representation theory of distributive lattices 06D10 Complete distributivity of lattices 06D15 Pseudocomplemented lattices 06D20 Heyting algebras 06D25 Post algebras 06D30 De Morgan algebras and generalizations 06D99 Distributive lattices 06Dxx Distributive lattices 06E05 Structure theory of Boolean algebras 06E10 Complete Boolean algebras 06E15 Stone space and related constructions 06E20 Ring theoretic properties (Boolean algebras) 06E25 Boolean algebras with additional operations 06E30 Boolean functions 06E99 Boolean algebras 06Exx Boolean algebras 06F05 Ordered semigroups 06F10 Noether lattices 06F15 Ordered groups 06F20 Ordered abelian groups, etc. 06F25 Ordered algebraic structures 06F30 Order topologies (ordertheoretic aspects) 06F35 BCKalgebras, etc. 06F99 Ordered structures (connections with other sections) 06Fxx Ordered structures (connections with other sections) 0800 Reference works (general algebraic systems) 0801 Textbooks (general algebraic systems) 0802 Research monographs (general algebraic systems) 0803 Historical (general algebraic systems) 0804 Machine computation, programs (general algebraic systems) 0806 Proceedings of conferences (general algebraic systems) 0899 General algebraic systems 08XX General algebraic systems 08A02 General relational systems 08A05 Structure theory of general algebraic systems 08A30 Subalgebras of general algebraic systems 08A35 Endomorphisms on general algebraic systems 08A40 Operations on general algebraic systems 08A45 Equational compactness 08A50 Word problems (universal algebra) 08A55 Partial algebras 08A60 Unary algebras 08A62 Finitary algebras 08A65 Infinitary algebras 08A70 Appl. of universal algebra in computer science 08A99 Universal algebra 08Axx Universal algebra 08B05 Equational logic in varieties of algebras 08B10 Congruence modularity and generalizations in varieties of algebras 08B15 Lattices of varieties of algebras 08B20 Free algebras in varieties of algebras 08B25 Limits in varieties of algebras 08B26 Subdirect products in varieties of algebras 08B30 Injectives or projectives in varieties of algebras 08B99 Varieties of algebras 08Bxx Varieties of algebras 08C05 Categories of algebras 08C10 Axiomatic model classes 08C15 Quasivarieties 08C99 Classes of algebras 08Cxx Other classes of algebras 1100 Reference works (number theory) 1101 Textbooks (number theory) 1102 Research monographs (number theory) 1103 Historical (number theory) 1104 Machine computation, programs (number theory) 1106 Proceedings of conferences (number theory) 1199 Number theory 11XX Number theory 11A05 Multiplicative structure of the integers 11A07 Congruences, etc. 11A15 Power residues, etc. 11A25 Arithmetic functions, etc. 11A41 Elemementary prime number theory 11A51 Factorization of numbers 11A55 Continued fractions (numbertheoretic results) 11A63 Radix representation 11A67 Representation systems for integers and rationals 11A99 Elementary number theory 11Axx Elementary number theory 11B05 Topology etc. of sets of numbers 11B13 Additive bases 11B25 Arithmetic progressions 11B34 Representation functions 11B37 Recurrences 11B39 Special numbers, etc. 11B50 Sequences (mod m) 11B57 Farey sequences; the sequences 11B65 Binomial coefficients, etc. 11B68 Bernoulli numbers, etc. 11B73 Bell and Stirling numbers 11B75 Combinatorial number theory 11B83 Special sequences of integers and polynomials 11B85 Automata sequences 11B99 Sequences and sets 11Bxx Sequences and sets of numbers 11C08 Polynomials 11C20 Matrices, determinants 11C99 Polynomials and matrices 11Cxx Polynomials and matrices 11D04 Linear diophantine equations 11D09 Quadratic and bilinear diophantine equations 11D25 Cubic and quartic diophantine equations 11D41 Higher degree diophantine equations 11D57 Multiplicative and norm form diophantine equations 11D61 Exponential diophantine equations 11D68 Rational numbers as sums of fractions 11D72 Equations in many variables 11D75 Diophantine inequalities 11D79 Congruences in many variables 11D85 Representation problems of integers 11D88 padic and power series fields 11D99 Diophantine equations 11Dxx Diophantine equations 11E04 Quadratic forms over general fields 11E08 Quadratic forms over local rings and fields 11E10 Forms over real fields 11E12 Quadratic forms over global rings and fields 11E16 General binary quadratic forms 11E20 General ternary and quaternary quadratic forms 11E25 Sums of squares, etc 11E39 Bilinear and Hermitian forms 11E41 Class numbers of quadratic and Hermitian forms 11E45 Analytic theory of forms 11E57 Arithmetic properties of classical groups 11E70 Ktheory of quadratic and Hermitian forms 11E72 Galois cohomology of linear algebraic groups 11E76 Forms of degree higher than two 11E81 Algebraic theory of quadratic forms 11E88 Quadratic spaces; Clifford algebras 11E95 padic theory of forms 11E99 Forms and linear algebraic groups 11Exx Forms and linear algebraic groups 11F03 Modular and automorphic functions 11F06 Structure of modular groups and generalizations 11F11 Modular forms, one variable 11F12 Automorphic forms, one variable 11F20 Dedekind eta function, Dedekind sums 11F22 Relationship of automorphic forms to Lie algebras, etc. 11F25 HeckePetersson operators, differential operators (one variable) 11F27 Theta series; Weil representation 11F30 Fourier coefficients of automorphic forms 11F32 Modular correspondences, etc. 11F33 Congruences for (padic) modular forms 11F37 Forms of halfinteger weight, etc. 11F41 Hilbert modular forms and surfaces 11F46 Siegel modular groups and their modular and automorphic forms 11F55 Groups and their modular and automorphic forms (several variables) 11F60 Differential operators, etc. (several variables) 11F66 Dirichlet series and functional equations related to modular forms 11F67 Special values of automorphic Lseries, etc 11F70 Representationtheoretic methods in automorphic theory 11F72 Spectral theory 11F75 Cohomology of arithmetic groups 11F80 Galois properties 11F85 padic theory, local fields 11F99 Discontinuous groups and automorphic forms 11Fxx Discontinuous groups and automorphic forms 11G05 Elliptic curves over global fields 11G07 Elliptic curves over local fields 11G09 Drinfel'd modules, etc. 11G10 Abelian varieties of dimension >1 11G15 Complex multiplication and moduli of abelian varieties 11G16 Elliptic and modular units 11G18 Arithmetic aspects of modular and Shimura varieties 11G20 Curves over finite and local fields 11G25 Varieties over finite and local fields 11G30 Curves of arbitrary genus 11G35 Varieties over global fields 11G40 Lfunctions of varieties over global fields 11G45 Geometric class field theory 11G99 Arithmetic algebraic geometry 11Gxx Arithmetic algebraic geometry (Diophantine geometry) 11H06 Lattices and convex bodies (number theoretic results) 11H16 Nonconvex bodies 11H31 Lattice packing and covering (numbertheoretic results) 11H46 Products of linear forms 11H50 Minima of forms 11H55 Quadratic forms 11H56 Automorphism groups of lattices 11H60 Mean value and transfer theorems 11H99 Geometry of numbers 11Hxx Geometry of numbers 11J04 Homogeneous approximation to one number 11J06 Markov and Lagrange spectra and generalizations 11J13 Simultaneous homogeneous approximation, linear forms 11J17 Approximation by numbers from a fixed field 11J20 Inhomogeneous linear forms 11J25 Diophantine inequalities 11J54 Small fractional parts of polynomials and generalizations 11J61 Approximation in nonArchimedean valuations 11J68 Approximation to algebraic numbers 11J70 Continued fractions and generalizations 11J71 Distribution modulo one 11J72 Irrationality 11J81 Transcendence (general theory) 11J82 Measures of irrationality and of transcendence 11J83 Metric theory 11J85 Algebraic independence results 11J86 Linear forms in logarithms; Baker's method 11J89 Transcendence theory of elliptic and abelian functions 11J91 Transcendence theory of other special functions 11J99 Diophantine approximation 11Jxx Diophantine approximation 11K06 General theory of distribution modulo 1 11K16 Normal numbers, etc. 11K31 Special sequences 11K36 Welldistributed sequences and other variations 11K38 Irregularities of distribution 11K41 Continuous, padic and abstract analogues 11K45 Pseudorandom numbers, etc. 11K50 Metric theory of continued fractions 11K55 Metric theory of other numbertheoretic algorithms and expansions 11K60 Diophantine approximation (probabilistic number theory) 11K65 Arithmetic functions (probabilistic number theory) 11K70 Harmonic analysis and almost periodicity 11K99 Probabilistic theory 11Kxx Probabilistic number theory 11L03 Trigonometric and exponential sums, general 11L05 Gauss and Kloosterman sums 11L07 Estimates on exponential sums 11L10 Complete character sums 11L15 Weyl sums 11L20 Sums over primes 11L26 Sums over arbitrary intervals 11L40 Estimates on character sums 11L99 Exponential sums and character sums 11Lxx Exponential sums and character sums 11M06 Riemannian zetafunction and Dirichlet Lfunction 11M20 Real zeros of L(s,chi) 11M26 Nonreal zeros of zeta(s) and L(s,chi) 11M35 Other zeta functions 11M36 Selberg zeta functions and regularized determinants 11M41 Other Dirichlet series and zeta functions 11M45 Tauberian theorems 11M99 Analytic theory of zeta and Lfunctions 11Mxx Analytic theory of zeta and Lfunctions 11N05 Distribution of primes 11N13 Primes in progressions 11N25 Distribution of integers with specified multiplicative constraints 11N30 Turan theory 11N32 Primes represented by polynomials 11N35 Sieves 11N36 Appl. of sieve methods 11N37 Asymptotic results on arithmetic functions 11N45 Asymptotic results on counting functions for other structures 11N56 Rate of growth of arithmetic functions 11N60 Distribution functions (additive and positive multipl. functions) 11N64 Characterization of arithmetic functions 11N69 Distribution of integers in special residue classes 11N75 Appl. of automorphic theory to multiplicative problems 11N80 Generalized primes and integers 11N99 Multiplicative number theory 11Nxx Multiplicative number theory 11P05 Waring's problem and variants 11P21 Lattice points in specified regions 11P32 Additive questions involving primes 11P55 Appl. of the HardyLittlewood method 11P81 Elementary theory of partitions 11P82 Analytic theory of partitions 11P83 Partitions: congruences and congruential restrictions 11P99 Additive number theory 11Pxx Additive number theory 11R04 Algebraic numbers 11R06 Special algebraic numbers 11R09 Polynomials over global fields 11R11 Quadratic extensions 11R16 Cubic and quartic extensions 11R18 Cyclotomic extensions 11R20 Other abelian and metabelian extensions 11R21 Other number fields 11R23 Iwasawa theory 11R27 Units and factorization 11R29 Class numbers, class groups, discriminants 11R32 Galois theory for global fields 11R33 Integral representations related to algebraic numbers 11R34 Galois cohomology for global fields 11R37 Class field theory for global fields 11R39 LanglandsWeil conjectures, nonabelian class field theory 11R42 Zeta functions and Lfunctions of global number fields 11R44 Distribution of prime ideals 11R45 Density theorems 11R47 Other analytic theory 11R52 Quaternion and other division algebras: arithmetic, zeta functions 11R54 Other algebras and orders, and their zeta and Lfunctions 11R56 Adele rings and groups 11R58 Arithmetic theory of algebraic function fields 11R65 Class groups and Picard groups of orders 11R70 Ktheory of global fields 11R80 Totally real fields, etc. 11R99 Algebraic number theory over global fields 11Rxx Algebraic number theory: global fields 11S05 Polynomials over local fields 11S15 Ramification and extension theory 11S20 Galois theory for local fields 11S23 Integral representations for local fields 11S25 Galois cohomology for local fields 11S31 Class field theory for local fields 11S37 LanglandsWeil conjectures, nonabelian class field theory 11S40 Zeta functions and Lfunctions of local number fields 11S45 Algebras and orders, and their zeta functions 11S70 Ktheory of local fields 11S80 Other analytic theory of local fields 11S85 Other nonanalytic theory of local fields 11S99 Algebraic number theory over local and padic fields 11Sxx Algebraic number theory: local and padic fields 11T06 Polynomials over finite fields or rings 11T22 Cyclotomy 11T23 Exponential sums 11T24 Other character sums and Gauss sums 11T30 Structure theory of finite fields 11T55 Arithmetic theory of polynomial rings over finite fields 11T71 Algebraic coding theory 11T99 Finite fields and commutative rings (numbertheoretic aspects) 11Txx Finite fields and finite commutative rings (numbertheoretic) 11U05 Decidability related to number theory 11U07 Ultraproducts in number theory 11U09 Connections of number theory with model theory 11U10 Nonstandard arithmetic in number theory 11U99 Connections of number theory with logic 11Uxx Connections of number theory with logic 11Y05 Factorization 11Y11 Primality 11Y16 Algorithms 11Y35 Analytic computations 11Y40 Algebraic number theory computations 11Y50 Computer solution of Diophantine equations 11Y55 Calculation of integer sequences 11Y60 Evaluation of constants 11Y65 Continued fraction calculations 11Y70 Values of arithmetic functions 11Y99 Computational number theory 11Yxx Computational number theory 11Z05 Miscellaneous appl. of number theory 1200 Reference works (field theory) 1201 Textbooks (field theory) 1202 Research monographs (field theory) 1203 Historical (field theory) 1204 Machine computation, programs (field theory) 1206 Proceedings of conferences (field theory) 1299 Field theory and polynomials 12XX Field theory and polynomials 12D05 Factorization of real or complex polynomials 12D10 Algebraic theorems of location of zeros of polynomials over R or C 12D15 Formally real fields 12D99 Real and complex fields 12Dxx Real and complex fields 12E05 Polynomials over general fields 12E10 Special polynomials over general fields 12E12 Algebraic equations 12E15 Skew fields over special fields 12E20 Finite fields (fieldtheoretic aspects) 12E25 Hilbertian fields; Hilbert's irreducibility theorem 12E99 General field theory 12Exx General field theory 12F05 Algebraic extensions 12F10 Galois theory 12F12 Inverse Galois theory 12F15 Inseparable extensions 12F20 Transcendental extensions 12F99 Field extensions 12Fxx Field extensions 12G05 Galois cohomology 12G10 Cohomological dimension 12G99 Homological methods in field theory 12Gxx Homological methods in field theory 12H05 Differential algebra 12H10 Difference algebra 12H20 Abstract differential equations 12H25 padic differential equations 12H99 Differential algebra 12Hxx Differential algebra, etc. 12J05 Normed fields 12J10 Valued fields 12J12 Formally padic fields 12J15 Ordered fields 12J17 Topological semifields 12J20 General valuation theory 12J25 NonArchimedean valued fields 12J27 KrasnerTate algebras 12J99 Topological fields 12Jxx Topological fields 12K05 Nearfields 12K10 Semifields 12K99 Generalizations of fields 12Kxx Generalizations of fields 12L05 Decidability related to field theory 12L10 Ultraproducts in field theory 12L12 Model theory for fields 12L15 Nonstandard arithmetic for fields 12L99 Connections of field theory with logic 12Lxx Connections of field theory with logic 12Y05 Computational aspects of field theory and polynomials 1300 Reference works (commutative rings and algebras) 1301 Textbooks (commutative rings and algebras) 1302 Research monographs (commutative rings and algebras) 1303 Historical (commutative rings and algebras) 1304 Machine computation, programs (commutative rings and algebras) 1306 Proceedings of conferences (commutative rings and algebras) 1399 Commutative rings and algebras 13XX Commutative rings and algebras 13A02 Graded rings 13A05 Divisibility 13A10 Radical theory on commutative rings 13A15 Ideals; multiplicative ideal theory 13A18 Valuations and their generalizations 13A20 Brauer group 13A30 Associated graded rings of ideals and related topics 13A35 Characteristic p methods 13A50 Invariant theory 13A99 General commutative ring theory 13Axx General commutative ring theory 13B02 Extension theory (commutative rings) 13B05 Galois theory (commutative rings) 13B10 Automorphisms, etc. (commutative rings) 13B15 Ramification theory 13B21 Integral dependence 13B22 Integral closure; integrally closed rings, related rings 13B24 Going up; going down; going between 13B25 Polynomials over commutative rings 13B30 Localization 13B35 Completion of rings 13B40 Etale extensions, etc. 13B99 Ring extensions 13Bxx Ring extensions and related topics 13C05 Structure of modules (commutative rings) 13C10 Projective modules, etc. 13C11 Injective modules etc. 13C12 Torsion modules 13C13 Other special types of modules (commutative rings) 13C14 CohenMacaulay modules 13C15 Dimension theory, etc. (commutative rings) 13C20 Class groups 13C40 Linkage, complete intersections and determinantal ideals 13C99 Theory of modules and ideals 13Cxx Theory of modules (commutative rings) 13D02 Syzygies 13D03 (Co)homology of commutative rings and algebras 13D05 Homological dimension (commutative rings) 13D10 Infinitesimal methods, etc. 13D15 Ktheory (commutative rings) 13D25 Complexes 13D30 Torsion theories (commutative rings) 13D40 HilbertSamuel functions and Poincare series 13D45 Local cohomology 13D99 Homological methods (commutative rings) 13Dxx Homological methods (commutative rings) 13E05 Noetherian rings and modules 13E10 Artinian rings and modules 13E15 Rings and modules of finite generation 13E99 Chain conditions, finiteness conditions 13Exx Chain conditions, finiteness conditions 13F05 Dedekind and Pruefer rings and their generalizations 13F07 Euclidean rings and generalizations 13F10 Principal ideal rings 13F15 Factorial rings, unique factorization domains 13F20 Polynomial rings 13F25 Formal power series rings 13F30 Valuation rings 13F40 Excellent rings 13F45 Seminormal rings 13F50 Rings with straightening laws, Hodge algebras 13F99 Arithmetic rings 13Fxx Arithmetic rings 13G05 Integral domains 13H05 Regular local rings 13H10 Special types of local rings 13H15 Multiplicity theory and related topics 13H99 Local rings 13Hxx Local rings and generalizations 13J05 Power series rings 13J07 Analytic algebras and rings 13J10 Complete rings, completion 13J15 Henselian rings 13J20 Global topological rings 13J25 Commutative ordered rings 13J99 Topological rings 13Jxx Topological rings 13K05 Witt vectors and related rings 13L05 Appl. of logic to commutative algebra 13M05 Structure of finite commutative rings 13M10 Polynomials over finite commutative rings 13M99 Finite commutative rings 13Mxx Finite commutative rings 13N05 Differential algebra (commutative algebra) 13N10 Rings of differential operators 13N99 Differential algebra 13Nxx Differential algebra 13P05 Polynomials, factorization 13P10 Polynomial ideals, Groebner bases 13P99 Computational aspects of commutative algebra 13Pxx Computational aspects of commutative algebra 1400 Reference works (algebraic geometry) 1401 Textbooks (algebraic geometry) 1402 Research monographs (algebraic geometry) 1403 Historical (algebraic geometry) 1404 Machine computation, programs (algebraic geometry) 1406 Proceedings of conferences (algebraic geometry) 1499 Algebraic geometry 14XX Algebraic geometry 14A05 Relevant commutative algebra 14A10 Varieties 14A15 Schemes 14A20 Generalizations (algebraic spaces, etc.) 14A22 Noncommutative algebraic geometry, etc. 14A25 Elementary questions of algebraic geometry 14A99 Foundations of algebraic geometry 14Axx Foundations of algebraic geometry 14B05 Singularities (algebraic geometry) 14B07 Deformations of singularities (local theory) 14B10 Infinitesimal methods 14B12 Local deformation theory 14B15 Local cohomology 14B20 Formal neighborhoods 14B99 Local algebraic geometry 14Bxx Local algebraic geometry 14C05 Parametrization 14C10 Equivalence relations (cycles) 14C15 Rational equivalence rings 14C17 Intersection theory 14C20 Divisors, linear systems, invertible sheaves 14C21 Webs, nets 14C22 Picard groups 14C25 Algebraic cycles 14C30 Transcendental methods 14C34 Torelli problem 14C35 Appl. of methods of algebraic Ktheory 14C40 RiemannRoch theorems 14C99 Cycles and subschemes 14Cxx Cycles and subschemes 14D05 Structure of families 14D07 Variation of Hodge structures 14D10 Arithmetic ground fields 14D15 (Formal) deformations 14D20 Algebraic moduli problems 14D22 Fine and coarse moduli spaces 14D25 Geometric invariants 14D99 Families, fibrations 14Dxx Families, fibrations 14E05 Birational correspondences 14E07 Birational automorphisms, Cremona group and generalizations 14E09 Automorphisms 14E10 General correspondences 14E15 Global theory of singularities 14E20 Coverings, fundamental group (mappings) 14E22 Ramification problems 14E25 Embeddings (algebraic varieties) 14E30 Minimal models 14E35 Results in dimension <=1 54F55 Unicoherence, multicoherence 54F65 Topological characterizations of particular spaces 54F99 Special properties of topological spaces 54Fxx Special properties of topological spaces 54G05 Extremally disconnected spaces, etc. 54G10 Pspaces 54G12 Scattered spaces 54G15 Pathological spaces 54G20 Counterexamples (general topology) 54G99 Peculiar topological spaces 54Gxx Peculiar topological spaces 54H05 Descriptive set theory (topological aspects) 54H10 Topological representations of algebraic systems 54H11 Topological groups (topological aspects) 54H12 Topological lattices (topological aspects) 54H13 Topological fields, etc. (topological aspects) 54H15 Transformation groups of topological spaces 54H20 Topological dynamics 54H25 Fixedpoint theorems in topological spaces 54H99 Connections of general topology with other structures 54Hxx Connections of general topology with other structures 54J05 Nonstandard topology 5500 Reference works (algebraic topology) 5501 Textbooks (algebraic topology) 5502 Research monographs (algebraic topology) 5503 Historical (algebraic topology) 5504 Machine computation, programs (algebraic topology) 5506 Proceedings of conferences (algebraic topology) 5599 Algebraic topology 55XX Algebraic topology 55M05 Topological duality 55M10 Dimension theory (algebraic topology) 55M15 Absolute neighborhood retracts 55M20 Fixed points and coincidences (algebraic topology) 55M25 Degree, etc. 55M30 LyusternikShnirel'man category of a space 55M35 Finite groups of transformations 55M99 Classical algebraic topology 55Mxx Classical topics of algebraic topology 55N05 Cech types 55N07 SteenrodSitnikov homologies 55N10 Singular theory 55N15 Ktheory (algebraic topology) 55N20 Generalized homology and cohomology theories 55N22 Bordism and cobordism theories, etc. 55N25 Homology with local coefficients, equivariant cohomology 55N30 Sheaf cohomology 55N33 Intersection homology and cohomology 55N35 Other homology theories 55N40 Axioms for homology theory and uniqueness theorems 55N45 Products and intersections 55N91 Equivariant homology and cohomology 55N99 Homology and cohomology theories 55Nxx Homology and cohomology theories 55P05 Homotopy extension properties, cofibrations 55P10 Homotopy equivalences 55P15 Classification of homotopy type 55P20 EilenbergMacLane spaces 55P25 SpanierWhitehead duality 55P30 EckmannHilton duality 55P35 Loop spaces 55P40 Suspensions 55P42 Stable homotopy theory 55P45 Hspaces and duals 55P47 Infinite loop spaces 55P50 Category and cocategory 55P55 Shape theory 55P60 Localization and completion 55P62 Rational homotopy theory 55P65 Homotopy functors 55P91 Equivariant homotopy theory 55P99 Homotopy theory 55Pxx Homotopy theory 55Q05 General theory of homotopy groups 55Q07 Shape groups 55Q10 Stable homotopy groups 55Q15 Whitehead products and generalizations 55Q20 Homotopy groups of wedges, etc. 55Q25 Hopf invariants 55Q30 Homotopy groups of triads, nads 55Q35 Operations in homotopy groups 55Q40 Homotopy groups of spheres 55Q45 Stable homotopy of spheres 55Q50 Jmorphism 55Q52 Homotopy groups of special spaces 55Q55 Cohomotopy groups 55Q70 Homotopy groups of special types 55Q91 Equivariant homotopy groups 55Q99 Homotopy groups 55Qxx Homotopy groups 55R05 Fiber spaces 55R10 Fiber bundles 55R12 Transfer 55R15 Classification 55R20 Spectral sequences and homology of fiber spaces 55R25 Sphere bundles and vector space bundles 55R35 Classifying spaces of groups and Hspaces 55R40 Homology of classifying spaces, characteristic classes 55R45 Homology and homotopy of BO and BU 55R50 Stable classes of vector space bundles, Ktheory 55R55 Fiberings with singularities 55R60 Microbundles and block bundles 55R65 Generalizations of fiber spaces and bundles 55R91 Equivariant fiber spaces and bundles 55R99 Fiber spaces and bundles 55Rxx Fiber spaces and bundles 55S05 Primary cohomology operations 55S10 Steenrod algebra 55S12 DyerLashof operations 55S15 Symmetric products, etc. 55S20 Secondary and higher cohomology operations 55S25 Ktheory operations and generalized cohomology operations 55S30 Massey products 55S35 Obstruction theory 55S36 Extension and compression of mappings 55S37 Classification of mappings 55S40 Sectioning fiber spaces and bundles 55S45 Postnikov system, kinvariants 55S91 Equivariant operations and obstructions 55S99 Operations and obstructions 55Sxx Operations and obstructions 55T05 General spectral sequences 55T10 Serre spectral sequences 55T15 Adams spectral sequences 55T20 EilenbergMoore spectral sequences 55T25 Generalized cohomology 55T99 Spectral sequences 55Txx Spectral sequences 55U05 Abstract complexes 55U10 Semisimplicial complexes 55U15 Chain complexes 55U20 Universal coefficient theorems, Bockstein operator 55U25 Homology of a product, Kuenneth formula 55U30 Duality (applied homological algebra) 55U35 Abstract homotopy theory 55U40 Topological categories 55U99 Applied homological algebra and category theory 55Uxx Applied homological algebra and category theory 5700 Reference works (manifolds) 5701 Textbooks (manifolds) 5702 Research monographs (manifolds) 5703 Historical (manifolds) 5704 Machine computation, programs (manifolds) 5706 Proceedings of conferences (manifolds) 5799 Manifolds and cell complexes 57XX Manifolds and cell complexes 57M05 Fundamental group, etc. 57M07 Topological methods in group theory 57M10 Covering spaces 57M12 Special coverings 57M15 Relations with graph theory 57M20 Twodimensional complexes 57M25 Knots and links in the 3sphere 57M30 Wild knots and surfaces, wild imbeddings 57M35 Dehn's lemma, sphere theorem, loop theorem, asphericity 57M40 Characterizations of Euclidean 3space and 3sphere 57M50 Geometric structures on lowdimensional manifolds 57M60 Group actions in low dimensions 57M99 Lowdimensional topology 57Mxx Lowdimensional topology 57N05 Topology of Euclidean 2space, 2manifolds 57N10 Topology of general 3manifolds 57N12 Topology of Euclidean 3space and 3sphere 57N13 Topology of Euclidean 4space, 4manifolds 57N15 Topology of Euclidean nspace, nmanifolds 57N17 Topology of topological vector spaces 57N20 Topology of infinitedimensional manifolds 57N25 Shapes 57N30 Engulfing 57N35 Imbeddings and immersions (topological manifolds) 57N37 Isotopy and pseudoisotopy 57N40 Neighborhoods of submanifolds 57N45 Flatness and tameness 57N50 (n1)sphere in Euclidean nspace 57N55 Microbundles and block bundles 57N60 Cellularity 57N65 Algebraic topology of manifolds 57N70 Cobordism and concordance 57N75 General position and transversality 57N80 Stratifications 57N99 Topological manifolds 57Nxx Topological manifolds 57P05 Local properties of generalized manifolds 57P10 Poincare duality spaces 57P99 Generalized manifolds 57Pxx Generalized manifolds 57Q05 General topology of complexes 57Q10 Simple homotopy type, etc. 57Q12 Wall finiteness obstruction for CWcomplexes 57Q15 Triangulating manifolds 57Q20 Cobordism (PLtopology) 57Q25 Comparison of PLstructures 57Q30 Engulfing (PLtopology) 57Q35 Imbeddings and immersions (PLtopology) 57Q37 Isotopy (PLtopology) 57Q40 Regular neighborhoods 57Q45 Knots and links in high dimensions (PLtopology) 57Q50 Microbundles and block bundles (PLtopology) 57Q55 Approximations (PLtopology) 57Q60 Cobordism and concordance (PLtopology) 57Q65 General position and transversality (PLtopology) 57Q91 Equivariant PLtopology 57Q99 PLtopology 57Qxx PLtopology 57R05 Triangulating 57R10 Smoothing 57R12 Smooth approximations 57R15 Specialized structures on manifolds 57R19 Algebraic topology on manifolds 57R20 Characteristic classes and numbers 57R22 Topology of vector bundles and fiber bundles 57R25 Vector fields, frame fields 57R27 Controllability of vector fields on Cinfinity (etc.) manifolds 57R30 Foliations; geometric theory 57R32 Classifying spaces for foliations 57R35 Differentiable mappings (differential topology) 57R40 Imbeddings (differential topology) 57R42 Immersions (differential topology) 57R45 Singularities of differentiable mappings 57R50 Diffeomorphisms 57R52 Isotopy (differential topology) 57R55 Differentiable structures 57R57 Appl. of global analysis to structures on manifolds 57R60 Homotopy spheres, Poincare conjecture 57R65 Surgery and handlebodies 57R67 Surgery obstructions, Wall groups 57R70 Critical points and critical submanifolds 57R75 O and SOcobordism 57R77 Complex cobordism (U and SUcobordism) 57R80 h and scobordism 57R85 Equivariant cobordism 57R90 Other types of cobordism 57R91 Equivariant algebraic topology of manifolds 57R95 Realizing cycles by submanifolds 57R99 Differential topology 57Rxx Differential topology 57S05 Topological properties of groups of homeomorphisms, etc. 57S10 Compact groups of homeomorphisms 57S15 Compact Lie groups of differentiable transformations 57S17 Finite transformation groups 57S20 Noncompact Lie groups of transformations 57S25 Groups acting on specific manifolds 57S30 Discontinuous groups of transformations 57S99 Topological transformation groups 57Sxx Topological transformation groups 57T05 Hopf algebras 57T10 Homology and cohomology of Lie groups 57T15 Homology and cohomology of homogeneous spaces of Lie groups 57T20 Homotopy groups of topological groups and homogeneous spaces 57T25 Homology and cohomology of Hspaces 57T30 Bar and cobar constructions 57T35 Appl. of EilenbergMoore spectral sequences 57T99 Homology and homotopy of topological groups 57Txx Homology and homotopy of topological groups and related structures 5800 Reference works (global analysis) 5801 Textbooks (global analysis) 5802 Research monographs (global analysis) 5803 Historical (global analysis) 5804 Machine computation, programs (global analysis) 5806 Proceedings of conferences (global analysis) 5899 Global analysis, analysis on manifolds 58XX Global analysis 58A03 Topostheoretic approach to differential manifolds 58A05 Foundations of differentiable manifolds 58A07 Realanalytic manifolds, etc. 58A10 Differential forms 58A12 de Rham theory (global analysis) 58A14 Hodge theory (global analysis) 58A15 Exterior differential systems (Cartan theory) 58A17 Pfaffian systems 58A20 Jets 58A25 Currents (global analysis) 58A30 Vector distributions (global analysis) 58A35 Stratified sets (global analysis) 58A40 Differential spaces (global analysis) 58A50 Supermanifolds, etc. (global analysis) 58A99 General theory of differentiable manifolds 58Axx General theory of differentiable manifolds 58B05 Topological questions of infinitedimensional manifolds 58B10 Differentiability questions in infinitedimensional manifolds 58B12 Questions of holomorphy in infinitedimensional manifolds 58B15 Fredholm structures on infinitedimensional manifolds 58B20 Geometric structures on infinitedimensional manifolds 58B25 Group structures and generalizations on infinitedim. manifolds 58B30 Noncommutative differential geometry and topology 58B99 Infinitedimensional manifolds 58Bxx Infinitedimensional manifolds 58C05 Realvalued functions on manifolds 58C06 Setvalued mappings etc. on manifolds 58C07 Continuity properties of mappings on manifolds 58C10 Holomorphic maps on manifolds (global analysis) 58C15 Implicit function theorems etc. on manifolds 58C20 Generalized differentiation theory on manifolds 58C25 Differentiable maps on manifolds (global analysis) 58C27 Singularities of differentiable maps on manifolds 58C28 Catastrophes 58C30 Fixed point theorems on manifolds 58C35 Integration on manifolds 58C40 Spectral theory on manifolds 58C50 Analysis on supermanifolds, etc. 58C99 Calculus on manifolds 58Cxx Calculus on manifolds 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 58D07 Groups and semigroups of nonlinear operators 58D10 Spaces of imbeddings and immersions 58D15 Manifolds of mappings 58D17 Manifolds of metrics 58D19 Global group actions and symmetry properties on manifolds 58D20 Measures on manifolds of maps 58D25 Differential equations in function spaces 58D27 Moduli problems for diff.geometric structures on spaces of mappings 58D29 Moduli problems for topological structures on manifolds of mappings 58D30 Spaces and manifolds of mappings in appl. to physics 58D99 Spaces and manifolds of mappings 58Dxx Spaces and manifolds of mappings 58E05 Abstract critical point theory 58E07 Abstract bifurcation theory 58E09 Groupinvariant bifurcation theory 58E10 Appl. of bifurcation theory to geodesics 58E11 Critical metrics in infinitedimensional spaces 58E12 Appl. of variational methods to minimal surfaces 58E15 Appl. of variational methods to extremal problems in sev.variables 58E17 Pareto optimality, etc., appl. to economics 58E20 Harmonic maps between infinitedimensional spaces 58E25 Appl. of variational methods to control theory 58E30 Variational principles on infinitedimensional spaces 58E35 Variational inequalities (global problems) 58E46 Variational problems under group actions on infinitedim. spaces 58E50 Appl. of variational methods in infinitedimensional spaces 58E99 Variational problems in infinitedimensional spaces 58Exx Variational problems in infinitedimensional spaces 58F03 Onedimensional dynamics, general; symbolic dynamics 58F05 Hamiltonian and Lagrangian systems on manifolds 58F06 Geometric quantization (appl. of representation theory) 58F07 Completely integrable dynamical systems 58F08 Pointmapping properties, iterations, completeness (dyn. systems) 58F09 MorseSmale systems 58F10 Stability theory of ODE on manifolds 58F11 Ergodic theory of dynamical systems on manifolds 58F12 Structure of attractors 58F13 Pathologies of dynamical systems 58F14 Bifurcation theory and singularities of dynamical systems 58F15 Hyperbolic structures of dynamical systems 58F17 Geodesic and horocycle flows 58F18 Relations of dynamical systems with foliations 58F19 Eigenvalue and spectral problems of ODE on manifolds 58F20 Periodic points, etc. (dynamical systems) 58F21 Limit cycles, etc. of ODE on manifolds 58F22 Periodic solutions of ODE on manifolds 58F23 Holomorphic flows 58F25 Flows on manifolds (general aspects) 58F27 Quasiperiodic flows 58F30 Perturbations of dynamical systems 58F32 Functionaldifferential equations on manifolds 58F35 Invariance properties (ODE on manifolds) 58F36 Normal forms for ODE or diffeomorphisms 58F37 Correspondences and other transformation methods (ODE on manifolds) 58F39 Dynamical systems treatment of PDE 58F40 Appl. of ODE on manifolds to physics 58F99 ODE on manifolds and dynamical systems 58Fxx Ordinary differential equations on manifolds; dynamical systems 58G03 Elliptic equations on manifolds; general theory 58G05 Differential complexes on manifolds; elliptic complexes 58G07 Hyperfunctions on manifolds 58G10 Index theory and fixed point theorems (global analysis) 58G11 Heat and other parabolic equation methods (global analysis) 58G12 Exotic index theories (global analysis) 58G15 Pseudodifferential and Fourier integral operators on manifolds 58G16 Hyperbolic equations on manifolds 58G17 Propagation of singularities (PDE on manifolds) 58G18 Perturbations and asymptotics (PDE on manifolds) 58G20 Boundary value problems of PDE on manifolds 58G25 Spectral problems of PDE on manifolds, etc. 58G26 Determinants and determinant bundles on manifolds 58G28 Bifurcations (PDE on manifolds) 58G30 Relations of PDE with special manifold structures 58G32 Diffusion processes and stochastic analysis on manifolds 58G35 Invariance properties (PDE on manifolds) 58G37 Correspondences and other transformation methods (PDE on manifolds) 58G40 Appl. of PDE on manifolds to physics 58G99 Partial differential equations on manifolds 58Gxx Partial differential equations on manifolds; differential operators 58H05 Pseudogroups on manifolds 58H10 Cohomology of classifying spaces for pseudogroup structures 58H15 Global deformations of structures on manifolds 58H99 Pseudogroups and general structures on manifolds 58Hxx Pseudogroups and general structures on manifolds 58Z05 Appl. of global analysis to physics 6000 Reference works (probability theory) 6001 Textbooks (probability theory) 6002 Research monographs (probability theory) 6003 Historical (probability theory) 6004 Machine computation, programs (probability theory) 6006 Proceedings of conferences (probability theory) 6099 Probability theory and stochastic processes 60XX Probability theory and stochastic processes 60A05 Axioms of probability theory 60A10 Probabilistic measure theory 60A99 Foundations of probability theory 60Axx Foundations of probability theory 60B05 Probability measures on topological spaces 60B10 Convergence of probability measures 60B11 Probability theory on linear topological spaces 60B12 Limit theorems for vectorvalued random variables (inf.dim.case) 60B15 Probability measures on groups 60B99 Probability theory on general structures 60Bxx Probability theory on general structures 60C05 Combinatorial probability 60D05 Geometric probability 60E05 General theory of probability distributions 60E07 Infinitely divisible distributions 60E10 Transforms of probability distributions 60E15 Inequalities in probability theory 60E99 Distribution theory in probability theory 60Exx Distribution theory in probability theory 60F05 Weak limit theorems 60F10 Large deviations 60F15 Strong limit theorems 60F17 Functional limit theorems 60F20 Zeroone laws 60F25 Lplimit theorems (probability) 60F99 Limit theorems (probability) 60Fxx Limit theorems (probability) 60G05 Foundations of stochastic processes 60G07 General theory of stochastic processes 60G09 Exchangeability 60G10 Stationary processes 60G12 General second order processes 60G15 Gaussian processes 60G17 Sample path properties 60G18 Selfsimilar processes 60G20 Generalized stochastic processes 60G25 Prediction theory 60G30 Induced measures of stochastic processes 60G35 Appl. of stochastic processes 60G40 Optimal stopping 60G42 Martingales with discrete parameter 60G44 Martingales with continuous parameter 60G46 Martingales and classical analysis 60G48 Generalizations of martingales 60G50 Sums of independent random variables 60G55 Point processes 60G57 Random measures 60G60 Random fields 60G70 Extreme value theory (probability) 60G99 Stochastic processes 60Gxx Stochastic processes 60H05 Stochastic integrals 60H07 Stochastic calculus of variations and the Malliavin calculus 60H10 Stochastic ordinary differential equations 60H15 Stochastic partial differential equations 60H20 Stochastic integral equations 60H25 Random operators, etc. 60H30 Appl. of stochastic analysis 60H99 Stochastic analysis 60Hxx Stochastic analysis 60J05 Markov processes with discrete parameter 60J10 Markov chains with discrete parameter 60J15 Random walk 60J20 Appl. of discrete Markov processes 60J25 Markov processes with continuous parameter 60J27 Markov chains with continuous parameter 60J30 Markov processes with independent increments 60J35 Transition functions 60J40 Right processes 60J45 Probabilistic potential theory 60J50 Boundary theory (probability) 60J55 Additive functionals 60J57 Multiplicative functionals 60J60 Diffusion processes 60J65 Brownian motion 60J70 Appl. of diffusion theory 60J75 Jump processes 60J80 Branching processes 60J85 Appl. of branching processes 60J99 Markov processes 60Jxx Markov processes 60K05 Renewal theory 60K10 Appl. of renewal theory 60K15 Markov renewal processes 60K20 Appl. of Markov renewal processes 60K25 Queueing theory 60K30 Appl. of queueing theory 60K35 Interacting random processes 60K40 Physical appl. of random processes 60K99 Special processes 60Kxx Special processes 6200 Reference works (statistics) 6201 Textbooks (statistics) 6202 Research monographs (statistics) 6203 Historical (statistics) 6204 Machine computation, programs (statistics) 6206 Proceedings of conferences (statistics) 6207 Data analysis (statistics) 6209 Graphical methods in statistics 6299 Statistics 62XX Statistics 62A05 Invariance and group considerations in statistics 62A10 The likelihood approach 62A15 The Bayesian approach 62A20 Classical approach in statistics 62A25 Structural approach in statistics 62A30 The fiducial approach 62A99 Foundations of statistics 62Axx Foundations of statistics 62B05 Sufficient statistics 62B10 Statistical information theory 62B15 Comparison of statistical experiments 62B20 Measuretheoretic results in statistics 62B99 Statistical sufficiency and information 62Bxx Statistical sufficiency and information 62C05 General considerations in statistical decision theory 62C07 Complete class results in statistical decision theory 62C10 Bayesian problems 62C12 Empirical statistical decision procedures 62C15 statistical admissibility 62C20 Statistical minimax procedures 62C25 Compound decision problems in statistics 62C99 Statistical decision theory 62Cxx Statistical decision theory 62D05 Statistical sampling theory 62E10 Structure theory of statistical distributions 62E15 Exact distribution theory in statistics 62E17 Approximations to statistical distributions (nonasymptotic) 62E20 Asymptotic distribution theory in statistics 62E25 Statistical Monte Carlo studies (distribution theory) 62E30 Formal computational methods for statistical distributions 62E99 Statistical distribution theory 62Exx Statistical distribution theory 62F03 Parametric hypothesis testing 62F04 Small sample properties of parametric tests 62F05 Asymptotic properties of parametric tests 62F07 Statistical ranking and selection procedures 62F10 Point estimation 62F11 Small sample properties of parametric estimators 62F12 Asymptotic properties of parametric estimators 62F15 Bayesian inference 62F25 Parametric confidence regions, etc. 62F30 Statistical inference under constraints 62F35 Robustness and adaptive procedures 62F99 Parametric inference 62Fxx Parametric inference 62G05 Nonparametric estimation 62G07 Curve estimation 62G09 Statistical resampling methods 62G10 Nonparametric hypothesis testing 62G15 Nonparametric confidence regions, etc. 62G20 Nonparametric asymptotic efficiency 62G30 Order statistics, etc. 62G35 Nonparametric robustness 62G99 Nonparametric inference 62Gxx Nonparametric inference 62H05 Multivariate structure theory 62H10 Multivariate distributions of statistics 62H11 Directional data; spatial statistics 62H12 Multivariate estimation 62H15 Multivariate hypothesis testing 62H17 Contingency (statistics) 62H20 Statistical measures of associations 62H25 Factor analysis, etc. 62H30 Statistical classification, etc. 62H40 Projection pursuit 62H99 Multivariate analysis 62Hxx Multivariate analysis 62J02 General nonlinear regression 62J05 Linear regression 62J07 Ridge regression 62J10 Analysis of variance, etc. 62J12 Generalized linear models 62J15 Multiple comparisons 62J20 Regression diagnostics 62J99 Linear statistical inference 62Jxx Linear statistical inference 62K05 Optimal statistical designs 62K10 Statistical block designs 62K15 Factorial statistical designs 62K99 Experimental statistical design 62Kxx Experimental statistical design 62L05 Sequential statistical designs 62L10 Sequential statistical analysis 62L12 Sequential estimation 62L15 Optimal stopping (statistics) 62L20 Stochastic approximation 62L99 Sequential statistical methods 62Lxx Sequential statistical methods 62M02 Markov processes: hypothesis testing 62M05 Markov processes: estimation 62M07 NonMarkovian processes: hypothesis testing 62M09 NonMarkovian processes: estimation 62M10 Time series, etc. (statistics) 62M15 Spectral analysis of processes 62M20 Prediction, etc. (statistics) 62M30 Statistics of spatial processes 62M40 Statistics of random fields 62M99 Inference from stochastic processes 62Mxx Inference from stochastic processes 62N05 Reliability, etc. (statistics) 62N10 Statistical quality control 62N99 Engineering statistics 62Nxx Engineering statistics 62P05 Appl. of statistics to actuarial sciences and financial mathematics 62P10 Appl. of statistics to biology 62P15 Appl. of statistics to psychology 62P20 Appl. of statistics to economics 62P25 Appl. of statistics to social sciences 62P99 Appl. of statistics 62Pxx Appl. of statistics 62Q05 Statistical tables 6500 Reference works (numerical analysis) 6501 Textbooks (numerical analysis) 6502 Research monographs (numerical analysis) 6503 Historical (numerical analysis) 6504 Machine computation, programs (numerical analysis) 6505 Experimental papers 6506 Proceedings of conferences (numerical analysis) 6599 Numerical analysis 65XX Numerical analysis 65A05 Tables 65B05 Extrapolation to the limit 65B10 Summation of series 65B15 EulerMaclaurin formula 65B99 Acceleration of convergence 65Bxx Acceleration of convergence 65C05 Monte Carlo methods 65C10 Random number generation 65C20 Models (numerical methods) 65C99 Numerical simulation 65Cxx Numerical simulation 65D05 Interpolation (numerical methods) 65D07 Splines (numerical methods) 65D10 Smoothing 65D15 Algorithms for functional approximation 65D17 Computer aided design (modeling of curves and surfaces) 65D20 Computation of special functions 65D25 Numerical differentiation 65D30 Numerical integration 65D32 Quadrature formulas (numerical methods) 65D99 Numerical approximation 65Dxx Numerical approximation 65E05 Numerical methods in complex analysis 65F05 Direct methods for linear systems 65F10 Iterative methods for linear systems 65F15 Eigenvalues (numerical linear algebra) 65F20 Overdetermined systems (numerical linear algebra) 65F25 Orthogonalization (numerical linear algebra) 65F30 Other matrix algorithms 65F35 Matrix norms, etc. (numerical linear algebra) 65F40 Determinants (numerical linear algebra) 65F50 Sparse matrices 65F99 Numerical linear algebra 65Fxx Numerical linear algebra 65G05 Roundoff error 65G10 Interval arithmetic 65G99 Error analysis 65Gxx Error analysis 65H05 Single nonlinear equations (numerical methods) 65H10 Systems of nonlinear equations (numerical methods) 65H17 Eigenvalue and bifurcation problems of nonlinear algebraic equations 65H20 Global methods, including homotopy approaches 65H99 Nonlinear algebraic or transcendental equations 65Hxx Nonlinear algebraic or transcendental equations 65J05 General theory of numerical methods in abstract spaces 65J10 Equations with linear operators (numerical methods) 65J15 Equations with nonlinear operators (numerical methods) 65J20 Improperly posed problems (numerical methods in abstract spaces) 65J99 Numerical analysis in abstract spaces 65Jxx Numerical analysis in abstract spaces 65K05 Mathematical programming (numerical methods) 65K10 Optimization techniques (numerical methods) 65K99 Numerical methods for mathematical programming and optimization 65Kxx Numerical methods in mathematical programming and optimization 65L05 Initial value problems for ODE (numerical methods) 65L06 Multistep, RungeKutta, and extrapolation methods 65L07 Numerical investigation of stability of solutions of ODE 65L08 Improperly posed problems for ODE (numerical methods) 65L10 Boundary value problems for ODE (numerical methods) 65L12 Finite difference methods for ODE 65L15 Eigenvalue problems for ODE (numerical methods) 65L20 Stability of numerical methods for ODE 65L50 Mesh generation and refinement (ODE) 65L60 Finite numerical methods for ODE 65L70 Error bounds (numerical methods for ODE) 65L99 Numerical methods for ODE 65Lxx Numerical methods for ODE 65M06 Finite difference methods (IVP of PDE) 65M12 Stability and convergence of numerical methods (IVP of PDE) 65M15 Error bounds (IVP of PDE) 65M20 Method of lines (IVP of PDE) 65M25 Method of characteristics (numerical) 65M30 Improperly posed problems (IVP of PDE, numerical methods) 65M50 Mesh generation and refinement (IVP of PDE) 65M55 Multigrid methods; domain decomposition (IVP of PDE) 65M60 Finite numerical methods (IVP of PDE) 65M70 Spectral, collocation and related methods (IVP of PDE) 65M99 Numerical methods for IVP of PDE 65Mxx Numerical methods for initial value problems (IVP) of PDE 65N06 Finite difference methods (BVP of PDE) 65N12 Stability and convergence of numerical methods (BVP of PDE) 65N15 Error bounds (BVP of PDE) 65N22 Solution of discretized equations (BVP of PDE) 65N25 Numerical methods for eigenvalue problems (BVP of PDE) 65N30 Finite numerical methods (BVP of PDE) 65N35 Collocation methods (BVP of PDE) 65N38 Boundary element methods (BVP of PDE) 65N40 Methods of lines (BVP of PDE) 65N45 Method of contraction of the boundary (BVP of PDE) 65N50 Mesh generation and refinement (BVP of PDE) 65N55 Multigrid methods; domain decomposition (BVP of PDE) 65N99 Numerical methods for BVP of PDE 65Nxx numerical methods for boundary value problems (BVP) of PDE 65P05 Numerical methods for miscellaneous problems of PDE 65Q05 Numerical methods for functional equations 65R10 Integral transforms (numerical methods) 65R20 Integral equations (numerical methods) 65R30 Improperly posed problems (integral equations, numerical methods) 65R99 Numerical methods for integral equations and transforms 65Rxx Numerical methods for integral equations and transforms 65S05 Graphical methods of numerical analysis 65T05 Numerical methods in harmonic analysis 65T10 Discrete and fast Fourier transforms 65T99 Numerical methods in Fourier analysis 65Txx Numerical methods in Fourier analysis 65U05 Numerical methods in probability and statistics 65Y05 Parallel computation (numerical methods) 65Y10 Algorithms for specific classes of architectures 65Y15 Packaged methods 65Y20 Complexity and performance of numerical algorithms 65Y25 Computer graphics and computational geometry 65Y99 Computer aspects of numerical algorithms 65Yxx Computer aspects of numerical algorithms 6800 Reference works (computer science) 6801 Textbooks (computer science) 6802 Research monographs (computer science) 6803 Historical (computer science) 6804 Machine computation, programs (computer science) 6806 Proceedings of conferences (computer science) 6899 Computer science 68XX Computer science 68M05 Computer system organization (general aspects) 68M07 Mathematical problems of computer architectures 68M10 Computer networks 68M15 Reliability and testing of computer systems 68M20 Performance evaluation of computer systems, etc. 68M99 Computer system organization 68Mxx Computer system organization 68N05 General theory of programming 68N15 Programming languages 68N17 Logic programming 68N20 Compilers and generators 68N25 Monitors and operating systems 68N99 Software 68Nxx Software 68P05 Data structures 68P10 Searching and sorting 68P15 Database theory 68P20 Information storage and retrieval 68P25 Data encryption 68P99 Theory of data 68Pxx Theory of data 68Q05 Models of computation 68Q10 Modes of computation 68Q15 Complexity classes of computation 68Q20 Nonnumerical algorithms 68Q22 Parallel and distributed algorithms 68Q25 Analysis of algorithms and problem complexity 68Q30 Algorithmic information theory 68Q35 VLSI algorithms 68Q40 Symbolic computation, algebraic computation 68Q42 Rewriting systems 68Q45 Formal languages 68Q50 Grammars 68Q52 Parsing 68Q55 Semantics 68Q60 Specification and verification of programs 68Q65 Abstract data types; algebraic specification 68Q68 Automata theory, general 68Q70 Algebraic theory of automata 68Q75 Stochastic and nondeterministic automata 68Q80 Cellular and array automata 68Q90 Transition nets 68Q99 Theory of computing 68Qxx Theory of computing 68R05 Combinatorics in connection with computer science 68R10 Graph theory in connection with computer science 68R15 Combinatorics on words 68R99 Discrete mathematics in relation to computer science 68Rxx Discrete mathematics in relation to computer science 68S05 Mathematical linguistics 68T01 Artificial intelligence (general aspects) 68T05 Learning and adaptive systems 68T10 Pattern recognition 68T15 Theorem proving 68T20 Problem solving 68T25 AI languages 68T27 AI logics 68T30 Knowledge representation 68T35 AI software systems 68T99 Artificial intelligence 68Txx Artificial intelligence 68U05 Computational geometry, etc. 68U07 Computer aided design 68U10 Image processing 68U15 Text processing 68U20 Simulation 68U30 Miscellaneous appl. of computers 68U99 Computing methodologies 68Uxx Computing methodologies 7000 Reference works (mechanics of particles and systems) 7001 Textbooks (mechanics of particles and systems) 7002 Research monographs (mechanics of particles and systems) 7003 Historical (mechanics of particles and systems) 7004 Machine computation, programs (mechanics of particles and systems) 7005 Experimental papers (mechanics of particles and systems) 7006 Proceedings of conferences (mechanics of particles and systems) 7008 Computational methods (mechanics of particles and systems) 7099 Mechanics of particles and systems 70XX Mechanics of particles and systems 70A05 Axiomatics, foundations (general mechanics) 70B05 Kinematics of particle 70B10 Kinematics of a rigid body 70B15 Mechanisms 70B99 Kinematics 70Bxx Kinematics 70C20 Statics 70D05 Newtonian dynamics 70D10 Lagrangian dynamics 70D99 Dynamics of a particle 70Dxx Dynamics of a particle 70E05 Motion of the gyroscope 70E10 Motion of streamlined bodies 70E15 Motion of rigid bodies 70E20 Perturbation methods for Euler's equations 70E99 Dynamics of a rigid body 70Exx Dynamics of a rigid body 70F05 Twobody problem 70F07 Threebody problem 70F10 nbody problem 70F15 Celestial mechanics 70F20 Holonomic systems 70F25 Nonholonomic systems 70F30 Impulsive motion 70F35 Collisions 70F99 Dynamics of a system of particles 70Fxx Dynamics of a system of particles 70G05 Geometrical methods in general mechanics 70G10 Generalized coordinates 70G15 Space of events 70G20 Impulseenergy space 70G25 Configuration space 70G30 State space 70G35 Phase space 70G50 Classical field theories (general) 70G99 General representations of dynamical systems 70Gxx General representations of dynamical systems 70H05 Hamilton's equations 70H10 Liouville's theorem 70H15 Canonical transformations 70H20 HamiltonJacobi equations 70H25 Hamilton's principle 70H30 Other variational principles (general mechanics) 70H33 Symmetries 70H35 Lagrange's equation of motion 70H40 Relativistic dynamics 70H99 Hamiltonian and Lagrangian mechanics 70Hxx Hamiltonian and Lagrangian mechanics 70J05 Linear vibrations of finite degree of freedom systems 70J10 Normal modes of linear vibrations 70J25 Stability of linear oscillatory motions 70J30 Free motions, etc. 70J35 Forced motions 70J40 Parametric resonances 70J99 Linear vibration theory 70Jxx Linear vibration theory (general mechanics) 70K05 Phase plane analysis (general mechanics) 70K10 Limit cycles (general mechanics) 70K15 Lyapunov theorems (general mechanics) 70K20 Stability of nonlinear oscillations (general mechanics) 70K25 Free motions 70K28 Parametric resonances 70K30 Nonlinear resonances (general mechanics) 70K40 Forced motions (general mechanics) 70K50 Transition to stochasticity (general mechanics) 70K99 Nonlinear motions 70Kxx Nonlinear oscillations (general mechanics) 70L05 Random vibrations (general mechanics) 70M20 Orbital mechanics 70P05 Variable mass 70Q05 Control of mechanical systems 7300 Reference works (mechanics of solids) 7301 Textbooks (mechanics of solids) 7302 Research monographs (mechanics of solids) 7303 Historical (mechanics of solids) 7304 Machine computation, programs (mechanics of solids) 7305 Experimental papers (mechanics of solids) 7306 Proceedings of conferences (mechanics of solids) 7399 Mechanics of solids 73XX Mechanics of solids 73A05 Axiomatics, foundations of solid mechanics 73B05 Constitutive equations (mechanics of solids) 73B10 symmetry groups (mechanics of solids) 73B18 Nonlocal theories 73B25 Polar theories 73B27 Nonhomogeneous materials. Homogenization 73B30 Thermodynamics of solids 73B35 Random materials (mechanics of solids) 73B40 Anisotropic materials 73B50 Stress concentrations 73B99 Continuum mechanics 73Bxx Continuum mechanics (mechanics of solids) 73C02 Classical linear elasticity 73C05 Stress functions (elasticity) 73C10 SaintVenant's principle 73C15 Uniqueness theorems in elasticity 73C35 Mixed boundary value problems in elasticity 73C50 Nonlinear elasticity 73C99 Elasticity 73Cxx Elasticity 73D05 Shock waves (mechanics of solids) 73D10 Integral transforms in solid mechanics 73D15 Body waves 73D20 Surface waves 73D25 Wave diffraction, etc. (mechanics of solids) 73D30 Linear vibrations of solids 73D35 Nonlinear vibrations of solids 73D40 Singular surfaces 73D50 Inverse problems in mechanics of solids 73D70 Random waves in mechanics of solids 73D99 Wave propagation in and vibrations of solids 73Dxx Wave propagation in and vibrations of solids 73E05 Constitutive specifications (Yield, flow, hardening) 73E10 Method of successive approximations in plasticity 73E20 Limit analysis in plasticity 73E50 Timedependent problems in plasticity 73E60 Viscoplasticity 73E70 Plastic waves 73E99 Plasticity 73Exx Plasticity 73F05 Response functions in viscoelasticity 73F10 Correspondence principle in viscoelasticity 73F15 Timedependent boundary value problems in viscoelasticity 73F20 Aging of materials 73F25 Environmentaldependent materials 73F99 Viscoelasticity 73Fxx Viscoelasticity 73G05 Finite elasticity 73G20 Finite plasticity 73G25 Finite viscoelasticity 73G99 Finite deformations 73Gxx Finite deformations (mechanics of solids) 73H05 Buckling 73H10 Dynamic stability (mechanics of solids) 73H99 Stability (mechanics of solids) 73Hxx Stability (mechanics of solids) 73K03 Strings 73K05 Rods, etc. 73K10 Plates, etc. 73K12 Dynamics of structures 73K15 Shells 73K20 Composite structures in mechanics of solids 73K35 Random excitation of structures 73K40 Optimization in structural mechanics 73K50 Control of structures 73K70 Aero or hydromechanic structure interactions 73K99 Mechanics of structures 73Kxx Mechanics of structures 73M25 Fracture mechanics 73N20 Geophysical solid mechanics 73P05 Biomechanics of solids 73Q05 Soil and rock mechanics 73R05 Electromagnetic elasticity 73S10 Micromechanics of solids 73T05 Contact and surface mechanics 73V05 Finite element methods 73V10 Boundary element methods 73V15 Finite difference methods 73V20 Other numerical methods 73V25 Variational methods 73V30 Stochastic analysis 73V35 Complex variable techniques 73V99 Basic methods in solid mechanics 73Vxx Basic methods in solid mechanics 7600 Reference works (fluid mechanics) 7601 Textbooks (fluid mechanics) 7602 Research monographs (fluid mechanics) 7603 Historical (fluid mechanics) 7604 Machine computation, programs (fluid mechanics) 7605 Experimental papers (fluid mechanics) 7606 Proceedings of conferences (fluid mechanics) 7699 Fluid mechanics 76XX Fluid mechanics 76A02 Foundations of fluid mechanics 76A05 NonNewtonian fluids 76A10 Viscoelastic fluids 76A15 Liquid crystals 76A99 Foundations, constitutive equations, rheology 76Axx Foundations, constitutive equations, etc. 76B05 Airfoil theory 76B10 Freestreamline theory and appl. 76B15 Wave motions (fluid mechanics) 76B20 Ship waves 76B25 Solitary waves, etc. (inviscid fluids) 76B35 Random waves (inviscid fluids) 76B40 Added mass computations (fluid mechanics) 76B45 Capillarity 76B99 Incompressible inviscid fluids, potential theory 76Bxx Incompressible inviscid fluids, potential theory 76C05 Vorticity flows 76C10 Internal waves (inviscid fluids) 76C15 Atmospheric waves 76C20 Rossby waves (fluid mechanics) 76C99 Incompressible inviscid fluids, vorticity flows 76Cxx Incompressible inviscid fluids, vorticity flows 76D05 NavierStokes equations (fluid dynamics) 76D07 Stokes flows 76D08 Lubrication theory 76D10 Boundarylayer theory (incompressible fluids) 76D15 Boundarylayer separation and reattachment 76D20 Higherorder effects in boundary layers 76D25 Wakes and jets (viscous fluids) 76D30 Singular perturbation problems (viscous fluids) 76D33 Waves in incompressible viscous fluids 76D35 Random waves (viscous fluids) 76D45 Capillarity 76D99 Incompressible viscous fluids 76Dxx Incompressible viscous fluids 76E05 Stability of parallel flows 76E10 Inertial instability (fluid mechanics) 76E15 Convective instability (fluid mechanics) 76E20 Instability of flows in nature 76E25 Instabilities in presence of electromagnetic forces 76E30 Nonlinear effects (fluid mechanics) 76E99 Hydrodynamic stability 76Exx Hydrodynamic stability 76F05 Homogeneous isotropic turbulence 76F10 Shear flows 76F20 Turbulence via chaos techniques 76F99 Turbulence 76Fxx Turbulence 76G25 General aerodynamics and subsonic flows 76H05 Transonic flows 76J20 Supersonic flows 76K05 Hypersonic flows 76L05 Shock waves (fluid mechanics) 76M10 Finite element methods 76M15 Boundary element methods 76M20 Finite difference methods 76M25 Other numerical methods 76M30 Variational methods 76M35 Stochastic analysis 76M99 Basic methods in fluid mechanics 76Mxx Basic methods in fluid mechanics 76N10 Compressible fluids, general 76N15 Gas dynamics, general 76N20 Boundary layer theory 76N99 Compressible fluids and gas dynamics, general 76Nxx Compressible fluids and gas dynamics, general 76P05 Molecular or atomic structure 76Q05 Density waves (fluid mechanics) 76R05 Forced convection 76R10 Free convection 76R50 Diffusion 76R99 Diffusion and convection 76Rxx Diffusion and convection (fluid mechanics) 76S05 Flows in porous media 76T05 Several phase flows 76U05 Rotating fluids 76V05 Interacting phases (fluid mechanics) 76W05 Flows in presence of electromagnetic forces 76X05 Plasmic flows 76Y05 Nonclassical hydrodynamics 76Z05 Physiological flows 76Z10 Biopropulsion 76Z99 Biological fluid mechanics 76Zxx Biological fluid mechanics 7800 Reference works (optics, electromagnetic theory) 7801 Textbooks (optics, electromagnetic theory) 7802 Research monographs (optics, electromagnetic theory) 7803 Historical (optics, electromagnetic theory) 7804 Machine computation, programs (optics, electromagnetic theory) 7805 Experimental papers (optics, electromagnetic theory) 7806 Proceedings of conferences (optics, electromagnetic theory) 7808 Computational methods (optics, electromagnetic theory) 7899 Optics, electromagnetic theory 78XX Optics, electromagnetic theory 78A02 Foundations of optics and electromagnetic theory 78A05 Geometric optics 78A10 Physical optics 78A15 Electron optics 78A20 Space charge waves 78A25 General electromagnetic theory 78A30 Electro and magnetostatics 78A35 Motion of charged particles 78A40 Waves and radiation 78A45 Diffraction, scattering (optics) 78A50 Antennas, waveguides 78A55 Technical appl. of optics and electromagnetic theory 78A60 Lasers, etc. 78A70 Biological appl. of optics and electromagnetic theory 78A97 Mathematically heuristic optics and electromagnetic theory 78A99 Miscellaneous topics in optics and electromagnetic theory 8000 Reference works (classical thermodynamics) 8001 Textbooks (classical thermodynamics) 8002 Research monographs (classical thermodynamics) 8003 Historical (classical thermodynamics) 8004 Machine computation, programs (classical thermodynamics) 8005 Experimental papers (classical thermodynamics) 8006 Proceedings of conferences (classical thermodynamics) 8008 Computational methods (classical thermodynamics) 8099 Classical thermodynamics, heat transfer 80XX Classical thermodynamics, heat transfer 80A05 Foundations of classical thermodynamics 80A10 Classical thermodynamics 80A15 Thermodynamics of mixtures 80A20 Heat and mass transfer 80A22 Stefan problems, etc. 80A23 Inverse problems (thermodynamics) 80A25 Combustion, interior ballistics 80A30 Chemical kinetics 80A32 Chemically reacting flows 80A50 Thermodynamical problems in chemistry 80A97 Mathematically heuristic classical thermodynamics 80A99 Miscellaneous topics in classical thermodynamics 8100 Reference works (quantum theory) 8101 Textbooks (quantum theory) 8102 Research monographs (quantum theory) 8103 Historical (quantum theory) 8104 Machine computation, programs (quantum theory) 8105 Experimental papers (quantum theory) 8106 Proceedings of conferences (quantum theory) 8108 Computational methods (quantum theory) 8199 Quantum theory 81XX Quantum Theory 81P05 General and philosophical topics in quantum theory 81P10 Logical foundations of quantum mechanics 81P15 Quantum measurement theory 81P20 Stochastic mechanics (including stochastic electrodynamics) 81P99 Axiomatics, foundations, philosophy of quantum theory 81Pxx Axiomatics, foundations, philosophy of quantum theory 81Q05 Closed and approximate solutions to quantummechanical equations 81Q10 Selfadjoint operator theory in quantum theory 81Q15 Perturbation theories for operators and differential equations 81Q20 Semiclassical techniques in quantum theory 81Q30 Feynman integrals and graphs 81Q40 Integral equations in quantum theory 81Q50 Quantum chaos 81Q60 Supersymmetric quantum mechanics 81Q99 General mathematical topics and methods in quantum theory 81Qxx General mathematical topics and methods in quantum theory 81R05 Repres. of finitedim. groups and algebras from quantum theory 81R10 Repres. of infinitedim. groups and algebras from quantum theory 81R20 Covariant wave equations 81R25 Spinor and twistor methods in quantum theory 81R30 Coherent states in quantum theory 81R40 Symmetry breaking 81R50 Quantum groups and related algebraic methods in quantum theory 81R99 Groups and algebras in quantum theory 81Rxx Groups and algebras in quantum theory 81S05 Commutation relations (quantum theory) 81S10 Geometric quantization, symplectic methods 81S20 Stochastic quantization 81S25 Quantum stochastic calculus 81S30 Phase space methods in quantum mechanics 81S40 Path integrals in quantum mechanics 81S99 General quantum mechanics and problems of quantization 81Sxx General quantum mechanics and problems of quantization 81T05 Axiomatic quantum field theory 81T08 Constructive quantum field theory 81T10 Model quantum field theories 81T13 Gauge theories 81T15 Perturbative methods of renormalization 81T16 Nonperturbative methods of renormalization 81T17 Renormalization group methods 81T18 Feynman diagrams 81T20 Quantum field theory on curved space backgrounds 81T25 Quantum field theory on lattices 81T27 Continuum limits 81T30 String and superstring theories 81T40 Twodimensional field theories, etc. 81T50 Anomalies in field theory 81T60 Supersymmetric field theories 81T70 Quantization in field theory; cohomological methods 81T80 Simulation and numerical modelling of fields 81T99 Quantum field theory 81Txx Quantum field theory and related classical field theories 81U05 2body potential scattering theory 81U10 nbody potential scattering theory 81U20 Smatrix theory, etc. 81U30 Dispersion theory, dispersion relations (quantum theory) 81U40 Inverse scattering problems (quantum theory) 81U99 Scattering theory (quantum theory) 81Uxx Scattering theory (quantum theory) 81V05 Strong interaction 81V10 Electromagnetic interaction 81V15 Weak interaction 81V17 Gravitational interaction 81V19 Other fundamental interactions 81V22 Unified theories of elementary partcles 81V25 Other elementary particle theory 81V35 Appl. of quantum theory to nuclear physics 81V45 Appl. of quantum theory to atomic physics 81V55 Appl. of quantum theory to molecular physics 81V70 Appl. of quantum theory to manybody systems 81V80 Appl. of quantum theory to quantum optics 81V99 Appl. of quantum theory to specific physical systems 81Vxx Appl. of quantum theory to specific physical systems 8200 Reference works (statistical mechanics) 8201 Textbooks (statistical mechanics) 8202 Research monographs (statistical mechanics) 8203 Historical (statistical mechanics) 8204 Machine computation, programs (statistical mechanics) 8205 Experimental papers (statistical mechanics) 8206 Proceedings of conferences (statistical mechanics) 8208 Computational methods (statistical mechanics) 8299 Statistical mechanics, structure of matter 82XX Statistical mechanics, structure of matter 82B03 Foundations of equilibrium statistical mechanics 82B05 Classical equilibrium statistical mechanics (general) 82B10 Quantum equilibrium statistical mechanics (general) 82B20 Lattice systems 82B21 Continuum models (systems of particles, etc.) 82B23 Exactly solvable models 82B24 Interface problems (equilibrium) 82B26 Phase transitions (general) 82B27 Critical phenomena 82B28 Renormalization group methods 82B30 Statistical thermodynamics 82B31 Stochastic methods in equilibrium statistical mechanics 82B35 Irreversible thermodynamics 82B40 Kinetic theory of gases 82B41 Random walks, etc. (statistical mechanics) 82B43 Percolation 82B44 Disordered systems 82B80 Numerical methods in equilibrium statistical mechanics 82B99 Equilibrium statistical mechanics 82Bxx Equilibrium statistical mechanics 82C03 Foundations of timedependent statistical mechanics 82C05 Classical dynamic and nonequilibrium statistical mechanics (general) 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general) 82C20 Dynamic lattice systems 82C21 Dynamic continuum models 82C22 Interacting particle systems 82C23 Exactly solvable dynamic models 82C24 Interface problems (dynamic and nonequilibrium) 82C26 Dynamic and nonequilibrium phase transitions (general) 82C27 Dynamic critical phenomena 82C28 Dynamic renormalization group methods 82C31 Stochastic methods in timedependent statistical mechanics 82C32 Neural nets 82C35 Irreversible thermodynamics 82C40 Kinetic theory of gases 82C41 Dynamics of random walks, etc. 82C43 Timedependent percolation 82C44 Dynamics of disordered systems 82C70 Transport processes 82C80 Numerical methods of timedependent statistical mechanics 82C99 Timedependent statistical mechanics 82Cxx Timedependent statistical mechanics (dynamic and nonequilibrium) 82D05 Gases 82D10 Plasmas 82D15 Liquids 82D20 Solids 82D25 Crystals 82D30 Random media, etc. 82D35 Metals 82D40 Magnetic materials 82D45 Ferroelectrics 82D50 Superfluids 82D55 Superconductors 82D60 Polymers 82D75 Nuclear reactor theory 82D99 Appl. to specific physical systems 82Dxx Appl. to specific physical systems 8300 Reference works (relativity) 8301 Textbooks (relativity) 8302 Research monographs (relativity) 8303 Historical (relativity) 8304 Machine computation, programs (relativity) 8305 Experimental papers (relativity) 8306 Proceedings of conferences (relativity) 8308 Computational methods (relativity) 8399 Relativity and gravitational theory 83XX Relativity and gravitational theory 83A05 Special relativity 83B05 Observational and experimental questions of relativity 83C05 Einstein's equations 83C10 Equations of motion 83C15 Closed form solutions of equations in general relativity 83C20 Classes of solutions of equations in general relativity 83C22 Electromagnetic fields, EinsteinMaxwell equations 83C25 Approximation procedures (general relativity) 83C27 Discrete methods in general relativity 83C30 Asymptotic procedures (general relativity) 83C35 Gravitational waves 83C40 Groups of motions, etc. 83C45 Quantization of the gravitational field 83C47 Quantum field theory on curved spacetimes 83C50 Electromagnetic fields 83C55 Hydrodynamics (general relativity) 83C57 Black holes 83C60 Spinor and twistor methods in general retativity 83C75 Spacetime singularities, etc. 83C99 General relativity 83Cxx General relativity 83D05 Relativistic gravitational theories other than Einstein's 83E05 Geometrodynamics 83E15 Higherdimensional field theories 83E30 String and superstring theories 83E50 Supergravity 83E99 Unified, higherdimensional and super field theories 83Exx Unified field theories, etc. 83F05 Relativistic cosmology 8500 Reference works (astronomy and astrophysics) 8501 Textbooks (astronomy and astrophysics) 8502 Research monographs (astronomy and astrophysics) 8503 Historical (astronomy and astrophysics) 8504 Machine computation, programs (astronomy and astrophysics) 8505 Experimental papers (astronomy and astrophysics) 8506 Proceedings of conferences (astronomy and astrophysics) 8508 Computational methods (astronomy and astrophysics) 8599 Astronomy and astrophysics 85XX Astronomy and astrophysics 85A04 General topics of astronomy and astrophysics 85A05 Galactic and stellar dynamics 85A15 Galactic and stellar structure 85A20 Stellar atmospheres 85A25 Radiative transfer 85A30 Hydrodynamic and hydromagnetic problems in astrophysics 85A35 Statistical astronomy 85A40 Nonrelativistic cosmology 85A45 Radio astronomy 85A99 Miscellaneous topics in astronomy and astrophysics 8600 Reference works (geophysics) 8601 Textbooks (geophysics) 8602 Research monographs (geophysics) 8603 Historical (geophysics) 8604 Machine computation, programs (geophysics) 8605 Experimental papers (geophysics) 8606 Proceedings of conferences (geophysics) 8608 Computational methods (geophysics) 8699 Geophysics 86XX Geophysics 86A04 General topics of geophysics 86A05 Hydrology, hydrography, oceanography 86A10 Meteorology 86A15 Seismology 86A17 Global dynamics, earthquake problems 86A20 Potentials, prospecting 86A22 Inverse problems in geophysics 86A25 Geoelectricity and geomagnetism 86A30 Geodesy 86A32 Geostatistics 86A40 Glaciology 86A60 Geological problems 86A99 Miscellaneous topics in geophysics 9000 Reference works (optimization) 9001 Textbooks (optimization) 9002 Research monographs (optimization) 9003 Historical (optimization) 9004 Machine computation, programs (optimization) 9006 Proceedings of conferences (optimization) 9008 Computational methods (optimization) 9099 Optimization 90XX Optimization 90A05 Decision theory 90A06 Individual preferences 90A07 Group preferences 90A08 Social welfare 90A09 Finance, etc. 90A10 Utility theory 90A11 Production theory, etc. 90A12 Price theory and market structure 90A14 General economic equilibrium theory 90A15 General economic models, etc. 90A16 Dynamic economic models, etc. 90A17 Multisectoral economic models 90A19 Statistical methods in mathematical economics 90A20 Economic time series analysis 90A25 Spatial economic models 90A27 Public goods 90A28 Voting theory 90A30 Environmental economics 90A35 Informational economics 90A36 Incentives theory 90A40 Consumer behavior, demand theory 90A43 Expected utility, etc. 90A46 Risk theory 90A50 Labor market 90A53 Special types of economies 90A56 Special types of economic equilibria 90A58 Models of real world systems, etc. 90A60 Market models 90A70 Macroeconomic policymaking 90A80 Resource allocation 90A99 Mathematical economics 90Axx Mathematical economics 90B05 Inventory management 90B06 Transportation, logistics 90B10 Flows in networks 90B12 Communication networks 90B15 Flows in networks with stochastic elements 90B20 Highway traffic 90B22 Queues and service 90B25 Reliability, etc. 90B30 Production models 90B35 Scheduling theory 90B40 Search theory 90B50 Multiplecriteria decision making 90B60 Marketing, advertising 90B70 Theory of organizations, etc. 90B80 Discrete location and assignment 90B85 Continuous location 90B90 Caseoriented studies in OR 90B99 Operations research and management science 90Bxx Operations research and management sience 90C05 Linear programming 90C06 Largescale problems 90C08 Special problems of linear programming 90C09 Boolean programming 90C10 Integer programming 90C11 Mixed integer programming 90C15 Stochastic programming 90C20 Quadratic programming 90C25 Convex programming 90C26 Nonconvex programming 90C27 Combinatorial programming 90C28 Geometric programming 90C29 Multiobjective programming, etc. 90C30 Nonlinear programming 90C31 Sensitivity, etc. 90C32 Fractional programming 90C33 Complementarity problems 90C34 Semiinfinite programming 90C35 Network programming 90C39 Dynamic programming 90C40 Markov decision processes, etc. 90C42 Markov and Markov renewal programming 90C48 Programming in abstract spaces 90C60 Abstract computational complexity for math. programming problems 90C70 Fuzzy programming 90C90 Appl. of mathematical programming 90C99 Mathematical programming 90Cxx Mathematical programming 90D05 2person games 90D06 nperson games (n>2) 90D10 Noncooperative games 90D12 Cooperative games 90D13 Games with infinitely many players 90D15 Stochastic games 90D20 Multistage games 90D25 Differential games 90D26 Pursuit and evasion games 90D35 Decision theory for games 90D40 Game theory models 90D42 Positional games 90D43 Games involving graphs 90D44 Games involving topology or set theory 90D46 Combinatorial games 90D50 Discretetime games 90D55 Games of timing 90D60 Probabilistic games 90D65 Hierarchical games 90D70 Spaces of games 90D80 Appl. of game theory 90D99 Game theory 90Dxx Game theory 9200 Reference works (appl. to natural and behavioral sciences) 9201 Textbooks (appl. to natural etc. sciences) 9202 Research monographs (appl. to natural/behavioral sciences) 9203 Historical (appl. to natural and behavioral sciences) 9204 Machine 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93B06 Relations between controllability and optimal solutions 93B07 Observability 93B10 Canonical structure of systems 93B11 System structure simplification 93B12 Variable structure systems 93B15 Realizability of systems from inputoutput data 93B17 System transformation 93B18 Linearizability of systems 93B20 Minimal systems representations 93B25 Algebraic theory of control systems 93B27 Geometric methods in systems theory 93B28 Operatortheoretic methods in systems theory 93B29 Differentialgeometric methods in systems theory 93B30 System identification 93B35 Sensitivity (robustness) of control systems 93B36 Hinfinitycontrol 93B40 Computational methods in systems theory 93B50 Synthesis problems 93B51 Design techniques in systems theory 93B52 Feedback control 93B55 Pole and zero placement problems 93B60 Eigenvalue problems in systems theory 93B99 Controllability, observability, and system structure 93Bxx Controllability, observability, and system structure 93C05 Linear control systems 93C10 Nonlinear control systems 93C15 Control systems governed by ODE 93C20 Control systems governed by PDE 93C22 Control systems governed by integral equations 93C25 Control systems in abstract spaces 93C30 Control systems governed by other functional relations 93C35 Multivariable, multidimensional control systems 93C40 Adaptive control systems 93C41 Control problems with incomplete information 93C42 Fuzzy control 93C45 Timeinvariant control systems 93C50 Timedependent control systems 93C55 Discretetime control systems 93C57 Sampleddata control systems 93C60 Continuoustime control systems 93C62 Digital control systems 93C70 Timescale analysis and related topics 93C73 Perturbations in control systems 93C80 Frequencyresponse methods 93C83 Control problems involving computers 93C85 Automated control systems 93C90 Random disturbances in control systems 93C95 Appl. of control theory 93C99 Control systems, guided systems 93Cxx Control systems, guided systems 93D05 Lyapunov and other classical stabilities of control systems 93D09 Robust stability of control systems 93D10 Popovtype stability of feedback systems 93D15 Stabilization of systems by feedback 93D20 Asymptotic stability of control systems 93D21 Adaptive and robust stabilization 93D22 Interrelations between stability problems and optimization problems 93D25 Inputoutput approaches to stability of control systems 93D30 Scalar and vector Lyapunov functions 93D99 Stability of control systems 93Dxx Stability of control systems 93E03 General theory of stochastic systems 93E05 Stochastic games, etc. 93E10 Estimation and detection in stochastic control 93E11 Filtering in stochastic control 93E12 System identification (stochastic systems) 93E14 Data smoothing (stochastic systems) 93E15 Stochastic stability 93E20 Optimal stochastic control (systems) 93E23 Stochastic gradient methods 93E24 Least squares and related methods in stochastic control 93E25 Computational methods in stochastic control 93E30 Computer simulations of stochastic systems 93E35 Stochastic learning and adaptive control 93E99 Stochastic systems and stochastic control 93Exx Stochastic systems and control 9400 Reference works (information and communication) 9401 Textbooks (information and communication) 9402 Research monographs (information and communication) 9403 Historical (information and communication) 9404 Machine computation, programs (information and communication) 9406 Proceedings of conferences (information and communication) 9499 Information and communication 94XX Information and communication 94A05 Communication theory 94A11 Application of orthogonal functions in communication 94A12 Signal theory 94A13 Detection theory 94A14 Modulation and demodulation 94A15 General topics of information theory 94A17 Measures of information 94A24 Coding theorems (Shannon theory) 94A29 Source coding 94A34 Ratedistortion theory 94A40 Channel models 94A45 Codes in connection with formal languages 94A50 Theory of questionnaires 94A55 Shift register sequences 94A60 Cryptography 94A99 Communication and information 94Axx Communication, information 94B05 General theory of linear codes 94B10 Convolutional codes 94B12 Combined modulation schemes 94B15 Cyclic codes 94B20 Burstcorrecting codes 94B25 Combinatorial codes 94B27 Geometric methods in coding theory 94B30 Majority codes 94B35 Decoding 94B40 Arithmetic codes 94B50 Synchronization errorcorrecting codes 94B60 Other types of codes 94B65 Bounds on codes 94B70 Error probability for codes 94B75 Appl. of convex sets and geometry of numbers in coding theory 94B99 Theory of errorcorrecting codes 94Bxx Theory of errorcorrecting codes 94C05 Analytic circuit theory 94C10 Switching theory 94C12 Fault detection 94C15 Appl. of graph theory to circuits and networks 94C30 Appl. of design theory to circuits and networks 94C99 Circuits, networks 94Cxx Circuits, networks 94D05 Fuzzy sets and logic in connection with communication  
