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## Index using Referativnyi Zhurnal System |

Here are the top-level areas of mathematics and related fields classified according to the Referativnyi Zhurnal classification system, used in reviewing journals in the Soviet Union. [Present status unknown]. This classification was prepared as a piece of the UDC (Universal Decimal Classification) which covers all knowledge in a fairly uniform way. Here we use the portion for Mathematics, every entry of which should have the field "271." prepended to the numbers below. The list is taken from an English translation at the AMS; here it is HTML-ized and a few obvious typos have been fixed. Note that there were a few questions inserted by the translators.

While this division reflects current mathematical reality well, the system used more commonly among (Western) mathematicians is the Mathematics Subject Classification (MSC) scheme, which is the basis for the organization of materials at this site. (Return to that index now.)

At this time there are links only for the broadest classifications of the
RZ scheme. (The RZ scheme includes some very deeply nested groups, e.g.
`21.19.27.21.17.15.17` for "Invariant objects in Riemann and pseudo-Riemann spaces".)

Since there are 2040 entries in this table, we provide bookmarks to the 19 top-level divisions on this page:

- 01 General questions of mathematics
- 03 Foundations of mathematics, mathematical logic
- 15 Number theory
- 17 Algebra
- 19 Topology
- 21 Geometry
- 23 Mathematical analysis
- 25 Theory of functions of a real variable
- 27 Theory of functions of complex variables
- 29 Ordinary differential equations
- 31 Partial differential equations
- 33 Integral equations
- 35 Differential and integral equations of mathematical models in the natural sciences
- 37 Calculus of variations and the mathematical theory of optimal control
- 39 Functional analysis
- 41 Numerical mathematics
- 43 Probability theory and mathematical statistics
- 45 Combinatorial analysis. Graph theory
- 47 Mathematical cybernetics

- 01.01 Instructional exposition
- 01.05 Publications of a general nature
- 01.05.15 Philosophy and the methodology of mathematics
- 01.05.17 Classification of the mathematical sciences

- 01.09 History of mathematics. Personalities
- 01.09.15 History of mathematics
- 01.09.17 Personalia

- 01.13 Scientific societies, meetings, congresses, conferences, symposia, seminars
- 01.17 International cooperation
- 01.21 Organization of scientific research activities
- 01.29 Informational activity
- 01.33 Terminology. Handbooks, dictionaries, textbooks
- 01.33.02 Monographs
- 01.33.03 Handbooks
- 01.33.04 Surveys
- 01.33.05 New journals and series
- 01.33.06 Publications of institutions and organizations (collectives)
- 01.33.07 Instructional material
- 01.33.15 Mathematical terminology

- 01.79 Mathematical training. Mathematical education
- 01.79.17 Popularization of the mathematical sciences

- 03.15 Foundations of mathematics
- 03.15.15 General philosophical problems
- 03.15.17 Set theory
- 03.15.17.17 Naive set theory
- 03.15.17.19 Axiomatic set theory. Axiomatization of analysis
- 03.15.17.25 Descriptive set theory
- 03.15.17.31 Theory of order types and of ordinal and cardinal numbers

- 03.15.19 Proof theory
- 03.15.21 Mathematical intuitionism
- 03.15.25 Constructive mathematics
- 03.15.31 Logical and semantic antinomies

- 03.17 Algorithms and computable functions
- 03.17.15 General problems in the theory of algorithms
- 03.17.15.15 General theory of calculi
- 03.17.15.17 General recursion theory

- 03.17.17 Complexity of algorithms
- 03.17.19 Algorithmic problems
- 03.17.19.17 Degrees of undecidability

- 03.17.21 Algorithmic set theory
- 03.17.31 Computable functions
- 03.17.33 Mathematical models of computational processes

- 03.17.15 General problems in the theory of algorithms
- 03.19 Mathematical logic
- 03.19.17 Logic and logico-mathematical languages
- 03.19.19 Classical logic theories
- 03.19.19.19 Propositional logic
- 03.19.19.25 Predicate logic
- 03.19.19.31 Higher-order logics

- 03.19.21 Nonclassical logics
- 03.19.21.17 Intuitionistic and intermediate logics
- 03.19.21.19 Modal logics
- 03.19.21.21 Many-valued logics
- 03.19.21.25 Formalization of traditional logics
- 03.19.21.27 Quantum logics
- 03.19.21.31 Probabilistic logic
- 03.19.21.33 Combinatorial logic
- 03.19.21.39 Other logic systems

- 03.19.25 Logico-mathematical theories
- 03.19.25.17 Formal arithmetic

- 03.19.27 Inference in logic and logico-mathematical calculi
- 03.19.29 Problems in the algorithmic decidability of logic and logico-mathematical theories
- 03.19.31 Theory of models
- 03.19.51 General mathematical systems

- 15.15 Elementary arithmetic
- 15.17 Elementary number theory
- 15.17.15 Elementary properties and methods
- 15.17.15.17 Multiplicative structure of integers (G.C.D, L.C.M, etc.). Comparisons, power residues, quadratic residues, etc.
- 15.17.15.27 Numerical sequences (Farey, et al.). Recurrent sequences
- 15.17.15.31 Special numbers and polynomials (Bernoulli, et al.)
- 15.17.15.33 Partitions (elementary methods, combinatorial number theory)

- 15.17.15 Elementary properties and methods
- 15.19 Analytic number theory
- 15.19.15 Riemann zeta function, Dirichlet function, etc.
- 15.19.17 Dirichlet series (general theory)
- 15.19.19 Distribution of prime numbers and divisors in number fields
- 15.19.21 Modular and quadratic forms
- 15.19.25 Asymptotics of number-theoretic functions
- 15.19.27 Method of trigonometric sums
- 15.19.31 Sieve. The sieve method (Eratosthenes, Brun, Selberg, et al.)

- 15.21 Additive number theory. Forms
- 15.21.17 Diophantine approximations
- 15.21.19 Metric and probabilistic number theory

- 15.23 Diophantine equations
- 15.23.15 Algebraic Diophantine equations
- 15.23.15.17 Linear, quadratic and bilinear equations
- 15.23.15.25 Diophantine equations of higher degrees

- 15.23.19 Nonalgebraic Diophantine equations (exponential and other equations)

- 15.23.15 Algebraic Diophantine equations
- 15.25 Algebraic number theory (algebraic number fields)
- 15.25.15 General theory of fields of algebraic numbers and complex units
- 15.25.17 Special classes of algebraic number fields
- 15.25.17.17 Quadratic fields
- 15.25.17.19 Cubic fields and fields of the fourth degree
- 15.25.17.25 Cyclic, abelian and metabelian number fields

- 15.25.27 Fields of functions of simple characteristic
- 15.25.33 Analytic and local methods in algebraic number theory
- 15.25.33.17 Analytic methods
- 15.25.33.31 Local methods

- 15.27 Geometry of numbers

- 17.15 Semigroups [Contiguous with 17.15.19]
- 17.15.19.15 Semigroups with finiteness conditions
- 17.15.19.15.17 Finite semigroups

- 17.15.19.17 Generating sets, relations and identities on semigroups
- 17.15.19.17.17 Varieties of semigroups. Free semigroups, defining relations
- 17.15.19.17.19 Commutative semigroups
- 17.15.19.17.25 Idempotent semigroups

- 17.15.19.19 Equivalences and complexes in semigroups. Homomorphisms
- 17.15.19.19.17 Semigroup homomorphisms
- 17.15.19.19.21 Special elements and complexes in semigroups
- 17.15.19.19.25 Semigroup ideals
- 17.15.19.19.27 Subsemigroups
- 17.15.19.19.33 Structures of subsemigroups, ideals and congruences of semigroups

- 17.15.19.21 Transformation semigroups
- 17.15.19.21.15 Semigroups of multivalued transformations (binary relations)
- 17.15.19.21.17 Semigroups of single-valued transformations
- 17.15.19.21.19 Representation of transformation semigroups
- 17.15.19.21.31 Matrix semigroups, linear semigroups

- 17.15.19.25 Inverse semigroups (generalized groups)
- 17.15.19.25.31 Regular semigroups. Other generalizations of inverse semigroups
- 17.15.19.25.33 Semiheaps and generalized heaps

- 17.15.19.27 Semigroups with complemented structures
- 17.15.19.27.15 Semigroups with operators of the -semigroup
- 17.15.19.27.17 Connection with ring theory, multiplicative ring semigroups
- 17.15.19.27.25 Quasi-ordered and ordered semigroups
- 17.15.19.27.31 Topological semigroups
- 17.15.19.27.31.17 Compact and connected semigroups
- 17.15.19.27.31.25 Topological semigroups of transformations of topological spaces

- 17.15.19.33 Different generalizations of associativity

- 17.15.19.15 Semigroups with finiteness conditions
- 17.17 Groups
- 17.17.15 Methods of mathematical logic, and algorithmic problems in group theory
- 17.17.15.15 Axiomatizable classes of groups
- 17.17.15.19 Elementary theories of different classes of groups
- 17.17.15.25 Algorithmic problems in group theory. Word problem

- 17.17.17 Abelian groups
- 17.17.17.15 Purity and its generalizations
- 17.17.17.17 Higher subgroups
- 17.17.17.19 Direct and subdirect sums (abelian groups)
- 17.17.17.21 Extensions of abelian groups
- 17.17.17.25 Mappings of a group into itself and into other subgroups
- 17.17.17.27 Primary abelian groups
- 17.17.17.31 Torsion-free abelian groups
- 17.17.17.33 Systems of generators. Factorization

- 17.17.19 Finite groups
- 17.17.19.15 Generators and defining relations
- 17.17.19.17 Automorphisms of finite groups
- 17.17.19.19 Finite p-groups
- 17.17.19.21 Finite solvable groups
- 17.17.19.25 Finite simple groups
- 17.17.19.25.17 Arithmetic and abstract properties
- 17.17.19.25.25 Methods in the theory of Lie algebras in finite groups

- 17.17.19.27 Arithmetic structure and normal structure of finite groups
- 17.17.19.27.17 Extensions of finite groups
- 17.17.19.27.19 Normal series in finite groups
- 17.17.19.27.21 Sylow-type theorems
- 17.17.19.27.27 Factorization of finite groups
- 17.17.19.27.33 Normal complements in finite groups

- 17.17.19.31 Permutation groups
- 17.17.19.31.17 Primitive and multiply transitive groups
- 17.17.19.31.21 Combined problems for permutation groups
- 17.17.19.31.25 Groups of collineations of finite projective and affine planes

- 17.17.21 Relationships between elementary groups
- 17.17.21.15 Systems of generators
- 17.17.21.17 Varieties of groups
- 17.17.21.25 Operations over groups
- 17.17.21.31 Equations over groups and embedding theorems in group theory

- 17.17.23 Relationships between subgroups. Generalized solvable groups and finiteness conditions
- 17.17.23.17 Structures of subgroups
- 17.17.23.17.17 Structural isomorphisms
- 17.17.23.17.31 Minimality and maximality conditions

- 17.17.23.19 Normal series and systems
- 17.17.23.19.17 Generalized solvable groups and finiteness conditions
- 17.17.23.19.19 Nilpotent and solvable groups
- 17.17.23.19.25 Generalized solvable groups
- 17.17.23.19.31 Radicals in groups

- 17.17.23.21 Characteristic subgroups, automorphisms and endomorphisms
- 17.17.23.21.17 Automorphism groups and representations of groups in automorphism groups of algebraic systems
- 17.17.23.21.19 Automorphisms and automorphism groups of specific groups

- 17.17.23.25 Locally finite groups
- 17.17.23.27 Linear groups
- 17.17.23.31 Approximation of groups

- 17.17.23.17 Structures of subgroups
- 17.17.25 Ordered groups
- 17.17.25.17 Linearly ordered groups
- 17.17.25.21 Structurally ordered groups
- 17.17.25.27 Partially ordered groups
- 17.17.25.33 Different types of preorderable groups

- 17.17.27 Topological groups
- 17.17.27.15 General theory of topological groups
- 17.17.27.15.17 Generators and relations in topological groups
- 17.17.27.15.25 Operations over topological groups. Products

- 17.17.27.17 Abelian topological groups
- 17.17.27.19 Locally compact groups
- 17.17.27.19.17 Measure and integral on topological groups
- 17.17.27.19.31 Pro-finite groups. Pro-p-groups

- 17.17.27.21 Representations of topological groups
- 17.17.27.27 Relations between subgroups in topological groups. Finiteness conditions and similar conditions
- 17.17.27.27.31 Groups with compact classes of conjugate elements
- 17.17.27.33 Generalizations of topological groups

- 17.17.27.15 General theory of topological groups
- 17.17.31 Linear representations of abstract groups. Characters of groups
- 17.17.31.17 Representations of finite groups
- 17.17.31.17.15 Classical theory
- 17.17.31.17.15.17 Representations of specific groups
- 17.17.31.17.15.21 Characters of representations

- 17.17.31.17.19 Representations over fields of nonzero characteristic
- 17.17.31.17.25 Representations over rings

- 17.17.31.17.15 Classical theory
- 17.17.31.21 Representations of infinite groups

- 17.17.31.17 Representations of finite groups
- 17.17.33 Generalizations of groups. Groupoids, etc.
- 17.17.33.17 Special classes of groupoids
- 17.17.33.21 Groupoids with complemented structures
- 17.17.33.31 Quasigroups
- 17.17.33.31.17 Isotopies and homotopies of quasigroups
- 17.17.33.31.21 Identities and generalized identities on quasigroups
- 17.17.33.31.31 Loops

- 17.17.15 Methods of mathematical logic, and algorithmic problems in group theory
- 17.19 Rings and modules
- 17.19.15 Methods of mathematical logic in rings and modules
- 17.19.19 Associative rings and algebras
- 17.19.19.15 Structure of rings
- 17.19.19.15.17 Ideals in rings. Radicals
- 17.19.19.15.19 Structure-theoretic problems for associative rings
- 17.19.19.15.27 Automorphisms, endomorphisms and derivation of rings

- 17.19.19.17 Rings with chain conditions
- 17.19.19.19 Rings with conditions on ideals and subrings
- 17.19.19.19.17 Skew fields
- 17.19.19.19.19 Prime rings
- 17.19.19.19.21 Primary and semiprimary rings
- 17.19.19.19.25 Regular, biregulator and strictly regulator rings
- 17.19.19.19.31 Rings of principal ideals

- 17.19.19.21 Defining and identity relations in rings. Varieties of rings
- 17.19.19.25 Embedding of rings
- 17.19.19.25.15 Quotient rings

- 17.19.19.27 Operations over rings
- 17.19.19.31 Semigroup and group rings
- 17.19.19.33 Representations of rings and algebras

- 17.19.19.15 Structure of rings
- 17.19.21 Modules
- 17.19.21.15 Structure of modules
- 17.19.21.17 Projective and flat modules
- 17.19.21.19 Injective modules
- 17.19.21.21 Quotient modules
- 17.19.21.25 Endomorphism rings
- 17.19.21.27 Equivalence and duality
- 17.19.21.31 Homology classification of rings
- 17.19.21.33 Submodules. Structure of submodules

- 17.19.23 Nonassociative rings and algebras
- 17.19.23.17 Nonassociative skew fields and their generalizations
- 17.19.23.19 Lie rings and algebras
- 17.19.23.19.15 Finite-dimensional Lie algebras
- 17.19.23.19.17 Infinite-dimensional Lie algebras
- 17.19.23.19.19 Generators, defining and identity relations. Varieties. Free algebras
- 17.19.23.19.21 Embeddings of Lie algebras into other types of algebras
- 17.19.23.19.21.17 Universal enveloping algebras of Lie algebras

- 17.19.23.19.25 Lie algebras of derivations
- 17.19.23.19.27 Subalgebras and ideals
- 17.19.23.19.31 Automorphisms, endomorphisms and derivations of Lie algebras
- 17.19.23.19.33 Generalizations of Lie algebras

- 17.19.23.25 Alternative rings and related rings
- 17.19.23.31 Jordan rings and algebras

- 17.19.25 Ordered rings and modules
- 17.19.27 Topological rings and modules
- 17.19.31 Rings and modules with valuation
- 17.19.33 Generalizations of rings and modules

- 17.21 Structures
- 17.21.17 Partially ordered sets
- 17.21.19 Boolean rings and algebras
- 17.21.19.27 Boolean algebras

- 17.21.25 Types of structures
- 17.21.25.17 Distributive structures
- 17.21.25.19 Dedekind structures and structures similar to them
- 17.21.25.27 Structures with complements
- 17.21.25.33 Complete structures

- 17.21.31 Representations of structures
- 17.21.33 Generalizations of structures
- 17.21.35 Algebraic theory of affine and projective geometries
- 17.21.35.17 On the basis of structure theory
- 17.21.35.19 Over skew fields
- 17.21.35.25 Finite projective spaces and other generalizations

- 17.23 Universal algebras
- 17.23.15 Structure of universal algebras
- 17.23.17 Varieties (primitive classes) of algebras and their free algebras
- 17.23.19 Algebra-theoretic constructions
- 17.23.25 Dependence in algebras
- 17.23.31 Types of universal algebras

- 17.25 Categories
- 17.25.15 General problems in category theory
- 17.25.15.17 Structural problems in category theory
- 17.25.15.19 Types and categories
- 17.25.15.31 Multiplicative structures on objects of categories

- 17.25.17 Functors
- 17.25.17.17 Union of functors
- 17.25.17.21 Duality of functors
- 17.25.17.27 Direct and inverse limits

- 17.25.19 Representations of categories
- 17.25.25 Abelian categories
- 17.25.25.19 Representations of abelian categories

- 17.25.15 General problems in category theory
- 17.27 Fields and polynomials
- 17.27.17 Polynomials, including binomials and prime factorization
- 17.27.19 General field theory
- 17.27.19.17 Extensions of fields
- 17.27.19.19 General Galois theory
- 17.27.19.19.17 Embedding problem
- 17.27.19.19.25 Construction of fields with a given Galois group

- 17.27.19.21 Valuations on fields
- 17.27.19.25 Ordered fields
- 17.27.19.25.17 Formally real fields

- 17.27.19.27 Topological fields
- 17.27.19.31 Special classes of fields
- 17.27.19.33 Generalizations of fields

- 17.27.21 Finite fields
- 17.27.25 Local fields
- 17.27.25.25 p-adic analysis
- 17.27.25.31 Forms over local fields

- 17.27.27 Fields of algebraic numbers and algebraic functions
- 17.27.27.15 Divisors and completions
- 17.27.27.17 Trims? and discriminant
- 17.27.27.19 Quadratic fields and division fields of a disk
- 17.27.27.21 Units of algebraic number fields
- 17.27.27.25 Group of classes of divisors
- 17.27.27.27 Idèles and adèles
- 17.27.27.31 Forms over number fields
- 17.27.27.33 Arithmetic problems of orders in semisimple algebras

- 17.27.31 Class field theory
- 17.27.31.25 Local class field theory

- 17.27.33 Differential and difference algebras
- 17.27.33.17 Differential algebra
- 17.27.33.21 Difference algebra

- 17.29 Linear algebra
- 17.29.17 Vector spaces. Theory of vector spaces
- 17.29.17.17 Vector spaces over skew fields

- 17.29.19 Matrices and linear mappings. Matrix theory
- 17.29.19.17 Determinants and their generalizations
- 17.29.19.21 Matrix equations
- 17.29.19.25 Eigenvalues of matrices
- 17.29.19.33 Special classes of matrices

- 17.29.21 Systems of linear equations and inequalities
- 17.29.31 Polylinear algebra. Forms
- 17.29.31.17 Bilinear and quadratic forms

- 17.29.17 Vector spaces. Theory of vector spaces
- 17.31 Homological algebra
- 17.31.17 Chain complexes
- 17.31.17.15 Homology theory of chain complexes
- 17.31.17.25 Homotopy theory of chain complexes
- 17.31.17.31 Chain complexes with a diagonal
- 17.31.17.33 Filtrations, exact pairs, spectral sequences

- 17.31.21 Derived functors
- 17.31.21.15 Homological algebra in abelian categories
- 17.31.21.17 Homology theory of associative rings and modules
- 17.31.21.19 Homology of Lie algebras and Hopf algebras
- 17.31.21.21 Homology of groups and semigroups
- 17.31.21.33 Deformations of algebraic structures
- 17.31.21.33.17 Deformations of discrete subgroups of Lie groups

- 17.31.27 Algebraic K-theory
- 17.31.31 Algebraic analogues of different constructions from topology and algebraic geometry
- 17.31.31.17 Homotopy groups in categories
- 17.31.31.25 General theory of topologies and sheaves on categories
- 17.31.31.31 General theory of co-algebras and Hopf algebras

- 17.31.17 Chain complexes
- 17.33 Algebraic geometry
- 17.33.15 Commutative rings and algebras, local theory and foundations of algebraic geometry
- 17.33.15.15 General theory of commutative rings
- 17.33.15.17 Valuations on commutative rings and divisibility theory
- 17.33.15.19 Arithmetic rings. Dedekind and Prüfer rings
- 17.33.15.21 Polynomial rings
- 17.33.15.25 Modules over commutative rings
- 17.33.15.31 Local algebra. Local theory
- 17.33.15.33 Foundations of algebraic geometry

- 17.33.17 Variations of structures of algebraic varieties, crossed products, fiber bundles
- 17.33.17.15 Moduli of algebraic varieties
- 17.33.17.17 Structure of families. Picard varieties
- 17.33.17.19 Vector algebraic bundles
- 17.33.17.21 Classification of algebraic varieties
- 17.33.17.25 Algebraic bundles with degenerate fibers

- 17.33.19 Cohomology theory of algebraic varieties and schemes
- 17.33.19.17 Algebraic sheaves and cohomology with coefficients in them
- 17.33.19.17.17 General properties of algebraic sheaves
- 17.33.19.17.27 The Riemann-Roch theorem for algebraic varieties and related questions

- 17.33.19.21 Cycles: intersection theory and equivalence
- 17.33.19.21.17 Foundations of intersection theory
- 17.33.19.21.19 Chow varieties and algebraic systems. Parametrization
- 17.33.19.21.25 Rational equivalence of cycles
- 17.33.19.21.31 Algebraic and numerical equivalence

- 17.33.19.27 Serre cohomology, K-theory
- 17.33.19.21 Grothendieck cohomology and topology

- 17.33.19.17 Algebraic sheaves and cohomology with coefficients in them
- 17.33.21 Algebraic groups, including abelian varieties
- 17.33.21.15 Formal groups
- 17.33.21.15.25 p-adic analytic groups

- 17.33.21.17 Abelian varieties and schemes
- 17.33.21.17.15 General theory of abelian varieties
- 17.33.21.17.17 Endomorphism rings of abelian varieties
- 17.33.21.17.19 Moduli of abelian varieties
- 17.33.21.17.21 Principal homogeneous spaces of abelian varieties
- 17.33.21.17.31 Arithmetic of abelian varieties
- 17.33.21.17.31.17 Arithmetic of elliptic curves

- 17.33.21.19 Linear algebraic groups
- 17.33.21.19.17 Adele groups and Tamagawa numbers
- 17.33.21.19.19 Groups of units
- 17.33.21.19.21 Approximation theorems
- 17.33.21.19.25 p-adic linear groups
- 17.33.21.19.31 Linear representations of linear algebraic groups

- 17.33.21.25 Algebraic transformation groups
- 17.33.21.25.17 Geometric theory of invariants of algebraic transformation groups
- 17.33.21.25.21 Infinite-dimensional algebraic groups

- 17.33.21.31 Pro-algebraic groups and group schemes

- 17.33.21.15 Formal groups
- 17.33.25 Arithmetic problems of algebraic varieties
- 17.33.25.17 Problems associated with rationality. Rational points on algebraic varieties
- 17.33.25.21 Zeta functions and related problems

- 17.33.27 Birational geometry. Mappings and the like
- 17.33.27.15 Singularities. Singular points of algebraic varieties
- 17.33.27.15.17 Resolution of singularities
- 17.33.27.15.19 Structure of varieties near singular points
- 17.33.27.15.25 Numerical invariants and classification of singularities

- 17.33.27.19 Linear systems and rational mappings
- 17.33.27.25 Modifications and problems of minimal models

- 17.33.27.15 Singularities. Singular points of algebraic varieties
- 17.33.31 Algebraic curves; surfaces and three-dimensional manifolds
- 17.33.31.17 Algebraic curves
- 17.33.31.17.15 Singular points of curves
- 17.33.31.17.17 Bundles over a curve
- 17.33.31.17.25 Modules over algebraic curves
- 17.33.31.17.31 Arithmetic problems on algebraic curves

- 17.33.31.21 Algebraic surfaces
- 17.33.31.21.15 Singular points of surfaces
- 17.33.31.21.15.19 Structure of a surface near singular points
- 17.33.31.21.15.17 Resolution of singularities
- 17.33.31.21.15.25 Numerical invariants and classification of singularities
- 17.33.31.21.15.31 Theory of intersections on singular surfaces

- 17.33.31.21.17 Birational transformations and minimal models
- 17.33.31.21.19 Algebraic and linear systems on algebraic surfaces
- 17.33.31.21.21 Algebraic geometry of different classes of surfaces
- 17.33.31.21.25 Moduli of algebraic surfaces
- 17.33.31.21.31 Arithmetic problems on algebraic surfaces

- 17.33.31.21.15 Singular points of surfaces
- 17.33.31.27 Algebraic varieties of dimension 3
- 17.33.31.33 Analytic spaces over arbitrary complete valued fields

- 17.33.31.17 Algebraic curves

- 17.33.15 Commutative rings and algebras, local theory and foundations of algebraic geometry
- 17.35 Lie groups
- 17.35.17 General theory of Lie groups, properties, structure and generalizations
- 17.35.17.17 Correspondence between Lie groups and Lie algebras. Exponential mapping
- 17.35.17.21 Structure of Lie groups and Lie algebras, deformation and contractions of Lie groups of automorphisms, and derivations
- 17.35.17.27 Related problems in the theory of topological groups
- 17.35.17.33 Generalizations of Lie groups

- 17.35.19 Special classes of Lie groups
- 17.35.19.19 Compact Lie groups and Lie algebras
- 17.35.19.21 Semisimple Lie groups and Lie algebras
- 17.35.19.25 Solvable Lie groups and Lie algebras
- 17.35.19.25.17 Nilpotent Lie groups and Lie algebras

- 17.35.21 Continuous subgroups of Lie groups
- 17.35.21.15 General properties of subgroups and subalgebras
- 17.35.21.17 Maximal subgroups and subalgebras
- 17.35.21.19 Compact and semisimple subgroups
- 17.35.21.25 Solvable subgroups and subalgebras
- 17.35.21.25.17 Cartan subgroups
- 17.35.21.31 Decomposition of Lie groups into the product of subgroups

- 17.35.25 Linear representations of Lie groups
- 17.35.25.15 Finite-dimensional linear representations of Lie groups and Lie algebras
- 17.35.25.17 Equivariant embeddings of spaces with a Lie transformation group into a Euclidean space
- 17.35.25.19 Representing functions. Duality theorems
- 17.35.25.21 Invariants of linear representations
- 17.35.25.27 Linear Lie groups and Lie algebras
- 17.35.25.31 Algebraic linear Lie groups
- 17.35.25.33 Linear representations of groups in theoretical physics

- 17.35.27 Lie transformation groups
- 17.35.27.15 General theory of Lie transformation groups
- 17.35.27.17 Orbits and quotient spaces of Lie transformation groups
- 17.35.27.19 Transitive Lie groups
- 17.35.27.21 Homogeneous spaces of semisimple Lie groups
- 17.35.27.25 Homogeneous spaces of solvable Lie groups
- 17.35.27.25.17 Simultaneous spaces of nilpotent Lie groups

- 17.35.27.31 Differential operators that are invariant with respect to Lie transformation groups
- 17.35.27.33 Invariant integration

- 17.35.31 Discrete subgroups and discrete transformation groups
- 17.35.31.15 General properties of discrete transformation groups and discrete subgroups of Lie groups
- 17.35.31.17 Discrete groups of linear-fractional transformations
- 17.35.31.19 Discrete subgroups of semisimple Lie groups
- 17.35.31.25 Discrete subgroups of of solvable and nilpotent Lie groups
- 17.35.31.27 Arithmetically defined discrete subgroups
- 17.35.31.31 Discrete groups of isometric transformations
- 17.35.31.31.17 Discrete groups generated by reflections

- 17.35.33 Theory of continuous pseudogroups (infinite Lie groups)
- 17.35.33.15 General concepts of the theory of topological pseudogroups and Lie pseudogroups
- 17.35.33.17 Methods of formal Lie groups in the theory of pseudogroups
- 17.35.33.19 Cartan pseudogroups
- 17.35.33.21 Infinite-dimensional filtered and graded Lie algebras

- 17.35.17 General theory of Lie groups, properties, structure and generalizations

- 19.15 General topology
- 19.15.17 Topological spaces
- 19.15.17.17 Axiomatic theory of topological spaces
- 19.15.17.17.17 Classes of spaces distinguished by separability axioms
- 19.15.17.17.19 Classes of spaces distinguished by conditions of a local nature
- 19.15.17.17.21 Cardinal-valued invariants of topological spaces
- 19.15.17.17.25 Classes of spaces distinguished by conditions for coverings
- 19.15.17.17.25.17 Compact spaces
- 19.15.17.17.25.21 Paracompact spaces

- 19.15.17.17.31 Classes of spaces distinguished by conditions that connect their topology with the properties of their subspaces
- 19.15.17.17.31.17 K-spaces

- 19.15.17.17.39 Other classes of topological spaces

- 19.15.17.19 Nonaxiomatic theory of topological spaces
- 19.15.17.19.17 Spaces that are embedded in another space of simple structure
- 19.15.17.19.25 Spaces that are continuous images of a given space of simple structure
- 19.15.17.19.25.17 Dyadic compact spaces

- 19.15.17.21 Topological properties of spaces with complemented structure, and topological groups of transformations
- 19.15.17.25 Construction of topological spaces and operations over them
- 19.15.17.25.19 Operations over topological spaces
- 19.15.17.25.19.17 Topological products
- 19.15.17.25.19.21 Hyperspaces
- 19.15.17.25.19.27 Compact extensions
- 19.15.17.25.19.31 Superextensions

- 19.15.17.25.25 Spaces of mappings (function spaces)
- 19.15.17.25.31 Passages to the limit in the category of topological spaces
- 19.15.17.25.31.17 Spectra of topological spaces

- 19.15.17.25.19 Operations over topological spaces
- 19.15.17.27 Shapes of topological spaces
- 19.15.17.31 Topological questions in category theory
- 19.15.17.33 Generalizations of topological spaces

- 19.15.17.17 Axiomatic theory of topological spaces
- 19.15.19 Uniform spaces and nearness spaces
- 19.15.19.17 Axioms of uniform and nearness spaces
- 19.15.19.17.17 Different classes of uniform and nearness spaces

- 19.15.19.21 Uniform spaces and uniformly continuous mappings
- 19.15.19.25 Nearness spaces
- 19.15.19.27 Nearness spaces and compact extensions
- 19.15.19.31 Comparison of topologies, uniformities and proximities
- 19.15.19.13.17 Topological properties of uniform spaces

- 19.15.19.17 Axioms of uniform and nearness spaces
- 19.15.21 Metric spaces
- 19.15.21.17 Axioms and generalizations of metric spaces
- 19.15.21.19 Topological properties of metric spaces
- 19.15.21.19.17 Metrizable spaces

- 19.15.21.21 Metric properties of metric spaces
- 19.15.21.25 Classes of metric spaces distinguished by topological properties
- 19.15.21.25.25 Compact metric spaces
- 19.15.21.25.25.17 Continua

- 19.15.21.25.25 Compact metric spaces
- 19.15.21.27 Classes of metric spaces distinguished by conditions of an external nature (for possible ambient spaces)
- 19.15.21.27.27 Absolute retracts

- 19.15.25 Topology of Euclidean spaces
- 19.15.25.25 Plane continua

- 19.15.27 Continuous mappings
- 19.15.27.17 Special types of continuous mappings
- 19.15.27.17.17 Quotient mappings
- 19.15.27.17.19 Open mappings
- 19.15.27.17.25 Perfect mappings and absolutes
- 19.15.27.17.31 Monotone mappings

- 19.15.27.21 Fixed points and coincidences
- 19.15.27.33 Generalizations of continuous mappings
- 19.15.27.33.19 Multivalued mappings

- 19.15.27.17 Special types of continuous mappings
- 19.15.31 Dimension and other topological numerical invariants
- 19.15.31.15 Dimension theory
- 19.15.31.15.17 Dimension theory of arbitrary spaces
- 19.15.31.15.17.25 Comparison of different types of dimensions

- 19.15.31.15.19 Dimension theory of compact spaces
- 19.15.31.15.21 Dimension theory of uniform and nearness spaces
- 19.15.31.15.25 Dimension theory of metric separable spaces
- 19.15.31.15.31 Theory of infinite dimensions

- 19.15.31.15.17 Dimension theory of arbitrary spaces
- 19.15.31.17 Invariants of dimension type

- 19.15.31.15 Dimension theory
- 19.15.33 Descriptive theory of sets of topological spaces

- 19.15.17 Topological spaces
- 19.17 Algebraic topology
- 19.17.17 General theorems on fundamental categories and functors
- 19.17.17.17 General topological categories
- 19.17.17.17.15 Homology and cohomology groups (definitions and basic properties). Axiomatics
- 19.17.17.17.17 Investigation of topological spaces and continuous mappings by homological methods
- 19.17.17.17.17.15 Homology theory of dimension
- 19.17.17.17.17.21 Spectral sequence of a continuous mapping
- 19.17.17.17.17.27 Homology theory of fixed points and coincidence points
- 19.17.17.17.17.33 Homology manifolds

- 19.17.17.17.19 Homology and cohomology with non-abelian coefficients
- 19.17.17.17.25 Homotopy and cohomotopy groups: definitions and basic properties. Axiomatics, etc.
- 19.17.17.17.25.25 Localization of topological spaces

- 19.17.17.17.27 Shape theory
- 19.17.17.17.31 Functors with values in general topological categories (operations over topological spaces)
- 19.17.17.17.31.17 General theory of such functors. Duality
- 19.17.17.17.31.25 Concrete functors

- 19.17.17.19 Polyhedral categories, i.e., categories whose volumes are polyhedra
- 19.17.17.19.17 Cellular partitions
- 19.17.17.19.19 Simplicial partitions (triangulations) and simplicial schemes

- 19.17.17.21 Categories that approximate general topological and polyhedral categories
- 19.17.17.21.17 Categories whose morphisms are stationary mappings or their homotopy classes (categories of spectra, S-categories)
- 19.17.17.21.17.17 S-duality
- 19.17.17.21.17.21 Adams spectral sequence
- 19.17.17.21.17.25 Extraordinary homology and cohomology theories
- 19.17.17.21.17.27 Bordism and cobordism

- 19.17.17.21.21 Categories of semi-exact functors

- 19.17.17.21.17 Categories whose morphisms are stationary mappings or their homotopy classes (categories of spectra, S-categories)
- 19.17.17.25 Simplicial sets

- 19.17.17.17 General topological categories
- 19.17.19 Homotopy theory: fundamental problems
- 19.17.19.17 Decompositions of spaces and mappings
- 19.17.19.17.17 Homotopic resolvents (Moore-Postnikov systems) and dual constructions
- 19.17.19.17.25 Homotopic convolutions of of spaces (decreasing homotopic groups)
- 19.17.19.17.33 Categories of spaces (in the sense of Lyusternik-Shnirel´man)

- 19.17.19.19 Obstruction theory. General classification and continuation theorems for continuous mappings and intersecting surfaces
- 19.17.19.25 Cohomology operations
- 19.17.19.25.33 Analogues of cohomology operations

- 19.17.19.17 Decompositions of spaces and mappings
- 19.17.25 Spaces with various complemented properties of a general nature or that are obtained by these or other general constructions
- 19.17.25.17 Fiber spaces and crossed products
- 19.17.25.17.17 Definition and basic properties, operations over fiber spaces and crossed products
- 19.17.25.17.19 Homotopy theory of bundles. Universal bundles and classifying spaces
- 19.17.25.17.25 Homology theory of fiber spaces
- 19.17.25.17.25.19 Crossed tensor products
- 19.17.25.17.25.27 Spectral sequences

- 19.17.25.17.31 General theorems on bundles with a vector fiber (K- and J-functors)

- 19.17.25.19 Spaces with operators
- 19.17.25.25 Spaces with multiplication (H-spaces) and loop spaces
- 19.17.25.27 Space with comultiplication, and surgeries
- 19.17.25.33 Spaces in which there are only a finite number of nonzero homotopy groups
- 19.17.25.33.21 Eilenberg-MacLane spaces
- 19.17.25.33.27 Spaces in which there are only two nonzero homotopy groups

- 19.17.25.17 Fiber spaces and crossed products
- 19.17.27 Concrete spaces. Calculation of homotopy invariants
- 19.17.27.17 Computation of homotopy groups
- 19.17.27.17.19 Homotopy groups of spheres

- 19.17.27.19 Computation of homology and cohomology groups
- 19.17.27.25 Computation of K- and J-functors
- 19.17.27.27 Computation of bordism and cobordism groups

- 19.17.27.17 Computation of homotopy groups
- 19.17.33 Isotopy theory

- 19.17.17 General theorems on fundamental categories and functors
- 19.19 Topology of manifolds
- 19.19.17 Topology of manifolds of lower dimensions
- 19.19.17.17 Topological surfaces
- 19.19.17.19 Three-dimensional topological manifolds
- 19.19.17.19.17 Classification of three-dimensional manifolds
- 19.19.17.19.17.19 Poincaré conjecture and related problems

- 19.19.17.19.17 Classification of three-dimensional manifolds
- 19.19.17.21 Four-dimensional topological manifolds
- 19.19.17.21.17 Classification of four-dimensional manifolds
- 19.19.17.21.17.19 Poincaré conjecture for four-dimensional manifolds

- 19.19.17.21.17 Classification of four-dimensional manifolds
- 19.19.17.27 Embeddings and immersions in lower dimensions
- 19.19.17.33 Knots. Wreaths. Braids

- 19.19.19 Topological manifolds
- 19.19.19.19 Microsheaves of topological manifolds
- 19.19.19.27 Topological embeddings and immersions

- 19.19.21 Topology of smooth and piecewise-linear manifolds
- 19.19.21.15 General questions
- 19.19.21.15.15 Homology theory of smooth manifolds
- 19.19.21.15.19 Differential forms on smooth manifolds
- 19.19.21.15.25 Singularities of smooth manifolds
- 19.19.21.15.25.17 Critical points of smooth mappings

- 19.19.21.15.31 Infinite-dimensional manifolds
- 19.19.21.15.31.21 Morse theory

- 19.19.21.17 Classification of smooth and piecewise-linear manifolds
- 19.19.21.17.17 Correspondences between homotopic, topological, combinatorial and smooth properties
- 19.19.21.17.17.25 Realization of cycles

- 19.19.21.17.21 Bordisms and cobordisms
- 19.19.21.17.25 Classification of manifolds up to diffeomorphism or piecewise-linear equivalence
- 19.19.21.17.25.15 Combinatorial equivalence of polyhedra. Simple homotopy type

- 19.19.21.17.17 Correspondences between homotopic, topological, combinatorial and smooth properties
- 19.19.21.19 Bundles of smooth manifolds and bundles whose bases are smooth manifolds
- 19.19.21.19.17 Characteristic classes of manifolds
- 19.19.21.19.17.17 Vector fields on manifolds

- 19.19.21.19.25 Microbundles

- 19.19.21.19.17 Characteristic classes of manifolds
- 19.19.21.27 Smooth and piecewise-linear embeddings and embeddings of manifolds
- 19.19.21.33 Groups that act on smooth and piecewise-linear manifolds
- 19.19.21.33.25 Groups of diffeomorphisms and piecewise-linear equivalences

- 19.19.21.15 General questions
- 19.19.25 Topology of smooth manifolds endowed with complemented structure
- 19.19.25.17 Topology of complex and almost complex manifolds
- 19.19.25.21 Topology of Kählerian and algebraic manifolds
- 19.19.25.31 Topology of manifolds with infinitesimal connection. Topology of Riemannian manifolds

- 19.19.33 Differential and integral operators on manifolds
- 19.19.33.19 Foliations. Integration of vector and tensor fields
- 19.19.33.25 Elliptic operators on manifolds

- 19.19.17 Topology of manifolds of lower dimensions
- 19.21 Analytic spaces
- 19.21.15 General theory of complex and real analytic spaces
- 19.21.15.15 Local theory
- 19.21.15.17 Classes of analytic spaces identified by local conditions
- 19.21.15.19 General theory of coherent analytic sheaves and their cohomology
- 19.21.15.19.19 A connection between the cohomologies of complex spaces and differential forms
- 19.21.15.19.19.21 Residues of differential forms

- 19.21.15.19.25 Computation of the cohomology of specific complex spaces
- 19.21.15.19.27 The Riemann-Roch theorem for complex manifolds, and related problems

- 19.21.15.19.19 A connection between the cohomologies of complex spaces and differential forms
- 19.21.15.25 Analytic sets, subspaces and submanifolds
- 19.21.15.27 Integration on analytic sets and analytic spaces
- 19.21.15.31 Intrinsic metrics on complex spaces

- 19.21.17 Analytic mappings and constructions of complex spaces
- 19.21.17.17 Holomorphic mappings of complex spaces
- 19.21.17.17.17 Holomorphic functions. Domains and holomorphy hulls in analytic spaces
- 19.21.17.17.19 Cohomology investigation of holomorphic mappings
- 19.21.17.17.25 Approximation theorems for holomorphic functions and mappings in analytic spaces. Runge pairs

- 19.21.17.19 Plurisubharmonic functions, pseudo-convex and pseudo-concave domains in analytic spaces and their generalizations
- 19.21.17.19.19 The Levi problem for analytic spaces

- 19.21.17.21 Meromorphic mappings
- 19.21.17.21.17 Fields of meromorphic functions
- 19.21.17.21.21 Cousin and Poincaré problems for analytic spaces

- 19.21.17.27 Quotient spaces of complex spaces
- 19.21.17.31 Analytic coverings
- 19.21.17.33 Modification of complex spaces
- 19.21.17.33.19 Resolution of singularities of complex spaces and mappings

- 19.21.17.17 Holomorphic mappings of complex spaces
- 19.21.19 Complex spaces of one, two and three dimensions
- 19.21.19.17 One-dimensional complex manifolds
- 19.21.19.21 Complex surfaces
- 19.21.19.21.15 Singular points of complex surfaces

- 19.21.19.27 Three-dimensional complex spaces

- 19.21.21 Classes of complex spaces distinguished by global conditions
- 19.21.21.17 Holomorphically convex spaces
- 19.21.21.19 Holomorphically complete spaces
- 19.21.21.21 q-pseudo-convex, q-pseudo-concave and q-complete spaces
- 19.21.21.25 Complex spaces that are close to algebraic manifolds
- 19.21.21.31 Global properties of real-analytic spaces

- 19.21.25 Generalizations of analytic spaces
- 19.21.25.17 Banach analytic spaces
- 19.21.25.21 Partially analytic and other spaces
- 19.21.25.31 Analytic investigation of almost complex manifolds

- 19.21.27 Holomorphic fiber spaces
- 19.21.27.17 Classification of holomorphic fiber spaces
- 19.21.27.19 Holomorphic vector fiber spaces and sheaves and related cohomologies
- 19.21.27.21 Holomorphic and meromorphic sections in fiber spaces
- 19.21.27.27 A connection between the theory of fiber spaces and some problems in analysis
- 19.21.27.33 Holomorphic connections in fiber spaces

- 19.21.31 Complex spaces with an automorphism group
- 19.21.31.17 Complex Lie transformation groups
- 19.21.31.21 Automorphism groups of complex and almost complex spaces
- 19.21.31.25 Complex homogeneous spaces
- 19.21.31.25.17 Compact complex homogeneous spaces
- 19.21.31.25.19 Kählerian homogeneous spaces. Homogeneous domains
- 19.21.31.25.21 Analytic functions on homogeneous spaces
- 19.21.31.25.27 Homogeneous vector fiber spaces and related cohomologies

- 19.21.33 Automorphic functions
- 19.21.33.15 Automorphic and modular forms
- 19.21.33.17 Abelian functions
- 19.21.33.19 Modular functions
- 19.21.33.25 Automorphic forms and related cohomologies
- 19.21.33.27 Automorphic functions in symmetric domains

- 19.21.39 Deformations of structures. Pseudogroups
- 19.21.39.15 Cohomology problems in the theory of pseudogroups
- 19.21.39.17 Deformations of complex structures
- 19.21.39.17.17 Deformations of submanifolds and holomorphic mappings
- 19.21.39.17.19 Extension of analytic objects
- 19.21.39.17.25 Theory of moduli of Riemann surfaces

- 19.21.39.19 Deformations of other pseudogroup structures
- 19.21.39.21 Deformations of G-structures and connections
- 19.21.39.25 Deformations of fiber spaces
- 19.21.39.33 Analytic theory of deformations of algebraic structures

- 19.21.15 General theory of complex and real analytic spaces

- 21.15 Geometry in spaces with fundamental groups
- 21.15.15 Elementary geometry, trigonometry, polygonometry
- 21.15.15.17 Planimetry
- 21.15.15.17.19 Triangle geometry
- 21.15.15.17.21 Geometry of polygons (including rectangles, etc.)
- 21.15.15.17.27 Elementary circle geometry

- 21.15.15.19 Stereometry
- 21.15.15.19.21 Geometry of tetrahedra
- 21.15.15.19.25 Geometry of polyhedra (polytopes)
- 21.15.15.19.27 Geometry of spheres and cylinders

- 21.15.15.21 Elementary geometry in multidimensional spaces
- 21.15.15.25 Theory of geometric constructions
- 21.15.15.27 Trigonometry and polygonometry
- 21.15.15.27.17 Plane trigonometry
- 21.15.15.27.19 Spherical trigonometry

- 21.15.15.17 Planimetry
- 21.15.17 Foundations of geometry. Axiomatics
- 21.15.19 Euclidean, pseudo-Euclidean and non-Euclidean geometries
- 21.15.19.15 Euclidean and pseudo-Euclidean geometries
- 21.15.19.15.21 Analytic geometry in Euclidean spaces
- 21.15.19.15.25 Pseudo-Euclidean spaces
- 21.15.19.15.27 Galilei spaces
- 21.15.19.15.31 Semi-Euclidean spaces
- 21.15.19.15.33 Flag spaces

- 21.15.19.17 Non-Euclidean geometries
- 21.15.19.17.17 Lobachevskii geometry
- 21.15.19.17.19 Other hyperbolic geometries
- 21.15.19.17.25 Elliptic geometries
- 21.15.19.17.27 Quasi-elliptic and quasi-hyperbolic spaces
- 21.15.19.17.31 Semi-elliptic and semi-hyperbolic spaces

- 21.15.19.15 Euclidean and pseudo-Euclidean geometries
- 21.15.21 Affine and projective geometries
- 21.15.21.17 Affine geometry
- 21.15.21.17.15 Synthetic geometry in affine space
- 21.15.21.17.17 Analytic geometry in affine space

- 21.15.21.21 Projective geometry
- 21.15.21.21.15 Synthetic geometry in projective space
- 21.15.21.21.17 Analytic geometry in projective space

- 21.15.21.17 Affine geometry
- 21.15.25 Geometry in spaces with other fundamental groups
- 21.15.25.17 Conformal geometry and its analogues
- 21.15.25.21 Symplectic geometry
- 21.15.25.31 Bi-axial geometry and its generalizations

- 21.15.27 Geometry over algebras
- 21.15.27.15 Affine and projective spaces over algebras
- 21.15.27.17 Quadratic Euclidean and non-Euclidean spaces
- 21.15.27.19 Hermitian Euclidean and non-Euclidean spaces
- 21.15.27.21 Symplectic spaces
- 21.15.27.39 Geometry of other spaces over algebras

- 21.15.31 Convex sets, arrangements of geometric figures, and geometric inequalities
- 21.15.31.17 Convex sets
- 21.15.31.17.17 Convex curves and surfaces
- 21.15.31.17.21 Convex bodies
- 21.15.31.17.21.25 Convex polygons and polyhedra

- 21.15.31.19 Generalizations of convex sets
- 21.15.31.21 Arrangements of geometric figures
- 21.15.31.21.17 Packings
- 21.15.31.21.19 Coverings
- 21.15.31.21.25 Partitions
- 21.15.31.21.27 Lattices

- 21.15.31.31 Geometric inequalities
- 21.15.31.31.17 Extremal problems in geometry

- 21.15.31.17 Convex sets
- 21.15.33 Descriptive geometry
- 21.15.33.15 Theoretical problems in descriptive geometry
- 21.15.33.17 Applied methods in descriptive geometry
- 21.15.33.25 Generalizations of descriptive geometry

- 21.15.15 Elementary geometry, trigonometry, polygonometry
- 21.17 Algebraic and analytic methods in geometry
- 21.17.17 Vector algebra and vector analysis
- 21.17.17.17 Vector algebra
- 21.17.17.21 Vector analysis (vector field theory)

- 21.17.19 Tensor algebra and tensor analysis
- 21.17.19.17 Tensor algebra
- 21.17.19.19 Tensor analysis

- 21.17.21 Spinors, spinor algebra and analysis
- 21.17.21.17 Spinor algebra
- 21.17.21.21 Spinor analysis

- 21.17.25 Calculus of exterior forms
- 21.17.25.17 Grassmannian algebra and its generalizations
- 21.17.25.21 Theory of exterior differential forms
- 21.17.25.25 Differential algebras and their geometric applications
- 21.17.25.33 Theory of the compatibility of systems of differential equations

- 21.17.31 Geometric objects
- 21.17.31.17 Representations of Lie groups, and geometric objects
- 21.17.31.19 Representations of infinite Lie pseudogroups, and differential-geometric objects
- 21.17.31.21 Extensions of geometric objects
- 21.17.31.27 Lie differentiation

- 21.17.33 Differential-geometric methods for investigations of embedded manifolds
- 21.17.33.17 Moving frame of a manifold
- 21.17.33.21 Geometric objects on embedded manifolds

- 21.17.17 Vector algebra and vector analysis
- 21.19 Differential geometry
- 21.19.25 Differential geometry in spaces with fundamental groups
- 21.19.25.17 Differential geometry in Euclidean, pseudo-Euclidean and semi-Euclidean spaces
- 21.19.25.17.17 Theory of curved lines
- 21.19.25.17.19 Theory of surface bands
- 21.19.25.17.21 Theory of surfaces
- 21.19.25.17.21.19 Surfaces in a three-dimensional space
- 21.19.25.17.21.21 Surfaces in a multidimensional space

- 21.19.25.17.25 Theory of families of straight lines and planes
- 21.19.25.17.27 Theory of families of curved lines and surfaces
- 21.19.25.17.31 Differential geometry of vector fields
- 21.19.25.17.33 Theory of nonholonomic manifolds

- 21.19.25.19 Differential geometry in non-Euclidean spaces
- 21.19.25.19.17 Differential geometry in non-Euclidean spaces with degenerate absolute
- 21.19.25.19.17.17 Theory of curved lines
- 21.19.25.19.17.19 Theory of surface bands
- 21.19.25.19.17.21 Theory of surfaces
- 21.19.25.19.17.25 Theory of families of straight lines and planes
- 21.19.25.19.17.27 Theory of families of lines and surfaces
- 21.19.25.19.17.33 Theory of nonholonomic manifolds

- 21.19.25.19.19 Differential geometry in non-Euclidean spaces with degenerate absolute
- 21.19.25.19.19.17 Theory of curved lines
- 21.19.25.19.19.21 Theory of surfaces
- 21.19.25.19.19.25 Theory of families of straight lines and planes

- 21.19.25.19.17 Differential geometry in non-Euclidean spaces with degenerate absolute
- 21.19.25.21 Affine differential geometry
- 21.19.25.21.17 Affine theory of curved lines
- 21.19.25.21.19 Affine theory of surface bands
- 21.19.25.21.21 Affine theory of surfaces
- 21.19.25.21.25 Affine theory of families of straight lines and planes
- 21.19.25.21.27 Affine theory of families of curved lines and surfaces
- 21.19.25.21.31 Affine differential geometry of vector fields
- 21.19.25.21.33 Affine theory of nonholonomic manifolds

- 21.19.25.25 Projective differential geometry
- 21.19.25.25.17 Projective theory of curved lines
- 21.19.25.25.19 Projective theory of surface bands
- 21.19.25.25.21 Projective theory of surfaces
- 21.19.25.25.25 Projective theory of families of straight lines and planes
- 21.19.25.25.27 Projective theory of families of curved lines and surfaces
- 21.19.25.25.33 Projective theory of nonholonomic manifolds

- 21.19.25.27 Differential geometry in spaces with other fundamental groups
- 21.19.25.27.17 Differential geometry in conformal and pseudo-conformal spaces
- 21.19.25.27.21 Differential geometry in symplectic spaces
- 21.19.25.27.31 Differential geometry in bi-axial and bi-affine spaces and their generalizations

- 21.19.25.31 Differential geometry of point mappings
- 21.19.25.31.17 Differential geometry of point mappings of affine and projective spaces
- 21.19.25.31.19 Differential geometry of point mappings of Euclidean, pseudo-Euclidean, conformal and other spaces with a metric
- 21.19.25.31.21 Mapping of submanifolds with point mappings of spaces with a fundamental group

- 21.19.25.33 Kinematic geometry

- 21.19.25.17 Differential geometry in Euclidean, pseudo-Euclidean and semi-Euclidean spaces
- 21.19.27 Geometry of differentiable manifolds and their submanifolds
- 21.19.27.17 Geometry of fiber spaces
- 21.19.27.17.17 General problems in the geometry of fiber spaces
- 21.19.27.17.17.31 Geometry of submanifolds in fiber spaces

- 21.19.27.17.19 Fiber spaces of geometric objects
- 21.19.27.17.19.17 Geometry of vector bundles
- 21.19.27.17.19.19 Geometry of tensor bundles
- 21.19.27.17.19.21 Fiber spaces of other geometric objects
- 21.19.27.17.19.27 Differential extension of spaces of geometric objects
- 21.19.27.17.19.31 Fields of geometric objects in fiber spaces and their extensions

- 21.19.27.17.25 Connections in fiber spaces
- 21.19.27.17.25.15 Nonlinear connections
- 21.19.27.17.25.17 Linear connections in principal fiber spaces
- 21.19.27.17.25.19 Linear connections in spaces with homogeneous fibers
- 21.19.27.17.25.21 Linear connections in spaces of geometric objects

- 21.19.27.17.31 Holonomy groups of fiber spaces

- 21.19.27.17.17 General problems in the geometry of fiber spaces
- 21.19.27.19 Infinitesimal structures and fields of geometric objects on differentiable manifolds
- 21.19.27.19.17 Differential geometry of vector and tensor fields on manifolds
- 21.19.27.19.19 G-structures on differentiable manifolds
- 21.19.27.19.19.15 General problems in the geometry of G-structures
- 21.19.27.19.19.17 Tensor G-structures
- 21.19.27.19.19.17.31 Submanifolds in manifolds of tensor G-structures

- 21.19.27.19.19.19 Symplectic and cosymplectic structures
- 21.19.27.19.19.19.31 Submanifolds in manifolds of symplectic and cosymplectic structures

- 21.19.27.19.19.21 Contact and almost contact structures
- 21.19.27.19.19.21.31 Submanifolds in manifolds of contact and almost contact structures

- 21.19.27.19.19.25 Structures of an almost product
- 21.19.27.19.19.25.31 Submanifolds in manifolds of structures of almost products

- 21.19.27.19.19.27 Structures defined by algebras
- 21.19.27.19.19.27.31 Submanifolds in manifolds of structures defined by algebras

- 21.19.27.19.19.31 Other special G-structures
- 21.19.27.19.19.31.31 Submanifolds in manifolds of other special G-structures

- 21.19.27.19.19.33 Mapping of manifolds with G-structures

- 21.19.27.19.21 Manifolds with complex or almost complex structure
- 21.19.27.19.21.17 Manifolds with complex structure
- 21.19.27.19.21.17.17 Hermitian manifolds
- 21.19.27.19.21.17.21 Kählerian manifolds

- 21.19.27.19.21.19 Manifolds with an almost complex structure
- 21.19.27.19.21.19.17 Almost Hermitian and subordinate structures

- 21.19.27.19.21.21 Connections on manifolds with complex or almost complex structure
- 21.19.27.19.21.25 Mappings of manifolds with complex structure
- 21.19.27.19.21.31 Submanifolds embedded in manifolds with complex or almost complex structure

- 21.19.27.19.21.17 Manifolds with complex structure
- 21.19.27.19.25 Infinitesimal structures and fields of of geometric objects of higher orders
- 21.19.27.19.25.15 General theory of tangent bundles (higher orders)
- 21.19.27.19.25.17 Jet theory
- 21.19.27.19.25.19 Tensors and tensor fields of higher orders
- 21.19.27.19.25.25 Fields of other geometric objects of higher orders
- 21.19.27.19.25.31 Higher-order connections on a differentiable manifold

- 21.19.27.19.27 Finsler geometry and its generalizations
- 21.19.27.19.27.17 Finsler geometry
- 21.19.27.19.27.17.21 Submanifolds of Finsler spaces

- 21.19.27.19.27.19 Interval geometry
- 21.19.27.19.27.19.31 Geometry of the calculus of variations

- 21.19.27.19.27.21 Geometry of a space of linear elements
- 21.19.27.19.27.25 Geometry of spaces with other generating elements

- 21.19.27.19.27.17 Finsler geometry
- 21.19.27.19.31 Web geometry
- 21.19.27.19.33 Geometry of differential equations

- 21.19.27.21 Classical spaces with connections and their generalizations
- 21.19.27.21.17 Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.15 General theory of Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.15.17 Invariant objects in Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.15.21 Holonomy groups of Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.15.27 Complete Riemann spaces

- 21.19.27.21.17.17 Special types of Riemann spaces
- 21.19.27.21.17.17.15 Subprojective spaces and their generalizations
- 21.19.27.21.17.17.19 Reducible and semi-reducible Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.17.21 Recurrent Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.17.27 Einstein spaces
- 21.19.27.21.17.17.31 Symmetric Riemann spaces and their generalizations

- 21.19.27.21.17.25 Mappings of Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.25.21 Isometric mappings, immersions and submersions of Riemann spaces

- 21.19.27.21.17.31 Submanifolds of Riemann and pseudo-Riemann spaces
- 21.19.27.21.17.31.17 Curves and families of curves
- 21.19.27.21.17.31.21 Hypersurfaces
- 21.19.27.21.17.31.33 Submanifolds of other dimensions

- 21.19.27.21.17.15 General theory of Riemann and pseudo-Riemann spaces
- 21.19.27.21.19 Spaces with affine connection
- 21.19.27.21.19.15 General theory of spaces with affine connection
- 21.19.27.21.19.17 Special types of spaces with affine connection
- 21.19.27.21.19.17.17 Spaces with equivalent connection
- 21.19.27.21.19.17.19 Weyl spaces
- 21.19.27.21.19.17.21 Projective-Euclidean spaces
- 21.19.27.21.19.17.27 Spaces with absolute parallelism
- 21.19.27.21.19.17.31 Symmetric spaces with affine connection
- 21.19.27.21.19.17.33 Semi-Riemann spaces

- 21.19.27.21.19.25 Mappings of spaces with affine connection
- 21.19.27.21.19.31 Submanifolds of spaces with affine connection

- 21.19.27.21.21 Spaces with projective connection
- 21.19.27.21.21.15 General theory of spaces with projective connection
- 21.19.27.21.21.31 Submanifolds of spaces with projective connection

- 21.19.27.21.25 Spaces with conformal connection
- 21.19.27.21.27 Spaces with symplectic connection
- 21.19.27.21.31 Spaces with generalized Euclidean and pseudo-Euclidean connections
- 21.19.27.21.39 Other classical spaces with connections

- 21.19.27.21.17 Riemann and pseudo-Riemann spaces
- 21.19.27.25 Geometry of homogeneous spaces. Geometry of Lie groups
- 21.19.27.25.15 Invariant infinitesimal structures in homogeneous spaces
- 21.19.27.25.17 Vector and tensor fields in homogeneous spaces
- 21.19.27.25.25 Manifolds embedded in homogeneous spaces
- 21.19.27.25.31 Integral geometry

- 21.19.27.17 Geometry of fiber spaces
- 21.19.31 Global differential geometry
- 21.19.31.17 Global differential geometry of submanifolds. Nonregular submanifolds
- 21.19.31.17.17 Global geometry of lines and surfaces in spaces with fundamental groups
- 21.19.31.17.17.17 Regular lines and surfaces
- 21.19.31.17.17.21 Nonregular lines and surfaces

- 21.19.31.17.19 Global images
- 21.19.31.17.19.17 Existence, embedding and realization of global images
- 21.19.31.17.19.25 Uniqueness, rigidity and bendability of global images

- 21.19.31.17.17 Global geometry of lines and surfaces in spaces with fundamental groups

- 21.19.31.17 Global differential geometry of submanifolds. Nonregular submanifolds
- 21.19.33 Geometry of metrized manifolds
- 21.19.33.17 Minkowski geometry
- 21.19.33.21 Hilbert geometry
- 21.19.33.33 Geometry of geodesics

- 21.19.25 Differential geometry in spaces with fundamental groups
- 21.21 Geometric investigation of objects in the natural sciences
- 21.21.17 Geometric problems and methods in the theory of relativity
- 21.21.17.15 Geometric problems in special relativity
- 21.21.17.17 Geometric problems in general relativity
- 21.21.17.19 Geometric problems in cosmology
- 21.21.17.21 Geometric problems in unified field theory

- 21.21.19 Geometric investigation of fields of physical objects
- 21.21.21 Geometric methods in quantum mechanics and elementary particle theory
- 21.21.25 Geometric methods in mechanics and engineering
- 21.21.25.15 Geometric methods in statistics
- 21.21.25.17 Geometric methods in kinematics
- 21.21.25.19 Geometric methods in dynamics
- 21.21.25.25 Geometric methods in engineering
- 21.21.25.31 Geometric methods in continuum mechanics
- 21.21.25.31.17 Geometric methods in the theory of shells

- 21.21.31 Geometric problems and methods in crystallography
- 21.21.33 Geometric problems and methods in optics

- 21.21.17 Geometric problems and methods in the theory of relativity

- 23.15 Introduction to analysis, and some special problems in analysis
- 23.15.19 Theory of real numbers
- 23.15.25 Asymptotic formulas and expressions
- 23.15.27 Analytic means. Inequalities
- 23.15.27.17 Means
- 23.15.27.25 Numerical inequalities and some elementary functional inequalities

- 23.15.33 Study of individual functions

- 23.17 Differential and integral calculus
- 23.17.17 Differential calculus
- 23.17.17.31 Mappings. Implicit functions
- 23.17.17.33 Other analytic applications of differential calculus

- 23.17.19 Integral calculus
- 23.17.19.31 Red? integrals
- 23.17.19.31.19 Integrals over curved manifolds (curvilinear and surface integrals)

- 23.17.19.33 Definite simple or multiple integrals
- 23.17.19.33.17 Improper integrals

- 23.17.19.31 Red? integrals

- 23.17.17 Differential calculus
- 23.19 Functional equations and the theory of finite differences
- 23.19.15 Theory of finite differences
- 23.19.15.17 Finite-difference equations
- 23.19.15.17.21 Recurrent relations and series

- 23.19.15.17 Finite-difference equations
- 23.19.19 Functional equations and inequalities

- 23.19.15 Theory of finite differences
- 23.21 Integral transformations, operational calculus
- 23.21.17 Laplace transform
- 23.21.19 Fourier integral and Fourier transform
- 23.21.21 Other integral transformations and their inversions. Convolutions
- 23.21.25 Operational calculus

- 23.23 Series and sequences
- 23.23.15 Numerical and functional series and sequences
- 23.23.15.15 Special numerical series and sequences
- 23.23.15.15.25 Sums of finite and infinite series

- 23.23.15.17 Convergence
- 23.23.15.25 Multiple series and sequences
- 23.23.15.31 Summation theory
- 23.23.15.31.25 Tauberian theorems

- 23.23.15.15 Special numerical series and sequences
- 23.23.19 Infinite products
- 23.23.21 Continued fractions

- 23.23.15 Numerical and functional series and sequences
- 23.25 Special functions
- 23.25.15 Euler integrals and their generalizations. The gamma function and related functions
- 23.25.17 Probability integral and related functions
- 23.25.19 Elliptic functions and integrals
- 23.25.21 Bessel functions and polynomials and other cylindrical functions
- 23.25.25 Mathieu functions
- 23.25.27 Spherical functions. Legendre polynomials and functions, harmonic polynomials, ultraspherical polynomials. Gegenbauer functions
- 23.25.31 Orthogonal polynomials and their generalizations (Chebyshev, Hermite, Jacobi, Laguerre, et al.)
- 23.25.33 Hypergeometric series and functions. Generalized and degenerate hypergeometric functions and their generalizations
- 23.25.39 Other special functions and special numbers

- 25.15 Descriptive function theory
- 25.17 Metric theory of functions
- 25.17.15 Measures, integration and differentiation
- 25.17.15.15 Measure, capacity
- 25.17.15.15.17 Lebesgue measure
- 25.17.15.15.19 Borel measure
- 25.17.15.15.21 Other measures
- 25.17.15.15.23 Measurable functions
- 25.17.15.15.25 Continuous functions
- 25.17.15.15.27 Additive set functions
- 25.17.15.15.29 Capacity

- 25.17.15.17 Integration theory
- 25.17.15.17.15 Riemann integral
- 25.17.15.17.17 Lebesgue integral
- 25.17.15.17.21 Stieltjes integral
- 25.17.15.17.25 Other integrals (theory)

- 25.17.15.19 Singular integrals
- 25.17.15.21 Integrals of potential type
- 25.17.15.23 Differentiation theory
- 25.17.15.23.17 Differentiable functions
- 25.17.15.23.19 Derivative
- 25.17.15.23.23 Symmetric derivatives

- 25.17.15.27 Mappings
- 25.17.15.29 Curved surfaces
- 25.17.15.29.17 Level sets of functions of several variables

- 25.17.15.15 Measure, capacity
- 25.17.17 Classes (sets) of functions
- 25.17.17.17 Compact families of function
- 25.17.17.17.17 Epsilon nets. Epsilon entropy
- 25.17.17.17.21 Widths

- 25.17.17.19 Embedding theorems for classes of differentiable functions
- 25.17.17.19.18 Inequalities between partial derivatives
- 25.17.17.19.21 Boundary properties of functions
- 25.17.17.19.25 Weight classes
- 25.17.17.19.31 Extension theorems
- 25.17.17.19.33 Integration of classes of functions

- 25.17.17.21 Functions of bounded variation
- 25.17.17.21.17 Absolutely continuous functions
- 25.17.17.21.21 Convex functions and their generalizations

- 25.17.17.25 Quasi-analytic functions
- 25.17.17.27 Other classes of functions
- 25.17.17.31 Superpositions
- 25.17.17.33 Inequalities

- 25.17.17.17 Compact families of function
- 25.17.19 Systems of functions and series in systems of functions
- 25.17.19.17 Completeness and closure of system of functions
- 25.17.19.21 Bases
- 25.17.19.27 Orthogonal systems
- 25.17.19.27.17 Convergence of orthogonal series
- 25.17.19.27.27 Summation of orthogonal series

- 25.17.21 Trigonometric series
- 25.17.21.17 Representation of a function in the form of a trigonometric series
- 25.17.21.19 Uniqueness problems
- 25.17.21.25 Fourier series
- 25.17.21.25.17 Convergence of Fourier series
- 25.17.21.25.19 Absolute convergence of Fourier series
- 25.17.21.25.21 Fourier coefficients
- 25.17.21.25.27 Summation of Fourier coefficients

- 25.17.21.31 Multiple trigonometric series
- 25.17.21.31.25 Multiple Fourier series
- 25.17.21.31.27 Summation of multiple Fourier series

- 25.17.25 Theory of the Fourier integral
- 25.17.25.27 Summability of Fourier integrals

- 25.17.27 Almost periodic functions
- 25.17.27.25 Compactness of systems of almost periodic functions
- 25.17.27.27 Convergence and summability of Fourier series of almost periodic functions
- 25.17.27.31 Interpolation, almost periodic extension of functions
- 25.17.27.33 Approximation of almost periodic functions

- 25.17.15 Measures, integration and differentiation
- 25.19 Approximation theory
- 25.19.17 Approximation by algebraic polynomials
- 25.19.17.17 On an infinite domain
- 25.19.17.19 Of several variables
- 25.19.17.27 Chebyshev-type problems
- 25.19.17.33 Approximation with exact constants

- 25.19.19 Approximation by trigonometric polynomials and entire functions of exponential type
- 25.19.19.17 Approximation in the sense of order
- 25.19.19.21 Approximation with exact constants
- 25.19.19.31 Approximation of functions of several variables

- 25.19.21 Approximation by rational functions
- 25.19.21.19 Nonlinear problems in approximation theory
- 25.19.21.25 Approximation in the Hausdorff metric

- 25.19.25 Integration
- 25.19.25.25 Approximation by spline functions

- 25.19.27 Extremal properties of polynomials and their generalizations
- 25.19.27.17 Inequalities for derivatives of polynomials and their generalizations
- 25.19.27.19 Other inequalities for polynomials and their generalizations
- 25.19.27.25 Zeros of polynomials and their generalizations

- 25.19.31 Theory of quadratures and cubatures
- 25.19.33 Moment theory

- 25.19.17 Approximation by algebraic polynomials

- 27.15 Functions of one complex variable
- 27.15.17 Elementary problems
- 27.15.25 Rational functions in a complex domain
- 27.15.31 Sequences and series of analytic functions
- 27.15.31.19 Power series
- 27.15.31.19.17 Properties of power series associated with the nature of the coefficients
- 27.15.31.19.21 Lacunary power series
- 27.15.31.19.27 Behavior of a power series on the boundary of the disk of convergence. Superconvergence
- 27.15.31.19.33 Analytic continuation. Singular points

- 27.15.31.19 Power series
- 27.15.31.27 Sequences and series of exponentials
- 27.15.31.27.17 Dirichlet series

- 27.15.33 Systems of functions
- 27.15.33.17 Problems of completeness. Closure of a system of functions. Bases
- 27.15.33.19 Sequences and series of polynomials. Orthogonal polynomials
- 27.15.33.25 Problems of approximation in a complex domain. Best approximation
- 27.15.33.25.17 Approximation by rational functions

- 27.15.33.27 Asymptotic representations in a complex domain
- 27.15.33.31 Interpolation. Iteration

- 27.17 Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalization
- 27.17.17 Mappings of special domains
- 27.17.21 Boundary properties of analytic functions, and boundary value problems
- 27.17.21.21 Bounded functions
- 27.17.21.21.19 Generalization of the Schwartz lemma
- 27.17.21.21.25 Generalization of the maximum modulus principle

- 27.17.21.25 Harmonic measure and capacity. Analytic capacity
- 27.17.21.31 Boundary properties of analytic functions
- 27.17.21.31.17 Theory of limit sets
- 27.17.21.31.19 Cauchy-type integral
- 27.17.21.31.27 Other integral representations of analytic functions

- 27.17.21.33 Boundary value problems in the theory of analytic functions

- 27.17.21.21 Bounded functions
- 27.17.25 Theory of Riemann surfaces. Uniformization
- 27.17.25.17 Conformal classes and automorphisms of Riemann surfaces

- 27.17.27 Univalent and multivalent functions
- 27.17.27.15 Univalent functions
- 27.17.27.15.17 Estimates for coefficients and other functionals
- 27.17.27.15.21 Geometric properties of mappings
- 27.17.27.15.31 Covering theorems

- 27.17.27.19 Multivalent functions

- 27.17.27.15 Univalent functions
- 27.17.31 Classes and spaces of analytic functions
- 27.17.31.17 Entire and meromorphic functions
- 27.17.31.17.17 Entire functions of finite order
- 27.17.31.17.21 Meromorphic functions
- 27.17.31.17.27 Generalization of Picard's theorem
- 27.17.31.17.33 Theory of the distribution of values

- 27.17.31.19 Analytic functions in the disk and other domains
- 27.17.31.25 Classes of analytic functions
- 27.17.31.25.17 Functions of bounded type
- 27.17.31.25.21 Noh? and related classes
- 27.17.31.25.27 Algebraic and algebroid functions
- 27.17.31.25.33 Analytic theory of automorphic functions
- 27.17.31.25.33.17 Elliptic and modular functions
- 27.17.31.25.39 Other classes of analytic functions

- 27.17.31.31 Spaces of analytic functions

- 27.17.31.17 Entire and meromorphic functions
- 27.17.33 Generalizations of analytic functions and conformal mappings
- 27.17.33.17 Quasiconformal mappings and their generalizations
- 27.17.33.19 Quasi-analytic classes in a complex domain
- 27.17.33.21 Generalized analytic functions
- 27.17.33.25 Monogenic functions
- 27.17.33.27 Analytic matrices, functions of a matrix argument
- 27.17.33.31 Functions of a hypercomplex variable
- 27.17.33.33 Functions of a discrete argument
- 27.17.33.39 Other generalizations of analytic functions

- 27.19 Functions of several complex variables
- 27.19.15 Series and sequences of functions of several variables
- 27.19.17 Approximation of functions and domains
- 27.19.19 Integral representations
- 27.19.21 Holomorphic functions of several variables. Domains and hulls of holomorphy. Pseudoconvexity
- 27.19.25 Analytic continuation. Singularities
- 27.19.27 Classes and boundary properties of functions of several variables
- 27.19.31 Meromorphic functions of several variables. Cousin and Poincaré problems
- 27.19.33 Entire functions of several complex variables

- 27.24 Harmonic functions and their mappings
- 27.24.17 General properties of harmonic functions
- 27.24.21 Subharmonic functions and their generalizations
- 27.24.25 Biharmonic and polyharmonic functions
- 27.24.27 Pluriharmonic and plurisubharmonic functions
- 27.24.31 Harmonic functions on Riemannian manifolds
- 27.24.33 Other generalizations of harmonic functions

- 29.15 General theory of ordinary differential equations and systems of equations
- 29.15.15 General problems. Existence theorems, uniqueness theorems and theorems on the differential properties of solutions
- 29.15.15.25 Differential equations with discontinuous and multivalued right-hand sides
- 29.15.15.31 Differential inequalities

- 29.15.17 Methods for solving various types of equations and systems of equations
- 29.15.19 First integrals
- 29.15.21 Equations that are not solved with respect to the highest derivative. Singular solutions
- 29.15.23 Special types of ordinary differential equations (Ricatti, hypergeometric, Bessel, Mathieu, Hill, etc.)
- 29.15.25 Pfaffian equations and Pfaffian systems
- 29.15.27 Infinite systems of differential equations

- 29.15.15 General problems. Existence theorems, uniqueness theorems and theorems on the differential properties of solutions
- 29.17 Qualitative theory of ordinary differential equations and systems of equations
- 29.17.15 Systems and analytic theory of ordinary differential equations
- 29.17.15.21 Theory of systems of second-order equations
- 29.17.15.21.15 Location of integral curves. Singular points
- 29.17.15.21.17 Limit cycles and periodic solutions. Oscillation in nonlinear systems
- 29.17.15.21.21 Properties of solutions of second-order equations and second-order systems (asymptotic behavior, monotonicity, estimates for the solutions etc.)
- 29.17.15.21.27 Zeros of solutions of second-order differential equations, oscillating and nonoscillating solutions

- 29.17.15.25 Theory of systems of arbitrary order and of equations of arbitrary order
- 29.17.15.25.15 Stability and asymptotic behavior of solutions
- 29.17.15.25.17 Equations with periodic and almost periodic right-hand sides Periodic and almost periodic solutions. Oscillations in nonlinear multidimensional systems
- 29.17.15.25.19 Integral manifolds
- 29.17.15.25.21 Properties of solutions of equations of arbitrary order and of systems of arbitrary order (asymptotic behavior, monotonicity, estimates for the solutions, etc.)
- 29.17.15.25.27 Zeros of solutions of higher-order equations and systems of equations

- 29.17.15.21 Theory of systems of second-order equations
- 29.17.17 Linear ordinary differential equations and systems
- 29.17.17.21 Linear ordinary differential equations with variable coefficients

- 29.17.19 Theory of dynamical systems
- 29.17.19.25 Topological problems in the theory of dynamical systems

- 29.17.15 Systems and analytic theory of ordinary differential equations
- 29.19 Boundary value problems and eigenvalue problems for ordinary differential equations and systems of equations
- 29.19.17 Boundary value problems for linear ordinary differential equations
- 29.19.17.15 Theorems on the existence, uniqueness and properties of solutions

- 29.19.25 Eigenvalues and eigenfunctions. Eigenfunction expansions
- 29.19.21 Boundary value problems for nonlinear ordinary differential equations
- 29.19.27 Multipoint boundary value problems and functional problems for ordinary differential equations

- 29.19.17 Boundary value problems for linear ordinary differential equations
- 29.21 Analytic theory of ordinary differential equations and systems of equations
- 29.21.15 Singular points of equations in a complex domain
- 29.21.25 Expansions of solutions in series in a complex domain
- 29.21.31 Expansions of solutions of equations and systems with a complex parameter

- 29.23 Asymptotic methods in the theory of ordinary differential equations and systems of equations
- 29.23.15 General theory of asymptotic methods
- 29.23.17 Linear ordinary differential equations and systems with small parameters multiplying the highest derivatives
- 29.23.31 Averaging methods and invariant manifolds. Problems in nonlinear mechanics

- 29.25 Functional-differential and discrete equations and systems of equations with one independent variable
- 29.25.17 Linear difference equations
- 29.25.21 Stability theory
- 29.25.25 Periodic solutions
- 29.25.31 Boundary value problems
- 29.25.33 Asymptotic methods

- 29.27 Equations of analytical mechanics, mathematical theory of the control of motion
- 29.27.19 Equations of analytical mechanics
- 29.27.25 Equations of automatic control systems
- 29.27.25.17 Equations of linear automatic control systems
- 29.27.25.21 Equations of nonlinear automatic control systems

- 31.15 General theory of partial differential equations and systems of partial differential equations
- 31.15.17 General first-order equations and systems: properties, types, etc.
- 31.15.19 General higher-order equations and systems: properties, types, etc.
- 31.15.21 Boundary value problems: general theory, equations on manifolds
- 31.15.25 The Cauchy problem for partial differential equations
- 31.15.25.17 Well-posedness theory
- 31.15.25.21 Semigroups associated with the Cauchy problem

- 31.17 Linear and quasilinear equations and systems of equations
- 31.17.17 Elliptic equations and systems
- 31.17.17.17 Linear equations of elliptic type
- 31.17.17.17.17 General properties
- 31.17.17.17.19 Boundary value problems
- 31.17.17.17.21 Potential theory. Potentials
- 31.17.17.17.25 Laplace and Poisson equations
- 31.17.17.17.27 Degenerate equations. Equations with a small parameter
- 31.17.17.17.31 Spectral theory

- 31.17.17.25 Quasilinear equations of elliptic type
- 31.17.17.31 Inverse problems
- 31.17.17.39 Ill-posed problems

- 31.17.17.17 Linear equations of elliptic type
- 31.17.19 Hyperbolic equations and systems
- 31.17.19.17 Linear hyperbolic equations
- 31.17.19.17.27 Degenerate equations. Equations with a small parameter
- 31.17.19.17.33 Spectral problems

- 31.17.19.25 Quasilinear hyperbolic equations
- 31.17.19.31 Inverse problems

- 31.17.19.17 Linear hyperbolic equations
- 31.17.21 Parabolic equations and systems
- 31.17.21.25 Nonlinear problems
- 31.17.21.31 Inverse problems

- 31.17.27 Equations of mixed and composite types

- 31.17.17 Elliptic equations and systems
- 31.19 Asymptotic behavior of solutions
- 31.21 Nonlinear equations and systems of equations

- 33.15 Linear integral equations
- 33.15.15 Fredholm integral equations
- 33.15.17 Volterra integral equations
- 33.15.19 Singular integral equations and related boundary value problems
- 33.15.25 Linear integral equations in function spaces
- 33.15.33 Systems of linear integral equations

- 33.17 Nonlinear integral equations
- 33.17.19 Nonlinear singular integral equations and related boundary value problems
- 33.17.33 Systems of nonlinear integral equations

- 33.19 Integro-differential equations
- 33.19.17 Linear integro-differential equations
- 33.19.19 Singular integro-differential equations
- 33.19.21 Nonlinear integro-differential equations
- 33.19.33 Systems of integro-differential equations

- 35.15 Mathematical models in aero- and hydrodynamics and acoustics
- 35.17 Mathematical models in gas dynamics
- 35.19 Flow problems
- 35.21 Mathematical models in hydrodynamics
- 35.21.15 Hydrodynamics of an ideal fluid
- 35.21.17 Hydrodynamics of a viscous fluid

- 35.23 Mathematical models in the theory of a boundary layer
- 35.25 Mathematical models in filtration
- 35.27 Mathematical models of the wave motions of a heavy fluid
- 35.29 Mathematical models in magnetohydrodynamics
- 35.31 Mathematical models in elasticity and plasticity
- 35.31.15 Dynamical problems
- 35.31.17 Plane and contact problems
- 35.31.19 Three-dimensional problems
- 35.31.21 Thermoelasticity
- 35.31.25 Plates and shells
- 35.31.27 Plastic media

- 35.33 Mathematical models in electrodynamics and optics
- 35.35 Mathematical theory of diffraction
- 35.37 Mathematical models of the electrodynamics of moving media
- 35.39 Mathematical models in gravitation and cosmology
- 35.41 Mathematical models of waveguides
- 35.43 Mathematical models in biology
- 35.45 Mathematical models in heat conduction and diffusion
- 35.45.17 The Stefan problem
- 35.45.19 Heat exchange problems

- 35.47 Transport equations
- 35.49 Mathematical models in statistical physics
- 35.51 Mathematical models in plasma physics, kinetic equations
- 35.53 Mathematical models of electromagnetic waves in plasma
- 35.55 Soliton solutions of evolution equations
- 35.57 Mathematical models in quantum physics
- 35.59 Methods in perturbation theory
- 35.63 Mathematical models in geophysics and meteorology

- 37.15 Calculus of variations
- 37.15.17 Functional analytic methods of the calculus of variations
- 37.15.17.17 Necessary conditions based on the theory of first and second variations
- 37.15.17.19 Sufficient conditions
- 37.15.17.21 Problems on the existence of solutions of variational problems. Theory of the existence of solutions
- 37.15.17.25 Variational methods for solving differential, integral, and other functional equations
- 37.15.17.27 Minimal surfaces
- 37.15.17.31 Inverse problems in the calculus of variations
- 37.15.17.33 Extremal problems in linear topological spaces and concepts associated these problems
- 37.15.17.39 Various special problems in the calculus of variations

- 37.15.21 Topological methods in the calculus of variations
- 37.15.21.33 Variational theory of geodesics

- 37.15.17 Functional analytic methods of the calculus of variations
- 37.17 Mathematical control theory. Optimal control
- 37.17.15 General theory of control systems, and controllability (mathematical theory)
- 37.17.25 Optimal control
- 37.17.25.17 Maximum principle
- 37.17.25.21 Dynamic programming methods
- 37.17.25.25 Theory of linear optimal systems
- 37.17.25.27 Optimal control of systems with distributed parameters
- 37.17.25.31 Problems of the existence of optimal solutions
- 37.17.25.35 Approximate methods for solving optimal control problems

- 37.19 Differential games
- 37.19.17 Two-person differential games
- 37.19.21 n-person differential games

- 39.15 Linear spaces endowed with topology, order, and other structures
- 39.15.15 Ordered and semi-ordered spaces
- 39.15.17 Linear topological spaces
- 39.15.17.17 Normed spaces. Banach space. Hilbert space
- 39.15.17.17.21 Hilbert spaces with an indefinite metric

- 39.15.17.25 Geometry of linear topological spaces
- 39.15.17.25.17 Convex sets in linear spaces
- 39.15.17.25.21 Bases in linear topological spaces
- 39.15.17.25.27 Geometric problems in approximation theory in linear spaces
- 39.15.17.25.31 Approximate dimension and related problems

- 39.15.17.27 Abstract potential theory
- 39.15.17.31 Concrete topological linear spaces. Interpolation theorems
- 39.15.17.31.17 Spaces of continuous functions
- 39.15.17.31.21 Spaces of analytic functions
- 39.15.17.31.27 Spaces of sequences and matrices

- 39.15.17.17 Normed spaces. Banach space. Hilbert space
- 39.15.19 Linear functionals and conjugate spaces
- 39.15.19.25 Positive-definite functionals in function spaces
- 39.15.19.25.21 Problems of the continuation of positive-definite functionals and positive-definite kernels

- 39.15.19.31 Moment theory

- 39.15.19.25 Positive-definite functionals in function spaces

- 39.17 Generalized functions
- 39.17.17 Homogeneous generalized functions
- 39.17.19 Fourier transform of generalized functions. Convolutions
- 39.17.25 Algebraic theory of generalized functions. (Operational calculus of Mikusinski, et al.)
- 39.17.27 Generalized distributions (hyperfunctions, ultradistributions, etc.)
- 39.17.31 Linear analytic functionals

- 39.19 Linear operators and operator equations
- 39.19.17 Linear operators in linear infinite-dimensional spaces; general properties
- 39.19.17.17 Linear operators in locally convex spaces
- 39.19.17.19 Linear operators in Banach spaces
- 39.19.17.21 Linear operators in Hilbert spaces
- 39.19.17.21.19 Normal and unitary operators in Hilbert spaces
- 39.19.17.21.27 Selfadjoint linear operators in Hilbert and pre-Hilbert spaces
- 39.19.17.21.33 Nonselfadjoint linear operators in Hilbert spaces

- 39.19.17.27 Completely continuous and nuclear operators
- 39.19.17.31 Linear operators in semi-ordered spaces
- 39.19.17.33 Theory of perturbations of linear operators

- 39.19.19 Study of concrete operators
- 39.19.19.19 Infinite matrices
- 39.19.19.21 Integral operators
- 39.19.19.25 Ordinary differential operators
- 39.19.19.27 Partial differential operators
- 39.19.19.31 Pseudodifferential operators

- 39.19.25 Linear equations in infinite-dimensional linear spaces
- 39.19.25.15 General theory of solvability of linear equations in function-spaces
- 39.19.25.19 Linear equations in concrete function spaces
- 39.19.25.21 Linear ill-posed problems

- 39.19.27 Vector functions and operator functions
- 39.19.33 Families of linear spaces and categories of linear operators

- 39.19.17 Linear operators in linear infinite-dimensional spaces; general properties
- 39.21 Spectral theory of linear operators
- 39.21.17 Spectral theory in general linear topological spaces and in spaces with a quasi-topology
- 39.21.17.17 Abstract operational calculus of linear operators
- 39.21.17.21 Spectral theory of completely continuous linear operators
- 39.21.17.27 Problems of completeness of (generalized) eigen- and associated vectors

- 39.21.19 Spectral theory in Banach spaces
- 39.21.19.17 Spectral theory of completely continuous and nuclear operators in Banach spaces
- 39.21.19.21 Spectral theory of Volterra operators in Banach spaces
- 39.21.19.27 Problems of linear similarity, and the equivalence of linear operators

- 39.21.21 Spectral theory in Hilbert spaces
- 39.21.21.17 Spectral theory of completely continuous and nuclear operators in Hilbert spaces
- 39.21.21.21 Spectral theory of Volterra operators in a Hilbert space
- 39.21.21.27 Spectral theory of selfadjoint operators in a Hilbert space
- 39.21.21.33 Spectral theory of nonselfadjoint operators in Hilbert spaces

- 39.21.25 Study of the spectrum of concrete operators
- 39.21.25.15 Spectra of infinite matrices
- 39.21.25.19 Spectra of integral operators
- 39.21.25.25 Spectra of ordinary differential operators
- 39.21.25.27 Spectra of partial differential operators
- 39.21.25.31 Spectra of pseudodifferential operators

- 39.21.27 Special problems in the spectral theory of linear operators
- 39.21.27.17 Expansions in eigen- and associated functions
- 39.21.27.21 Inverse problems in spectral analysis
- 39.21.27.27 Perturbation of the spectrum of linear operators
- 39.21.27.31 Extension of operators

- 39.21.17 Spectral theory in general linear topological spaces and in spaces with a quasi-topology
- 39.23 Topological algebras and the theory of infinite-dimensional representations
- 39.23.17 Topological algebras (rings) and their continuous representations
- 39.23.17.17 Normed algebras and their representations
- 39.23.17.17.25 Commutative Banach algebras

- 39.23.17.21 Algebras (rings) with involution
- 39.23.17.21.17 Positive-definite functions on algebras (rings) with involution

- 39.23.17.17 Normed algebras and their representations
- 39.23.19 Algebras (rings) of linear operators
- 39.23.19.17 C*-algebras
- 39.23.19.19 Von Neumann algebras (W*-algebras)

- 39.23.21 Infinite-dimensional representation of groups
- 39.23.25 Infinite-dimensional representation of Lie algebras
- 39.23.27 Harmonic analysis of functions on groups and homogeneous spaces
- 39.23.27.17 Harmonic analysis on abelian groups
- 39.23.27.19 Almost periodic functions on groups
- 39.23.27.27 Group algebras
- 39.23.27.33 Special functions that arise in the theory of finite- and infinite dimensional representations of Lie groups

- 39.23.31 Semigroups of linear and nonlinear operators. Evolution equations
- 39.23.37 Other algebraic structures in functional analysis
- 39.23.39 Applications of functional analysis to quantum mechanics and field theory

- 39.23.17 Topological algebras (rings) and their continuous representations
- 39.25 Measure theory, representations of Boolean algebras, dynamical systems
- 39.25.15 Measure and integral theory
- 39.25.19 Representations of Boolean algebras
- 39.25.21 Functional integrals and their applications to evolution equations
- 39.25.25 Metric theory of dynamical systems

- 39.27 Nonlinear functional analysis
- 39.27.17 Analysis on manifolds
- 39.27.17.17 Function spaces and sections of bundles
- 39.27.17.21 Infinite-dimensional functional analysis (global analysis)
- 39.27.17.27 Operators on manifolds
- 39.27.17.33 Integral geometry

- 39.27.19 Nonlinear functionals
- 39.27.19.17 General topological properties
- 39.27.19.21 Differential calculus for nonlinear functionals
- 39.27.19.31 Differential and analytic properties of nonlinear functionals
- 39.27.19.31.17 Analytic functionals

- 39.27.19.33 Extrema of nonlinear functionals

- 39.27.25 Nonlinear operators
- 39.27.25.17 General properties of nonlinear operators
- 39.27.25.17.15 Condensing operators
- 39.27.25.17.17 Fixed points of nonlinear operators
- 39.27.25.17.25 Monotone operators

- 39.27.25.21 Differential and integral calculus for nonlinear operators
- 39.27.25.31 Eigenvalues of nonlinear operators

- 39.27.25.17 General properties of nonlinear operators
- 39.27.27 Nonlinear equations in function spaces
- 39.27.27.19 Existence and uniqueness theorems for nonlinear equations
- 39.27.27.31 Continuability and branching of solutions of nonlinear equations
- 39.27.27.33 Nonlinear ill-posed problems

- 39.27.17 Analysis on manifolds
- 39.29 Approximate methods in functional analysis

- 41.15 Numerical methods in algebra
- 41.15.17 Numerical methods for solving systems of linear algebraic equations
- 41.15.17.17 The case of a square matrix
- 41.15.17.21 The case of a matrix of general form

- 41.15.19 Numerical methods for inverting matrices
- 41.15.19.17 The case of symmetric matrices
- 41.15.19.19 The case of nonsymmetric matrices

- 41.15.21 Numerical methods for computing the eigenvalues and eigenvectors of matrices
- 41.15.21.17 Partial eigenvalue problem
- 41.15.21.21 Complete eigenvalue problem

- 41.15.25 Numerical methods for solving transcendental equations and systems of equations
- 41.15.25.17 Localization of solutions
- 41.15.25.21 Numerical methods for determining all the zeros of polynomials
- 41.15.25.25 Numerical methods for solving nonlinear systems

- 41.15.17 Numerical methods for solving systems of linear algebraic equations
- 41.17 Numerical methods in analysis
- 41.17.15 Approximation of functions
- 41.17.15.15 Determination of constants
- 41.17.15.17 Uniform approximation
- 41.17.15.19 Mean-square approximation

- 41.17.17 Interpolation and extrapolation
- 41.17.17.15 Parabolic interpolation
- 41.17.17.17 Nonparabolic interpolation
- 41.17.17.19 Spline interpolation

- 41.17.19 Numerical differentiation
- 41.17.21 The method of least squares
- 41.17.31 Empirical formulas
- 41.17.33 Optimization of functions
- 41.17.33.17 Unconstrained optimization
- 41.17.33.21 Constrained optimization

- 41.17.35 Quadrature formulas
- 41.17.35.17 Definite integrals
- 41.17.35.19 Singular integrals
- 41.17.35.25 Improper integrals
- 41.17.35.31 Multiple integrals

- 41.17.15 Approximation of functions
- 41.19 Numerical methods for solving differential and integral equations
- 41.19.15 Numerical methods for solving ordinary differential equations
- 41.19.15.17 The Cauchy problem for ordinary differential equations
- 41.19.15.17.15 First-order differential equations
- 41.19.15.17.17 Systems of ordinary differential equations

- 41.19.15.21 Boundary value problems for ordinary differential equations
- 41.19.15.21.15 First-order differential equations
- 41.19.15.21.17 Second-order differential equations
- 41.19.15.21.19 Higher-order differential equations

- 41.19.15.27 Optimal control problems
- 41.19.15.27.15 Linear problems
- 41.19.15.27.17 Nonlinear problems

- 41.19.15.33 Inverse problems and intensification problems
- 41.19.15.33.15 The case of initial conditions
- 41.19.15.33.17 The case of boundary conditions

- 41.19.15.17 The Cauchy problem for ordinary differential equations
- 41.19.17 Numerical methods for solving partial differential equations
- 41.19.17.13 First-order differential equations and their systems
- 41.19.17.17 Second-order differential equations of elliptic type
- 41.19.17.17.21 Boundary value problems
- 41.19.17.17.27 Problems with characteristic parameters
- 41.19.17.17.33 Inverse problems

- 41.19.17.19 Second-order differential equations of parabolic and hyperbolic types
- 41.19.17.19.17 The Cauchy problem
- 41.19.17.19.27 Mixed problems
- 41.19.17.17.33 Systems of equations
- 41.19.17.17.39 Inverse problems

- 41.19.17.21 Systems of nonlinear differential equations in continuum mechanics
- 41.19.17.25 Higher-order partial differential equations and systems of such equations
- 41.19.17.25.15 Biharmonic equation
- 41.19.17.25.17 Cauchy problems
- 41.19.17.25.21 Boundary value problems
- 41.19.17.25.27 Mixed problems
- 41.19.17.25.31 Inverse problems

- 41.19.19 Numerical methods for solving integral equations
- 41.19.19.17 Integro-differential equations
- 41.19.19.19 Fredholm equations of the first kind
- 41.19.19.21 Fredholm equations of the second kind
- 41.19.19.25 Volterra equations
- 41.19.19.27 Nonlinear equations
- 41.19.19.31 Singular equations
- 41.19.19.33 Operator equations

- 41.19.15 Numerical methods for solving ordinary differential equations
- 41.21 Mathematical tables
- 41.23 Computer, graphic and other methods in numerical mathematics
- 41.23.15 Computer programming
- 41.23.17 Mechanical methods for computations
- 41.23.19 Solution of mathematical problems by means of modeling systems
- 41.23.21 Graphic methods for computations
- 41.23.25 Nomography and nomograms
- 41.23.27 Probabilistic methods for computations
- 41.23.31 Solution of problems in mathematical analysis and of applied problems

- 43.15 Probability theory and random processes
- 43.15.15 Foundations and axioms of probability theory
- 43.15.17 Abstract probability theory
- 43.15.17.17 Combinatorial probabilities
- 43.15.17.19 Geometric probabilities

- 43.15.19 Probability distributions and distribution densities
- 43.15.19.15 The normal distribution
- 43.15.19.17 Characteristic functions, moments, semimartingales and other characteristics
- 43.15.19.19 Measures of dependency
- 43.15.19.25 Infinitely divisible laws
- 43.15.19.31 Stable laws

- 43.15.21 Limit theorems
- 43.15.21.21 for sums of independent random variables
- 43.15.21.25 for sums of weakly dependent random variables
- 43.15.21.27 for functionals and random processes
- 43.15.21.31 on groups and other algebraic structures
- 43.15.21.33 Large deviations

- 43.15.27 Random processes (general questions)
- 43.15.27.17 General theory of random processes
- 43.15.27.17.17 Measures in function spaces
- 43.15.27.17.21 Limit theorems for sequences of random processes

- 43.15.27.19 Prediction theory
- 43.15.27.25 Stopping times
- 43.15.27.33 Martingales

- 43.15.27.17 General theory of random processes
- 43.15.31 Markov processes
- 43.15.31.15 General theory of Markov processes
- 43.15.31.15.17 Properties of sample functions
- 43.15.31.15.19 Infinitesimal and characteristic operators
- 43.15.31.15.21 A strictly Markov process
- 43.15.31.15.27 Topologies associated with a process

- 43.15.31.17 Markov chains: processes with finite or countable set of states
- 43.15.31.19 Processes with independent increments
- 43.15.31.25 Additive functionals. Probabilistic potential theory
- 43.15.31.27 Transformation of Markov processes
- 43.15.31.27.17 Random time change
- 43.15.31.27.19 Subprocesses
- 43.15.31.27.25 Transformations of measures

- 43.15.31.31 Boundary theory of Markov processes
- 43.15.31.31.17 Martin boundary
- 43.15.31.31.21 General boundary conditions

- 43.15.31.15 General theory of Markov processes
- 43.15.33 Random processes of a special type
- 43.15.33.15 Diffusion processes and processes that are solutions of stochastic differential equations
- 43.15.33.17 Branching processes and epidemic processes
- 43.15.33.17.17 General branching processes
- 43.15.33.17.19 Markov branching processes
- 43.15.33.17.21 Processes with increments that depend on the age of the particles
- 43.15.33.17.25 Processes with increments that depend on the location of the particles
- 43.15.33.17.27 Processes with increments that depend on the energy or mass of the particles

- 43.15.33.19 Controlled random processes
- 43.15.33.21 Renewal processes
- 43.15.33.25 Point random processes
- 43.15.33.31 Gaussian processes and measures
- 43.15.33.31.17 Properties of sample functions
- 43.15.33.31.21 Asymptotic weakening of dependence
- 43.15.33.31.25 Derivatives of Gaussian measures

- 43.15.33.33 Stationary and harmonizable sequences and processes
- 43.15.33.33.17 Extrapolation, interpolation, filtering
- 43.15.33.33.21 Ergodic theorems

- 43.15.39 Random functions of several variables
- 43.15.39.17 Homogeneous random fields
- 43.15.39.25 Point random fields

- 43.17 Mathematical statistics
- 43.17.15 Foundations of statistical theory
- 43.17.17 Statistical scattering and dependence. Statistical means, deviations, etc.
- 43.17.19 Sufficiency, sufficient statistics
- 43.17.21 Distribution theory
- 43.17.21.17 Distributions of sample characteristics
- 43.17.21.17.17 Point distributions
- 43.17.21.17.21 Asymptotic theory

- 43.17.21.19 Characterization and structural theory

- 43.17.21.17 Distributions of sample characteristics
- 43.17.27 Theory of statistical inferences and decisions
- 43.17.27.17 Likelihood
- 43.17.27.19 Bayesian theory and problems
- 43.17.27.25 Compound decision problems
- 43.17.27.31 Fiducial probability

- 43.17.31 Methods of statistical analysis and inference
- 43.17.31.19 Parametric methods
- 43.17.31.19.17 Estimation of parameters and functionals
- 43.17.31.19.17.17 Point estimation
- 43.17.31.19.17.21 Confidence regions, tolerance bounds

- 43.17.31.19.19 Hypothesis testing
- 43.17.31.19.19.17 Properties of individual tests
- 43.17.31.19.19.19 Goodness-of-fit tests
- 43.17.31.19.19.25 Discrimination

- 43.17.31.19.21 Variance and covariance analysis
- 43.17.31.19.25 Correlation and regression analysis
- 43.17.31.19.27 Ranking and selection
- 43.17.31.19.33 Paired and multiple comparisons

- 43.17.31.19.17 Estimation of parameters and functionals
- 43.17.31.21 Nonparametric methods
- 43.17.31.21.17 Estimation of parameters and functionals
- 43.17.31.21.17.17 Point estimation
- 43.17.31.21.17.21 Confidence regions, tolerance bounds

- 43.17.31.21.19 Hypothesis testing
- 43.17.31.21.19.17 Properties of individual tests
- 43.17.31.21.19.19 Goodness-of-fit tests
- 43.17.31.21.19.25 Discrimination

- 43.17.31.21.21 Variance and covariance analysis
- 43.17.31.21.25 Correlation and regression analysis
- 43.17.31.21.27 Ranking and selection
- 43.17.31.21.31 Order statistics
- 43.17.31.21.33 Paired comparison methods

- 43.17.31.21.17 Estimation of parameters and functionals
- 43.17.31.25 Statistics of independent random variables. Contingency tables
- 43.17.31.31 Multidimensional statistical methods
- 43.17.31.31.17 Estimation of parameter and functionals
- 43.17.31.31.17.17 Point estimation
- 43.17.31.31.17.21 Confidence regions, tolerance bounds

- 43.17.31.31.19 Hypothesis testing
- 43.17.31.31.19.17 Properties of individual tests
- 43.17.31.31.19.19 Goodness-of-fit tests
- 43.17.31.31.19.25 Discrimination

- 43.17.31.31.21 Variance and covariance analysis
- 43.17.31.31.25 Correlation and regression analysis
- 43.17.31.31.27 Ranking and selection
- 43.17.31.31.31 Factor analysis
- 43.17.31.31.33 Cluster analysis. Classification

- 43.17.31.31.17 Estimation of parameter and functionals

- 43.17.31.19 Parametric methods
- 43.17.33 Special statistical applications and models
- 43.17.33.17 Design of an experiment (general theory)
- 43.17.33.17.25 Optimal designs
- 43.17.33.17.27 Block designs
- 43.17.33.17.31 Factor designs

- 43.17.33.19 Sampling and sampling theory
- 43.17.33.21 Sequential methods
- 43.17.33.21.17 Sequential designs
- 43.17.33.21.19 Sequential analysis
- 43.17.33.21.21 Sequential estimation
- 43.17.33.21.25 Optimal stopping
- 43.17.33.21.33 Cumulative sum technique

- 43.17.33.25 Stochastic approximation. Monte Carlo methods
- 43.17.33.27 Statistics of random processes
- 43.17.33.27.17 Estimation for random processes
- 43.17.33.27.17.17 Mean of a stationary process
- 43.17.33.27.17.25 Correlation function of a stationary process
- 43.17.33.27.17.31 Spectrum of a stationary process

- 43.17.33.27.19 Hypothesis testing for random processes
- 43.17.33.27.25 Statistics of point processes
- 43.17.33.27.33 Analysis of time series
- 43.17.33.27.33.25 Autocorrelation, regression
- 43.17.33.27.33.31 Spectral analysis of time series

- 43.17.33.27.17 Estimation for random processes

- 43.17.33.17 Design of an experiment (general theory)

- 43.51 Application of probability-theoretic and statistical methods
- 43.51.17 Application to the mathematical physical sciences
- 43.51.17.15 Multicomponent random systems. Processes with a large number of locally interacting components
- 43.51.17.17 Gibbs random fields, cluster expansions
- 43.51.17.19 Applications to classical statistical mechanics
- 43.51.17.21 Generalized Gibbs fields. Euclidean quantum field theory
- 43.51.17.25 Random evolution in nonequilibrium statistical mechanics

- 43.51.19 Noncommutative probability theory and its application to quantum physics
- 43.51.21 Application of probability-theoretic and statistical methods to engineering and the humanities
- 43.51.21.15 Applications to mechanics
- 43.51.21.17 Applications to physics
- 43.51.21.21 Applications to geophysics
- 43.51.21.23 Applications to astronomy and geodesy
- 43.51.21.25 Applications to chemistry
- 43.51.21.27 Applications to geography and geology
- 43.51.21.29 Applications to engineering
- 43.51.21.31 Statistical methods in production control
- 43.51.21.33 Applications to radio-engineering
- 43.51.21.35 Applications to automation
- 43.51.21.37 Probability-theoretic reliability theory
- 43.51.21.39 Applications of mathematical statistical methods to psychology, biology and medicine
- 43.51.21.41 Applications to economics and sociology
- 43.51.21.45 Design of specific experiments
- 43.51.21.47 Statistical tables

- 43.51.23 Processing of statistical data
- 43.51.23.17 Data collection and survey design
- 43.51.23.19 Sample surveys: methods, questionnaires; editing, errors and corrections
- 43.51.23.21 Computational processing of data, algorithms
- 43.51.23.25 Formulation of data; format, etc,
- 43.51.23.27 Data storage. Data banks
- 43.51.23.31 Use of statistical data
- 43.51.23.33 Types of statistical data

- 43.51.17 Application to the mathematical physical sciences

- 45.15 General theory of combinatorial analysis
- 45.15.17 Combinatorial choice problems
- 45.15.17.15 Matroids
- 45.15.17.17 Transversals
- 45.15.17.21 Ramsey theory
- 45.15.17.27 Combinatorics of finite lattices
- 45.15.17.31 Extremal combinatorial problems
- 45.15.17.31.15 Problems on a covering and on minimal systems of representatives
- 45.15.17.31.21 Intersections of systems of sets. Spencer theory

- 45.15.19 General enumeration methods
- 45.15.19.15 Polya's theory
- 45.15.19.19 Combinatorics of formal power series. Generating functions
- 45.15.19.25 Incidence algebras, the inclusion-exclusion principle, Möbius theory
- 45.15.19.27 Finite-difference method. Recurrent sequences
- 45.15.19.33 Asymptotic methods

- 45.15.21 Combinatorial sequences of numbers and polynomials
- 45.15.23 Enumeration problems of combinatorial analysis
- 45.15.24 Probability-theoretic approach to combinatorial problems
- 45.15.27 Combinatorial theory of partitions
- 45.15.31 Combinatorial identities
- 45.15.33 Combinatorial inequalities
- 45.15.35 Combinatorial theory of substitutions and permutations
- 45.15.39 Special combinatorial tables and configurations
- 45.15.39.17 Matrix combinatorial problems
- 45.15.39.17.15 (0,1)-matrices
- 45.15.39.17.19 Combinatorial problems in the theory of permanents
- 45.15.39.17.27 Hadamard matrices

- 45.15.39.19 Orthogonal tables: Latin squares, etc.
- 45.15.39.21 Block designs
- 45.15.39.22 Applications of combinatorial analysis to the design of experiments
- 45.15.39.25 Finite, affine and projective geometries as block designs
- 45.15.39.31 Packings and coverings
- 45.15.39.32 Combinatorics of the placement of geometric objects
- 45.15.39.33 Tessellation and tiling problems

- 45.15.39.17 Matrix combinatorial problems
- 45.15.41 Algorithmic problems of combinatorial analysis

- 45.15.17 Combinatorial choice problems
- 45.17 Graph theory
- 45.17.15 General graph theory and graph representations
- 45.17.15.15 General graph theory
- 45.17.15.17 Graph representations

- 45.17.17 Study of individual classes of graphs
- 45.17.17.15 Trees
- 45.17.17.17 Planar graphs
- 45.17.17.19 Directed graphs. Tournaments
- 45.17.17.21 Other classes

- 45.17.19 Topological problems in graph theory
- 45.17.21 Graph coloring
- 45.17.25 Algebraic problems in graph theory
- 45.17.25.15 Isomorphism of graphs. Symmetries of graphs
- 45.17.25.17 Operations over graphs
- 45.17.25.19 Computation? and enumerations of graphs

- 45.17.27 Extremal problems in graph theory
- 45.17.31 Combinatorial problems in graph theory
- 45.17.31.15 Connectivity
- 45.17.31.17 Graph circuits
- 45.17.31.19 Partitions, coverings, packings

- 45.17.33 Algorithmic problems in graph theory
- 45.17.39 Generalizations of graphs
- 45.17.39.15 Hypergraphs
- 45.17.39.17 Matroids
- 45.17.39.19 Nets
- 45.17.39.21 Random graphs

- 45.17.51 Applications of graph theory
- 45.17.51.17 Applications of graph theory in the natural sciences
- 45.17.51.19 Applications of graph theory in engineering
- 45.17.51.21 Applications of graph theory in the social sciences
- 45.17.51.21.17 Applications of graph theory in economics

- 45.17.15 General graph theory and graph representations

- 47.15 Mathematical theory of control systems
- 47.15.15 Mathematical problems in modeling control systems
- 47.15.16 Combinatorial-logic problems in coding
- 47.15.17 Cybernetic problems in the theory of algorithms
- 47.15.19 Automata theory
- 47.15.19.15 Methods for the specification and realization of automata
- 47.15.19.17 Algebraic problems in automata theory
- 47.15.19.19 Problems of the representability of events in automata
- 47.15.19.21 Experiments with automata
- 47.15.19.25 Automata games
- 47.15.19.27 Probabilistic automata
- 47.15.19.31 Asynchronous automata
- 47.15.19.33 Generalizations of automata

- 47.15.21 Design problems in the theory of control systems
- 47.15.21.21 Estimates for the complexity of the realization of functions by circuits
- 47.15.21.25 Problems of circuit design with special constraints on the topology of the circuits and the form of the elements
- 47.15.21.31 Minimization of Boolean and many-valued functions
- 47.15.21.33 Application of Boolean algebra to circuit design

- 47.15.27 Functional systems
- 47.15.27.19 Completeness problems for specific functional systems
- 47.15.27.19.17 Finite-valued logics
- 47.15.27.19.19 Infinite-valued logics
- 47.15.27.19.21 Fuzzy logics and sets
- 47.15.27.19.25 Automata mappings
- 47.15.27.19.31 Recursive functions
- 47.15.27.19.39 Other systems

- 47.15.27.25 Study of the structure of closed classes
- 47.15.27.31 Metric problems in functional systems

- 47.15.27.19 Completeness problems for specific functional systems
- 47.15.31 Identity transformations
- 47.15.33 Stability; reliability and control
- 47.15.33.19 Design of stable and reliable circuits
- 47.15.33.31 Tests

- 47.17 Mathematical theory of information
- 47.17.17 Entropy, quantity of information and their properties
- 47.17.19 Asymptotic theorems on optimal coding (Shannon's theory)
- 47.17.19.17 Multisided channels
- 47.17.19.21 Channels with feedback
- 47.17.19.27 Channels with partially known parameters

- 47.17.21 Computation of information-theoretic characteristics for specific channels and messages
- 47.17.21.17 Computation of capacity
- 47.17.21.21 Epsilon entropy
- 47.17.21.27 Computation of error probability

- 47.17.25 Algebraic theory of codes and of correcting errors
- 47.17.25.17 Cyclic codes
- 47.17.25.19 Convolutional codes
- 47.17.25.21 Majority decoding
- 47.17.25.25 Concatenated codes
- 47.17.25.27 Codes for correcting errors in arithmetic operations
- 47.17.25.31 Synchronization error-correcting codes

- 47.17.27 Nonuniform codes for messages
- 47.17.31 Sequential decoding methods
- 47.17.33 Coding methods in continuous channels
- 47.17.33.17 Quantization of messages
- 47.17.33.21 Gaussian channels
- 47.17.33.27 Channels with fading

- 47.17.39 Complexity of coding and decoding methods

- 47.19 Operations research
- 47.19.15 Utility and decision-making theory
- 47.19.15.17 General utility theory
- 47.19.15.17.15 Theory of binary relations
- 47.19.15.17.17 Axiomatic utility theory
- 47.19.15.17.25 Theory of group behavior

- 47.19.15.19 Games of chance and experimental games
- 47.19.15.19.19 Games of chance (mathematical problems)
- 47.19.15.19.31 Experimental games

- 47.19.15.21 Theory of statistical decisions
- 47.19.15.27 Decision-making theory
- 47.19.15.27.17 Decision-making under fuzzy conditions
- 47.19.15.27.21 Multi-criterial optimization
- 47.19.15.27.27 Stochastic decision-making models

- 47.19.15.17 General utility theory
- 47.19.19 Game theory
- 47.19.19.17 Antagonistic games
- 47.19.19.17.19 Matrix games
- 47.19.19.17.21 Two-person zero-sum infinite games (on the unit square on function spaces)

- 47.19.19.19 Noncooperative games
- 47.19.19.19.17 Equilibrium situations
- 47.19.19.19.19 Bimatrix games
- 47.19.19.19.21 Supergames and metagames
- 47.19.19.19.25 Cooperative theory
- 47.19.19.19.25.17 Arbitrage schemes

- 47.19.19.19.31 Games without side payments
- 47.19.19.19.33 Games with an infinite number of players
- 47.19.19.19.51 Market games and related problems

- 47.19.19.31 Dynamic games
- 47.19.19.31.17 Positional games
- 47.19.19.31.19 Discrete-time games (recursive, survival, stochastic)
- 47.19.19.31.21 Continuous-time games

- 47.19.19.17 Antagonistic games
- 47.19.25 Mathematical programming
- 47.19.25.17 Linear programming
- 47.19.25.17.17 Linear inequalities, convex cones and polyhedra
- 47.19.25.17.19 Special linear programming problems
- 47.19.25.17.19.19 Transportation problem
- 47.19.25.17.19.25 Flows in networks

- 47.19.25.17.27 Computation methods of linear programming
- 47.19.25.17.27.15 Simplex method
- 47.19.25.17.27.21 Block programming
- 47.19.25.17.27.31 Solution of large-scale problems

- 47.19.25.19 Nonlinear programming
- 47.19.25.19.17 Duality theory
- 47.19.25.19.17.21 Optimality conditions, saddle points, Lagrange functions

- 47.19.25.19.19 Convex programming
- 47.19.25.19.19.17 Quadratic programming
- 47.19.25.19.19.17.21 Complementarity problems

- 47.19.25.19.19.17 Quadratic programming
- 47.19.25.19.21 Nonconvex and multi-extremal problems
- 47.19.25.19.25 Nonsmooth optimization
- 47.19.25.19.25.19 Minimax problems

- 47.19.25.19.27 Computational methods of nonlinear programming
- 47.19.25.19.27.25 Relaxation methods
- 47.19.25.19.27.25.15 Linearization methods, including gradient methods

- 47.19.25.19.27.25 Relaxation methods
- 47.19.25.19.27.27 Nonrelaxation methods
- 47.19.25.19.27.27.19 Feasible directions methods
- 47.19.25.19.27.27.27 Second- and higher-order methods
- 47.19.25.19.27.27.21 Conjugate gradient methods
- 47.19.25.19.27.27.17 Penalty methods

- 47.19.25.19.17 Duality theory
- 47.19.25.21 Discrete programming
- 47.19.25.21.15 Complexity theory for discrete problems
- 47.19.25.21.17 Combinatorial problems (the traveling salesman problem, scheduling theory, etc.)
- 47.19.25.21.19 Integer programming
- 47.19.25.21.19.19 Boolean programming

- 47.19.25.21.21 Computational methods for discrete programming
- 47.19.25.21.27.17 Truncation methods; group approach
- 47.19.25.21.27.21 Partial sorting method. The branch and bound method
- 47.19.25.21.27.31 Approximate and heuristic methods

- 47.19.25.25 Parametric programming
- 47.19.25.27 Stochastic programming
- 47.19.25.27.17 Problems with random constraints
- 47.19.25.27.19 Probability characteristics of solutions

- 47.19.25.31 Dynamic programming
- 47.19.25.31.19 Markov decision-making processes
- 47.19.25.31.27 Computational methods for dynamic programming

- 47.19.25.17 Linear programming
- 47.19.27 Theory of mathematical economic models
- 47.19.27.17 Static models
- 47.19.27.17.17 Input-output-type models
- 47.19.27.17.25 Macro-economic models
- 47.19.27.17.25.19 Production functions

- 47.19.27.17.27 Econometrics
- 47.19.27.17.33 Optimization models

- 47.19.27.19 Dynamic models
- 47.19.27.19.17 Single- and two-commodity models
- 47.19.27.19.19 Multicommodity models
- 47.19.27.19.19.17 Leontief-type models
- 47.19.27.19.19.21 Von Neumann-type models. Optimal trajectories

- 47.19.27.19.27 Consumption models

- 47.19.27.21 Probabilistic models
- 47.19.27.21.19 Selection of a portfolio of securities

- 47.19.27.25 Theory of economic behavior
- 47.19.27.25.15 Supply and demand models
- 47.19.27.25.17 Exchange models
- 47.19.27.25.19 Equilibrium models
- 47.19.27.25.25 Theory of a firm
- 47.19.27.25.31 Models for the control of an economy

- 47.19.27.27 Modeling of separate aspects of an economy
- 47.19.27.27.17 Price models; monetary economics
- 47.19.27.27.21 Models that take into account ecological and demographic factors
- 47.19.27.27.27 Resource-allocation models

- 47.19.27.33 Sector and regional models

- 47.19.27.17 Static models
- 47.19.31 Mathematical models in operations research
- 47.19.31.17 Queueing theory
- 47.19.31.17.25 Queueing system networks
- 47.19.31.17.27 Theory of transportation flows and traffic
- 47.19.31.17.31 Service optimization models

- 47.19.31.19 Reliability and backup theory (optimization models). Quality control
- 47.19.31.21 Inventory control theory. Storage theory
- 47.19.31.21.17 Storage models
- 47.19.31.21.21 Exchange models

- 47.19.31.27 Large-scale systems
- 47.19.31.27.17 Modeling control processes
- 47.19.31.27.19 Network design
- 47.19.31.27.25 Digital simulation and modeling of systems

- 47.19.31.33 Search theory

- 47.19.31.17 Queueing theory
- 47.19.51 Applications to operations research
- 47.19.51.15 Organization of research
- 47.19.51.17 Applications to design problems
- 47.19.51.19 Applications to sociology
- 47.19.51.21 Location of production
- 47.19.51.23 Applications to economic problems
- 47.19.51.27 Financial and actuarial applications
- 47.19.51.29 Preservation of the environment
- 47.19.51.31 Applications to public health
- 47.19.51.33 Applications to industry
- 47.19.51.35 Energy applications
- 47.19.51.37 Applications to mining
- 47.19.51.39 Military applications
- 47.19.51.41 Applications to forestry
- 47.19.51.43 Applications to agriculture
- 47.19.51.45 Applications to communications problems
- 47.19.51.47 Applications to transportation problems
- 47.19.51.51 Applications to the organization of production
- 47.19.51.53 Applications to chemistry
- 47.19.51.55 Automated control systems
- 47.19.51.57 Applications to construction problems
- 47.19.51.59 Urban economics

- 47.19.15 Utility and decision-making theory
- 47.21 Theory of mathematical machines, and programming
- 47.21.17 Theory of mathematical machines
- 47.21.17.17 Computer networks
- 47.21.17.21 Multiprocessor systems
- 47.21.17.27 Special processors and multiprocessors
- 47.21.17.33 Number systems and carrying out of operations

- 47.21.21 Computer programming
- 47.21.21.15 Programming theory
- 47.21.21.15.15 Writing and verifying programs
- 47.21.21.15.17 Computational complexity
- 47.21.21.15.19 Abstract data types
- 47.21.21.15.21 Transformation of programs
- 47.21.21.15.25 Parallel programming

- 47.21.21.17 Programming methods and examples
- 47.21.21.17.15 Software reliability

- 47.21.21.19 Programming languages and systems
- 47.21.21.19.15 Methods for describing languages
- 47.21.21.19.17 Programming languages
- 47.21.21.19.19 Programming systems
- 47.21.21.19.21 Applied program packages

- 47.21.21.21 Storage, retrieval and information processing
- 47.21.21.21.15 Data structures
- 47.21.21.21.17 Databases
- 47.21.21.21.19 Information-retrieval systems
- 47.21.21.21.21 Automated control systems
- 47.21.21.21.27 Computer graphics

- 47.21.21.25 Operating systems
- 47.21.21.27 Programs and algorithms for solving specific problems

- 47.21.21.15 Programming theory

- 47.21.17 Theory of mathematical machines
- 47.23 Mathematical problems in artificial intelligence
- 47.23.15 Pattern recognition and image analysis (distinguishing of contours recognition of characters and oral speech; taking into account context languages for describing patterns and images)
- 47.23.17 Mathematical investigation of the behavior of individuals and groups (games and computer behavior; activity of operators; psychological tests and their analysis; problems concerning the interaction of computers with society)
- 47.23.19 Mathematical description and modeling of neurons, neural networks, brains and other organs of human beings and animals
- 47.23.21 Complex systems (investigation of the activity of complex systems investigation of their structure, languages for their description)
- 47.23.25 Robots (theory, control languages; operations design, specific robots and their applications)
- 47.23.27 Algorithmization of creative activity (decision-makers, question-answer type systems, heuristic methods)

- 47.25 Mathematical problems in semiotics
- 47.25.17 Syntactical investigation of symbolic systems
- 47.25.19 Meaningful interpretation of symbolic systems
- 47.25.21 Decoding of symbolic systems
- 47.25.25 Mathematical linguistics (general aspects). Mathematical investigation of languages of a general nature)
- 47.25.25.51 Algorithmic languages

- 47.25.27 Models of languages and language structures
- 47.25.27.17 Algebro-logic and set-theoretic models of languages and language structures
- 47.25.27.17.19 Models defined by a generating investigation (grammar)
- 47.25.27.17.21 Languages that admit and are generated by automata
- 47.25.27.17.23 Models defined by means of internal correspondences configurations, control relations, word connectives)
- 47.25.27.17.25 Transformation of languages

- 47.25.27.21 Probability-statistical models for languages and language structures

- 47.25.27.17 Algebro-logic and set-theoretic models of languages and language structures
- 47.25.31 Language semantics (mathematical aspects)
- 47.25.33 Mathematical problems of machine translation
- 47.25.39 Other mathematical problems of semiotics and mathematical linguistics

Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org