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Referativni Zhurnal Classification

Math on the Web  >  Classifications  >  Referativni Zhurnal Classification  [Updated: June 1, 2011]


Referativni Zhurnal Classification Scheme

Translated by Bogdan Dudzik
With the editorial assistance of Andrei Iacob and Smilka Zdravkovska

PRELIMINARY VERSION -- 29 August 1995

Updated Tue, Aug 29, 1995. Feedback to mathweb at MR

This classification was prepared as a piece of the UDC (Universal Decimal Classification) which covers all knowledge in a fairly uniform way.


RzhMat Classification

271 Mathematics

271.01  General questions of mathematics
271.01.01  Instructional exposition
271.01.05  Publications of a general nature
271.01.05.15  Philosophy and the methodology of mathematics
271.01.05.17  Classification of the mathematical sciences
271.01.09  History of mathematics.  Personalities
271.01.09.15  History of mathematics
271.01.09.17  Personalia
271.01.13  Scientific societies, meetings, congresses, 			
	conferences, symposia, seminars
271.01.17  International cooperation
271.01.21  Organization of scientific research activities
271.01.29  Informational activity
271.01.33  Terminology.  Handbooks, dictionaries, textbooks
271.01.33.02  Monographs
271.01.33.03  Handbooks
271.01.33.04  Surveys
271.01.33.05  New journals and series
271.01.33.06  Publications of institutions and organizations (collectives)
271.01.33.07  Instructional material
271.01.33.15  Mathematical terminology
271.01.79  Mathematical training.  Mathematical education
271.01.79.17  Popularization of the mathematical sciences

271.03  Foundations of mathematics, mathematical logic

271.03.15  Foundations of mathematics
271.03.15.15  General philosophical problems
271.03.15.17  Set theory
271.03.15.17.17 Naive set theory
271.03.15.17.19  Axiomatic set theory.  Axiomatization of analysis
271.03.15.17.25  Descriptive set theory
271.03.15.17.31  Theory of order types and of ordinal and cardinal numbers
271.03.15.19  Proof theory
271.03.15.21  Mathematical intuitionism
271.03.15.25  Constructive mathematics
271.03.15.31  Logical and semantic antinomies
271.03.17  Algorithms and computable functions
271.03.17.15  General problems in the theory of algorithms
271.03.17.15.15  General theory of calculi
271.03.17.15.17  General recursion theory
271.03.17.17  Complexity of algorithms
271.03.17.19  Algorithmic problems
271.03.17.19.17  Degrees of undecidability
271.03.17.21  Algorithmic set theory
271.03.17.31  Computable functions
271.03.17.33  Mathematical models of computational processes
271.03.19  Mathematical logic
271.03.19.17  Logic and logico-mathematical languages
271.03.19.19  Classical logic theories
271.03.19.19.19  Propositional logic
271.03.19.19.25  Predicate logic
271.03.19.19.31  Higher-order logics
271.03.19.21  Nonclassical logics
271.03.19.21.17  Intuitionistic and intermediate logics
271.03.19.21.19  Modal logics
271.03.19.21.21.  Many-valued logics
271.03.19.21.25  Formalization of traditional logics
271.03.19.21.27  Quantum logics
271.03.19.21.31  Probabilistic logic
271.03.19.21.33  Combinatorial logic
271.03.19.21.39  Other logic systems
271.03.19.25  Logico-mathematical theories
271.03.19.25.17  Formal arithmetic
271.03.19.27  Inference in logic and logico-mathematical calculi
271.03.19.29  Problems in the algorithmic decidability of logic and logico-mathematical 
		theories
271.03.19.31  Theory of models
271.03.19.51  General mathematical systems
	
271.15  Number theory

271.15.15  Elementary arithmetic
271.15.17  Elementary number theory
271.15.17.15  Elementary properties and methods
271.15.17.15.17  Multiplicative structure of integers (G.C.D, L.C.M, etc.).  Comparisons, 
		power residues, quadratic residues, etc.
271.15.17.15.27  Numerical sequences (Farey, et al.).  Recurrent sequences
271.15.17.15.31  Special numbers and polynomials (Bernoulli, et al.)
271.15.17.15.33  Partitions (elementary methods, combinatorial number theory)
271.15.19  Analytic number theory
271.15.19.15  Riemann zeta function,  Dirichlet function, etc.
271.15.19.17  Dirichlet series (general theory)
271.15.19.19  Distribution of prime numbers and divisors in number fields
271.15.19.21  Modular and quadratic forms
271.15.19.25  Asymptotics of number-theoretic functions
271.15.19.27  Method of trigonometric sums
271.15.19.31  Sieve.  The sieve method (Eratosthenes, Brun, Selberg, et al.)
271.15.21  Additive number theory.  Forms
271.15.21.17  Diophantine approximations
271.15.21.19  Metric and probabilistic number theory
271.15.23  Diophantine equations
271.15.23.15  Algebraic  Diophantine equations
271.15.23.15.17  Linear, quadratic and bilinear equations
271.15.23.15.25  Diophantine equations of higher degrees
271.15.23.19  Nonalgebraic  Diophantine equations (exponential and other equations)
271.15.25  Algebraic number theory (algebraic number fields)
271.15.25.15  General theory of fields of algebraic numbers and complex units
271.15.25.17  Special classes of algebraic number fields
271.15.25.17.17  Quadratic fields
271.15.25.17.19  Cubic fields and fields of the fourth degree
271.15.25.17.25  Cyclic, abelian and metabelian number fields
271.15.25.27  Fields oƒ functions of simple characteristic
271.15.25.33  Analytic and local methods in algebraic number theory
271.15.25.33.17  Analytic methods
271.15.25.33.31  Local methods
271.15.27  Geometry of numbers


271.17  Algebra

271.17.15  Semigroups
271.17.15.19.15  Semigroups with finiteness conditions
271.17.15.19.15.17  Finite semigroups
271.17.15.19.17  Generating sets, relations and identities on semigroups
271.17.15.19.17.17  Varieties of semigroups.  Free semigroups, defining relations
271.17.15.19.17.19  Commutative semigroups
271.17.15.19.17.25  Idempotent semigroups
271.17.15.19.19  Equivalences and complexes in semigroups.  Homomorphisms
271.17.15.19.19.17  Semigroup homomorphisms
271.17.15.19.19.21  Special elements and complexes in semigroups
271.17.15.19.19.25  Semigroup ideals
271.17.15.19.19.27   Subsemigroups
271.17.15.19.19.33  Structures of subsemigroups, ideals and congruences of semigroups
271.17.15.19.21  Transformation semigroups
271.17.15.19.21.15  Semigroups of multivalued transformations (binary relations)
271.17.15.19.21.17  Semigroups of single-valued transformations
271.17.15.19.21.19  Representation of transformation semigroups
271.17.15.19.21.31  Matrix semigroups, linear semigroups
271.17.15.19.25  Inverse semigroups (generalized groups)
271.17.15.19.25.31  Regular semigroups.  Other generalizations of inverse semigroups
271.17.15.19.25.33  Semiheaps and generalized heaps
271.17.15.19.27  Semigroups with complemented structures
271.17.15.19.27.15  Semigroups with operators of the  -semigroup
271.17.15.19.27.17  Connection with ring theory, multiplicative ring semigroups
271.17.15.19.27.25  Quasi-ordered and ordered semigroups
271.17.15.19.27.31  Topological semigroups
271.17.15.19.27.31.17  Compact and connected semigroups
271.17.15.19.27.31.25  Topological semigroups of transformations of topological spaces
271.17.15.19.33  Different generalizations of associativity
271.17.17  Groups
271.17.17.15  Methods of mathematical logic, and algorithmic problems in group theory
271.17.17.15.15  Axiomatizable classes of groups
271.17.17.15.19  Elementary theories of different classes of groups
271.17.17.15.25  Algorithmic problems in group theory.  Word problem
271.17.17.17  Abelian groups
271.17.17.17.15  Purity and its generalizations
271.17.17.17.17  Higher subgroups
271.17.17.17.19  Direct and subdirect sums (abelian groups)
271.17.17.17.21  Extensions of abelian groups
271.17.17.17.25  Mappings of a group into itself and into other subgroups
271.17.17.17.27  Primary abelian groups
271.17.17.17.31  Torsion-free abelian groups
271.17.17.17.33  Systems of generators.  Factorization
271.17.17.19  Finite groups
271.17.17.19.15  Generators and defining relations
271.17.17.19.17  Automorphisms of finite groups
271.17.17.19.19  Finite p-groups
271.17.17.19.21  Finite solvable groups
271.17.17.19.25  Finite simple groups
271.17.17.19.25.17  Arithmetic and abstract properties
271.17.17.19.25.25  Methods in the theory of Lie algebras in finite groups
271.17.17.19.27  Arithmetic structure and normal structure of finite groups
271.17.17.17.27.17  Extensions of finite groups
271.17.17.17.27.19  Normal series in finite groups
271.17.17.17.27.21  Sylow-type theorems
271.17.17.17.27.27  Factorization of finite groups
271.17.17.17.27.33  Normal complements in finite groups
271.17.17.19.31  Permutation groups
271.17.17.19.31.17  Primitive and multiply transitive groups
271.17.17.19.31.21  Combined problems for permutation groups
271.17.17.19.31.25  Groups of collineations of finite projective and affine planes
271.17.17.21  Relationships between elementary groups
271.17.17.21.15  Systems of generators
271.17.17.21.17  Varieties of groups
271.17.17.21.25  Operations over groups
271.17.17.21.31  Equations over groups and embedding theorems in group theory
271.17.17.23  Relationships between subgroups.  Generalized solvable groups and 
		finiteness conditions
271.17.17.23.17  Structures of subgroups
271.17.17.23.17.17  Structural isomorphisms
271.17.17.23.17.31  Minimality and maximality  conditions
271.17.17.23.19  Normal series and systems
271.17.17.23.19.17  Generalized solvable groups and finiteness conditions
271.17.17.23.19.19  Nilpotent and solvable groups
271.17.17.23.19.25  Generalized solvable groups
271.17.17.23.19.31  Radicals in groups
271.17.17.23.21  Characteristic subgroups, automorphisms and endomorphisms
271.17.17.23.21.17  Automorphism groups and representations of groups in 	
		automorphism groups of algebraic systems
271.17.17.23.21.19  Automorphisms and automorphism groups of specific groups
271.17.17.23.25  Locally finite groups
271.17.17.23.27  Linear groups
271.17.17.23.31  Approximation of groups
271.17.17.25  Ordered groups
271.17.17.25.17  Linearly ordered groups
271.17.17.25.21  Structurally ordered groups
271.17.17.25.27  Partially ordered groups
271.17.17.25.33  Different types of preorderable groups
271.17.17.27  Topological groups
271.17.17.27.15  General theory of topological groups
271.17.17.27.15.17  Generators and relations in topological groups
271.17.17.27.15.25  Operations over topological groups.  Products
271.17.17.27.17  Abelian topological groups
271.17.17.27.19  Locally compact groups
271.17.17.27.19.17  Measure and integral on topological groups
271.17.17.27.19.31  Pro-finite groups.  Pro-p-groups
271.17.17.27.21  Representations of topological groups
271.17.17.27.27  Relations between subgroups in topological groups.  Finiteness 	
		conditions and similar conditions
271.17.17.27.27.31  Groups with compact classes of conjugate elements
271.17.17.27.33  Generalizations of topological groups
271.17.17.31  Linear representations of abstract groups.  Characters of groups
271.17.17.31.17  Representations of finite groups
271.17.17.31.17.15  Classical theory
271.17.17.31.17.15.17  Representations of specific groups
271.17.17.31.17.15.21  Characters of representations
271.17.17.31.17.19  Representations over fields of nonzero characteristic
271.17.17.31.17.25  Representations over rings
271.17.17.31.21  Representations of infinite groups
271.17.17.33  Generalizations of groups.  Groupoids, etc.
271.17.17.33.17  Special classes of groupoids
271.17.17.33.21  Groupoids with complemented structures
271.17.17.33.31  Quasigroups
271.17.17.33.31.17  Isotopies and homotopies of quasigroups
271.17.17.33.31.21  Identities and generalized identities on quasigroups
271.17.17.33.31.31  Loops
271.17.19  Rings and modules
271.17.19.15  Methods of mathematical logic in rings and modules
271.17.19.19  Associative rings and algebras
271.17.19.19.15  Structure of rings
271.17.19.19.15.17  Ideals in rings.  Radicals
271.17.19.19.15.19  Structure-theoretic problems for associative rings
271.17.19.19.15.27  Automorphisms, endomorphisms and derivation of rings
271.17.19.19.17  Rings with chain conditions
271.17.19.19.19  Rings with conditions on ideals and subrings
271.17.19.19.19.17  Skew fields
271.17.19.19.19.19  Prime rings
271.17.19.19.19.21  Primary and semiprimary rings
271.17.19.19.19.25  Regular, biregulator and strictly regulator rings
271.17.19.19.19.31  Rings of principal ideals
271.17.19.19.21  Defining and identity relations in rings.  Varieties of rings
271.17.19.19.25  Embedding of rings
271.17.19.19.25.15  Quotient rings
271.17.19.19.27  Operations over rings
271.17.19.19.31  Semigroup and group rings
271.17.19.19.33  Representations of rings and algebras
271.17.19.21  Modules
271.17.19.21.15  Structure of modules
271.17.19.21.17  Projective and flat modules
271.17.19.21.19  Injective modules
271.17.19.21.21  Quotient modules
271.17.19.21.25  Endomorphism rings
271.17.19.21.27  Equivalence and duality
271.17.19.21.31  Homology classification of rings
271.17.19.21.33  Submodules.  Structure of submodules
271.17.19.23  Nonassociative rings and algebras
271.17.19.23.17  Nonassociative skew fields and their generalizations
271.17.19.23.19  Lie rings and algebras
271.17.19.23.19.15  Finite-dimensional Lie algebras
271.17.19.23.19.17  Infinite-dimensional Lie algebras
271.17.19.23.19.19  Generators, defining and identity relations.  Varieties.  Free algebras
271.17.19.23.19.21  Embeddings of Lie algebras into other types of algebras
271.17.19.23.19.21.17  Universal enveloping algebras of Lie algebras
271.17.19.23.19.25  Lie algebras of derivations
271.17.19.23.19.27  Subalgebras and ideals
271.17.19.23.19.31  Automorphisms, endomorphisms and derivations of Lie algebras
271.17.19.23.19.33  Generalizations of Lie algebras
271.17.19.23.25  Alternative rings and related rings
271.17.19.23.31  Jordan rings and algebras
271.17.19.25  Ordered rings and modules
271.17.19.27  Topological rings and modules
271.17.19.31  Rings and modules with valuation
271.17.19.33  Generalizations of rings and modules
271.17.21  Structures
271.17.21.17  Partially ordered sets
271.17.21.19  Boolean rings and algebras
271.17.21.19.27  Boolean algebras
271.17.21.25  Types of structures
271.17.21.25.17  Distributive structures
271.17.21.25.19  Dedekind structures and structures similar to them
271.17.21.25.27  Structures with complements
271.17.21.25.33  Complete structures
271.17.21.31  Representations of structures
271.17.21.33  Generalizations of structures
271.17.21.35  Algebraic theory of affine and projective geometries
271.17.21.35.17  On the basis of structure theory
271.17.21.35.19  Over skew fields
271.17.21.35.25  Finite projective spaces and other generalizations
271.17.23  Universal algebras
271.17.23.15  Structure of universal algebras
271.17.23.17  Varieties (primitive classes) of algebras and their free algebras
271.17.23.19  Algebra-theoretic constructions
271.17.23.25  Dependence in algebras
271.17.23.31  Types of universal algebras
271.17.25  Categories
271.17.25.15  General problems in category theory
271.17.25.15.17  Structural  problems in category theory
271.17.25.15.19  Types and categories
271.17.25.15.31  Multiplicative structures on objects of categories
271.17.25.17  Functors
271.17.25.17.17  Union of functors
271.17.25.17.21  Duality of functors
271.17.25.17.27  Direct and inverse limits
271.17.25.19  Representations of categories
271.17.25.25  Abelian categories
271.17.25.25.19  Representations of abelian categories
271.17.27  Fields and polynomials
271.17.27.17  Polynomials, including binomials and prime factorization
271.17.27.19  General field theory
271.17.27.19.17  Extensions of fields
271.17.27.19.19  General Galois theory
271.17.27.19.19.17  Embedding problem
271.17.27.19.19.25  Construction of fields with a given Galois group
271.17.27.19.21  Valuations on fields
271.17.27.19.25  Ordered fields
271.17.27.19.25.17  Formally real fields
271.17.27.19.27  Topological fields
271.17.27.19.31  Special classes of fields
271.17.27.19.33  Generalizations of fields
271.17.27.21  Finite fields
271.17.27.25  Local fields
271.17.27.25.25  p-adic analysis
271.17.27.25.31  Forms over local fields
271.17.27.27  Fields of algebraic numbers and algebraic functions
271.17.27.27.15  Divisors and completions
271.17.27.27.17  Trims? and discriminant
271.17.27.27.19  Quadratic fields and division fields of a disk
271.17.27.27.21  Units of algebraic number fields
271.17.27.27.25  Group of classes of divisors
271.17.27.27.27  Ideles and adeles
271.17.27.27.31  Forms over number fields
271.17.27.27.33  Arithmetic problems of orders in semisimple algebras
271.17.27.31  Class field theory
271.17.27.31.25  Local class field theory
271.17.27.33  Differential and difference algebras
271.17.27.33.17  Differential algebra
271.17.27.33.21  Difference algebra
271.17.29  Linear algebra
271.17.29.17  Vector spaces.  Theory of vector spaces
271.17.29.17.17  Vector spaces over skew fields
271.17.29.19  Matrices and linear mappings.  Matrix theory
271.17.29.19.17  Determinants and their generalizations
271.17.29.19.21  Matrix equations
271.17.29.19.25  Eigenvalues of matrices
271.17.29.19.33  Special classes of matrices
271.17.29.21  Systems of linear equations and inequalities
271.17.29.31  Polylinear algebra.  Forms
271.17.29.31.17  Bilinear and quadratic forms
271.17.31  Homological algebra
271.17.31.17  Chain complexes
271.17.31.17.15  Homology theory of chain complexes
271.17.31.17.25  Homotopy theory of chain complexes
271.17.31.17.31  Chain complexes with a diagonal
271.17.31.17.33  Filtrations, exact pairs, spectral sequences
271.17.31.21  Derived functors
271.17.31.21.15  Homological algebra in abelian categories 
271.17.31.21.17  Homology theory of associative rings and modules
271.17.31.21.19 Homology of Lie algebras and Hopf algebras
271.17.31.21.21  Homology of groups and semigroups
271.17.31.21.33. Deformations of algebraic structures
271.17.31.21.33.17  Deformations of discrete subgroups of Lie groups
271.17.31.27  Algebraic K-theory
271.17.31.31  Algebraic analogues of different constructions from topology and algebraic 
		geometry
271.17.31.31.17  Homotopy groups in categories
271.17.31.31.25  General theory of topologies and sheaves on categories
271.17.31.31.31  General theory of co-algebras and Hopf algebras
271.17.33  Algebraic geometry
271.17.33.15  Commutative rings and algebras, local theory and foundations of algebraic 
		geometry
271.17.33.15.15  General theory of commutative rings
271.17.33.15.17  Valuations on commutative rings and divisibility theory
271.17.33.15.19  Arithmetic rings.  Dedekind and Prufer rings
271.17.33.15.21  Polynomial rings
271.17.33.15.25  Modules over commutative rings
271.17.33.15.31  Local algebra.  Local theory
271.17.33.15.33  Foundations of algebraic geometry
271.17.33.17  Variations of structures of algebraic varieties, crossed products, fiber 
		bundles
271.17.33.17.15  Moduli of algebraic varieties
271.17.33.17.17  Structure of families.  Picard varieties
271.17.33.17.19  Vector algebraic bundles
271.17.33.17.21  Classification of algebraic varieties
271.17.33.17.25  Algebraic bundles with degenerate fibers
271.17.33.19  Cohomology theory of algebraic varieties and schemes
271.17.33.19.17  Algebraic sheaves and cohomology with coefficients in them
271.17.33.19.17.17  General properties of algebraic sheaves
271.17.33.19.17.27  The Riemann-Roch theorem for algebraic varieties and related 
			questions
271.17.33.19.21  Cycles:  intersection theory and equivalence
271.17.33.19.21.17  Foundations of intersection theory
271.17.33.19.21.19  Chow varieties and algebraic systems.  Parametrization
271.17.33.19.21.25  Rational equivalence of cycles
271.17.33.19.21.31  Algebraic and numerical equivalence
271.17.33.19.27  Serre cohomology, K-theory
271.17.33.19.21  Grothendieck cohomology and topology
271.17.33.21  Algebraic groups, including abelian varieties
271.17.33.21.15  Formal groups
271.17.33.21.15.25  p-adic analytic groups
271.17.33.21.17  Abelian varieties and schemes
271.17.33.21.17.15  General theory of abelian varieties
271.17.33.21.17.17  Endomorphism rings of abelian varieties
271.17.33.21.17.19  Moduli of abelian varieties
271.17.33.21.17.21  Principal homogeneous spaces of abelian varieties
271.17.33.21.17.31  Arithmetic of abelian varieties
271.17.33.21.17.31.17  Arithmetic of elliptic curves
271.17.33.21.19  Linear algebraic groups
271.17.33.21.19.17  Adele groups and Tamagawa numbers
271.17.33.21.19.19  Groups of units 
271.17.33.21.19.21  Approximation theorems
271.17.33.21.19.25  p-adic linear groups
271.17.33.21.19.31  Linear representations of linear algebraic groups
271.17.33.21.25  Algebraic transformation groups
271.17.33.21.25 .17  Geometric theory of invariants of algebraic transformation groups
271.17.33.21.25 .21  Infinite-dimensional algebraic groups
271.17.33.21.31  Pro-algebraic groups and group schemes
271.17.33.25  Arithmetic problems of algebraic varieties
271.17.33.25.17  Problems associated with rationality.  Rational points on algebraic 
		varieties
271.17.33.25.21  Zeta functions and related problems
271.17.33.27  Birational geometry.  Mappings and the like
271.17.33.27.15  Singularities.  Singular points of algebraic varieties
271.17.33.27.15.17  Resolution of singularities
271.17.33.27.15.19  Structure of varieties near singular points
271.17.33.27.15.25  Numerical invariants and classification of singularities
271.17.33.27.19  Linear systems and rational mappings
271.17.33.27.25  Modifications and problems of minimal models
271.17.33.31  Algebraic curves; surfaces and three-dimensional manifolds
271.17.33.31.17  Algebraic curves
271.17.33.31.17.15  Singular points of curves
271.17.33.31.17.17  Bundles over a curve
271.17.33.31.17.25  Modules over algebraic curves
271.17.33.31.17.31  Arithmetic problems on algebraic curves
271.17.33.31.21  Algebraic surfaces
271.17.33.31.21.15  Singular points of surfaces
271.17.33.31.21.15.19  Structure of a surface near singular points
271.17.33.31.21.15.17  Resolution of singularities
271.17.33.31.21.15.25  Numerical invariants and classification of singularities
271.17.33.31.21.15.31  Theory of intersections on singular surfaces
271.17.33.31.21.17  Birational transformations and minimal models
271.17.33.31.21.19  Algebraic and linear systems on algebraic surfaces
271.17.33.31.21.21  Algebraic geometry of different classes of surfaces
271.17.33.31.21.25  Moduli of algebraic surfaces
271.17.33.31.21.31  Arithmetic problems on algebraic surfaces
271.17.33.31.27  Algebraic varieties of dimension 3
271.17.33.31.33  Analytic spaces over arbitrary complete valued fields
271.17.35  Lie groups
271.17.35.17  General theory of Lie groups, properties, structure and generalizations
271.17.35.17.17  Correspondence between Lie groups and Lie algebras.  Exponential 
		mapping
271.17.35.17.21  Structure of Lie groups and Lie algebras, deformation and contractions of 
		Lie groups of automorphisms, and derivations
271.17.35.17.27  Related problems in the theory of topological groups
271.17.35.17.33  Generalizations of Lie groups
271.17.35.19  Special classes of Lie groups
271.17.35.19.19  Compact Lie groups and Lie algebras
271.17.35.19.21  Semisimple Lie groups and Lie algebras
271.17.35.19.25  Solvable Lie groups and Lie algebras
271.17.35.19.25.17  Nilpotent Lie groups and Lie algebras
271.17.35.21  Continuous subgroups of Lie groups
271.17.35.21.15  General properties of subgroups and subalgebras
271.17.35.21.17  Maximal subgroups and subalgebras
271.17.35.21.19  Compact and semisimple subgroups
271.17.35.21.25  Solvable subgroups and subalgebras
271.17.35.21.25.17  Cartan subgroups
271.17.35.21.31  Decomposition of Lie groups into the product of subgroups
271.17.35.25  Linear representations of Lie groups
271.17.35.25.15  Finite-dimensional linear representations of Lie groups and Lie algebras
271.17.35.25.17  Equivariant embeddings of spaces with a Lie transformation group into 
		a Euclidean space
271.17.35.25.19  Representing functions.  Duality theorems
271.17.35.25.21  Invariants of linear representations
271.17.35.25.27  Linear Lie groups and Lie algebras
271.17.35.25.31  Algebraic linear Lie groups
271.17.35.25.33  Linear representations of groups in theoretical physics
271.17.35.27  Lie transformation groups
271.17.35.27.15  General theory of Lie transformation groups
271.17.35.27.17  Orbits and quotient spaces of Lie transformation groups 
271.17.35.27.19  Transitive Lie groups
271.17.35.27.21  Homogeneous spaces of semisimple Lie groups
271.17.35.27.25  Homogeneous spaces of solvable Lie groups
271.17.35.27.25.17  Simultaneous spaces of nilpotent Lie groups
271.17.35.27.31  Differential operators that are invariant with respect to Lie transformation 
		groups
271.17.35.27.33  Invariant integration
271.17.35.31  Discrete subgroups and discrete transformation groups
271.17.35.31.15  General properties of discrete transformation groups and discrete 
		subgroups of Lie groups
271.17.35.31.17  Discrete groups of linear-fractional transformations
271.17.35.31.19  Discrete subgroups of semisimple Lie groups
271.17.35.31.25  Discrete subgroups of of solvable and nilpotent Lie groups
271.17.35.31.27  Arithmetically defined discrete subgroups
271.17.35.31.31  Discrete groups of isometric transformations
271.17.35.31.31.17  Discrete groups generated by reflections
271.17.35.33  Theory of continuous pseudogroups (infinite Lie groups)
271.17.35.33.15  General concepts of the theory of topological pseudogroups and Lie 
		pseudogroups
271.17.35.33.17  Methods of formal Lie groups in the theory of pseudogroups
271.17.35.33.19  Cartan pseudogroups
271.17.35.33.21  Infinite-dimensional filtered and graded Lie algebras

271.19  Topology

271.19.15  General topology
271.19.15.17  Topological spaces
271.19.15.17.17  Axiomatic theory of topological spaces
271.19.15.17.17.17  Classes of spaces distinguished by separability axioms
271.19.15.17.17.19  Classes of spaces distinguished by conditions of a local nature
271.19.15.17.17.21  Cardinal-valued invariants of topological spaces
271.19.15.17.17.25  Classes of spaces distinguished by conditions for coverings
271.19.15.17.17.25.17  Compact spaces
271.19.15.17.17.25.21  Paracompact spaces
271.19.15.17.17.31  Classes of spaces distinguished by conditions that connect their 
		topology with the properties of their subspaces
271.19.15.17.17.31.17  K-spaces
271.19.15.17.17.39  Other classes of topological spaces
271.19.15.17.19  Nonaxiomatic theory of topological spaces
271.19.15.17.19.17  Spaces that are embedded in another space of simple structure
271.19.15.17.19.25  Spaces that are continuous images of a given space of simple structure
271.19.15.17.19.25.17  Dyadic compact spaces
271.19.15.17.21  Topological properties of spaces with complemented structure, and 
		topological groups of transformations
271.19.15.17.25  Construction of topological spaces and operations over them
271.19.15.17.25.19  Operations over topological spaces
271.19.15.17.25.19.17  Topological products
271.19.15.17.25.19.21  Hyperspaces
271.19.15.17.25.19.27  Compact extensions
271.19.15.17.25.19.31  Superextensions
271.19.15.17.25.25  Spaces of mappings (function spaces)
271.19.15.17.25.31  Passages to the limit in the category of topological spaces
271.19.15.17.25.31.17  Spectra of topological spaces
271.19.15.17.27  Shapes of topological spaces
271.19.15.17.31  Topological questions in category theory
271.19.15.17.33  Generalizations of topological spaces
271.19.15.19  Uniform spaces and nearness spaces
271.19.15.19.17  Axioms of uniform and nearness spaces
271.19.15.19.17.17  Different classes of uniform and nearness spaces 
271.19.15.19.21  Uniform spaces and uniformly continuous mappings
271.19.15.19.25  Nearness spaces
271.19.15.19.27  Nearness spaces and compact extensions
271.19.15.19.31  Comparison of topologies, uniformities and proximities
271.19.15.19.13.17  Topological properties of uniform spaces
271.19.15.21  Metric spaces
271.19.15.21.17  Axioms and generalizations of metric spaces
271.19.15.21.19  Topological properties of metric spaces
271.19.15.21.19.17  Metrizable spaces
271.19.15.21.21  Metric properties of metric spaces
271.19.15.21.25  Classes of metric spaces distinguished by topological properties 
271.19.15.21.25.25  Compact metric spaces
271.19.15.21.25.25.17  Continua
271.19.15.21.27  Classes of metric spaces distinguished by conditions of an external nature 
		( for possible ambient spaces)
271.19.15.21.27.27  Absolute retracts
271.19.15.25  Topology of Euclidean spaces
271.19.15.25.25  Plane continua
271.19.15.27  Continuous mappings
271.19.15.27.17  Special types of continuous mappings
271.19.15.27.17.17  Quotient mappings
271.19.15.27.17.19  Open mappings
271.19.15.27.17.25  Perfect mappings and absolutes
271.19.15.27.17.31  Monotone mappings
271.19.15.27.21  Fixed points and coincidences
271.19.15.27.33  Generalizations of continuous mappings
271.19.15.27.33.19  Multivalued mappings
271.19.15.31  Dimension and other topological numerical invariants
271.19.15.31.15  Dimension theory
271.19.15.31.15.17  Dimension theory of arbitrary spaces
271.19.15.31.15.17.25  Comparison of different types of dimensions
271.19.15.31.15.19  Dimension theory of compact spaces
271.19.15.31.15.21  Dimension theory of uniform and nearness spaces
271.19.15.31.15.25  Dimension theory of metric separable spaces
271.19.15.31.15.31  Theory of infinite dimensions
271.19.15.31.17  Invariants of dimension type
271.19.15.33  Descriptive theory of sets of topological spaces

271.19.17  Algebraic topology

271.19.17.17  General theorems on fundamental categories and functors
271.19.17.17.17  General topological categories
271.19.17.17.17.15  Homology and cohomology groups (definitions and basic properties).  
		Axiomatics
271.19.17.17.17.17  Investigation of topological spaces and continuous mappings by 
		homological methods
271.19.17.17.17.17.15  Homology theory of dimension
271.19.17.17.17.17.21  Spectral sequence of a continuous mapping
271.19.17.17.17.17.27  Homology theory of fixed points and coincidence points
271.19.17.17.17.17.33  Homology manifolds
271.19.17.17.17.19  Homology and cohomology with nonabelian coefficients
271.19.17.17.17.25  Homotopy and cohomotopy groups:  definitions and basic 	
		properties.  Axiomatics, etc.
271.19.17.17.17.25.25  Localization of topological spaces
271.19.17.17.17.27  Shape theory
271.19.17.17.17.31  Functors with values in general topological categories (operations over 
		topological spaces)
271.19.17.17.17.31.17  General theory of such functors.  Duality
271.19.17.17.17.31.25  Concrete functors
271.19.17.17.19  Polyhedral categories, i.e., categories whose volumes are polyhedra
271.19.17.17.19.17  Cellular partitions
271.19.17.17.19.19  Simplicial partitions (triangulations) and simplicial schemes
271.19.17.17.21  Categories that approximate general topological and polyhedral categories
271.19.17.17.21.17  Categories whose morphisms are stationary mappings or their 
		homotopy classes (categories of spectra, S-categories)
271.19.17.17.21.17.17  S-duality
271.19.17.17.21.17.21  Adams spectral sequence
271.19.17.17.21.17.25  Extraordinary homology and cohomology theories
271.19.17.17.21.17.27  Bordism and cobordism
271.19.17.17.21.21  Categories of semi-exact functors
271.19.17.17.25  Simplicial sets
271.19.17.19  Homotopy theory:  fundamental problems
271.19.17.19.17  Decompositions of spaces and mappings
271.19.17.19.17.17  Homotopic resolvents ( Moore-Postnikov systems)  and dual 
		constructions
271.19.17.19.17.25  Homotopic convolutions of of spaces (decreasing homotopic groups)
271.19.17.19.17.33  Categories of spaces  (in the sense of Lyusternik-Shnirel'man)
271.19.17.19.19  Obstruction theory.  General classification and continuation theorems for 
		continuous mappings and intersecting surfaces
271.19.17.19.25  Cohomology operations
271.19.17.19.25.33  Analogues of cohomology operations
271.19.17.25  Spaces with various complemented properties of a general nature or that are 
		obtained by these or other general constructions
271.19.17.25.17  Fiber spaces and crossed products
271.19.17.25.17.17  Definition and basic properties, operations over fiber spaces and 
		crossed products
271.19.17.25.17.19  Homotopy theory of bundles.  Universal bundles and classifying 
		spaces
271.19.17.25.17.25  Homology theory of fiber spaces
271.19.17.25.17.25.19  Crossed tensor products
271.19.17.25.17.25.27  Spectral sequences
271.19.17.25.17.31  General theorems on bundles with a vector fiber (K- and J-functors)
271.19.17.25.19  Spaces with operators
271.19.17.25.25  Spaces with multiplication  (H-spaces) and loop spaces
271.19.17.25.27  Space with comultiplication,  and surgeries
271.19.17.25.33  Spaces in which there are only a finite number of nonzero homotopy 
		groups
271.19.17.25.33.21  Eilenberg-MacLane spaces
271.19.17.25.33.27  Spaces in which there are only two nonzero homotopy groups
271.19.17.27  Concrete spaces.  Calculation of homotopy invariants
271.19.17.27.17  Computation of homotopy groups
271.19.17.27.17.19  Homotopy groups of spheres
271.19.17.27.19  Computation of homology and cohomology groups
271.19.17.27.25  Computation of K- and J-functors
271.19.17.27.27  Computation of bordism and cobordism groups
271.19.17.33  Isotopy theory

271.19.19.  Topology of manifolds

271.19.19.17  Topology of manifolds of lower dimensions
271.19.19.17.17  Topological surfaces
271.19.19.17.19  Three-dimensional topological manifolds
271.19.19.17.19.17  Classification of three-dimensional manifolds
271.19.19.17.19.17.19  Poincare conjecture and related problems
271.19.19.17.21  Four-dimensional topological manifolds
271.19.19.17.21.17  Classification of four-dimensional manifolds
271.19.19.17.21.17.19  Poincare conjecture for four-dimensional manifolds
271.19.19.17.27  Embeddings and immersions in lower dimensions
271.19.19.17.33  Knots.  Wreaths.  Braids
271.19.19.19  Topological manifolds
271.19.19.19.19  Microsheaves of topological manifolds
271.19.19.19.27  Topological embeddings and immersions
271.19.19.21  Topology of smooth and piecewise-linear manifolds
271.19.19.21.15  General questions
271.19.19.21.15.15  Homology theory of smooth manifolds
271.19.19.21.15.19  Differential forms on smooth manifolds
271.19.19.21.15.25  Singularities of smooth manifolds
271.19.19.21.15.25.17  Critical points of smooth mappings
271.19.19.21.15.31  Infinite-dimensional manifolds
271.19.19.21.15.31.21  Morse theory
271.19.19.21.17  Classification of smooth and piecewise-linear manifolds
271.19.19.21.17.17  Correspondences between homotopic, topological, combinatorial and 
		smooth properties
271.19.19.21.17.17.25  Realization of cycles
271.19.19.21.17.21  Bordisms and cobordisms
271.19.19.21.17.25  Classification of manifolds up to diffeomorphism or piecewise-linear 
		equivalence
271.19.19.21.17.25.15  Combinatorial equivalence of polyhedra.  Simple homotopy type 
271.19.19.21.19  Bundles of smooth manifolds and bundles whose bases are smooth 
		manifolds
271.19.19.21.19.17  Characteristic classes of manifolds
271.19.19.21.19.17.17  Vector fields on manifolds
271.19.19.21.19.25  Microbundles
271.19.19.21.27  Smooth and piecewise-linear embeddings and embeddings of manifolds
271.19.19.21.33  Groups that act on smooth and piecewise-linear manifolds
271.19.19.21.33.25  Groups of diffeomorphisms and piecewise-linear equivalences
271.19.19.25  Topology of smooth manifolds endowed with complemented structure
271.19.19.25.17  Topology of complex and almost complex manifolds
271.19.19.25.21  Topology of Kahlerian and algebraic manifolds
271.19.19.25.31  Topology of manifolds with infinitesimal connection.  Topology of 
		Riemannian manifolds
271.19.19.33  Differential and integral operators on manifolds
271.19.19.33.19  Foliations.  Integration of vector and tensor fields
271.19.19.33.25  Elliptic operators on manifolds
271.19.21  Analytic spaces
271.19.21.15  General theory of complex and real analytic spaces
271.19.21.15.15  Local theory
271.19.21.15.17  Classes of analytic spaces identified by local conditions
271.19.21.15.19  General theory of coherent analytic sheaves and their cohomology
271.19.21.15.19.19  A connection between the cohomologies of complex spaces and 
		differential forms
271.19.21.15.19.19.21  Residues of differential forms
271.19.21.15.19.25   Computation of the cohomology of specific complex spaces 
271.19.21.15.19.27  The Riemann-Roch theorem for complex manifolds, and related 
		problems
271.19.21.15.25  Analytic sets, subspaces and submanifolds
271.19.21.15.27  Integration on analytic sets and analytic spaces
271.19.21.15.31  Intrinsic metrics on complex spaces
271.19.21.17  Analytic mappings and constructions of complex spaces
271.19.21.17.17  Holomorphic mappings of complex spaces
271.19.21.17.17.17  Holomorphic functions.  Domains and holomorphy hulls in analytic 
		spaces
271.19.21.17.17.19  Cohomology investigation of holomorphic mappings
271.19.21.17.17.25  Approximation theorems for holomorphic functions and mappings in 
		analytic spaces.  Runge pairs
271.19.21.1719  Plurisubharmonic functions, pseudo-convex and pseudo-concave 
		domains in analytic spaces and their generalizations
271.19.21.17.19.19  The Levi problem for analytic spaces
271.19.21.17.21  Meromorphic mappings
271.19.21.17.21.17  Fields of meromorphic functions
271.19.21.17.21.21  Cousin and Poincare problems for analytic spaces
271.19.21.17.27  Quotient spaces of complex spaces 
271.19.21.17.31  Analytic coverings
271.19.21.17.33  Modification of complex spaces
271.19.21.17.33.19  Resolution of singularities of complex spaces and mappings
271.19.21.19  Complex spaces of one, two and three dimensions
271.19.21.19.17  One-dimensional complex manifolds
271.19.21.19.21  Complex surfaces
271.19.21.19.21.15  Singular points of complex surfaces
271.19.21.19.27  Three-dimensional complex spaces
271.19.21.21  Classes of complex spaces distinguished by global conditions
271.19.21.21.17  Holomorphically convex spaces
271.19.21.21.19  Holomorphically complete spaces
271.19.21.21.21.  q-pseudo-convex, q-pseudo-concave and q-complete spaces
271.19.21.21.25  Complex spaces that are close to algebraic manifolds
271.19.21.21.31  Global properties of real-analytic spaces
271.19.21.25  Generalizations of analytic spaces
271.19.21.25.17  Banach analytic spaces
271.19.21.25.21  Partially analytic and other spaces
271.19.21.25.31  Analytic investigation of almost complex manifolds
271.19.21.27  Holomorphic fiber spaces
271.19.21.27.17  Classification of holomorphic fiber spaces 
271.19.21.27.19  Holomorphic vector fiber spaces and sheaves and related cohomologies
271.19.21.27.21  Holomorphic and meromorphic sections in fiber spaces
271.19.21.27.27  A connection between the theory of fiber spaces and some problems in 
		analysis
271.19.21.27.33  Holomorphic connections in fiber spaces
271.19.21.31  Complex spaces with an automorphism group
271.19.21.31.17  Complex Lie transformation groups
271.19.21.31.21  Automorphism groups of complex and almost complex spaces
271.19.21.21.25  Complex homogeneous spaces
271.19.21.21.25.17  Compact complex homogeneous spaces
271.19.21.21.25.19  Kahlerian homogeneous spaces.  Homogeneous domains
271.19.21.21.25.21  Analytic functions on homogeneous spaces
271.19.21.21.25.27  Homogeneous vector fiber spaces and related cohomologies
271.19.21.33  Automorphic functions
271.19.21.33.15  Automorphic and modular forms
271.19.21.33.17  Abelian functions
271.19.21.33.19  Modular functions
271.19.21.33.25  Automorphic forms and related cohomologies
271.19.21.33.27  Automorphic functions in symmetric domains
271.19.21.39  Deformations of structures.  Pseudogroups
271.19.21.39.15  Cohomology problems in the theory of pseudogroups
271.19.21.39.17  Deformations of complex structures
271.19.21.39.17.17  Deformations of submanifolds and holomorphic mappings
271.19.21.39.17.19  Extension of analytic objects
271.19.21.39.17.25  Theory of moduli of Riemann surfaces
271.19.21.39.19  Deformations of other pseudogroup structures
271.19.21.39.21  Deformations of G-structures and connections
271.19.21.39.25  Deformations of fiber spaces
271.19.21.39.33  Analytic theory of deformations of algebraic structures

271.21  Geometry

271.21.15  Geometry in spaces with fundamental groups
271.21.15.15  Elementary geometry, trigonometry, polygonometry
271.21.15.15.17  Planimetry
271.21.15.15.17.19  Triangle geometry
271.21.15.15.17.21  Geometry of polygons (including rectangles, etc.)
271.21.15.15.17.27  Elementary circle geometry
271.21.15.15.19  Stereometry
271.21.15.15.19.21  Geometry of tetrahedra
271.21.15.15.19.25  Geometry of polyhedra (polytopes)
271.21.15.15.19.27  Geometry of spheres and cylinders
271.21.15.15.21  Elementary geometry in multidimensional spaces
271.21.15.15.25  Theory of geometric constructions
271.21.15.15.27  Trigonometry and polygonometry
271.21.15.15.27.17  Plane trigonometry
271.21.15.15.27.19  Spherical trigonometry
271.21.15.17  Foundations of geometry.  Axiomatics
271.21.15.19  Euclidean, pseudo-Euclidean and non-Euclidean geometries
271.21.15.19.15  Euclidean and pseudo-Euclidean geometries
271.21.15.19.15.21  Analytic geometry in Euclidean spaces
271.21.15.19.15.25  Pseudo-Euclidean spaces
271.21.15.19.15.27  Galilei spaces
271.21.15.19.15.31  Semi-Euclidean spaces
271.21.15.19.15.33  Flag spaces
271.21.15.19.17  Non-Euclidean geometries
271.21.15.19.17.17  Lobachevskii geometry
271.21.15.19.17.19  Other hyperbolic geometries
271.21.15.19.17.25  Elliptic geometries
271.21.15.19.17.27  Quasi-elliptic and quasi-hyperbolic spaces
271.21.15.19.17.31  Semi-elliptic and semi-hyperbolic spaces
271.21.15.21  Affine and projective geometries
271.21.15.21.17  Affine geometry
271.21.15.21.17.15  Synthetic geometry in affine space
271.21.15.21.17.17  Analytic geometry in affine space
271.21.15.21.21  Projective geometry
271.21.15.21.21.15  Synthetic geometry in  projective space
271.21.15.21.21.17  Analytic geometry in  projective space
271.21.15.25  Geometry in spaces with other fundamental groups
271.21.15.25.17  Conformal geometry and its analogues
271.21.15.25.21  Symplectic geometry
271.21.15.25.31  Bi-axial geometry and its generalizations
271.21.15.27  Geometry over algebras
271.21.15.27.15  Affine and projective spaces over algebras
271.21.15.27.17  Quadratic Euclidean and non-Euclidean spaces
271.21.15.27.19  Hermitian Euclidean and non-Euclidean spaces
271.21.15.27.21  Symplectic spaces
271.21.15.27.39  Geometry of other spaces over algebras
271.21.15.31  Convex sets, arrangements of geometric figures, and geometric inequalties
271.21.15.31.17  Convex sets
271.21.15.31.17.17  Convex curves and surfaces
271.21.15.31.17.21  Convex bodies
271.21.15.31.17.21.25  Convex polygons and polyhedra
271.21.15.31.19  Generalizations of convex sets
271.21.15.31.21  Arrangements of geometric figures
271.21.15.31.21.17  Packings
271.21.15.31.21.19  Coverings
271.21.15.31.21.25  Partitions
271.21.15.31.21.27   Lattices
271.21.15.31.31  Geometric inequalities
271.21.15.31.31.17  Extremal problems in geometry
271.21.15.33  Descriptive geometry
271.21.15.33.15  Theoretical problems in descriptive geometry
271.21.15.33.17  Applied methods in descriptive geometry
271.21.15.33.25  Generalizations of descriptive geometry
271.21.17  Algebraic and analytic methods in geometry
271.21.17.17  Vector algebra and vector analysis
271.21.17.17.17  Vector algebra
271.21.17.17.21  Vector analysis (vector field theory)
271.21.17.19  Tensor algebra and tensor analysis
271.21.17.19.17  Tensor algebra
271.21.17.19.19  Tensor analysis
271.21.17.21  Spinors, spinor algebra and analysis
271.21.17.21.17  Spinor algebra
271.21.17.21.21  Spinor analysis
271.21.17.25  Calculus of exterior forms
271.21.17.25.17  Grassmannian algebra and its generalizations
271.21.17.25.21  Theory of exterior differential forms
271.21.17.25.25  Differential algebras and their geometric applications
271.21.17.25.33  Theory of the compatability of systems of differential equations
271.21.17.31  Geometric objects
271.21.17.31.17  Representations of Lie groups, and geometric objects
271.21.17.31.19  Representations of infinite Lie pseudogroups, and differential-geometric 
		objects
271.21.17.31.21  Extensions of geometric objects
271.21.17.31.27  Lie differentiation
271.21.17.33  Differential-geometric methods for investigations of embedded manifolds
271.21.17.33.17  Moving frame of a manifold
271.21.17.33.21  Geometric objects on embedded manifolds
271.21.19  Differential geometry
271.21.19.25  Differential geometry in spaces with fundamental groups
271.21.19.25.17  Differential geometry in Euclidean, pseudo-Euclidean and semi-	
		Euclidean spaces
271.21.19.25.17.17  Theory of curved lines
271.21.19.25.17.19  Theory of surface bands
271.21.19.25.17.21  Theory of surfaces
271.21.19.25.17.21.19  Surfaces in a three-dimensional space
271.21.19.25.17.21.21  Surfaces in a multidimensional space
271.21.19.25.17.25  Theory of families of straight lines and planes
271.21.19.25.17.27  Theory of families of curved lines and surfaces
271.21.19.25.17.31  Differential geometry of vector fields
271.21.19.25.17.33  Theory of nonholonomic manifolds
271.21.19.25.19  Differential geometry in non-Euclidean spaces
271.21.19.25.19.17  Differential geometry in non-Euclidean spaces with degenerate 
		absolute
271.21.19.25.19.17.17  Theory of curved lines
271.21.19.25.19.17.19  Theory of surface bands
271.21.19.25.19.17.21  Theory of surfaces
271.21.19.25.19.17.25  Theory of families of straight lines and planes
271.21.19.25.19.17.27  Theory of families of lines and surfaces
271.21.19.25.19.17.33  Theory of nonholonomic manifolds
271.21.19.25.19.19  Differential geometry in non-Euclidean spaces with degenerate 
		absolute
271.21.19.25.19.19.17  Theory of curved lines
271.21.19.25.19.19.21  Theory of surfaces
271.21.19.25.19.19.25  Theory of families of straight lines and planes
271.21.19.25.21  Affine differential geometry
271.21.19.25.21.17  Affine theory of curved lines
271.21.19.25.21.19  Affine theory of surface bands
271.21.19.25.21.21  Affine theory of surfaces
271.21.19.25.21.25  Affine theory of families of straight lines and planes
271.21.19.25.21.27  Affine theory of families of curved lines and surfaces
271.21.19.25.21.31  Affine differential geometry of vector fields
271.21.19.25.21.33  Affine theory of nonholonomic manifolds
271.21.19.25.25  Projective differential geometry
271.21.19.25.25.17  Projective theory of curved lines
271.21.19.25.25.19  Projective theory of surface bands
271.21.19.25.25.21  Projective theory of surfaces
271.21.19.25.25.25  Projective theory of families of straight lines and planes
271.21.19.25.25.27  Projective theory of families of curved lines and surfaces
271.21.19.25.25.33  Projective theory of nonholonomic manifolds
271.21.19.25.27  Differential geometry in spaces with other fundamental groups
271.21.19.25.27.17  Differential geometry in conformal and pseudo-conformal spaces
271.21.19.25.27.21  Differential geometry in symplectic spaces
271.21.19.25.27.31  Differential geometry in bi-axial and  bi-affine spaces and their 
		generalizations
271.21.19.25.31  Differential geometry of point mappings
271.21.19.25.31.17  Differential geometry of point mappings of affine and projective 
		spaces
271.21.19.25.31.19  Differential geometry of point mappings of Euclidean, pseudo-
		Euclidean, conformal and other spaces with a metric
271.21.19.25.31.21  Mapping of submanifolds with point mappings of spaces with a 
		fundamental group
271.21.19.25.33  Kinematic geometry
271.21.19.27  Geometry of differentiable manifolds and their submanifolds
271.21.19.27.17  Geometry of fiber spaces
271.21.19.27.17.17  General problems in the geometry of fiber spaces
271.21.19.27.17.17.31  Geometry of submanifolds in fiber spaces 
271.21.19.27.17.19  Fiber spaces of geometric objects
271.21.19.27.17.19.17  Geometry of vector bundles
271.21.19.27.17.19.19  Geometry of tensor bundles
271.21.19.27.17.19.21  Fiber spaces of other geometric objects
271.21.19.27.17.19.27  Differential extension of spaces of geometric objects
271.21.19.27.17.19.31  Fields of geometric objects in fiber spaces and their extensions
271.21.19.27.17.25  Connections in fiber spaces
271.21.19.27.17.25.15  Nonlinear connections
271.21.19.27.17.25.17  Linear connections in principal fiber spaces
271.21.19.27.17.25.19  Linear connections in spaces with homogeneous fibers
271.21.19.27.17.25.21  Linear connections in spaces of geometric objects
271.21.19.27.17.31  Holonomy groups of fiber spaces
271.21.19.27.19  Infinitesimal structures and fields of geometric objects on differentiable 
		manifolds
271.21.19.27.19.17  Differential geometry of vector and tensor fields on manifolds
271.21.19.27.19.19  G-structures on differentiable manifolds
271.21.19.27.19.19.15  General problems in the geometry of G-structures
271.21.19.27.19.19.17  Tensor G-structures
271.21.19.27.19.19.17.31  Submanifolds in manifolds of tensor G-structures
271.21.19.27.19.19.19  Symplectic and cosymplectic structures
271.21.19.27.19.19.19.31  Submanifolds in manifolds of symplectic and cosymplectic 
		structures
271.21.19.27.19.19.21  Contact and almost contact structures
271.21.19.27.19.19.21.31  Submanifolds in manifolds of contact and almost contact 
		structures
271.21.19.27.19.19.25  Structures of an almost product
271.21.19.27.19.19.25.31  Submanifolds in manifolds of structures of almost products
271.21.19.27.19.19.27  Structures defined by algebras
271.21.19.27.19.19.27.31  Submanifolds in manifolds of structures defined by algebras
271.21.19.27.19.19.31  Other special G-structures
271.21.19.27.19.19.31.31  Submanifolds in manifolds of other special G-structures
271.21.19.27.19.19.33  Mapping of manifolds with G-structures
271.21.19.27.19.21  Manifolds with complex or almost complex structure
271.21.19.27.19.21.17  Manifolds with complex structure
271.21.19.27.19.21.17.17  Hermitian manifolds
271.21.19.27.19.21.17.21  Kahlerian manifolds
271.21.19.27.19.21.19  Manifolds with an almost complex structure
271.21.19.27.19.21.19.17  Almost Hermitian and subordinate structures
271.21.19.27.19.21.21  Connections on manifolds with complex or almost complex 
		structure
271.21.19.27.19.21.25  Mappings of manifolds with complex structure
271.21.19.27.19.21.31  Submanifolds embedded in manifolds with complex or almost 
		complex structure
271.21.19.27.19.25  Infinitesimal structures and fields of of geometric objects of higer 
		orders
271.21.19.27.19.25.15  General theory of tangent bundles (higher orders)
271.21.19.27.19.25.17  Jet theory
271.21.19.27.19.25.19  Tensors and tensor fields of higher orders
271.21.19.27.19.25.25  Fields of other geometric objects of higher orders
271.21.19.27.19.25.31  Higher-order connections on a differentiable manifold
271.21.19.27.19.27  Finsler geometry and its generalizations
271.21.19.27.19.27.17  Finsler geometry
271.21.19.27.19.27.17.21  Submanifolds of Finsler spaces
271.21.19.27.19.27.19  Interval geometry
271.21.19.27.19.27.19.31  Geometry of the calculus of variations
271.21.19.27.19.27.21  Geometry of a space of linear elements
271.21.19.27.19.27.25  Geometry of spaces with other generating elements
271.21.19.27.19.31  Web geometry
271.21.19.27.19.33  Geometry of differential equations
271.21.19.27.21  Classical spaces with connections and their generalizations
271.21.19.27.21.17  Riemann and pseudo-Riemann spaces
271.21.19.27.21.17.15  General theory of  Riemann and pseudo-Riemann spaces
271.21.19.27.21.17.15.17  Invariant objects in Riemann and pseudo-Riemann spaces
271.21.19.27.21.17.15.21  Holonomy groups of Riemann and pseudo-Riemann spaces
271.21.19.27.21.17.15.27  Complete Riemann spaces
271.21.19.27.21.17.17  Special types of Riemann spaces
271.21.19.27.21.17.17.15  Subprojective spaces and their generalizations
271.21.19.27.21.17.17.19  Reducible and semi-reducible Riemann and pseudo-Riemann 
		spaces
271.21.19.27.21.17.17.21    Recurrent Riemann and pseudo-Riemann spaces
271.21.19.27.21.17.17.27  Einstein spaces
271.21.19.27.21.17.17.31  Symmetric Riemann spaces and their generalizations
271.21.19.27.21.17.25  Mappings of Riemann and pseudo-Riemann spaces
271.21.19.27.21.17.25.21  Isometric mappings, immersions and submersions of Riemann 
		spaces 
271.21.19.27.21.17.31  Submanifolds of Riemann and pseudo-Riemann spaces
271.21.19.27.21.17.31.17  Curves and families of curves
271.21.19.27.21.17.31.21  Hypersurfaces
271.21.19.27.21.17.31.33  Submanifolds of other dimensions
271.21.19.27.21.19  Spaces with affine connection
271.21.19.27.21.19.15  General theory of spaces with affine connection
271.21.19.27.21.19.17  Special types of spaces with affine connection
271.21.19.27.21.19.17.17  Spaces with equivalent connection
271.21.19.27.21.19.17.19  Weyl spaces
271.21.19.27.21.19.17.21  Projective-Euclidean spaces
271.21.19.27.21.19.17.27  Spaces with absolute parallelism
271.21.19.27.21.19.17.31  Symmetric spaces with affine connection
271.21.19.27.21.19.17.33  Semi-Riemann spaces
271.21.19.27.21.19.25  Mappings of spaces with affine connection
271.21.19.27.21.19.31  Submanifolds of spaces with affine connection
271.21.19.27.21.21  Spaces with projective connection
271.21.19.27.21.21.15  General theory of spaces with projective connection
271.21.19.27.21.21.31  Submanifolds of spaces with projective connection
271.21.19.27.21.25  Spaces with conformal connection
271.21.19.27.21.27  Spaces with symplectic connection
271.21.19.27.21.31  Spaces with generalized Euclidean and pseud-Euclidean connections
271.21.19.27.21.39  Other classical spaces with connections
271.21.19.27.25  Geometry of homogeneous spaces.  Geometry of Lie groups
271.21.19.27.25.15  Invariant infinitesimal structures in homogeneous spaces
271.21.19.27.25.17  Vector and tensor fields in homogeneous spaces
271.21.19.27.25.25  Manifolds embedded in homogeneous spaces
271.21.19.27.25.31  Integral geometry
271.21.19.31  Global differential geometry
271.21.19.31.17  Global differential geometry of submanifolds.  Nonregular submanifolds
271.21.19.31.17.17  Global geometry of lines and surfaces in spaces with fundamental 
		groups
271.21.19.31.17.17.17  Regular lines and surfaces
271.21.19.31.17.17.21  Nonregular lines and surfaces
271.21.19.31.17.19  Global images
271.21.19.31.17.19.17  Existence, embedding and realizationof global images
271.21.19.31.17.19.25  Uniqueness, rigidity and bendability of global images
271.21.19.33  Geometry of metrized manifolds
271.21.19.33.17  Minkowski geometry
271.21.19.33.21  Hilbert geometry
271.21.19.33.33  Geometry of geodesics
271.21.21  Geometric investigation of objects in the natural sciences
271.21.21.17  Geometric problems and methods in the theory of relativity
271.21.21.17.15  Geometric problems in special relativity
271.21.21.17.17  Geometric problems in general relativity
271.21.21.17.19  Geometric problems in cosmology
271.21.21.17.21  Geometric problems in unified field theory
271.21.21.19  Geometric investigation of fields of physical objects
271.21.21.21  Geometric methods in quantum mechanics and elementary particle theory
271.21.21.25  Geometric methods in mechanics and engineering
271.21.21.25.15  Geometric methods in statistics
271.21.21.25.17  Geometric methods in kinematics
271.21.21.25.19  Geometric methods in dynamics
271.21.21.25.25  Geometric methods in engineering
271.21.21.25.31  Geometric methods in continuum mechanics
271.21.21.25.31.17  Geometric methods in the theory of shells
271.21.21.31  Geometric problems and methods in crystallography
271.21.21.33  Geometric problems and methods in optics

271.23  Mathematical analysis

271.23.15  Introduction to analysis, and some special problems in analysis
271.23.15.19  Theory of real numbers
271.23.15.25  Asymptotic formulas and expressions
271.23.15.27  Analytic means.  Inequalities
271.23.15.27.17  Means
271.23.15.27.25  Numerical inequalities and some elementary functional inequalities
271.23.15.33  Study of individual functions
271.23.17  Differential and integral calculus
271.23.17.17  Differential calculus
271.23.17.17.31  Mappings.  Implicit functions
271.23.17.17.33   Other analytic applications of differential calculus
271.23.17.19  Integral calculus
271.23.17.19.31  Red?  integrals
271.23.17.19.31.19  Integrals over curved manifolds (curvilinear and surface integrals)
271.23.17.19.33  Definite simple or multiple integrals
271.23.17.19.33.17  Improper integrals
271.23.19  Functional equations and the theory of finite differences
271.23.19.15.  Theory of finite differences
271.23.19.15.17  Finite-difference equations
271.23.19.15.17.21  Recurrent relations and series
271.23.19.19  Functional equations and inequalities
271.23.21  Integral transformations, operational calculus
271.23.21.17  Laplace transform
271.23.21.19  Fourier integral and Fourier transform
271.23.21.21  Other integral transformations and their inversions.  Convolutions
271.23.21.25  Operational calculus
271.23.23  Series and sequences
271.23.23.15  Numerical and functional series and sequences
271.23.23.15.15  Special numerical series and sequences
271.23.23.15.15.25  Sums of finite and infinite series
271.23.23.15.17  Convergence
271.23.23.15.25  Multiple series and sequences
271.23.23.15.31  Summation theory
271.23.23.15.31.25  Tauberian theorems
271.23.23.19  Infinite products
271.23.23.21  Continued fractions
271.23.25  Special functions
271.23.25.15  Euler integrals and their generalizations.  The gamma function and related 
		functions
271.23.25.17  Probability integral and related functions
271.23.25.19  Elliptic functions and integrals
271.23.25.21  Bessel functions and polynomials and other cylindrical functions
271.23.25.25  Mathieu functions
271.23.25.27  Spherical functions.  Legendre polynomials and functions,  harmonic 
		polynomials, ultraspherical polynomials.  Gegenbauer functions
271.23.25.31  Orthogonal polynomials and their generalizations (Chebyshev, Hermite, 
		Jacobi, Laguerre, et al.)
271.23.25.33  Hypergeometric series and functions.  Generalized and degenerate 	
		hypergeometric  functions and their generalizations
271.23.25.39  Other special functions and special numbers

271.25  Theory of functions of a real variable

271.25.15  Descriptive function theory 
271.25.17  Metric theory of functions
271.25.17.15  Measures, integration and differentiation
271.25.17.15.15  Measure, capacity
271.25.17.15.15.17  Lebesgue measure
271.25.17.15.15.19  Borel measure
271.25.17.15.15.21  Other measures
271.25.17.15.15.23  Measurable functions
271.25.17.15.15.25  Continuous functions
271.25.17.15.15.27  Additive set functions
271.25.17.15.15.29  Capacity
271.25.17.15.17  Integration theory
271.25.17.15.17.15  Riemann integral
271.25.17.15.17.17  Lebesgue integral
271.25.17.15.17.21  Stieltjes integral
271.25.17.15.17.25  Other integrals (theory)
271.25.17.15.19  Singular integrals
271.25.17.15.21  Integrals of potential type
271.25.17.15.23  Differentiation theory
271.25.17.23.17  Differentiable functions
271.25.17.15.23.19  Derivative
271.25.17.15.23.23  Symmetric derivatives
271.25.17.15.27  Mappings
271.25.17.15.29  Curved surfaces
271.25.17.15.29.17  Level sets of functions of several variables
271.25.17.17  Classes (sets) of functions
271.25.17.17.17  Compact families of function
271.25.17.17.17.17  Epsilon nets.  Epsilon entropy
271.25.17.17.17.21  Widths
271.25.17.17.19  Embedding theorems for classes of differentiable functions
271.25.17.17.19.18  Inequalities between partial derivatives
271.25.17.17.19.21  Boundary properties of functions
271.25.17.17.19.25  Weight classes
271.25.17.17.19.31  Extension theorems
271.25.17.17.19.33  Integration of classes of functions
271.25.17.17.21 Functions of bounded variation
271.25.17.17.21.17  Absolutely continuous functions
271.25.17.17.21.21  Convex functions and their generalizations
271.25.17.17.25  Quasi-analytic functions
271.25.17.17.27  Other classes of functions
271.25.17.17.31  Superpositions
271.25.17.17.33  Inequalities
271.25.17.19  Systems of functions and series in systems of functions
271.25.17.19.17  Completeness and closure of system of functions
271.25.17.19.21  Bases
271.25.17.19.27  Orthogonal systems
271.25.17.19.27.17  Convergence of orthogonal series
271.25.17.19.27.27  Summation of orthogonal series
271.25.17.21  Trigonometric series
271.25.17.21.17  Representation of a function in the form of a trigonometric series
271.25.17.21.19  Uniqueness problems
271.25.17.21.25  Fourier series
271.25.17.21.25.17  Convergence of Fourier series
271.25.17.21.25.19 Absolute convergence of Fourier series
271.25.17.21.25.21  Fourier coefficients
271.25.17.21.25.27  Summation of Fourier coefficients
271.25.17.21.31  Multiple trigonometric series
271.25.17.21.31.25  Multiple Fourier series
271.25.17.21.31.27  Summation of multiple Fourier series
271.25.17.25  Theory of the Fourier integral
271.25.17.25.27  Summability of Fourier integrals
271.25.17.27  Almost periodic functions
271.25.17.27.25  Compactness of systems of almost periodic functions
271.25.17.27.27  Convergence and summability of Fourier series of almost periodic 
		functions
271.25.17.27.31  Interpolation, almost periodic extension of functions
271.25.17.27.33  Approximation of almost periodic functions
271.25.19.  Approximation theory 
271.25.19.17  Approximation by algebraic polynomials
271.25.19.17.17  On an infinite domain
271.25.19.17.19  Of several variables
271.25.19.17.27  Chebyshev-type problems
271.25.19.17.33  Approximation with exact constants
271.25.19.19  Approximation by trigonometric polynomials and entire functions of 
		exponential type
271.25.19.19.17  Approximation in the sense of order
271.25.19.19.21  Approximation with exact constants
271.25.19.19.31  Approximation of functions of several variables
271.25.19.21  Approximation by rational functions
271.25.19.21.19  Nonlinear problems in approximation theory
271.25.19.21.25  Approximation in the Hausdorff metric
271.25.19.25  Integration
271.25.19.25.25  Approximation by spline functions
271.25.19.27  Extremal properties of polynomials and their generalizations
271.25.19.27.17  Inequalities for derivatives of polynomials and their generalizations
271.25.19.27.19  Other inequalities for polynomials and their generalizations
271.25.19.27.25  Zeros of polynomials and their generalizations
271.25.19.31  Theory of quadratures and cubatures
271.25.19.33  Moment theory

271.27  Theory of functions of complex variables

271.27.15  Functions of one complex variable
271.27.15.17  Elementary problems
271.27.15.25  Rational functions in a complex domain
271.27.15.31  Sequences and series of analytic functions
271.27.15.31.19  Power series
271.27.15.31.19.17  Properties of power series associated with the nature of the 	
		coefficients
271.27.15.31.19.21  Lacunary power series
271.27.15.31.19.27  Behavior of a power series on the boundary of the disk of 	
		convergence.  Superconvergence
271.27.15.31.19.33  Analytic continuation.  Singular points
271.27.15.31.27  Sequences and series of exponentials
271.27.15.31.27.17  Dirichlet series
271.27.15.33  Systems of functions
271.27.15.33.17  Problems of completeness.  Closure of a system of functions.  Bases
271.27.15.33.19  Sequences and series of polynomials.  Orthogonal polynomials
271.27.15.33.25  Problems of approximation in a complex domain.  Best approximation
271.27.15.33.25.17  Approximation by rational functions
271.27.15.33.27  Asymptotic representations in a complex domain
271.27.15.33.31  Interpolation.  Iteration
271.27.17  Conformal mapping and geometric problems in the theory of functions of a 
		complex variable.  Analytic functions and their generalization
271.27.17.17  Mappings of special domains
271.27.17.21  Boundary properties of analytic functions, and boundary value problems
271.27.17.21.21  Bounded functions
271.27.17.21.21.19  Generalization of the Schwartz lemma
271.27.17.21.21.25  Generalization of the maximum modulus principle
271.27.17.21.25  Harmonic measure and capacity.  Analytic capacity
271.27.17.21.31  Boundary properties of analytic functions
271.27.17.21.31.17  Theory of limit sets
271.27.17.21.31.19  Cauchy-type integral
271.27.17.21.31.27  Other integral representations of analytic functions
271.27.17.21.33  Boundary value problems in the theory of analytic functions
271.27.17.25  Theory of Riemann surfaces.  Uniformization
271.27.17.25.17  Conformal classes and automorphisms of Riemann surfaces
271.27.17.27  Univalent and multivalent functions
271.27.17.27.15  Univalent functions
271.27.17.27.15 .17  Estimates for coefficients and other functionals
271.27.17.27.15 .21  Geometric properties of mappings
271.27.17.27.15.31  Covering theorems
271.27.17.27.19  Multivalent functions
271.27.17.31  Classes and spaces of analytic functions
271.27.17.31.17  Entire and meromorphic functions
271.27.17.31.17.17  Entire functions of finite order
271.27.17.31.17.21  Meromorphic functions
271.27.17.31.17.27  Generalization of Picard's theorem
271.27.17.31.17.33  Theory of the distribution of values
271.27.17.31.19  Analytic functions in the disk and other domains
271.27.17.31.25  Classes of analytic functions
271.27.17.31.25.17  Functions of bounded type
271.27.17.31.25.21  Noh? and related classes 
271.27.17.31.25.27  Algebraic and algebroid functions
271.27.17.31.25.33  Analytic theory of automorphic functions
271.27.17.31.25.33.17  Elliptic and modular functions
271.27.17.31.25.39  Other classes of analytic functions
271.27.17.31.31  Spaces of analytic functions
271.27.17.33  Generalizations of analytic functions and conformal mappings
271.27.17.33.17  Quasiconformal mappings and their generalizations
271.27.17.33.19  Quasi-analytic classes in a complex domain
271.27.17.33.21  Generalized analytic functions
271.27.17.33.25  Monogenic functions
271.27.17.33.27  Analytic matrices, functions of a matrix argument
271.27.17.33.31  Functions of a hypercomplex variable
271.27.17.33.33  Functions of a discrete argument
271.27.17.33.39  Other generalizations of analytic functions
271.27.19  Functions of several complex variables
271.27.19.15  Series and sequences of functions of several variables
271.27.19.17  Approximation of functions and domains
271.27.19.19  Integral representations
271.27.19.21  Holomorphic functions of several variables.  Domains and hulls of 	
		holomorphy.  Pseudoconvexity
271.27.19.25  Analytic continuation.  Singularities
271.27.19.27  Classes and boundary properties of functions of several variables
271.27.19.31  Meromorphic functions of several variables.  Cousin and Poincare problems
271.27.19.33  Entire functions of several complex variåbles
271.27.24  Harmonic functions and their mappings
271.27.24.17  General properties of harmonic functions
271.27.24.21  Subharmonic functions and their generalizations
271.27.24.25  Biharmonic and polyharmonic functions
271.27.24.27  Pluriharmonic and plurisubharmonic functions
271.27.24.31  Harmonic functions on Riemannian manifolds
271.27.24.33  Other generalizations of harmonic functions 

271.29  Ordinary differential equations

271.29.15  General theory of ordinary differential equations and systems of equations
271.29.15.15  General problems.  Existence theorems, uniqueness theorems and theorems 
		on the differential properties of solutions
271.29.15.15.25  Differential equations with discontinuous and multivalued right-hand 
		sides
271.29.15.15.31  Differential inequalities
271.29.15.17  Methods for solving various types of equations and systems of equations
271.29.15.19  First integrals
271.29.15.21  Equations that are not solved with respect to the highest derivative.  Singular 
		solutions
271.29.15.23  Special types of ordinary differential equations (Riccati, hypergeometric, 
		Bessel, Mathieu, Hill, etc.)
271.29.15.25  Pfaffian equations and Pfaffian systems
271.29.15.27  Infinite systems of differential equations
271.29.17  Qualitative theory of ordinary differential equations and systems of equations
271.29.17.15  Systems and analytic theory of ordinary differential equations
271.29.17.15.21  Theory of systems of second-order equations
271.29.17.15.21.15  Location  of integral curves.  Singular points
271.29.17.15.21.17  Limit cycles and periodic solutions.  Oscillation in nonlinear systems
271.29.17.15.21.21  Properties of solutions of second-order equations and second-order 
		systems (asymptotic behavior, monotonicity, estimates for the solutions, 
		etc.)
271.29.17.15.21.27  Zeros of solutions of second-order differential equations, oscillating 
		and nonoscillating solutions
271.29.17.15.25  Theory of systems of arbitrary order and of equations of 	
	arbitrary order
271.29.17.15.25.15  Stability and asymptotic behavior of solutions
271.29.17.15.25.17  Equations with periodic and almost periodic right-hand sides.  
		Periodic and almost periodic solutions.  Oscillations in nonlinear 	
		multidimensional systems
271.29.17.15.25.19  Integral manifolds
271.29.17.15.25.21  Properties of solutions of equations of arbitrary order and of systems 
		of arbitrary order (asymptotic behavior, monotonicity, estimates for the 
		solutions, etc.)
271.29.17.15.25.27  Zeros of solutions of higher-order equations and systems of equations
271.29.17.17  Linear ordinary differential equations and systems
271.29.17.17.21  Linear ordinary differential equations with variable coefficients
271.29.17.19  Theory of dynamical systems
271.29.17.19.25  Topological problems in the theory of dynamical systems
271.29.19  Boundary value problems and eigenvalue problems for ordinary differential 
		equations and systems of equations 
271.29.19.17  Boundary value problems for linear ordinary differential equations
271.29.19.17.15  Theorems on the existence, uniqueness and properties of solutions
271.29.19.25  Eigenvalues and eigenfunctions.  Eigenfunction expansions
271.29.19.21  Boundary value problems for nonlinear ordinary differential equations
271.29.19.27  Multipoint boundary value problems and functional problems for ordinary 
		differential equations
271.29.21  Analytic theory of ordinary differential equations and systems of equations
271.29.21.15  Singular points of equations in a complex domain
271.29.21.25  Expansions of solutions in series in a complex domain
271.29.21.31  Expansions of solutions of equations and systems with a complex 	
		parameter
271.29.23  Asymptotic methods in the theory of ordinary differential equations and 
		systems of equations
271.29.23.15  General theory of asymptotic methods
271.29.23.17  Linear ordinary differential equations and systems with small parameters 
		multiplying the highest derivatives
271.29.23.31  Averaging methods and  invariant manifolds.  Problems in nonlinear 
		mechanics
271.29.25  Functional-differential and discrete equations and systems of equations with 
		one independent variable
271.29.25.17  Linear difference equations
271.29.25.21  Stability theory
271.29.25.25  Periodic solutions
271.29.25.31  Boundary value problems
271.29.25.33  Asymptotic methods
271.29.27  Equations of analytical mechanics, mathematical theory of the control of 
		motion
271.29.27.19  Equations of analytical mechanics
271.29.27.25  Equations of automatic control systems
271.29.27.25.17  Equations of linear automatic control systems
271.29.27.25.21  Equations of nonlinear automatic control systems

271.31  Partial differential equations 

271.31.15  General theory of partial differential equations and systems of partial differential 
		equations
271.31.15.17  General first-order equations and systems:  properties, types, etc.
271.31.15.19  General higher-order equations and systems:  properties, types, etc.
271.31.15.21  Boundary value problems:  general theory, equations on manifolds
271.31.15.25  The Cauchy problem for partial differential equations
271.31.15.25.17  Well-posedness theory
271.31.15.25.21  Semigroups associated with the Cauchy problem
271.31.17  Linear and quasilinear equations and systems of equations
271.31.17.17  Elliptic equations and systems
271.31.17.17.17  Linear equations of elliptic type
271.31.17.17.17.17  General properties
271.31.17.17.17.19  Boundary value problems
271.31.17.17.17.21  Potential theory.  Potentials
271.31.17.17.17.25  Laplace and Poisson equations
271.31.17.17.17.27  Degenerate equations.  Equations with a small parameter
271.31.17.17.17.31  Spectral theory
271.31.17.17.25  Quasilinear equations of elliptic type
271.31.17.17.31  Inverse problems 
271.31.17.17.39  Ill-posed problems
271.31.17.19  Hyperbolic equations and systems
271.31.17.19.17  Linear hyperbolic equations
271.31.17.19.17.27  Degenerate equations.  Equations with a small parameter
271.31.17.19.17.33  Spectral problems
271.31.17.19.25  Quasilinear hyperbolic equations
271.31.17.19.31  Inverse problems
271.31.17.21  Parabolic equations and systems
271.31.17.21.25  Nonlinear problems
271.31.17.21.31  Inverse problems
271.31.17.27  Equations of mixed and composite types
271.31.19  Asymptotic behavior of solutions
271.31.21  Nonlinear equations and systems of equations

271.33  Integral equations

271.33.15  Linear integral equations
271.33.15.15  Fredholm integral equations
271.33.15.17  Volterra integral equations
271.33.15.19  Singular integral equations and related boundary value problems
271.33.15.25  Linear integral equations in function spaces
271.33.15.33  Systems of linear integral equations
271.33.17  Nonlinear integral equations
271.33.17.19  Nonlinear singular integral equations and related boundary value problems
271.33.17.33  Systems of nonlinear integral equations
271.33.19  Integro-differential equations
271.33.19.17  Linear integro-differential equations
271.33.19.19  Singular integro-differential equations
271.33.19.21  Nonlinear inegro-differential equations
271.33.19.33  Systems of integro-differential equations

271.35  Differential and integral equations of mathematical models in the natural 
		sciences

271.35.15  Mathematical models in aero- and hydrodynamics and acoustics
271.35.17  Mathematical models in gas dynamics
271.35.19  Flow problems
271.35.21  Mathematical models in hydrodynamics
271.35.21.15  Hydrodynamics of an ideal fluid
271.35.21.17  Hydrodynamics of a viscous fluid
271.35.23  Mathematical models in the theory of a boundary layer
271.35.25  Mathematical models in filtration
271.35.27  Mathematical models of the wave motions of a heavy fluid
271.35.29  Mathematical models in magnetohydrodynamics
271.35.31  Mathematical models in elasticity and plasticity
271.35.31.15  Dynamical problems
271.35.31.17  Plane and contact problems
271.35.31.19  Three-dimensional problems
271.35.31.21  Thermoelasticity
271.35.31.25  Plates and shells
271.35.31.27  Plastic media
271.35.33  Mathematical models in electrodynamics and optics
271.35.35  Mathematical theory of diffraction
271.35.37  Mathematical models of the electrodynamics of moving media
271.35.39  Mathematical models in gravitation and cosmology
271.35.41  Mathematical models of waveguides
271.35.43  Mathematical models in biology
271.35.45  Mathematical models in heat conduction and diffusion
271.35.45.17  The Stefan problem
271.35.45.19  Heat exchange problems
271.35.47  Transport equations
271.35.49  Mathematical models in statistical physics
271.35.51  Mathematical models in plasma physics, kinetic equations
271.35.53  Mathematical models of electromagnetic waves in plasma
271.35.55  Soliton solutions of evolution equations
271.35.57  Mathematical models in quantum physics
271.35.59  Methods in perturbation theory
271.35.63  Mathematical models in geophysics and meteorology

271.37  Calculus of variations and the mathematical theory of optimal control

271.37.15  Calculus of variations 
271.37.15.17  Functional analytic methods of the calculus of variations
271.37.15.17.17  Necessary conditions based on the theory of first and second variations
271.37.15.17.19  Sufficient conditions
271.37.15.17.21  Problems on the existence of solutions of variational problems.  Theory 
		of the existence of solutions
271.37.15.17.25  Variational methods for solving differential, integral, and other functional 
		equations
271.37.15.17.27  Minimal surfaces
271.37.15.17.31  Inverse problems in the calculus of variations
271.37.15.17.33  Extremal problems in linear topological spaces and concepts associated 
		these problems
271.37.15.17.39  Various special problems in the calculus of variations
271.37.15.21  Topological methods in the calculus of variations
271.37.15.21.33  Variational theory of geodesics
271.37.17  Mathematical control theory.  Optimal control
271.37.17.15  General theory of control systems, and controllability (mathematical theory)
271.37.17.25  Optimal control
271.37.17.25.17  Maximum principle
271.37.17.25.21  Dynamic programming methods
271.37.17.25.25  Theory of linear optimal systems
271.37.17.25.27  Optimal control of systems with distributed parameters
271.37.17.25.31  Problems of the existence of optimal solutions
271.37.17.25.35  Approximate methods for solving optimal control problems
271.37.19  Differential games
271.37.19.17  Two-person differential games
271.37.19.21  n-person differential games

271.39  Functional analysis

271.39.15  Linear spaces endowed with topology, order, and other structures
271.39.15.15  Ordered and semi-ordered spaces
271.39.15.17  Linear topological spaces
271.39.15.17.17  Normed spaces.  Banach space.  Hilbert space
271.39.15.17.17.21  Hilbert spaces with an indefinite metric
271.39.15.17.25  Geometry of linear topological spaces
271.39.15.17.25.17  Convex sets in linear spaces
271.39.15.17.25.21  Bases in linear topological spaces
271.39.15.17.25.27  Geometric problems in approximation theory in linear spaces
271.39.15.17.25.31  Approximate dimension and related problems
271.39.15.17.27  Abstract potential theory
271.39.15.17.31  Concrete topological  linear spaces.  Interpolation theorems
271.39.15.17.31.17  Spaces of continuous functions
271.39.15.17.31.21  Spaces of analytic functions
271.39.15.17.31.27  Spaces of sequences and matrices
271.39.15.19  Linear functionals and conjugate spaces
271.39.15.19.25  Positive-definite functionals in function spaces
271.39.15.19.25.21  Problems of the continuation of positive-definite functionals and 
		positive-definite kernels
271.39.15.19.31  Moment theory
271.39.17  Generalized functions
271.39.17.17  Homogeneous generalized functions
271.39.17.19  Fourier transform of generalized functions.  Convolutions
271.39.17.25  Algebraic theory of generalized functions.  (Operational calculus of 	
		Mikusinski, et al.)
271.39.17.27  Generalized distributions (hyperfunctions, ultradistributions, etc.)
271.39.17.31  Linear analytic functionals
271.39.19  Linear operators and operator equations
271.39.19.17  Linear operators in linear infinite-dimensional spaces; general properties
271.39.19.17.17  Linear operators in locally convex spaces
271.39.19.17.19  Linear operators in Banach spaces
271.39.19.17.21  Linear operators in Hilbert spaces
271.39.19.17.21.19  Normal and unitary operators in Hilbert spaces
271.39.19.17.21.27  Selfadjoint linear operators in Hilbert and pre-Hilbert spaces
271.39.19.17.21.33  Nonselfadjoint linear operators in Hilbert spaces
271.39.19.17.27  Completely continuous and nuclear operators
271.39.19.17.31  Linear operators in semi-ordered spaces
271.39.19.17.33  Theory of perturbations of linear operators
271.39.19.19  Study of concrete operators
271.39.19.19.19  Infinite matrices
271.39.19.19.21  Integral operators
271.39.19.19.25  Ordinary differential operators
271.39.19.19.27  Partial differential operators
271.39.19.19.31  Pseudodifferential operators
271.39.19.25  Linear equations in infinite-dimensional linear spaces
271.39.19.25.15  General theory of solvability of linear equations in function spaces
271.39.19.25.19  Linear equations in concrete function spaces
271.39.19.25.21  Linear ill-posed problems
271.39.19.27  Vector functions and operator functions
271.39.19.33  Families of linear spaces and categories of linear operators
271.39.21  Spectral theory of linear operators
271.39.21.17  Spectral theory in general linear topological spaces and in spaces with a 
		quasi-topology
271.39.21.17.17  Abstract operational calculus of linear operators
271.39.21.17.21  Spectral theory of completely continuous linear operators
271.39.21.17.27  Problems of completeness of (generalized) eigen- and associated vectors
271.39.21.19  Spectral theory in Banach spaces
271.39.21.19.17  Spectral theory of completely continuous and nuclear operators in Banach 
		spaces
271.39.21.19.21  Spectral theory of Volterra operators in Banach spaces
271.39.21.19.27  Problems of linear similarity, and the equivalence of linear operators
271.39.21.21  Spectral theory in Hilbert spaces
271.39.21.21.17  Spectral theory of completely continuous and nuclear operators in Hilbert 
		spaces
271.39.21.21.21.  Spectral theory of Volterra operators in a Hilbert space
271.39.21.21.27  Spectral theory of selfadjoint operators in a Hilbert space
271.39.21.21.33  Spectral theory of nonselfadjoint operators in Hilbert spaces
271.39.21.25  Study of the spectrum of concrete operators
271.39.21.25 .15  Spectra of infinite matrices
271.39.21.25 .19  Spectra of integral operators
271.39.21.25.25  Spectra of ordinary differential operators
271.39.21.25.27  Spectra of partial differential operators
271.39.21.25.31  Spectra of pseudodifferential operators
271.39.21.27  Special problems in the spectral theory of linear operators
271.39.21.27.17  Expansions in eigen- and associated functions
271.39.21.27.21  Inverse problems in spectral analysis
271.39.21.27.27  Perturbation of the spectrum of linear operators
271.39.21.27.31  Extension of operators
271.39.23  Topological algebras and the theory of infinite-dimensional representations
271.39.23.17  Topological algebras (rings) and their continuous representations
271.39.23.17.17  Normed algebras and their representations
271.39.23.17.17.25  Commutative Banach algebras
271.39.23.17.21  Algebras (rings) with involution
271.39.23.17.21.17  Positive-definite functions on algebras (rings) with involution
271.39.23.19  Algebras (rings) of linear operators
271.39.23.19.17  C*-algebras
271.39.23.19.19  Von Neumann algebras (W*-algebras)
271.39.23.21  Infinite-dimensional representation of groups
271.39.23.25  Infinite-dimensional representation of Lie algebras
271.39.23.27  Harmonic analysis of functions on groups and homogeneous spaces
271.39.23.27.17  Harmonic analysis on abelian groups
271.39.23.27.19  Almost periodic functions on groups
271.39.23.27.27  Group algebras
271.39.23.27.33  Special functions that arise in the theory of finite- and infinite-	
		dimensional representations of Lie groups
271.39.23.31  Semigroups of linear and nonlinear operators.  Evolution equations
271.39.23.37  Other algebraic structures in functional analysis
271.39.23.39  Applications of functional analysis to quantum mechanics and field theory
271.39.25  Measure theory, representations of Boolean algebras, dynamical systems
271.39.25.15  Measure and integral theory
271.39.25.19  Representations of Boolean algebras
271.39.25.21  Functional integrals and their applications to evolution equations
271.39.25.25  Metric theory of dynamical systems
271.39.27  Nonlinear functional analysis
271.39.27.17  Analysis on manifolds
271.39.27.17.17  Function spaces and sections of bundles
271.39.27.17.21  Infinite-dimensional functional analysis (global analysis)
271.39.27.17.27  Operators on manifolds
271.39.27.17.33  Integral geometry
271.39.27.19  Nonlinear functionals
271.39.27.19.17  General topological properties
271.39.27.19.21  Differential calculus for nonlinear functionals
271.39.27.19.31  Differential and analytic properties of nonlinear functionals
271.39.27.19.31.17  Analytic functionals
271.39.27.19.33  Extrema of nonlinear functionals
271.39.27.25  Nonlinear operators
271.39.27.25.17  General properties of nonlinear operators
271.39.27.25.17.15  Condensing operators
271.39.27.25.17.17  Fixed points of nonlinear operators
271.39.27.25.17.25  Monotone operators
271.39.27.25.21  Differential and integral calculus for nonlinear operators
271.39.27.25.31  Eigenvalues of nonlinear operators
271.39.27.27  Nonlinear equations in function spaces
271.39.27.27.19  Existence and uniqueness theorems for nonlinear equations
271.39.27.27.31  Continuability and branching of solutions of nonlinear equations
271.39.27.27.33  Nonlinear ill-posed problems
271.39.29  Approximate methods in functional analysis

271.41  Numerical mathematics

271.41.15  Numerical methods in algebra
271.41.15.17  Numerical methods for solving systems of linear algebraic equations
271.41.15.17.17  The case of a square matrix
271.41.15.17.21  The case of a matrix of general form
271.41.15.19  Numerical methods for inverting matrices
271.41.15.19.17  The case of symmetric matrices
271.41.15.19.19  The case of nonsymmetric matrices
271.41.15.21  Numerical methods for computing the eigenvalues and eigenvectors of 
		matrices
271.41.15.21.17  Partial eigenvalue problem
271.41.15.21.21  Complete eigenvalue problem
271.41.15.25  Numerical methods for solving transcendental equations and systems of 
		equations
271.41.15.25.17  Localization of solutions
271.41.15.25.21  Numerical methods for determining all the zeros of polynomials
271.41.15.25.25  Numerical methods for  solving nonlinear systems
271.41.17  Numerical methods in analysis
271.41.17.15  Approximation of functions
271.41.17.15.15  Determination of constants
271.41.17.15.17  Uniform approximation
271.41.17.15.19  Mean-square approximation
271.41.17.17  Interpolation and extrapolation
271.41.17.17.15  Parabolic interpolation
271.41.17.17.17  Nonparabolic interpolation
271.41.17.17.19  Spline interpolation
271.41.17.19  Numerical differentiation
271.41.17.21  The method of least squares
271.41.17.31  Empirical formulas
271.41.17.33  Optimization of functions
271.41.17.33.17  Unconstrained optimization
271.41.17.33.21  Constrained optimization
271.41.17.35  Quadrature formulas
271.41.17.35.17  Definite integrals
271.41.17.35.19  Singular integrals
271.41.17.35.25  Improper integrals
271.41.17.35.31  Multiple integrals
271.41.19  Numerical methods for solving differential and integral equations
271.41.19.15  Numerical methods for solving ordinary differential equations
271.41.19.15.17  The Cauchy problem for ordinary differential equations 
271.41.19.15.17.15  First-order differential equations
271.41.19.15.17.17  Systems of ordinary differential equations
271.41.19.15.21  Boundary value problems for ordinary differential equations
271.41.19.15.21.15  First-order differential equations
271.41.19.15.21.17  Second-order differential equations
271.41.19.15.21.19  Higher-order differential equations
271.41.19.15.27  Optimal control problems
271.41.19.15.27.15  Linear problems
271.41.19.15.27.17  Nonlinear problems
271.41.19.15.33  Inverse problems and intensification problems
271.41.19.15.33.15  The case of initial conditions
271.41.19.15.33.17  The case of boundary conditions
271.41.19.17  Numerical methods for solving partial differential equations
271.41.19.17.13  First-order differential equations and their systems
271.41.19.17.17  Second-order differential equations of elliptic type 
271.41.19.17.17.21  Boundary value problems
271.41.19.17.17.27  Problems with characteristic parameters
271.41.19.17.17.33  Inverse problems
271.41.19.17.19  Second-order differential equations of parabolic and hyperbolic types
271.41.19.17.19.17  The Cauchy problem
271.41.19.17.19.27  Mixed problems
271.41.19.17.17.33  Systems of equations
271.41.19.17.17.39  Inverse problems
271.41.19.17.21  Systems of nonlinear differential equations in continuum mechanics
271.41.19.17.25  Higher-order partial differential equations and systems of such equations
271.41.19.17.25.15  Biharmonic equation
271.41.19.17.25.17  Cauchy problems
271.41.19.17.25.21  Boundary value problems
271.41.19.17.25.27  Mixed problems
271.41.19.17.25.31  Inverse problems
271.41.19.19  Numerical methods for solving integral equations
271.41.19.19.17  Integro-differential equations
271.41.19.19.19  Fredholm equations of the first kind
271.41.19.19.21  Fredholm equations of the second kind
271.41.19.19.25  Volterra equations 
271.41.19.19.27  Nonlinear equations 
271.41.19.19.31  Singular equations 
271.41.19.19.33  Operator equations 
271.41.21  Mathematical tables
271.41.23  Computer, graphic and other methods in numerical mathematics
271.41.23.15  Computer programming
271.41.23.17  Mechanical methods for computations
271.41.23.19  Solution of mathematical problems by means of modeling systems
271.41.23.21  Graphic methods for computations
271.41.23.25  Nomography and nomograms
271.41.23.27  Probabilistic methods for computations
271.41.23.31  Solution of problems in mathematical analysis and of applied problems

271.43  Probability theory and mathematical statistics

271.43.15  Probability theory and random processes
271.43.15.15  Foundations and axioms of probability theory
271.43.15.17  Abstract probability theory
271.43.15.17.17  Combinatorial probabilities
271.43.15.17.19  Geometric probabilities
271.43.15.19  Probability distributions and distribution densities
271.43.15.19.15  The normal distribution
271.43.15.19.17  Characteristic functions, moments, semimartingales and other 	
		characteristics
271.43.15.19.19  Measures of dependency
271.43.15.19.25  Infinitely divisible laws
271.43.15.19.31  Stable laws
271.43.15.21  Limit theorems
271.43.15.21.21  for sums of independent random variables
271.43.15.21.25  for sums of weakly dependent random variables
271.43.15.21.27  for functionals and random processes
271.43.15.21.31  on groups and other algebraic structures
271.43.15.21.33  Large deviations 
271.43.15.27  Random processes  (general questions)
271.43.15.27.17  General theory of random processes
271.43.15.27.17.17  Measures in function spaces
271.43.15.27.17.21  Limit theorems for sequences of random processes
271.43.15.27.19  Prediction theory
271.43.15.27.25  Stopping times
271.43.15.27.33 Martingales
271.43.15.31  Markov processes
271.43.15.31.15  General theory of Markov processes
271.43.15.31.15.17  Properties of sample functions
271.43.15.31.15.19  Infinitesimal and characteristic operators
271.43.15.31.15.21  A strictly Markov process
271.43.15.31.15.27  Topologies associated with a process
271.43.15.31.17  Markov chains:  processes with finite  or countable set of states
271.43.15.31.19  Processes with independent increments
271.43.15.31.25  Additive functionals.  Probabilistic potential theory
271.43.15.31.27  Transformation of Markov processes
271.43.15.31.27.17  Random time change
271.43.15.31.27.19  Subprocesses
271.43.15.31.27.25  Transformations of measures
271.43.15.31.31  Boundary theory of Markov processes
271.43.15.31.31.17  Martin boundary
271.43.15.31.31.21  General boundary conditions
271.43.15.33  Random processes of a special type
271.43.15.33.15  Diffusion processes and processes that are solutions of stochastic 
		differential equations
271.43.15.33.17  Branching processes and epidemic processes
271.43.15.33.17.17  General branching processes
271.43.15.33.17.19  Markov branching processes
271.43.15.33.17.21  Processes with increments that depend on the age of the particles
271.43.15.33.17.25  Processes with increments that depend on the location of the particles
271.43.15.33.17.27  Processes with increments that depend on the energy or mass of the 
		particles
271.43.15.33.19  Controlled random processes
271.43.15.33.21  Renewal processes
271.43.15.33.25  Point random processes
271.43.15.33.31  Gaussian processes and measures
271.43.15.33.31.17  Properties of sample functions 
271.43.15.33.31.21  Asymptotic weakening of dependence
271.43.15.33.31.25  Derivatives of Gaussian measures
271.43.15.33.33  Stationary and harmonizable sequences and processes
271.43.15.33.33.17  Extrapolation, interpolation, filtering
271.43.15.33.33.21  Ergodic theorems
271.43.15.39  Random functions of several variables
271.43.15.39.17  Homogeneous random fields
271.43.15.39.25  Point random fields
271.43.17  Mathematical statistics
271.43.17.15  Foundations of statistical theory
271.43.17.17  Statistical scattering and dependence.  Statistical means, deviations, etc.
271.43.17.19  Sufficiency, sufficient statistics
271.43.17.21  Distribution theory
271.43.17.21.17  Distributions of sample characteristics
271.43.17.21.17.17  Point distributions
271.43.17.21.17.21  Asymptotic theory
271.43.17.21.19  Characterization and structural theory
271.43.17.27  Theory of statistical inferences and decisions
271.43.17.27.17  Likelihood
271.43.17.27.19  Bayesian theory and problems
271.43.17.27.25  Compound decision problems
271.43.17.27.31  Fiducial probability
271.43.17.31  Methods of statistical analysis and inference
271.43.17.31.19  Parametric methods
271.43.17.31.19.17  Estimation of parameters and functionals
271.43.17.31.19.17.17  Point estimation
271.43.17.31.19.17.21  Confidence regions, tolerance bounds
271.43.17.31.19.19  Hypothesis testing
271.43.17.31.19.19.17  Properties of individual tests
271.43.17.31.19.19.19  Goodness-of-fit tests
271.43.17.31.19.19.25  Discrimination
271.43.17.31.19.21  Variance and covariance analysis
271.43.17.31.19.25  Correlation and regression analysis
271.43.17.31.19.27  Ranking and selection
271.43.17.31.19.33  Paired and multiple comparisons
271.43.17.31.21  Nonparametric methods
271.43.17.31.21.17  Estimation of parameters and functionals
271.43.17.31.21.17.17  Point estimation
271.43.17.31.21.17.21  Confidence regions, tolerance bounds
271.43.17.31.21.19  Hypothesis testing
271.43.17.31.21.19.17  Properties of individual tests
271.43.17.31.21.19.19  Goodness-of-fit tests
271.43.17.31.21.19.25  Discrimination
271.43.17.31.21.21  Variance and covariance analysis
271.43.17.31.21.25  Correlation and regression analysis
271.43.17.31.21.27  Ranking and selection
271.43.17.31.21.31  Order statistics
271.43.17.31.21.33  Paired comparison methods
271.43.17.31.25  Statistics of independent random variables.  Contingency tables
271.43.17.31.31  Multidimensional statistical methods
271.43.17.31.31.17  Estimation of parameter and functionals
271.43.17.31.31.17.17  Point estimation
271.43.17.31.31.17.21  Confidence regions, tolerance bounds
271.43.17.31.31.19  Hypothesis testing
271.43.17.31.31.19.17  Properties of individual tests
271.43.17.31.31.19.19  Goodness-of-fit tests
271.43.17.31.31.19.25  Discrimination
271.43.17.31.31.21  Variance and covariance analysis
271.43.17.31.31.25  Correlation and regression analysis
271.43.17.31.31.27  Ranking and selection
271.43.17.31.31.31  Factor analysis
271.43.17.31.31.33  Cluster analysis.  Classification
271.43.17.33  Special statistical applications and models
271.43.17.33.17  Design of an experiment (general theory)
271.43.17.33.17.25  Optimal designs
271.43.17.33.17.27  Block designs
271.43.17.33.17.31  Factor designs
271.43.17.33.19  Sampling and sampling theory
271.43.17.33.21  Sequential methods
271.43.17.33.21.17  Sequential designs
271.43.17.33.21.19  Sequential analysis
271.43.17.33.21.21  Sequential estimation
271.43.17.33.21.25  Optimal stopping 
271.43.17.33.21.33  Cumulative sum technique
271.43.17.33.25  Stochastic approximation.  Monte Carlo methods
271.43.17.33.27  Statistics of random processes
271.43.17.33.27.17  Estimation for random processes
271.43.17.33.27.17.17  Mean of a stationary process
271.43.17.33.27.17.25  Correlation function of a stationary process
271.43.17.33.27.17.31  Spectrum of a stationary process
271.43.17.33.27.19  Hypothesis testing for random processes
271.43.17.33.27.25  Statistics of point processes
271.43.17.33.27.33  Analysis of time series
271.43.17.33.27.33.25  Autocorrelation, regression
271.43.17.33.27.33.31  Spectral analysis of time series
271.43.51  Application of probability-theoretic and statistical methods
271.43.51.17  Application to the mathematical physical sciences
271.43.51.17.15  Multicomponent random systems.  Processes with a large number of 
		locally interacting components
271.43.51.17.17  Gibbs random fields, cluster expansions
271.43.51.17.19  Applications to classical statistical mechanics
271.43.51.17.21  Generalized Gibbs fields.  Euclidean quantum field theory
271.43.51.17.25  Random evolution in nonequilibrium statistical mechanics
271.43.51.19  Noncommutative probability theory and its application to quantum physics
271.43.51.21  Application of probability-theoretic and statistical methods to engineering 
		and the humanities
271.43.51.21.15  Applications to mechanics 
271.43.51.21.17  Applications to physics
271.43.51.21.21 Applications to geophysics                                                                    
271.43.51.21.23  Applications to astronomy and geodesy
271.43.51.21.25  Applications to  chemistry
271.43.51.21.27  Apllications to geography and geology
271.43.51.21.29  Apllications to engineering
271.43.51.21.31  Statistical methods in production control
271.43.51.21.33  Applications to radio-engineering
271.43.51.21.35  Applications to automation
271.43.51.21.37  Probability-theoretic reliability theory
271.43.51.21.39  Applications of mathematical statistical methods to psychology, biology 
		and medicine
271.43.51.21.41  Applications to economics and sociology
271.43.51.21.45  Design of specific experiments
271.43.51.21.47  Statistical tables
271.43.51.23  Processing of statistical data
271.43.51.23.17  Data collection and survey design
271.43.51.23.19  Sample surveys:  methods, questionnaires; editing, errors and 	
		corrections
271.43.51.23.21  Computational processing of data, algorithms
271.43.51.23.25  Formulation of data; format, etc,
271.43.51.23.27  Data storage.  Data banks
271.43.51.23.31  Use of statistical data
271.43.51.23.33  Types of statistical data

271.45  Combinatorial analysis.  Graph theory

271.45.15  General theory of combinatorial analysis
271.45.15 .17  Combinatorial choice problems
271.45.15.17.15  Matroids
271.45.15.17.17  Transversals
271.45.15.17.21  Ramsey theory
271.45.15.17.27  Combinatorics of finite lattices
271.45.15.17.31  Extremal combinatorial problems
271.45.15.17.31.15  Problems on a covering and on minimal systems of representatives
271.45.15.17.31.21  Intersections of systems of sets.  Spencer theory
271.45.15.19  General enumeration methods
271.45.15.19.15  Polya's theory
271.45.15.19.19.  Combinatorics of formal power series.  Generating functions
271.45.15.19.25  Incidence algebras, the inclusion-exclusion principle, Mobius theory
271.45.15.19.27  Fnite-difference method.  Recurrent sequences
271.45.15.19.33  Asymptotic methods
271.45.15.21  Combinatorial sequences of numbers and polynomials
271.45.15.23  Enumeration problems of combinatorial analysis
271.45.15.24  Probability-theoretic approach to combinatorial problems
271.45.15.27  Combinatorial theory of partitions
271.45.15.31  Combinatorial identities
271.45.15.33  Combinatorial inequalities
271.45.15.35  Combinatorial theory of substitutions and permutations
271.45.15.39  Special combinatorial tables and configurations
271.45.15.39.17  Matrix combinatorial problems
271.45.15.39.17.15  (0,1)-matrices
271.45.15.39.17.19  Combinatorial problems in the theory of permanents
271.45.15.39.17.27  Hadamard matrices
271.45.15.39.19  Orthogonal tables:  Latin squares, etc.
271.45.15.39.21  Block designs
271.45.15.39.22  Applications of combinatorial analysis to the design of experiments
271.45.15.39.25  Finite, affine and projective geometries as block designs
271.45.15.39.31  Packings and coverings
271.45.15.39.32  Combinatorics of the placement of geometric objects
271.45.15.39.33  Tesselation and tiling problems 
271.45.15.41  Algorithmic problems of combinatorial analysis
271.45.17  Graph theory
271.45.17.15  General graph theory and graph representations
271.45.17.15.15  General graph theory
271.45.17.15.17  Graph representations
271.45.17.17  Study of individual classes of graphs
271.45.17.17.15  Trees
271.45.17.17.17  Planar graphs
271.45.17.17.19  Directed graphs.  Tournaments
271.45.17.17.21  Other classes
271.45.17.19  Topological problems in graph theory
271.45.17.21  Graph coloring
271.45.17.25  Algebraic problems in graph theory
271.45.17.25.15  Isomorphism of graphs.  Symmetries of graphs
271.45.17.25.17  Operations over graphs
271.45.17.25.19  Computation? and enumerations of graphs
271.45.17.27  Extremal problems in graph theory
271.45.17.31  Combinatorial problems in graph theory
271.45.17.31.15  Connectivity
271.45.17.31.17  Graph circuits
271.45.17.31.19  Partitions, coverings, packings
271.45.17.33  Algorithmic problems in graph theory
271.45.17.39  Generalizations of graphs
271.45.17.39.15  Hypergraphs
271.45.17.39.17  Matroids
271.45.17.39.19  Nets
271.45.17.39.21  Random graphs
271.45.17.51  Applications of graph theory
271.45.17.51.17  Applications of graph theory in the natural sciences
271.45.17.51.19  Applications of graph theory in engineering
271.45.17.51.21  Applications of graph theory in the social sciences
271.45.17.51.21.17  Applications of graph theory in economics

271.47  Mathematical cybernetics

271.47.15  Mathematical theory of control systems
271.47.15.15  Mathematical problems in modeling control systems
271.47.15.16  Combinatorial-logic problems in coding
271.47.15.17  Cybernetic problems in the theory of algorithms
271.47.15.19  Automata theory
271.47.15.19.15  Methods for the specification and realization of automata
271.47.15.19.17  Algebraic problems in automata theory
271.47.15.19.19  Problems of the representability of events in automata
271.47.15.19.21  Experiments with automata
271.47.15.19.25  Automata games
271.47.15.19.27  Probabilistic automata 
271.47.15.19.31  Asynchronous automata 
271.47.15.19.33  Generalizations of automata
271.47.15.21  Design problems in the theory of control systems
271.47.15.21.21  Estimates for the complexity of the realization of functions by circuits
271.47.15.21.25  Problems of circuit design with special constraints on the topology of the
                        circuits and the form of the elements
271.47.15.21.31  Minimization of Boolean and many-valued functions
271.47.15.21.33  Application of Boolean algebra to circuit design
271.47.15.27  Functional systems
271.47.15.27.19  Completeness problems for specific functional systems
271.47.15.27.19.17  Finite-valued logics
271.47.15.27.19.19  Infinite-valued logics
271.47.15.27.19.21  Fuzzy logics and sets
271.47.15.27.19.25  Automata mappings
271.47.15.27.19.31  Recursive functions
271.47.15.27.19.39  Other systems
271.47.15.27.25  Study of the structure of closed classes
271.47.15.27.31  Metric problems in functional systems
271.47.15.31  Identity transformations
271.47.15.33   Stability; reliability and control
271.47.15.33.19  Design of stable and reliable circuits
271.47.15.33.31  Tests
271.47.17  Mathematical theory of information
271.47.17.17  Entropy, quantity of information and their properties
271.47.17.19  Asymptotic theorems on optimal coding (Shannon's theory)
271.47.17.19.17  Multisided channels
271.47.17.19.21  Channels with feedback
271.47.17.19.27  Channels with partially known parameters
271.47.17.21  Computation of information-theoretic characteristics for specific channels       
                        and messages
271.47.17.21.17  Computation of capacity
271.47.17.21.21  Epsilon entropy
271.47.17.21.27  Computation of error probability
271.47.17.25  Algebraic theory of codes and of correcting errors
271.47.17.25.17  Cyclic codes
271.47.17.25.19  Convolutional codes
271.47.17.25.21  Majority decoding
271.47.17.25.25  Concatenated codes
271.47.17.25.27  Codes for correcting errors in arithmetic operations
271.47.17.25.31  Synchronization error-correcting codes
271.47.17.27  Nonuniform codes for messages
271.47.17.31  Sequential decoding methods
271.47.17.33  Coding methods in continuous channels
271.47.17.33.17  Quantization of messages
271.47.17.33.21  Gaussian channels
271.47.17.33.27  Channels with fading
271.47.17.39  Complexity of coding and decoding methods
271.47.19  Operations research
271.47.19.15  Utility and decision-making theory
271.47.19.15.17  General utility theory
271.47.19.15.17.15  Theory of binary relations
271.47.19.15.17.17  Axiomatic utility theory
271.47.19.15.17.25  Theory of group behavior
271.47.19.15.19  Games of chance and experimental games
271.47.19.15.19.19  Games of chance (mathematical problems)
271.47.19.15.19.31  Experimental games
271.47.19.15.21  Theory of statistical decisions
271.47.19.15.27   Decision-making theory	
271.47.19.15.27.17  Decision-making under fuzzy conditions
271.47.19.15.27.21  Multicriterial optimization
271.47.19.15.27.27  Stochastic decision-making models
271.47.19.19  Game theory
271.47.19.19.17  Antagonistic games
271.47.19.19.17.19  Matrix games
271.47.19.19.17.21  Two-person zero-sum infinite games (on the unit square on function 
                        spaces)
271.47.19.19.19  Noncooperative games
271.47.19.19.19.17  Equilibrium situations
271.47.19.19.19.19  Bimatrix games
271.47.19.19.19.21  Supergames and metagames
271.47.19.19.19.25  Cooperative theory
271.47.19.19.19.25.17  Arbitrage schemes
271.47.19.19.19.31  Games without side payments
271.47.19.19.19.33  Games with an infinite number of players  
271.47.19.19.19.51  Market games and related problems
271.47.19.19.31  Dynamic games
271.47.19.19.31.17  Positional games
271.47.19.19.31.19   Discrete-time games (recursive, survival, stochastic)
271.47.19.19.31.21  Continuous-time games
271.47.19.25  Mathematical programming
271.47.19.25.17  Linear programming
271.47.19.25.17.17  Linear inequalities, convex cones and polyhedra
271.47.19.25.17.19  Special linear programming problems
271.47.19.25.17.19.19  Transportation problem
271.47.19.25.17.19.25  Flows in networks
271.47.19.25.17.27  Computation methods of linear programming
271.47.19.25.17.27.15  Simplex method
271.47.19.25.17.27.21  Block programming
271.47.19.25.17.27.31  Solution of large-scale problems
271.47.19.25.19  Nonlinear programing
271.47.19.25.19.17  Duality theory
271.47.19.25.19.17.21  Optimality conditions, saddle points, Lagrange functions
271.47.19.25.19.19  Convex programming
271.47.19.25.19.19.17  Quadratic programming
271.47.19.25.19.19.17.21  Complementarity problems
271.47.19.25.19.21  Nonconvex and multi-extremal problems
271.47.19.25.19.25  Nonsmooth optimization
271.47.19.25.19.25.19  Minimax problems
271.47.19.25.19.27  Computational methods of nonlinear programming
271.47.19.25.19.27.25.15  Linearization methods, including gradient methods
271.47.19.25.19.27.25  Relaxation methods          
271.47.19.25.19.27.27   Nonrelaxation methods                      
271.47.19.25.19.27.27.19  Feasible directions methods		            
271.47.19.25.19.27.27.27  Second- and higher-order methods
271.47.19.25.19.27.27.21  Conjugate gradient methods
271.47.19.25.19.27.27.17  Penalty methods
271.47.19.25.21  Discrete programming
271.47.19.25.21.15  Complexity theory for discrete problems
271.47.19.25.21.17  Combinatorial problems (the traveling salesman problem, scheduling       
                        theory, etc.)
271.47.19.25.21.19  Integer programming
271.47.19.25.21.19.19  Boolean programming
271.47.19.25.21.21  Computational methods for discrete programming
271.47.19.25.21.27.17  Truncation methods; group approach
271.47.19.25.21.27.21  Partial sorting  method.  The branch and bound method
271.47.19.25.21.27.31  Approximate and heuristic methods
271.47.19.25.25  Parametric programming
271.47.19.25.27  Stochastic programming
271.47.19.25.27.17  Problems with random constraints
271.47.19.25.27.19  Probability characteristics of solutions
271.47.19.25.31  Dynamic programming
271.47.19.25.31.19  Markov decision-making processes
271.47.19.25.31.27  Computational methods for dynamic programming
271.47.19.27  Theory of mathematical economic models
271.47.19.27.17  Static models
271.47.19.27.17.17  Input-output-type models
271.47.19.27.17.25  Macroeconomic models
271.47.19.27.17.25.19  Production functions
271.47.19.27.17.27  Econometrics
271.47.19.27.17.33  Optimization models
271.47.19.27.19  Dynamic models
271.47.19.27.19.17  Single- and two-commodity models
271.47.19.27.19.19  Multicommodity models
271.47.19.27.19.19.17  Leontief-type models
271.47.19.27.19.19.21  Von Neumann-type models.  Optimal trajectories
271.47.19.27.19.27  Consumption models
271.47.19.27.21  Probabilistic models
271.47.19.27.21.19  Selection of a portfolio of securities
271.47.19.27.25  Theory of economic behavior
271.47.19.27.25.15  Supply and demand models
271.47.19.27.25.17  Exchange models
271.47.19.27.25.19  Equilibrium models
271.47.19.27.25.25  Theory of a firm
271.47.19.27.25.31  Models for the control of an economy
271.47.19.27.27  Modeling of separate aspects of an economy
271.47.19.27.27.17  Price models; monetary economics
271.47.19.27.27.21  Models that take into account ecological and demographic factors
271.47.19.27.27.27  Resource-allocation models
271.47.19.27.33  Sector and regional models
271.47.19.31  Mathematical models in operations research
271.47.19.31.17  Queueing theory
271.47.19.31.17.25  Queueing system networks
271.47.19.31.17.27  Theory of transportation flows and traffic
271.47.19.31.17.31  Service optimization models
271.47.19.31.19  Reliability and backup theory (optimization models).  Quality control
271.47.19.31.21  Inventory control theory.  Storage theory
271.47.19.31.21.17  Storage models
271.47.19.31.21.21  Exchange models
271.47.19.31.27  Large-scale systems
271.47.19.31.27.17  Modeling control processes
271.47.19.31.27.19  Network design
271.47.19.31.27.25  Digital simulation and modeling of systems
271.47.19.31.33  Search theory
271.47.19.51  Applications to operations research
271.47.19.51.15  Organization of research
271.47.19.51.17  Applications to design problems
271.47.19.51.19  Applications to sociology
271.47.19.51.21  Location of production
271.47.19.51.23  Applications to economic problems
271.47.19.51.27  Financial and actuarial applications
271.47.19.51.29  Preservation of the environment
271.47.19.51.31  Applications to public health
271.47.19.51.33  Applications to industry
271.47.19.51.35  Energy applications
271.47.19.51.37  Applications to mining
271.47.19.51.39  Military applications
271.47.19.51.41  Applications to forestry
271.47.19.51.43  Applications to agriculture
271.47.19.51.45  Applications to communications problems
271.47.19.51.47  Applications to transportation problems
271.47.19.51.51  Applications to the organization of production
271.47.19.51.53  Applications to chemistry
271.47.19.51.55  Automated control systems
271.47.19.51.57  Applications to construction problems
271.47.19.51.59  Urban economics
271.47.21  Theory of mathematical machines, and programming
271.47.21.17  Theory of mathematical machines
271.47.21.17.17.  Computer networks
271.47.21.17.21  Multiprocessor systems
271.47.21.17.27  Special processors and multiprocessors
271.47.21.17.33  Number systems and carrying out of operations
271.47.21.21  Computer programming
271.47.21.21.15  Programming theory
271.47.21.21.15.15  Writing and verifying programs
271.47.21.21.15.17  Computational complexity
271.47.21.21.15.19  Abstract data types
271.47.21.21.15.21  Transformation of programs
271.47.21.21.15.25  Parallel programming
271.47.21.21.17  Programming methods and examples
271.47.21.21.17.15  Software reliability
271.47.21.21.19  Programming languages and systems
271.47.21.21.19.15  Methods for describing languages
271.47.21.21.19.17  Programming languages
271.47.21.21.19.19  Programming systems
271.47.21.21.19.21  Applied program packages
271.47.21.21.21  Storage, retrieval and information processing
271.47.21.21.21.15  Data structures
271.47.21.21.21.17  Databases
271.47.21.21.21.19  Information-retrieval systems
271.47.21.21.21.21  Automated control systems
271.47.21.21.21.27  Computer graphics
271.47.21.21.25  Operating systems
271.47.21.21.27  Programs and algorithms for solving specific problems
271.47.23  Mathematical problems in artificial intelligence
271.47.23.15  Pattern recognition and image analysis (distinguishing of contours, 	 
		recognition of  characters and oral speech; taking into account context; 
		languages for describing patterns and images)
271.47.23.17  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)
271.47.23.19  Mathematical description and modeling of neurons, neural networks, brains 
		and other organs of human beings and animals
271.47.23.21  Complex systems (investigation of the activity of complex systems,     
                        investigation of their structure, languages for their description)
271.47.23.25  Robots (theory, control languages; operations design, specific robots and
                        their applications)
271.47.23.27  Algorithmization of creative activity  (decision-makers, question-answer-	
                        type systems, heuristic methods)
271.47.25  Mathematical problems in semiotics
271.47.25.17  Syntactical investigation of symbolic systems
271.47.25.19  Meaningful interpretation of symbolic systems
271.47.25.21  Decoding of symbolic systems
271.47.25.25  Mathematical linguistics (general aspects).  Mathematical investigation of      
                        languages of a general nature)
271.47.25.25.51  Algorithmic languages
271.47.25.27  Models of languages and language structures	                  
271.47.25.27.17  Algebro-logic and set-theoretic models of languages and language 
                        stuctures
271.47.25.27.17.19  Models defined by a generating investigation (grammar)
271.47.25.27.17.21  Languages that admit and are generated by automata
271.47.25.27.17.23  Models defined by means of internal correspondences 
                         (configurations, control relations, word connectives)
271.47.25.27.17.25  Transformation of languages
271.47.2527.21  Probability-statistical models for languages and language structures
271.47.25.31  Language semantics (mathematical aspects)
271.47.25.33  Mathematical problems of machine translation
271.47.25.39  Other mathematical problems of semiotics and mathematical linguistics                          
	                                     

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