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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


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  Philosophy and the methodology of mathematics  Classification of the mathematical sciences
271.01.09  History of mathematics.  Personalities  History of mathematics  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  Monographs  Handbooks  Surveys  New journals and series  Publications of institutions and organizations (collectives)  Instructional material  Mathematical terminology
271.01.79  Mathematical training.  Mathematical education  Popularization of the mathematical sciences

271.03  Foundations of mathematics, mathematical logic

271.03.15  Foundations of mathematics  General philosophical problems  Set theory Naive set theory  Axiomatic set theory.  Axiomatization of analysis  Descriptive set theory  Theory of order types and of ordinal and cardinal numbers  Proof theory  Mathematical intuitionism  Constructive mathematics  Logical and semantic antinomies
271.03.17  Algorithms and computable functions  General problems in the theory of algorithms  General theory of calculi  General recursion theory  Complexity of algorithms  Algorithmic problems  Degrees of undecidability  Algorithmic set theory  Computable functions  Mathematical models of computational processes
271.03.19  Mathematical logic  Logic and logico-mathematical languages  Classical logic theories  Propositional logic  Predicate logic  Higher-order logics  Nonclassical logics  Intuitionistic and intermediate logics  Modal logics  Many-valued logics  Formalization of traditional logics  Quantum logics  Probabilistic logic  Combinatorial logic  Other logic systems  Logico-mathematical theories  Formal arithmetic  Inference in logic and logico-mathematical calculi  Problems in the algorithmic decidability of logic and logico-mathematical 
		theories  Theory of models  General mathematical systems
271.15  Number theory

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

271.17  Algebra

271.17.15  Semigroups  Semigroups with finiteness conditions  Finite semigroups  Generating sets, relations and identities on semigroups  Varieties of semigroups.  Free semigroups, defining relations  Commutative semigroups  Idempotent semigroups  Equivalences and complexes in semigroups.  Homomorphisms  Semigroup homomorphisms  Special elements and complexes in semigroups  Semigroup ideals   Subsemigroups  Structures of subsemigroups, ideals and congruences of semigroups  Transformation semigroups  Semigroups of multivalued transformations (binary relations)  Semigroups of single-valued transformations  Representation of transformation semigroups  Matrix semigroups, linear semigroups  Inverse semigroups (generalized groups)  Regular semigroups.  Other generalizations of inverse semigroups  Semiheaps and generalized heaps  Semigroups with complemented structures  Semigroups with operators of the  -semigroup  Connection with ring theory, multiplicative ring semigroups  Quasi-ordered and ordered semigroups  Topological semigroups  Compact and connected semigroups  Topological semigroups of transformations of topological spaces  Different generalizations of associativity
271.17.17  Groups  Methods of mathematical logic, and algorithmic problems in group theory  Axiomatizable classes of groups  Elementary theories of different classes of groups  Algorithmic problems in group theory.  Word problem  Abelian groups  Purity and its generalizations  Higher subgroups  Direct and subdirect sums (abelian groups)  Extensions of abelian groups  Mappings of a group into itself and into other subgroups  Primary abelian groups  Torsion-free abelian groups  Systems of generators.  Factorization  Finite groups  Generators and defining relations  Automorphisms of finite groups  Finite p-groups  Finite solvable groups  Finite simple groups  Arithmetic and abstract properties  Methods in the theory of Lie algebras in finite groups  Arithmetic structure and normal structure of finite groups  Extensions of finite groups  Normal series in finite groups  Sylow-type theorems  Factorization of finite groups  Normal complements in finite groups  Permutation groups  Primitive and multiply transitive groups  Combined problems for permutation groups  Groups of collineations of finite projective and affine planes  Relationships between elementary groups  Systems of generators  Varieties of groups  Operations over groups  Equations over groups and embedding theorems in group theory  Relationships between subgroups.  Generalized solvable groups and 
		finiteness conditions  Structures of subgroups  Structural isomorphisms  Minimality and maximality  conditions  Normal series and systems  Generalized solvable groups and finiteness conditions  Nilpotent and solvable groups  Generalized solvable groups  Radicals in groups  Characteristic subgroups, automorphisms and endomorphisms  Automorphism groups and representations of groups in 	
		automorphism groups of algebraic systems  Automorphisms and automorphism groups of specific groups  Locally finite groups  Linear groups  Approximation of groups  Ordered groups  Linearly ordered groups  Structurally ordered groups  Partially ordered groups  Different types of preorderable groups  Topological groups  General theory of topological groups  Generators and relations in topological groups  Operations over topological groups.  Products  Abelian topological groups  Locally compact groups  Measure and integral on topological groups  Pro-finite groups.  Pro-p-groups  Representations of topological groups  Relations between subgroups in topological groups.  Finiteness 	
		conditions and similar conditions  Groups with compact classes of conjugate elements  Generalizations of topological groups  Linear representations of abstract groups.  Characters of groups  Representations of finite groups  Classical theory  Representations of specific groups  Characters of representations  Representations over fields of nonzero characteristic  Representations over rings  Representations of infinite groups  Generalizations of groups.  Groupoids, etc.  Special classes of groupoids  Groupoids with complemented structures  Quasigroups  Isotopies and homotopies of quasigroups  Identities and generalized identities on quasigroups  Loops
271.17.19  Rings and modules  Methods of mathematical logic in rings and modules  Associative rings and algebras  Structure of rings  Ideals in rings.  Radicals  Structure-theoretic problems for associative rings  Automorphisms, endomorphisms and derivation of rings  Rings with chain conditions  Rings with conditions on ideals and subrings  Skew fields  Prime rings  Primary and semiprimary rings  Regular, biregulator and strictly regulator rings  Rings of principal ideals  Defining and identity relations in rings.  Varieties of rings  Embedding of rings  Quotient rings  Operations over rings  Semigroup and group rings  Representations of rings and algebras  Modules  Structure of modules  Projective and flat modules  Injective modules  Quotient modules  Endomorphism rings  Equivalence and duality  Homology classification of rings  Submodules.  Structure of submodules  Nonassociative rings and algebras  Nonassociative skew fields and their generalizations  Lie rings and algebras  Finite-dimensional Lie algebras  Infinite-dimensional Lie algebras  Generators, defining and identity relations.  Varieties.  Free algebras  Embeddings of Lie algebras into other types of algebras  Universal enveloping algebras of Lie algebras  Lie algebras of derivations  Subalgebras and ideals  Automorphisms, endomorphisms and derivations of Lie algebras  Generalizations of Lie algebras  Alternative rings and related rings  Jordan rings and algebras  Ordered rings and modules  Topological rings and modules  Rings and modules with valuation  Generalizations of rings and modules
271.17.21  Structures  Partially ordered sets  Boolean rings and algebras  Boolean algebras  Types of structures  Distributive structures  Dedekind structures and structures similar to them  Structures with complements  Complete structures  Representations of structures  Generalizations of structures  Algebraic theory of affine and projective geometries  On the basis of structure theory  Over skew fields  Finite projective spaces and other generalizations
271.17.23  Universal algebras  Structure of universal algebras  Varieties (primitive classes) of algebras and their free algebras  Algebra-theoretic constructions  Dependence in algebras  Types of universal algebras
271.17.25  Categories  General problems in category theory  Structural  problems in category theory  Types and categories  Multiplicative structures on objects of categories  Functors  Union of functors  Duality of functors  Direct and inverse limits  Representations of categories  Abelian categories  Representations of abelian categories
271.17.27  Fields and polynomials  Polynomials, including binomials and prime factorization  General field theory  Extensions of fields  General Galois theory  Embedding problem  Construction of fields with a given Galois group  Valuations on fields  Ordered fields  Formally real fields  Topological fields  Special classes of fields  Generalizations of fields  Finite fields  Local fields  p-adic analysis  Forms over local fields  Fields of algebraic numbers and algebraic functions  Divisors and completions  Trims? and discriminant  Quadratic fields and division fields of a disk  Units of algebraic number fields  Group of classes of divisors  Ideles and adeles  Forms over number fields  Arithmetic problems of orders in semisimple algebras  Class field theory  Local class field theory  Differential and difference algebras  Differential algebra  Difference algebra
271.17.29  Linear algebra  Vector spaces.  Theory of vector spaces  Vector spaces over skew fields  Matrices and linear mappings.  Matrix theory  Determinants and their generalizations  Matrix equations  Eigenvalues of matrices  Special classes of matrices  Systems of linear equations and inequalities  Polylinear algebra.  Forms  Bilinear and quadratic forms
271.17.31  Homological algebra  Chain complexes  Homology theory of chain complexes  Homotopy theory of chain complexes  Chain complexes with a diagonal  Filtrations, exact pairs, spectral sequences  Derived functors  Homological algebra in abelian categories  Homology theory of associative rings and modules Homology of Lie algebras and Hopf algebras  Homology of groups and semigroups Deformations of algebraic structures  Deformations of discrete subgroups of Lie groups  Algebraic K-theory  Algebraic analogues of different constructions from topology and algebraic 
		geometry  Homotopy groups in categories  General theory of topologies and sheaves on categories  General theory of co-algebras and Hopf algebras
271.17.33  Algebraic geometry  Commutative rings and algebras, local theory and foundations of algebraic 
		geometry  General theory of commutative rings  Valuations on commutative rings and divisibility theory  Arithmetic rings.  Dedekind and Prufer rings  Polynomial rings  Modules over commutative rings  Local algebra.  Local theory  Foundations of algebraic geometry  Variations of structures of algebraic varieties, crossed products, fiber 
		bundles  Moduli of algebraic varieties  Structure of families.  Picard varieties  Vector algebraic bundles  Classification of algebraic varieties  Algebraic bundles with degenerate fibers  Cohomology theory of algebraic varieties and schemes  Algebraic sheaves and cohomology with coefficients in them  General properties of algebraic sheaves  The Riemann-Roch theorem for algebraic varieties and related 
			questions  Cycles:  intersection theory and equivalence  Foundations of intersection theory  Chow varieties and algebraic systems.  Parametrization  Rational equivalence of cycles  Algebraic and numerical equivalence  Serre cohomology, K-theory  Grothendieck cohomology and topology  Algebraic groups, including abelian varieties  Formal groups  p-adic analytic groups  Abelian varieties and schemes  General theory of abelian varieties  Endomorphism rings of abelian varieties  Moduli of abelian varieties  Principal homogeneous spaces of abelian varieties  Arithmetic of abelian varieties  Arithmetic of elliptic curves  Linear algebraic groups  Adele groups and Tamagawa numbers  Groups of units  Approximation theorems  p-adic linear groups  Linear representations of linear algebraic groups  Algebraic transformation groups .17  Geometric theory of invariants of algebraic transformation groups .21  Infinite-dimensional algebraic groups  Pro-algebraic groups and group schemes  Arithmetic problems of algebraic varieties  Problems associated with rationality.  Rational points on algebraic 
		varieties  Zeta functions and related problems  Birational geometry.  Mappings and the like  Singularities.  Singular points of algebraic varieties  Resolution of singularities  Structure of varieties near singular points  Numerical invariants and classification of singularities  Linear systems and rational mappings  Modifications and problems of minimal models  Algebraic curves; surfaces and three-dimensional manifolds  Algebraic curves  Singular points of curves  Bundles over a curve  Modules over algebraic curves  Arithmetic problems on algebraic curves  Algebraic surfaces  Singular points of surfaces  Structure of a surface near singular points  Resolution of singularities  Numerical invariants and classification of singularities  Theory of intersections on singular surfaces  Birational transformations and minimal models  Algebraic and linear systems on algebraic surfaces  Algebraic geometry of different classes of surfaces  Moduli of algebraic surfaces  Arithmetic problems on algebraic surfaces  Algebraic varieties of dimension 3  Analytic spaces over arbitrary complete valued fields
271.17.35  Lie groups  General theory of Lie groups, properties, structure and generalizations  Correspondence between Lie groups and Lie algebras.  Exponential 
		mapping  Structure of Lie groups and Lie algebras, deformation and contractions of 
		Lie groups of automorphisms, and derivations  Related problems in the theory of topological groups  Generalizations of Lie groups  Special classes of Lie groups  Compact Lie groups and Lie algebras  Semisimple Lie groups and Lie algebras  Solvable Lie groups and Lie algebras  Nilpotent Lie groups and Lie algebras  Continuous subgroups of Lie groups  General properties of subgroups and subalgebras  Maximal subgroups and subalgebras  Compact and semisimple subgroups  Solvable subgroups and subalgebras  Cartan subgroups  Decomposition of Lie groups into the product of subgroups  Linear representations of Lie groups  Finite-dimensional linear representations of Lie groups and Lie algebras  Equivariant embeddings of spaces with a Lie transformation group into 
		a Euclidean space  Representing functions.  Duality theorems  Invariants of linear representations  Linear Lie groups and Lie algebras  Algebraic linear Lie groups  Linear representations of groups in theoretical physics  Lie transformation groups  General theory of Lie transformation groups  Orbits and quotient spaces of Lie transformation groups  Transitive Lie groups  Homogeneous spaces of semisimple Lie groups  Homogeneous spaces of solvable Lie groups  Simultaneous spaces of nilpotent Lie groups  Differential operators that are invariant with respect to Lie transformation 
		groups  Invariant integration  Discrete subgroups and discrete transformation groups  General properties of discrete transformation groups and discrete 
		subgroups of Lie groups  Discrete groups of linear-fractional transformations  Discrete subgroups of semisimple Lie groups  Discrete subgroups of of solvable and nilpotent Lie groups  Arithmetically defined discrete subgroups  Discrete groups of isometric transformations  Discrete groups generated by reflections  Theory of continuous pseudogroups (infinite Lie groups)  General concepts of the theory of topological pseudogroups and Lie 
		pseudogroups  Methods of formal Lie groups in the theory of pseudogroups  Cartan pseudogroups  Infinite-dimensional filtered and graded Lie algebras

271.19  Topology

271.19.15  General topology  Topological spaces  Axiomatic theory of topological spaces  Classes of spaces distinguished by separability axioms  Classes of spaces distinguished by conditions of a local nature  Cardinal-valued invariants of topological spaces  Classes of spaces distinguished by conditions for coverings  Compact spaces  Paracompact spaces  Classes of spaces distinguished by conditions that connect their 
		topology with the properties of their subspaces  K-spaces  Other classes of topological spaces  Nonaxiomatic theory of topological spaces  Spaces that are embedded in another space of simple structure  Spaces that are continuous images of a given space of simple structure  Dyadic compact spaces  Topological properties of spaces with complemented structure, and 
		topological groups of transformations  Construction of topological spaces and operations over them  Operations over topological spaces  Topological products  Hyperspaces  Compact extensions  Superextensions  Spaces of mappings (function spaces)  Passages to the limit in the category of topological spaces  Spectra of topological spaces  Shapes of topological spaces  Topological questions in category theory  Generalizations of topological spaces  Uniform spaces and nearness spaces  Axioms of uniform and nearness spaces  Different classes of uniform and nearness spaces  Uniform spaces and uniformly continuous mappings  Nearness spaces  Nearness spaces and compact extensions  Comparison of topologies, uniformities and proximities  Topological properties of uniform spaces  Metric spaces  Axioms and generalizations of metric spaces  Topological properties of metric spaces  Metrizable spaces  Metric properties of metric spaces  Classes of metric spaces distinguished by topological properties  Compact metric spaces  Continua  Classes of metric spaces distinguished by conditions of an external nature 
		( for possible ambient spaces)  Absolute retracts  Topology of Euclidean spaces  Plane continua  Continuous mappings  Special types of continuous mappings  Quotient mappings  Open mappings  Perfect mappings and absolutes  Monotone mappings  Fixed points and coincidences  Generalizations of continuous mappings  Multivalued mappings  Dimension and other topological numerical invariants  Dimension theory  Dimension theory of arbitrary spaces  Comparison of different types of dimensions  Dimension theory of compact spaces  Dimension theory of uniform and nearness spaces  Dimension theory of metric separable spaces  Theory of infinite dimensions  Invariants of dimension type  Descriptive theory of sets of topological spaces

271.19.17  Algebraic topology  General theorems on fundamental categories and functors  General topological categories  Homology and cohomology groups (definitions and basic properties).  
		Axiomatics  Investigation of topological spaces and continuous mappings by 
		homological methods  Homology theory of dimension  Spectral sequence of a continuous mapping  Homology theory of fixed points and coincidence points  Homology manifolds  Homology and cohomology with nonabelian coefficients  Homotopy and cohomotopy groups:  definitions and basic 	
		properties.  Axiomatics, etc.  Localization of topological spaces  Shape theory  Functors with values in general topological categories (operations over 
		topological spaces)  General theory of such functors.  Duality  Concrete functors  Polyhedral categories, i.e., categories whose volumes are polyhedra  Cellular partitions  Simplicial partitions (triangulations) and simplicial schemes  Categories that approximate general topological and polyhedral categories  Categories whose morphisms are stationary mappings or their 
		homotopy classes (categories of spectra, S-categories)  S-duality  Adams spectral sequence  Extraordinary homology and cohomology theories  Bordism and cobordism  Categories of semi-exact functors  Simplicial sets  Homotopy theory:  fundamental problems  Decompositions of spaces and mappings  Homotopic resolvents ( Moore-Postnikov systems)  and dual 
		constructions  Homotopic convolutions of of spaces (decreasing homotopic groups)  Categories of spaces  (in the sense of Lyusternik-Shnirel'man)  Obstruction theory.  General classification and continuation theorems for 
		continuous mappings and intersecting surfaces  Cohomology operations  Analogues of cohomology operations  Spaces with various complemented properties of a general nature or that are 
		obtained by these or other general constructions  Fiber spaces and crossed products  Definition and basic properties, operations over fiber spaces and 
		crossed products  Homotopy theory of bundles.  Universal bundles and classifying 
		spaces  Homology theory of fiber spaces  Crossed tensor products  Spectral sequences  General theorems on bundles with a vector fiber (K- and J-functors)  Spaces with operators  Spaces with multiplication  (H-spaces) and loop spaces  Space with comultiplication,  and surgeries  Spaces in which there are only a finite number of nonzero homotopy 
		groups  Eilenberg-MacLane spaces  Spaces in which there are only two nonzero homotopy groups  Concrete spaces.  Calculation of homotopy invariants  Computation of homotopy groups  Homotopy groups of spheres  Computation of homology and cohomology groups  Computation of K- and J-functors  Computation of bordism and cobordism groups  Isotopy theory

271.19.19.  Topology of manifolds  Topology of manifolds of lower dimensions  Topological surfaces  Three-dimensional topological manifolds  Classification of three-dimensional manifolds  Poincare conjecture and related problems  Four-dimensional topological manifolds  Classification of four-dimensional manifolds  Poincare conjecture for four-dimensional manifolds  Embeddings and immersions in lower dimensions  Knots.  Wreaths.  Braids  Topological manifolds  Microsheaves of topological manifolds  Topological embeddings and immersions  Topology of smooth and piecewise-linear manifolds  General questions  Homology theory of smooth manifolds  Differential forms on smooth manifolds  Singularities of smooth manifolds  Critical points of smooth mappings  Infinite-dimensional manifolds  Morse theory  Classification of smooth and piecewise-linear manifolds  Correspondences between homotopic, topological, combinatorial and 
		smooth properties  Realization of cycles  Bordisms and cobordisms  Classification of manifolds up to diffeomorphism or piecewise-linear 
		equivalence  Combinatorial equivalence of polyhedra.  Simple homotopy type  Bundles of smooth manifolds and bundles whose bases are smooth 
		manifolds  Characteristic classes of manifolds  Vector fields on manifolds  Microbundles  Smooth and piecewise-linear embeddings and embeddings of manifolds  Groups that act on smooth and piecewise-linear manifolds  Groups of diffeomorphisms and piecewise-linear equivalences  Topology of smooth manifolds endowed with complemented structure  Topology of complex and almost complex manifolds  Topology of Kahlerian and algebraic manifolds  Topology of manifolds with infinitesimal connection.  Topology of 
		Riemannian manifolds  Differential and integral operators on manifolds  Foliations.  Integration of vector and tensor fields  Elliptic operators on manifolds
271.19.21  Analytic spaces  General theory of complex and real analytic spaces  Local theory  Classes of analytic spaces identified by local conditions  General theory of coherent analytic sheaves and their cohomology  A connection between the cohomologies of complex spaces and 
		differential forms  Residues of differential forms   Computation of the cohomology of specific complex spaces  The Riemann-Roch theorem for complex manifolds, and related 
		problems  Analytic sets, subspaces and submanifolds  Integration on analytic sets and analytic spaces  Intrinsic metrics on complex spaces  Analytic mappings and constructions of complex spaces  Holomorphic mappings of complex spaces  Holomorphic functions.  Domains and holomorphy hulls in analytic 
		spaces  Cohomology investigation of holomorphic mappings  Approximation theorems for holomorphic functions and mappings in 
		analytic spaces.  Runge pairs  Plurisubharmonic functions, pseudo-convex and pseudo-concave 
		domains in analytic spaces and their generalizations  The Levi problem for analytic spaces  Meromorphic mappings  Fields of meromorphic functions  Cousin and Poincare problems for analytic spaces  Quotient spaces of complex spaces  Analytic coverings  Modification of complex spaces  Resolution of singularities of complex spaces and mappings  Complex spaces of one, two and three dimensions  One-dimensional complex manifolds  Complex surfaces  Singular points of complex surfaces  Three-dimensional complex spaces  Classes of complex spaces distinguished by global conditions  Holomorphically convex spaces  Holomorphically complete spaces  q-pseudo-convex, q-pseudo-concave and q-complete spaces  Complex spaces that are close to algebraic manifolds  Global properties of real-analytic spaces  Generalizations of analytic spaces  Banach analytic spaces  Partially analytic and other spaces  Analytic investigation of almost complex manifolds  Holomorphic fiber spaces  Classification of holomorphic fiber spaces  Holomorphic vector fiber spaces and sheaves and related cohomologies  Holomorphic and meromorphic sections in fiber spaces  A connection between the theory of fiber spaces and some problems in 
		analysis  Holomorphic connections in fiber spaces  Complex spaces with an automorphism group  Complex Lie transformation groups  Automorphism groups of complex and almost complex spaces  Complex homogeneous spaces  Compact complex homogeneous spaces  Kahlerian homogeneous spaces.  Homogeneous domains  Analytic functions on homogeneous spaces  Homogeneous vector fiber spaces and related cohomologies  Automorphic functions  Automorphic and modular forms  Abelian functions  Modular functions  Automorphic forms and related cohomologies  Automorphic functions in symmetric domains  Deformations of structures.  Pseudogroups  Cohomology problems in the theory of pseudogroups  Deformations of complex structures  Deformations of submanifolds and holomorphic mappings  Extension of analytic objects  Theory of moduli of Riemann surfaces  Deformations of other pseudogroup structures  Deformations of G-structures and connections  Deformations of fiber spaces  Analytic theory of deformations of algebraic structures

271.21  Geometry

271.21.15  Geometry in spaces with fundamental groups  Elementary geometry, trigonometry, polygonometry  Planimetry  Triangle geometry  Geometry of polygons (including rectangles, etc.)  Elementary circle geometry  Stereometry  Geometry of tetrahedra  Geometry of polyhedra (polytopes)  Geometry of spheres and cylinders  Elementary geometry in multidimensional spaces  Theory of geometric constructions  Trigonometry and polygonometry  Plane trigonometry  Spherical trigonometry  Foundations of geometry.  Axiomatics  Euclidean, pseudo-Euclidean and non-Euclidean geometries  Euclidean and pseudo-Euclidean geometries  Analytic geometry in Euclidean spaces  Pseudo-Euclidean spaces  Galilei spaces  Semi-Euclidean spaces  Flag spaces  Non-Euclidean geometries  Lobachevskii geometry  Other hyperbolic geometries  Elliptic geometries  Quasi-elliptic and quasi-hyperbolic spaces  Semi-elliptic and semi-hyperbolic spaces  Affine and projective geometries  Affine geometry  Synthetic geometry in affine space  Analytic geometry in affine space  Projective geometry  Synthetic geometry in  projective space  Analytic geometry in  projective space  Geometry in spaces with other fundamental groups  Conformal geometry and its analogues  Symplectic geometry  Bi-axial geometry and its generalizations  Geometry over algebras  Affine and projective spaces over algebras  Quadratic Euclidean and non-Euclidean spaces  Hermitian Euclidean and non-Euclidean spaces  Symplectic spaces  Geometry of other spaces over algebras  Convex sets, arrangements of geometric figures, and geometric inequalties  Convex sets  Convex curves and surfaces  Convex bodies  Convex polygons and polyhedra  Generalizations of convex sets  Arrangements of geometric figures  Packings  Coverings  Partitions   Lattices  Geometric inequalities  Extremal problems in geometry  Descriptive geometry  Theoretical problems in descriptive geometry  Applied methods in descriptive geometry  Generalizations of descriptive geometry
271.21.17  Algebraic and analytic methods in geometry  Vector algebra and vector analysis  Vector algebra  Vector analysis (vector field theory)  Tensor algebra and tensor analysis  Tensor algebra  Tensor analysis  Spinors, spinor algebra and analysis  Spinor algebra  Spinor analysis  Calculus of exterior forms  Grassmannian algebra and its generalizations  Theory of exterior differential forms  Differential algebras and their geometric applications  Theory of the compatability of systems of differential equations  Geometric objects  Representations of Lie groups, and geometric objects  Representations of infinite Lie pseudogroups, and differential-geometric 
		objects  Extensions of geometric objects  Lie differentiation  Differential-geometric methods for investigations of embedded manifolds  Moving frame of a manifold  Geometric objects on embedded manifolds
271.21.19  Differential geometry  Differential geometry in spaces with fundamental groups  Differential geometry in Euclidean, pseudo-Euclidean and semi-	
		Euclidean spaces  Theory of curved lines  Theory of surface bands  Theory of surfaces  Surfaces in a three-dimensional space  Surfaces in a multidimensional space  Theory of families of straight lines and planes  Theory of families of curved lines and surfaces  Differential geometry of vector fields  Theory of nonholonomic manifolds  Differential geometry in non-Euclidean spaces  Differential geometry in non-Euclidean spaces with degenerate 
		absolute  Theory of curved lines  Theory of surface bands  Theory of surfaces  Theory of families of straight lines and planes  Theory of families of lines and surfaces  Theory of nonholonomic manifolds  Differential geometry in non-Euclidean spaces with degenerate 
		absolute  Theory of curved lines  Theory of surfaces  Theory of families of straight lines and planes  Affine differential geometry  Affine theory of curved lines  Affine theory of surface bands  Affine theory of surfaces  Affine theory of families of straight lines and planes  Affine theory of families of curved lines and surfaces  Affine differential geometry of vector fields  Affine theory of nonholonomic manifolds  Projective differential geometry  Projective theory of curved lines  Projective theory of surface bands  Projective theory of surfaces  Projective theory of families of straight lines and planes  Projective theory of families of curved lines and surfaces  Projective theory of nonholonomic manifolds  Differential geometry in spaces with other fundamental groups  Differential geometry in conformal and pseudo-conformal spaces  Differential geometry in symplectic spaces  Differential geometry in bi-axial and  bi-affine spaces and their 
		generalizations  Differential geometry of point mappings  Differential geometry of point mappings of affine and projective 
		spaces  Differential geometry of point mappings of Euclidean, pseudo-
		Euclidean, conformal and other spaces with a metric  Mapping of submanifolds with point mappings of spaces with a 
		fundamental group  Kinematic geometry  Geometry of differentiable manifolds and their submanifolds  Geometry of fiber spaces  General problems in the geometry of fiber spaces  Geometry of submanifolds in fiber spaces  Fiber spaces of geometric objects  Geometry of vector bundles  Geometry of tensor bundles  Fiber spaces of other geometric objects  Differential extension of spaces of geometric objects  Fields of geometric objects in fiber spaces and their extensions  Connections in fiber spaces  Nonlinear connections  Linear connections in principal fiber spaces  Linear connections in spaces with homogeneous fibers  Linear connections in spaces of geometric objects  Holonomy groups of fiber spaces  Infinitesimal structures and fields of geometric objects on differentiable 
		manifolds  Differential geometry of vector and tensor fields on manifolds  G-structures on differentiable manifolds  General problems in the geometry of G-structures  Tensor G-structures  Submanifolds in manifolds of tensor G-structures  Symplectic and cosymplectic structures  Submanifolds in manifolds of symplectic and cosymplectic 
		structures  Contact and almost contact structures  Submanifolds in manifolds of contact and almost contact 
		structures  Structures of an almost product  Submanifolds in manifolds of structures of almost products  Structures defined by algebras  Submanifolds in manifolds of structures defined by algebras  Other special G-structures  Submanifolds in manifolds of other special G-structures  Mapping of manifolds with G-structures  Manifolds with complex or almost complex structure  Manifolds with complex structure  Hermitian manifolds  Kahlerian manifolds  Manifolds with an almost complex structure  Almost Hermitian and subordinate structures  Connections on manifolds with complex or almost complex 
		structure  Mappings of manifolds with complex structure  Submanifolds embedded in manifolds with complex or almost 
		complex structure  Infinitesimal structures and fields of of geometric objects of higer 
		orders  General theory of tangent bundles (higher orders)  Jet theory  Tensors and tensor fields of higher orders  Fields of other geometric objects of higher orders  Higher-order connections on a differentiable manifold  Finsler geometry and its generalizations  Finsler geometry  Submanifolds of Finsler spaces  Interval geometry  Geometry of the calculus of variations  Geometry of a space of linear elements  Geometry of spaces with other generating elements  Web geometry  Geometry of differential equations  Classical spaces with connections and their generalizations  Riemann and pseudo-Riemann spaces  General theory of  Riemann and pseudo-Riemann spaces  Invariant objects in Riemann and pseudo-Riemann spaces  Holonomy groups of Riemann and pseudo-Riemann spaces  Complete Riemann spaces  Special types of Riemann spaces  Subprojective spaces and their generalizations  Reducible and semi-reducible Riemann and pseudo-Riemann 
		spaces    Recurrent Riemann and pseudo-Riemann spaces  Einstein spaces  Symmetric Riemann spaces and their generalizations  Mappings of Riemann and pseudo-Riemann spaces  Isometric mappings, immersions and submersions of Riemann 
		spaces  Submanifolds of Riemann and pseudo-Riemann spaces  Curves and families of curves  Hypersurfaces  Submanifolds of other dimensions  Spaces with affine connection  General theory of spaces with affine connection  Special types of spaces with affine connection  Spaces with equivalent connection  Weyl spaces  Projective-Euclidean spaces  Spaces with absolute parallelism  Symmetric spaces with affine connection  Semi-Riemann spaces  Mappings of spaces with affine connection  Submanifolds of spaces with affine connection  Spaces with projective connection  General theory of spaces with projective connection  Submanifolds of spaces with projective connection  Spaces with conformal connection  Spaces with symplectic connection  Spaces with generalized Euclidean and pseud-Euclidean connections  Other classical spaces with connections  Geometry of homogeneous spaces.  Geometry of Lie groups  Invariant infinitesimal structures in homogeneous spaces  Vector and tensor fields in homogeneous spaces  Manifolds embedded in homogeneous spaces  Integral geometry  Global differential geometry  Global differential geometry of submanifolds.  Nonregular submanifolds  Global geometry of lines and surfaces in spaces with fundamental 
		groups  Regular lines and surfaces  Nonregular lines and surfaces  Global images  Existence, embedding and realizationof global images  Uniqueness, rigidity and bendability of global images  Geometry of metrized manifolds  Minkowski geometry  Hilbert geometry  Geometry of geodesics
271.21.21  Geometric investigation of objects in the natural sciences  Geometric problems and methods in the theory of relativity  Geometric problems in special relativity  Geometric problems in general relativity  Geometric problems in cosmology  Geometric problems in unified field theory  Geometric investigation of fields of physical objects  Geometric methods in quantum mechanics and elementary particle theory  Geometric methods in mechanics and engineering  Geometric methods in statistics  Geometric methods in kinematics  Geometric methods in dynamics  Geometric methods in engineering  Geometric methods in continuum mechanics  Geometric methods in the theory of shells  Geometric problems and methods in crystallography  Geometric problems and methods in optics

271.23  Mathematical analysis

271.23.15  Introduction to analysis, and some special problems in analysis  Theory of real numbers  Asymptotic formulas and expressions  Analytic means.  Inequalities  Means  Numerical inequalities and some elementary functional inequalities  Study of individual functions
271.23.17  Differential and integral calculus  Differential calculus  Mappings.  Implicit functions   Other analytic applications of differential calculus  Integral calculus  Red?  integrals  Integrals over curved manifolds (curvilinear and surface integrals)  Definite simple or multiple integrals  Improper integrals
271.23.19  Functional equations and the theory of finite differences  Theory of finite differences  Finite-difference equations  Recurrent relations and series  Functional equations and inequalities
271.23.21  Integral transformations, operational calculus  Laplace transform  Fourier integral and Fourier transform  Other integral transformations and their inversions.  Convolutions  Operational calculus
271.23.23  Series and sequences  Numerical and functional series and sequences  Special numerical series and sequences  Sums of finite and infinite series  Convergence  Multiple series and sequences  Summation theory  Tauberian theorems  Infinite products  Continued fractions
271.23.25  Special functions  Euler integrals and their generalizations.  The gamma function and related 
		functions  Probability integral and related functions  Elliptic functions and integrals  Bessel functions and polynomials and other cylindrical functions  Mathieu functions  Spherical functions.  Legendre polynomials and functions,  harmonic 
		polynomials, ultraspherical polynomials.  Gegenbauer functions  Orthogonal polynomials and their generalizations (Chebyshev, Hermite, 
		Jacobi, Laguerre, et al.)  Hypergeometric series and functions.  Generalized and degenerate 	
		hypergeometric  functions and their generalizations  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  Measures, integration and differentiation  Measure, capacity  Lebesgue measure  Borel measure  Other measures  Measurable functions  Continuous functions  Additive set functions  Capacity  Integration theory  Riemann integral  Lebesgue integral  Stieltjes integral  Other integrals (theory)  Singular integrals  Integrals of potential type  Differentiation theory  Differentiable functions  Derivative  Symmetric derivatives  Mappings  Curved surfaces  Level sets of functions of several variables  Classes (sets) of functions  Compact families of function  Epsilon nets.  Epsilon entropy  Widths  Embedding theorems for classes of differentiable functions  Inequalities between partial derivatives  Boundary properties of functions  Weight classes  Extension theorems  Integration of classes of functions Functions of bounded variation  Absolutely continuous functions  Convex functions and their generalizations  Quasi-analytic functions  Other classes of functions  Superpositions  Inequalities  Systems of functions and series in systems of functions  Completeness and closure of system of functions  Bases  Orthogonal systems  Convergence of orthogonal series  Summation of orthogonal series  Trigonometric series  Representation of a function in the form of a trigonometric series  Uniqueness problems  Fourier series  Convergence of Fourier series Absolute convergence of Fourier series  Fourier coefficients  Summation of Fourier coefficients  Multiple trigonometric series  Multiple Fourier series  Summation of multiple Fourier series  Theory of the Fourier integral  Summability of Fourier integrals  Almost periodic functions  Compactness of systems of almost periodic functions  Convergence and summability of Fourier series of almost periodic 
		functions  Interpolation, almost periodic extension of functions  Approximation of almost periodic functions
271.25.19.  Approximation theory  Approximation by algebraic polynomials  On an infinite domain  Of several variables  Chebyshev-type problems  Approximation with exact constants  Approximation by trigonometric polynomials and entire functions of 
		exponential type  Approximation in the sense of order  Approximation with exact constants  Approximation of functions of several variables  Approximation by rational functions  Nonlinear problems in approximation theory  Approximation in the Hausdorff metric  Integration  Approximation by spline functions  Extremal properties of polynomials and their generalizations  Inequalities for derivatives of polynomials and their generalizations  Other inequalities for polynomials and their generalizations  Zeros of polynomials and their generalizations  Theory of quadratures and cubatures  Moment theory

271.27  Theory of functions of complex variables

271.27.15  Functions of one complex variable  Elementary problems  Rational functions in a complex domain  Sequences and series of analytic functions  Power series  Properties of power series associated with the nature of the 	
		coefficients  Lacunary power series  Behavior of a power series on the boundary of the disk of 	
		convergence.  Superconvergence  Analytic continuation.  Singular points  Sequences and series of exponentials  Dirichlet series  Systems of functions  Problems of completeness.  Closure of a system of functions.  Bases  Sequences and series of polynomials.  Orthogonal polynomials  Problems of approximation in a complex domain.  Best approximation  Approximation by rational functions  Asymptotic representations in a complex domain  Interpolation.  Iteration
271.27.17  Conformal mapping and geometric problems in the theory of functions of a 
		complex variable.  Analytic functions and their generalization  Mappings of special domains  Boundary properties of analytic functions, and boundary value problems  Bounded functions  Generalization of the Schwartz lemma  Generalization of the maximum modulus principle  Harmonic measure and capacity.  Analytic capacity  Boundary properties of analytic functions  Theory of limit sets  Cauchy-type integral  Other integral representations of analytic functions  Boundary value problems in the theory of analytic functions  Theory of Riemann surfaces.  Uniformization  Conformal classes and automorphisms of Riemann surfaces  Univalent and multivalent functions  Univalent functions .17  Estimates for coefficients and other functionals .21  Geometric properties of mappings  Covering theorems  Multivalent functions  Classes and spaces of analytic functions  Entire and meromorphic functions  Entire functions of finite order  Meromorphic functions  Generalization of Picard's theorem  Theory of the distribution of values  Analytic functions in the disk and other domains  Classes of analytic functions  Functions of bounded type  Noh? and related classes  Algebraic and algebroid functions  Analytic theory of automorphic functions  Elliptic and modular functions  Other classes of analytic functions  Spaces of analytic functions  Generalizations of analytic functions and conformal mappings  Quasiconformal mappings and their generalizations  Quasi-analytic classes in a complex domain  Generalized analytic functions  Monogenic functions  Analytic matrices, functions of a matrix argument  Functions of a hypercomplex variable  Functions of a discrete argument  Other generalizations of analytic functions
271.27.19  Functions of several complex variables  Series and sequences of functions of several variables  Approximation of functions and domains  Integral representations  Holomorphic functions of several variables.  Domains and hulls of 	
		holomorphy.  Pseudoconvexity  Analytic continuation.  Singularities  Classes and boundary properties of functions of several variables  Meromorphic functions of several variables.  Cousin and Poincare problems  Entire functions of several complex variåbles
271.27.24  Harmonic functions and their mappings  General properties of harmonic functions  Subharmonic functions and their generalizations  Biharmonic and polyharmonic functions  Pluriharmonic and plurisubharmonic functions  Harmonic functions on Riemannian manifolds  Other generalizations of harmonic functions 

271.29  Ordinary differential equations

271.29.15  General theory of ordinary differential equations and systems of equations  General problems.  Existence theorems, uniqueness theorems and theorems 
		on the differential properties of solutions  Differential equations with discontinuous and multivalued right-hand 
		sides  Differential inequalities  Methods for solving various types of equations and systems of equations  First integrals  Equations that are not solved with respect to the highest derivative.  Singular 
		solutions  Special types of ordinary differential equations (Riccati, hypergeometric, 
		Bessel, Mathieu, Hill, etc.)  Pfaffian equations and Pfaffian systems  Infinite systems of differential equations
271.29.17  Qualitative theory of ordinary differential equations and systems of equations  Systems and analytic theory of ordinary differential equations  Theory of systems of second-order equations  Location  of integral curves.  Singular points  Limit cycles and periodic solutions.  Oscillation in nonlinear systems  Properties of solutions of second-order equations and second-order 
		systems (asymptotic behavior, monotonicity, estimates for the solutions, 
		etc.)  Zeros of solutions of second-order differential equations, oscillating 
		and nonoscillating solutions  Theory of systems of arbitrary order and of equations of 	
	arbitrary order  Stability and asymptotic behavior of solutions  Equations with periodic and almost periodic right-hand sides.  
		Periodic and almost periodic solutions.  Oscillations in nonlinear 	
		multidimensional systems  Integral manifolds  Properties of solutions of equations of arbitrary order and of systems 
		of arbitrary order (asymptotic behavior, monotonicity, estimates for the 
		solutions, etc.)  Zeros of solutions of higher-order equations and systems of equations  Linear ordinary differential equations and systems  Linear ordinary differential equations with variable coefficients  Theory of dynamical systems  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  Boundary value problems for linear ordinary differential equations  Theorems on the existence, uniqueness and properties of solutions  Eigenvalues and eigenfunctions.  Eigenfunction expansions  Boundary value problems for nonlinear ordinary differential equations  Multipoint boundary value problems and functional problems for ordinary 
		differential equations
271.29.21  Analytic theory of ordinary differential equations and systems of equations  Singular points of equations in a complex domain  Expansions of solutions in series in a complex domain  Expansions of solutions of equations and systems with a complex 	
271.29.23  Asymptotic methods in the theory of ordinary differential equations and 
		systems of equations  General theory of asymptotic methods  Linear ordinary differential equations and systems with small parameters 
		multiplying the highest derivatives  Averaging methods and  invariant manifolds.  Problems in nonlinear 
271.29.25  Functional-differential and discrete equations and systems of equations with 
		one independent variable  Linear difference equations  Stability theory  Periodic solutions  Boundary value problems  Asymptotic methods
271.29.27  Equations of analytical mechanics, mathematical theory of the control of 
		motion  Equations of analytical mechanics  Equations of automatic control systems  Equations of linear automatic control systems  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  General first-order equations and systems:  properties, types, etc.  General higher-order equations and systems:  properties, types, etc.  Boundary value problems:  general theory, equations on manifolds  The Cauchy problem for partial differential equations  Well-posedness theory  Semigroups associated with the Cauchy problem
271.31.17  Linear and quasilinear equations and systems of equations  Elliptic equations and systems  Linear equations of elliptic type  General properties  Boundary value problems  Potential theory.  Potentials  Laplace and Poisson equations  Degenerate equations.  Equations with a small parameter  Spectral theory  Quasilinear equations of elliptic type  Inverse problems  Ill-posed problems  Hyperbolic equations and systems  Linear hyperbolic equations  Degenerate equations.  Equations with a small parameter  Spectral problems  Quasilinear hyperbolic equations  Inverse problems  Parabolic equations and systems  Nonlinear problems  Inverse problems  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  Fredholm integral equations  Volterra integral equations  Singular integral equations and related boundary value problems  Linear integral equations in function spaces  Systems of linear integral equations
271.33.17  Nonlinear integral equations  Nonlinear singular integral equations and related boundary value problems  Systems of nonlinear integral equations
271.33.19  Integro-differential equations  Linear integro-differential equations  Singular integro-differential equations  Nonlinear inegro-differential equations  Systems of integro-differential equations

271.35  Differential and integral equations of mathematical models in the natural 

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  Hydrodynamics of an ideal fluid  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  Dynamical problems  Plane and contact problems  Three-dimensional problems  Thermoelasticity  Plates and shells  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  The Stefan problem  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  Functional analytic methods of the calculus of variations  Necessary conditions based on the theory of first and second variations  Sufficient conditions  Problems on the existence of solutions of variational problems.  Theory 
		of the existence of solutions  Variational methods for solving differential, integral, and other functional 
		equations  Minimal surfaces  Inverse problems in the calculus of variations  Extremal problems in linear topological spaces and concepts associated 
		these problems  Various special problems in the calculus of variations  Topological methods in the calculus of variations  Variational theory of geodesics
271.37.17  Mathematical control theory.  Optimal control  General theory of control systems, and controllability (mathematical theory)  Optimal control  Maximum principle  Dynamic programming methods  Theory of linear optimal systems  Optimal control of systems with distributed parameters  Problems of the existence of optimal solutions  Approximate methods for solving optimal control problems
271.37.19  Differential games  Two-person differential games  n-person differential games

271.39  Functional analysis

271.39.15  Linear spaces endowed with topology, order, and other structures  Ordered and semi-ordered spaces  Linear topological spaces  Normed spaces.  Banach space.  Hilbert space  Hilbert spaces with an indefinite metric  Geometry of linear topological spaces  Convex sets in linear spaces  Bases in linear topological spaces  Geometric problems in approximation theory in linear spaces  Approximate dimension and related problems  Abstract potential theory  Concrete topological  linear spaces.  Interpolation theorems  Spaces of continuous functions  Spaces of analytic functions  Spaces of sequences and matrices  Linear functionals and conjugate spaces  Positive-definite functionals in function spaces  Problems of the continuation of positive-definite functionals and 
		positive-definite kernels  Moment theory
271.39.17  Generalized functions  Homogeneous generalized functions  Fourier transform of generalized functions.  Convolutions  Algebraic theory of generalized functions.  (Operational calculus of 	
		Mikusinski, et al.)  Generalized distributions (hyperfunctions, ultradistributions, etc.)  Linear analytic functionals
271.39.19  Linear operators and operator equations  Linear operators in linear infinite-dimensional spaces; general properties  Linear operators in locally convex spaces  Linear operators in Banach spaces  Linear operators in Hilbert spaces  Normal and unitary operators in Hilbert spaces  Selfadjoint linear operators in Hilbert and pre-Hilbert spaces  Nonselfadjoint linear operators in Hilbert spaces  Completely continuous and nuclear operators  Linear operators in semi-ordered spaces  Theory of perturbations of linear operators  Study of concrete operators  Infinite matrices  Integral operators  Ordinary differential operators  Partial differential operators  Pseudodifferential operators  Linear equations in infinite-dimensional linear spaces  General theory of solvability of linear equations in function spaces  Linear equations in concrete function spaces  Linear ill-posed problems  Vector functions and operator functions  Families of linear spaces and categories of linear operators
271.39.21  Spectral theory of linear operators  Spectral theory in general linear topological spaces and in spaces with a 
		quasi-topology  Abstract operational calculus of linear operators  Spectral theory of completely continuous linear operators  Problems of completeness of (generalized) eigen- and associated vectors  Spectral theory in Banach spaces  Spectral theory of completely continuous and nuclear operators in Banach 
		spaces  Spectral theory of Volterra operators in Banach spaces  Problems of linear similarity, and the equivalence of linear operators  Spectral theory in Hilbert spaces  Spectral theory of completely continuous and nuclear operators in Hilbert 
		spaces  Spectral theory of Volterra operators in a Hilbert space  Spectral theory of selfadjoint operators in a Hilbert space  Spectral theory of nonselfadjoint operators in Hilbert spaces  Study of the spectrum of concrete operators .15  Spectra of infinite matrices .19  Spectra of integral operators  Spectra of ordinary differential operators  Spectra of partial differential operators  Spectra of pseudodifferential operators  Special problems in the spectral theory of linear operators  Expansions in eigen- and associated functions  Inverse problems in spectral analysis  Perturbation of the spectrum of linear operators  Extension of operators
271.39.23  Topological algebras and the theory of infinite-dimensional representations  Topological algebras (rings) and their continuous representations  Normed algebras and their representations  Commutative Banach algebras  Algebras (rings) with involution  Positive-definite functions on algebras (rings) with involution  Algebras (rings) of linear operators  C*-algebras  Von Neumann algebras (W*-algebras)  Infinite-dimensional representation of groups  Infinite-dimensional representation of Lie algebras  Harmonic analysis of functions on groups and homogeneous spaces  Harmonic analysis on abelian groups  Almost periodic functions on groups  Group algebras  Special functions that arise in the theory of finite- and infinite-	
		dimensional representations of Lie groups  Semigroups of linear and nonlinear operators.  Evolution equations  Other algebraic structures in functional analysis  Applications of functional analysis to quantum mechanics and field theory
271.39.25  Measure theory, representations of Boolean algebras, dynamical systems  Measure and integral theory  Representations of Boolean algebras  Functional integrals and their applications to evolution equations  Metric theory of dynamical systems
271.39.27  Nonlinear functional analysis  Analysis on manifolds  Function spaces and sections of bundles  Infinite-dimensional functional analysis (global analysis)  Operators on manifolds  Integral geometry  Nonlinear functionals  General topological properties  Differential calculus for nonlinear functionals  Differential and analytic properties of nonlinear functionals  Analytic functionals  Extrema of nonlinear functionals  Nonlinear operators  General properties of nonlinear operators  Condensing operators  Fixed points of nonlinear operators  Monotone operators  Differential and integral calculus for nonlinear operators  Eigenvalues of nonlinear operators  Nonlinear equations in function spaces  Existence and uniqueness theorems for nonlinear equations  Continuability and branching of solutions of nonlinear equations  Nonlinear ill-posed problems
271.39.29  Approximate methods in functional analysis

271.41  Numerical mathematics

271.41.15  Numerical methods in algebra  Numerical methods for solving systems of linear algebraic equations  The case of a square matrix  The case of a matrix of general form  Numerical methods for inverting matrices  The case of symmetric matrices  The case of nonsymmetric matrices  Numerical methods for computing the eigenvalues and eigenvectors of 
		matrices  Partial eigenvalue problem  Complete eigenvalue problem  Numerical methods for solving transcendental equations and systems of 
		equations  Localization of solutions  Numerical methods for determining all the zeros of polynomials  Numerical methods for  solving nonlinear systems
271.41.17  Numerical methods in analysis  Approximation of functions  Determination of constants  Uniform approximation  Mean-square approximation  Interpolation and extrapolation  Parabolic interpolation  Nonparabolic interpolation  Spline interpolation  Numerical differentiation  The method of least squares  Empirical formulas  Optimization of functions  Unconstrained optimization  Constrained optimization  Quadrature formulas  Definite integrals  Singular integrals  Improper integrals  Multiple integrals
271.41.19  Numerical methods for solving differential and integral equations  Numerical methods for solving ordinary differential equations  The Cauchy problem for ordinary differential equations  First-order differential equations  Systems of ordinary differential equations  Boundary value problems for ordinary differential equations  First-order differential equations  Second-order differential equations  Higher-order differential equations  Optimal control problems  Linear problems  Nonlinear problems  Inverse problems and intensification problems  The case of initial conditions  The case of boundary conditions  Numerical methods for solving partial differential equations  First-order differential equations and their systems  Second-order differential equations of elliptic type  Boundary value problems  Problems with characteristic parameters  Inverse problems  Second-order differential equations of parabolic and hyperbolic types  The Cauchy problem  Mixed problems  Systems of equations  Inverse problems  Systems of nonlinear differential equations in continuum mechanics  Higher-order partial differential equations and systems of such equations  Biharmonic equation  Cauchy problems  Boundary value problems  Mixed problems  Inverse problems  Numerical methods for solving integral equations  Integro-differential equations  Fredholm equations of the first kind  Fredholm equations of the second kind  Volterra equations  Nonlinear equations  Singular equations  Operator equations 
271.41.21  Mathematical tables
271.41.23  Computer, graphic and other methods in numerical mathematics  Computer programming  Mechanical methods for computations  Solution of mathematical problems by means of modeling systems  Graphic methods for computations  Nomography and nomograms  Probabilistic methods for computations  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  Foundations and axioms of probability theory  Abstract probability theory  Combinatorial probabilities  Geometric probabilities  Probability distributions and distribution densities  The normal distribution  Characteristic functions, moments, semimartingales and other 	
		characteristics  Measures of dependency  Infinitely divisible laws  Stable laws  Limit theorems  for sums of independent random variables  for sums of weakly dependent random variables  for functionals and random processes  on groups and other algebraic structures  Large deviations  Random processes  (general questions)  General theory of random processes  Measures in function spaces  Limit theorems for sequences of random processes  Prediction theory  Stopping times Martingales  Markov processes  General theory of Markov processes  Properties of sample functions  Infinitesimal and characteristic operators  A strictly Markov process  Topologies associated with a process  Markov chains:  processes with finite  or countable set of states  Processes with independent increments  Additive functionals.  Probabilistic potential theory  Transformation of Markov processes  Random time change  Subprocesses  Transformations of measures  Boundary theory of Markov processes  Martin boundary  General boundary conditions  Random processes of a special type  Diffusion processes and processes that are solutions of stochastic 
		differential equations  Branching processes and epidemic processes  General branching processes  Markov branching processes  Processes with increments that depend on the age of the particles  Processes with increments that depend on the location of the particles  Processes with increments that depend on the energy or mass of the 
		particles  Controlled random processes  Renewal processes  Point random processes  Gaussian processes and measures  Properties of sample functions  Asymptotic weakening of dependence  Derivatives of Gaussian measures  Stationary and harmonizable sequences and processes  Extrapolation, interpolation, filtering  Ergodic theorems  Random functions of several variables  Homogeneous random fields  Point random fields
271.43.17  Mathematical statistics  Foundations of statistical theory  Statistical scattering and dependence.  Statistical means, deviations, etc.  Sufficiency, sufficient statistics  Distribution theory  Distributions of sample characteristics  Point distributions  Asymptotic theory  Characterization and structural theory  Theory of statistical inferences and decisions  Likelihood  Bayesian theory and problems  Compound decision problems  Fiducial probability  Methods of statistical analysis and inference  Parametric methods  Estimation of parameters and functionals  Point estimation  Confidence regions, tolerance bounds  Hypothesis testing  Properties of individual tests  Goodness-of-fit tests  Discrimination  Variance and covariance analysis  Correlation and regression analysis  Ranking and selection  Paired and multiple comparisons  Nonparametric methods  Estimation of parameters and functionals  Point estimation  Confidence regions, tolerance bounds  Hypothesis testing  Properties of individual tests  Goodness-of-fit tests  Discrimination  Variance and covariance analysis  Correlation and regression analysis  Ranking and selection  Order statistics  Paired comparison methods  Statistics of independent random variables.  Contingency tables  Multidimensional statistical methods  Estimation of parameter and functionals  Point estimation  Confidence regions, tolerance bounds  Hypothesis testing  Properties of individual tests  Goodness-of-fit tests  Discrimination  Variance and covariance analysis  Correlation and regression analysis  Ranking and selection  Factor analysis  Cluster analysis.  Classification  Special statistical applications and models  Design of an experiment (general theory)  Optimal designs  Block designs  Factor designs  Sampling and sampling theory  Sequential methods  Sequential designs  Sequential analysis  Sequential estimation  Optimal stopping  Cumulative sum technique  Stochastic approximation.  Monte Carlo methods  Statistics of random processes  Estimation for random processes  Mean of a stationary process  Correlation function of a stationary process  Spectrum of a stationary process  Hypothesis testing for random processes  Statistics of point processes  Analysis of time series  Autocorrelation, regression  Spectral analysis of time series
271.43.51  Application of probability-theoretic and statistical methods  Application to the mathematical physical sciences  Multicomponent random systems.  Processes with a large number of 
		locally interacting components  Gibbs random fields, cluster expansions  Applications to classical statistical mechanics  Generalized Gibbs fields.  Euclidean quantum field theory  Random evolution in nonequilibrium statistical mechanics  Noncommutative probability theory and its application to quantum physics  Application of probability-theoretic and statistical methods to engineering 
		and the humanities  Applications to mechanics  Applications to physics Applications to geophysics                                                             Applications to astronomy and geodesy  Applications to  chemistry  Apllications to geography and geology  Apllications to engineering  Statistical methods in production control  Applications to radio-engineering  Applications to automation  Probability-theoretic reliability theory  Applications of mathematical statistical methods to psychology, biology 
		and medicine  Applications to economics and sociology  Design of specific experiments  Statistical tables  Processing of statistical data  Data collection and survey design  Sample surveys:  methods, questionnaires; editing, errors and 	
		corrections  Computational processing of data, algorithms  Formulation of data; format, etc,  Data storage.  Data banks  Use of statistical data  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  Matroids  Transversals  Ramsey theory  Combinatorics of finite lattices  Extremal combinatorial problems  Problems on a covering and on minimal systems of representatives  Intersections of systems of sets.  Spencer theory  General enumeration methods  Polya's theory  Combinatorics of formal power series.  Generating functions  Incidence algebras, the inclusion-exclusion principle, Mobius theory  Fnite-difference method.  Recurrent sequences  Asymptotic methods  Combinatorial sequences of numbers and polynomials  Enumeration problems of combinatorial analysis  Probability-theoretic approach to combinatorial problems  Combinatorial theory of partitions  Combinatorial identities  Combinatorial inequalities  Combinatorial theory of substitutions and permutations  Special combinatorial tables and configurations  Matrix combinatorial problems  (0,1)-matrices  Combinatorial problems in the theory of permanents  Hadamard matrices  Orthogonal tables:  Latin squares, etc.  Block designs  Applications of combinatorial analysis to the design of experiments  Finite, affine and projective geometries as block designs  Packings and coverings  Combinatorics of the placement of geometric objects  Tesselation and tiling problems  Algorithmic problems of combinatorial analysis
271.45.17  Graph theory  General graph theory and graph representations  General graph theory  Graph representations  Study of individual classes of graphs  Trees  Planar graphs  Directed graphs.  Tournaments  Other classes  Topological problems in graph theory  Graph coloring  Algebraic problems in graph theory  Isomorphism of graphs.  Symmetries of graphs  Operations over graphs  Computation? and enumerations of graphs  Extremal problems in graph theory  Combinatorial problems in graph theory  Connectivity  Graph circuits  Partitions, coverings, packings  Algorithmic problems in graph theory  Generalizations of graphs  Hypergraphs  Matroids  Nets  Random graphs  Applications of graph theory  Applications of graph theory in the natural sciences  Applications of graph theory in engineering  Applications of graph theory in the social sciences  Applications of graph theory in economics

271.47  Mathematical cybernetics

271.47.15  Mathematical theory of control systems  Mathematical problems in modeling control systems  Combinatorial-logic problems in coding  Cybernetic problems in the theory of algorithms  Automata theory  Methods for the specification and realization of automata  Algebraic problems in automata theory  Problems of the representability of events in automata  Experiments with automata  Automata games  Probabilistic automata  Asynchronous automata  Generalizations of automata  Design problems in the theory of control systems  Estimates for the complexity of the realization of functions by circuits  Problems of circuit design with special constraints on the topology of the
                        circuits and the form of the elements  Minimization of Boolean and many-valued functions  Application of Boolean algebra to circuit design  Functional systems  Completeness problems for specific functional systems  Finite-valued logics  Infinite-valued logics  Fuzzy logics and sets  Automata mappings  Recursive functions  Other systems  Study of the structure of closed classes  Metric problems in functional systems  Identity transformations   Stability; reliability and control  Design of stable and reliable circuits  Tests
271.47.17  Mathematical theory of information  Entropy, quantity of information and their properties  Asymptotic theorems on optimal coding (Shannon's theory)  Multisided channels  Channels with feedback  Channels with partially known parameters  Computation of information-theoretic characteristics for specific channels       
                        and messages  Computation of capacity  Epsilon entropy  Computation of error probability  Algebraic theory of codes and of correcting errors  Cyclic codes  Convolutional codes  Majority decoding  Concatenated codes  Codes for correcting errors in arithmetic operations  Synchronization error-correcting codes  Nonuniform codes for messages  Sequential decoding methods  Coding methods in continuous channels  Quantization of messages  Gaussian channels  Channels with fading  Complexity of coding and decoding methods
271.47.19  Operations research  Utility and decision-making theory  General utility theory  Theory of binary relations  Axiomatic utility theory  Theory of group behavior  Games of chance and experimental games  Games of chance (mathematical problems)  Experimental games  Theory of statistical decisions   Decision-making theory  Decision-making under fuzzy conditions  Multicriterial optimization  Stochastic decision-making models  Game theory  Antagonistic games  Matrix games  Two-person zero-sum infinite games (on the unit square on function 
                        spaces)  Noncooperative games  Equilibrium situations  Bimatrix games  Supergames and metagames  Cooperative theory  Arbitrage schemes  Games without side payments  Games with an infinite number of players  Market games and related problems  Dynamic games  Positional games   Discrete-time games (recursive, survival, stochastic)  Continuous-time games  Mathematical programming  Linear programming  Linear inequalities, convex cones and polyhedra  Special linear programming problems  Transportation problem  Flows in networks  Computation methods of linear programming  Simplex method  Block programming  Solution of large-scale problems  Nonlinear programing  Duality theory  Optimality conditions, saddle points, Lagrange functions  Convex programming  Quadratic programming  Complementarity problems  Nonconvex and multi-extremal problems  Nonsmooth optimization  Minimax problems  Computational methods of nonlinear programming  Linearization methods, including gradient methods  Relaxation methods    Nonrelaxation methods               Feasible directions methods		     Second- and higher-order methods  Conjugate gradient methods  Penalty methods  Discrete programming  Complexity theory for discrete problems  Combinatorial problems (the traveling salesman problem, scheduling       
                        theory, etc.)  Integer programming  Boolean programming  Computational methods for discrete programming  Truncation methods; group approach  Partial sorting  method.  The branch and bound method  Approximate and heuristic methods  Parametric programming  Stochastic programming  Problems with random constraints  Probability characteristics of solutions  Dynamic programming  Markov decision-making processes  Computational methods for dynamic programming  Theory of mathematical economic models  Static models  Input-output-type models  Macroeconomic models  Production functions  Econometrics  Optimization models  Dynamic models  Single- and two-commodity models  Multicommodity models  Leontief-type models  Von Neumann-type models.  Optimal trajectories  Consumption models  Probabilistic models  Selection of a portfolio of securities  Theory of economic behavior  Supply and demand models  Exchange models  Equilibrium models  Theory of a firm  Models for the control of an economy  Modeling of separate aspects of an economy  Price models; monetary economics  Models that take into account ecological and demographic factors  Resource-allocation models  Sector and regional models  Mathematical models in operations research  Queueing theory  Queueing system networks  Theory of transportation flows and traffic  Service optimization models  Reliability and backup theory (optimization models).  Quality control  Inventory control theory.  Storage theory  Storage models  Exchange models  Large-scale systems  Modeling control processes  Network design  Digital simulation and modeling of systems  Search theory  Applications to operations research  Organization of research  Applications to design problems  Applications to sociology  Location of production  Applications to economic problems  Financial and actuarial applications  Preservation of the environment  Applications to public health  Applications to industry  Energy applications  Applications to mining  Military applications  Applications to forestry  Applications to agriculture  Applications to communications problems  Applications to transportation problems  Applications to the organization of production  Applications to chemistry  Automated control systems  Applications to construction problems  Urban economics
271.47.21  Theory of mathematical machines, and programming  Theory of mathematical machines  Computer networks  Multiprocessor systems  Special processors and multiprocessors  Number systems and carrying out of operations  Computer programming  Programming theory  Writing and verifying programs  Computational complexity  Abstract data types  Transformation of programs  Parallel programming  Programming methods and examples  Software reliability  Programming languages and systems  Methods for describing languages  Programming languages  Programming systems  Applied program packages  Storage, retrieval and information processing  Data structures  Databases  Information-retrieval systems  Automated control systems  Computer graphics  Operating systems  Programs and algorithms for solving specific problems
271.47.23  Mathematical problems in artificial intelligence  Pattern recognition and image analysis (distinguishing of contours, 	 
		recognition of  characters and oral speech; taking into account context; 
		languages for describing patterns and images)  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)  Mathematical description and modeling of neurons, neural networks, brains 
		and other organs of human beings and animals  Complex systems (investigation of the activity of complex systems,     
                        investigation of their structure, languages for their description)  Robots (theory, control languages; operations design, specific robots and
                        their applications)  Algorithmization of creative activity  (decision-makers, question-answer-	
                        type systems, heuristic methods)
271.47.25  Mathematical problems in semiotics  Syntactical investigation of symbolic systems  Meaningful interpretation of symbolic systems  Decoding of symbolic systems  Mathematical linguistics (general aspects).  Mathematical investigation of      
                        languages of a general nature)  Algorithmic languages  Models of languages and language structures	           Algebro-logic and set-theoretic models of languages and language 
                        stuctures  Models defined by a generating investigation (grammar)  Languages that admit and are generated by automata  Models defined by means of internal correspondences 
                         (configurations, control relations, word connectives)  Transformation of languages
271.47.2527.21  Probability-statistical models for languages and language structures  Language semantics (mathematical aspects)  Mathematical problems of machine translation  Other mathematical problems of semiotics and mathematical linguistics                          

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