
Referativni Zhurnal Classification 
Math on the Web > Classifications > Referativni Zhurnal Classification [Updated: June 1, 2011]
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 logicomathematical 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 Higherorder 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. Manyvalued 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 Logicomathematical theories 271.03.19.25.17 Formal arithmetic 271.03.19.27 Inference in logic and logicomathematical calculi 271.03.19.29 Problems in the algorithmic decidability of logic and logicomathematical 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 numbertheoretic 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 singlevalued 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 Quasiordered 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 Torsionfree 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 pgroups 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 Sylowtype 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 Profinite groups. Propgroups 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 Structuretheoretic 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 Finitedimensional Lie algebras 271.17.19.23.19.17 Infinitedimensional 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 Algebratheoretic 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 padic 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 Ktheory 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 coalgebras 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 RiemannRoch 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, Ktheory 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 padic 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 padic 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 Infinitedimensional algebraic groups 271.17.33.21.31 Proalgebraic 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 threedimensional 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 Finitedimensional 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 linearfractional 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 Infinitedimensional 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 Cardinalvalued 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 Kspaces 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, Scategories) 271.19.17.17.21.17.17 Sduality 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 semiexact 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 ( MoorePostnikov 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 LyusternikShnirel'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 Jfunctors) 271.19.17.25.19 Spaces with operators 271.19.17.25.25 Spaces with multiplication (Hspaces) 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 EilenbergMacLane 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 Jfunctors 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 Threedimensional topological manifolds 271.19.19.17.19.17 Classification of threedimensional manifolds 271.19.19.17.19.17.19 Poincare conjecture and related problems 271.19.19.17.21 Fourdimensional topological manifolds 271.19.19.17.21.17 Classification of fourdimensional manifolds 271.19.19.17.21.17.19 Poincare conjecture for fourdimensional 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 piecewiselinear 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 Infinitedimensional manifolds 271.19.19.21.15.31.21 Morse theory 271.19.19.21.17 Classification of smooth and piecewiselinear 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 piecewiselinear 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 piecewiselinear embeddings and embeddings of manifolds 271.19.19.21.33 Groups that act on smooth and piecewiselinear manifolds 271.19.19.21.33.25 Groups of diffeomorphisms and piecewiselinear 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 RiemannRoch 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, pseudoconvex and pseudoconcave 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 Onedimensional 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 Threedimensional 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. qpseudoconvex, qpseudoconcave and qcomplete spaces 271.19.21.21.25 Complex spaces that are close to algebraic manifolds 271.19.21.21.31 Global properties of realanalytic 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 Gstructures 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, pseudoEuclidean and nonEuclidean geometries 271.21.15.19.15 Euclidean and pseudoEuclidean geometries 271.21.15.19.15.21 Analytic geometry in Euclidean spaces 271.21.15.19.15.25 PseudoEuclidean spaces 271.21.15.19.15.27 Galilei spaces 271.21.15.19.15.31 SemiEuclidean spaces 271.21.15.19.15.33 Flag spaces 271.21.15.19.17 NonEuclidean 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 Quasielliptic and quasihyperbolic spaces 271.21.15.19.17.31 Semielliptic and semihyperbolic 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 Biaxial 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 nonEuclidean spaces 271.21.15.27.19 Hermitian Euclidean and nonEuclidean 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 differentialgeometric objects 271.21.17.31.21 Extensions of geometric objects 271.21.17.31.27 Lie differentiation 271.21.17.33 Differentialgeometric 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, pseudoEuclidean 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 threedimensional 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 nonEuclidean spaces 271.21.19.25.19.17 Differential geometry in nonEuclidean 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 nonEuclidean 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 pseudoconformal spaces 271.21.19.25.27.21 Differential geometry in symplectic spaces 271.21.19.25.27.31 Differential geometry in biaxial and biaffine 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 Gstructures on differentiable manifolds 271.21.19.27.19.19.15 General problems in the geometry of Gstructures 271.21.19.27.19.19.17 Tensor Gstructures 271.21.19.27.19.19.17.31 Submanifolds in manifolds of tensor Gstructures 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 Gstructures 271.21.19.27.19.19.31.31 Submanifolds in manifolds of other special Gstructures 271.21.19.27.19.19.33 Mapping of manifolds with Gstructures 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 Higherorder 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 pseudoRiemann spaces 271.21.19.27.21.17.15 General theory of Riemann and pseudoRiemann spaces 271.21.19.27.21.17.15.17 Invariant objects in Riemann and pseudoRiemann spaces 271.21.19.27.21.17.15.21 Holonomy groups of Riemann and pseudoRiemann 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 semireducible Riemann and pseudoRiemann spaces 271.21.19.27.21.17.17.21 Recurrent Riemann and pseudoRiemann 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 pseudoRiemann 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 pseudoRiemann 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 ProjectiveEuclidean 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 SemiRiemann 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 pseudEuclidean 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 Finitedifference 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 Quasianalytic 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 Chebyshevtype 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 Cauchytype 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 Quasianalytic 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 righthand 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 secondorder 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 secondorder equations and secondorder systems (asymptotic behavior, monotonicity, estimates for the solutions, etc.) 271.29.17.15.21.27 Zeros of solutions of secondorder 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 righthand 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 higherorder 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 Functionaldifferential 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 firstorder equations and systems: properties, types, etc. 271.31.15.19 General higherorder 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 Wellposedness 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 Illposed 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 Integrodifferential equations 271.33.19.17 Linear integrodifferential equations 271.33.19.19 Singular integrodifferential equations 271.33.19.21 Nonlinear inegrodifferential equations 271.33.19.33 Systems of integrodifferential 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 Threedimensional 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 Twoperson differential games 271.37.19.21 nperson differential games 271.39 Functional analysis 271.39.15 Linear spaces endowed with topology, order, and other structures 271.39.15.15 Ordered and semiordered 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 Positivedefinite functionals in function spaces 271.39.15.19.25.21 Problems of the continuation of positivedefinite functionals and positivedefinite 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 infinitedimensional 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 preHilbert 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 semiordered 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 infinitedimensional 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 illposed 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 quasitopology 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 infinitedimensional 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 Positivedefinite 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 Infinitedimensional representation of groups 271.39.23.25 Infinitedimensional 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 Infinitedimensional 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 illposed 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 Meansquare 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 Firstorder 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 Firstorder differential equations 271.41.19.15.21.17 Secondorder differential equations 271.41.19.15.21.19 Higherorder 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 Firstorder differential equations and their systems 271.41.19.17.17 Secondorder 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 Secondorder 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 Higherorder 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 Integrodifferential 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 Goodnessoffit 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 Goodnessoffit 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 Goodnessoffit 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 probabilitytheoretic 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 probabilitytheoretic 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 radioengineering 271.43.51.21.35 Applications to automation 271.43.51.21.37 Probabilitytheoretic 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 inclusionexclusion principle, Mobius theory 271.45.15.19.27 Fnitedifference 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 Probabilitytheoretic 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 Combinatoriallogic 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 manyvalued 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 Finitevalued logics 271.47.15.27.19.19 Infinitevalued 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 informationtheoretic 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 errorcorrecting 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 decisionmaking 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 Decisionmaking theory 271.47.19.15.27.17 Decisionmaking under fuzzy conditions 271.47.19.15.27.21 Multicriterial optimization 271.47.19.15.27.27 Stochastic decisionmaking 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 Twoperson zerosum 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 Discretetime games (recursive, survival, stochastic) 271.47.19.19.31.21 Continuoustime 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 largescale 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 multiextremal 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 higherorder 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 decisionmaking 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 Inputoutputtype 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 twocommodity models 271.47.19.27.19.19 Multicommodity models 271.47.19.27.19.19.17 Leontieftype models 271.47.19.27.19.19.21 Von Neumanntype 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 Resourceallocation 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 Largescale 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 Informationretrieval 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 (decisionmakers, questionanswer 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 Algebrologic and settheoretic 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 Probabilitystatistical 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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