SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 5847 papers in Mathematics
The paper proves that every normal topological space of weight τ can be represented as the image of a zero-dimensional subspace of a generalized Cantor discontinuum of the same weight. The construction uses directed refining systems of finite canonical coverings, forms an inverse spectrum of finite …
The paper studies numerical continuation for initial value problems for ordinary differential equations using piecewise linear approximate solutions associated with Euler, Runge, and Adams type schemes, including versions affected by bounded round-off errors. It formulates conditions under which the…
The paper studies the simultaneous reduction of two bilinear forms whose matrices are symmetric or skew-symmetric, over the real or complex numbers. It gives a canonical decomposition of any such pair into a direct sum of explicitly listed elementary pairs, with uniqueness up to the order of summand…
This paper studies spaces of fractional order defined by difference norms, comparing them with related Sobolev, Slobodetskii, Besov, and Gagliardo type spaces. It presents a simpler method, based on integral representation formulas due to Il’in, for proving trace, extension, embedding, and regularit…
This paper studies how far a continuous mapping from a finite-dimensional compactum into a polyhedron can be approximated so that the dimensions of point preimages are controlled. It introduces a defect function on a polyhedron and proves that if such a function satisfies certain local approximation…
This paper describes an algorithm for a universal program automating the numerical solution of the plane Dirichlet problem for the Laplace equation on general domains using finite difference methods. The proposed procedure encodes parametrically given boundaries, replaces them by a grid polygon, cla…
This paper gives a sufficient criterion for a sequence of real numbers in the unit interval to be completely uniformly distributed. The criterion assumes a uniform upper bound, proportional to volume, for the limiting frequency with which consecutive blocks of any dimension fall in an arbitrary para…
This paper completes the proof of a comparison theorem for complete twice continuously differentiable Riemannian spaces whose sectional curvature is bounded below by a positive constant. Extending earlier work and using limiting arguments, nonbranching of shortest arcs, and comparison with the const…
This note studies extremal problems for real polynomials with multiple monotonicity conditions on an interval or on the real line, under admissible linear constraints on their coefficients. It proves existence theorems describing extremal elements with minimal oscillation in the classes of multiply …
This note develops Linnik’s method of computing variance in arithmetic progressions to treat binary additive equations of the form n equals uv plus a binary quadratic form, where u and v range over broad prescribed sequences. As an illustrative case, it proves an asymptotic formula for representatio…
This note extends the theory of defining relations from models to general categories, using homomorphisms to express substructures, products, free compositions, and related notions. It introduces replicas of objects in subcategories as a categorical formulation of structures determined by generators…
This paper studies direct and inverse problems for approximation of functions on a finite interval by algebraic polynomials in the spaces Lp, with attention to endpoint-weighted estimates involving the function g(x,n). It proves several direct theorems giving polynomial approximation bounds under as…
The paper derives an expansion formula for arbitrary vector functions associated with a boundary value problem for a system of linear differential equations on several intervals, with piecewise smooth coefficients depending on a complex parameter and including negative powers of that parameter. Usin…
The paper derives inversion formulas for the Sommerfeld integral representation of solutions of the two-dimensional wave equation, with emphasis on functions defined by contour integrals in wedge diffraction problems. It proves existence and uniqueness of an odd analytic density satisfying specified…
This paper introduces entropy per unit time as a new metric invariant for transitive dynamical systems and automorphisms of Lebesgue spaces, addressing whether systems with countable Lebesgue spectrum are all isomorphic modulo zero. It develops the needed notions of conditional entropy and condition…
The paper constructs an analogue of the Laplace transform for Mikusiński’s operational calculus, motivated by the simplifying role of Laplace integrals in operational formulas. It defines rings of Laplace transforms modulo ideals determined by exponential shifts, forms a direct sum of quotient rings…
This note gives a homotopic classification of nonsingular unit tangent vector fields on orientable smooth closed manifolds with Euler characteristic zero. Using obstruction and difference cohomology, together with a classification theorem for section surfaces, it identifies the homotopy classes firs…
This paper studies a boundary value problem for uniformly elliptic first order linear systems in a simply connected planar domain, with Hölder continuous oblique real boundary condition. The system is reduced by complex notation and conformal mapping to a generalized Beltrami type equation in the di…
This paper studies boundedness and global stability of a class of nonlinear differential equations arising in indirect automatic control with one scalar nonlinearity satisfying a sign condition. Using Lur’e’s Lyapunov method and resolving equations, it derives conditions for continuability, boundedn…
The paper develops general criteria for the existence of subgroups and factorizations in finite groups using divisors associated with the indices of a chief series. It introduces indexials and directed indices, proving that an indexial yields a subgroup whose order differs only by primes already div…
This paper extends the notion of a maximal correlation coefficient to the nonsymmetric case of two random variables with a joint density on a rectangular, possibly infinite, domain. Using Hilbert-Schmidt theory, it associates the nonsymmetric density with two symmetric kernels having the same eigenv…
The paper studies extremal problems for normalized quasiconformal mappings of the disk, where a differentiable real functional depends on the images of finitely many prescribed points. Using a variational method applied to the complex characteristic of the inverse mapping, it derives necessary extre…
This note extends Sobolev embedding theorems to spaces of functions whose generalized derivatives of order l belong to Orlicz spaces generated by complementary N-functions. It defines the spaces, quotient structure modulo polynomials, and equivalent norms, then establishes embedding and compactness …
This note studies when a category of structures can be represented, in the stronger sense of structural equivalence, by a subclass of algebras of a fixed type. It develops conditions involving free structures, homomorphic closure, additivity, boundedness, regularity, divisible homomorphisms, and fin…
This paper studies uniform approximation of periodic differentiable functions by de la Vallée Poussin sums, focusing on the worst case deviation over the classes of functions with bounded rth derivative and over their conjugate classes. It derives asymptotic formulas for these deviations as the poly…
This note studies the image of the natural homomorphism from the group of internal homologies to the group of internal homologies modulo 2, using the known Thom and Dold description of the unoriented cobordism algebra by generators. Rokhlin proves that several conditions on a manifold are equivalent…
The paper studies the relation between weak and strong convergence in Banach spaces and proves that every separable Banach space admits an equivalent norm for which weak convergence together with convergence of norms implies norm convergence. The proof is first carried out for the space of continuou…
This paper studies generalized minimizers of multidimensional variational integrals whose integrands depend on the first derivatives and satisfy growth, ellipticity, and differentiability assumptions of order p at least 2. Using difference quotient arguments and weak variational identities, it estab…
This note develops expansion formulas for non-self-adjoint singular differential operators on the half-axis, generalizing Weyl’s spectral representation for self-adjoint boundary-value problems. It introduces spectral functions as generalized functions on a space of even entire functions of exponent…
This paper addresses Aleksandrov’s problem of defining a class of irregular surfaces in three-dimensional Euclidean space whose intrinsic metrics have bounded curvature while also including smooth surfaces of bounded extrinsic curvature, general convex surfaces, and DC surfaces. The author replaces …
The paper proposes a method for solving finite difference equations arising from the planar Dirichlet problem by using a normal sequence of signs. It first proves a theorem on the asymptotic frequency with which variable length combinations from a prescribed set occur in a normal sequence, under con…
This note studies the relationship between integral equations of convolution type on the real line and singular integral equations with a Cauchy kernel. It introduces weighted function classes for the unknown function, kernels, and right hand side, then uses Fourier transforms and analytic continuat…
This paper studies boundary-layer asymptotics for solutions of first boundary-value problems for elliptic partial differential equations of arbitrary even order when the boundary data oscillate rapidly. Using local boundary coordinates, a rescaling normal to the boundary, and an iterative expansion …
Smirnov generalizes Dowker’s example of a normal space with small inductive dimension zero but larger covering dimension. The paper studies convergent subsets of the product of the space of countable ordinals with a separable metric space, proving that such subsets are normal, countably paracompact,…
The paper derives an expansion formula for arbitrary functions in \(L_2\) in terms of fundamental functions associated with a class of parameter-dependent boundary-value problems for linear partial differential equations. The class considered permits partial separation of variables, reducing the ana…
The paper studies bicompact extensions of semibicompact Hausdorff spaces, focusing on when the remainder of an extension is zero-dimensional. Using special bases of open sets with bicompact boundaries and methods from proximity space theory, it constructs compatible proximities and the corresponding…
This note extends the Weyl and Vishik projection method for elliptic boundary value problems from Hilbert space settings to \(L_p\) and Sobolev spaces in a smooth bounded domain. Using the Calderón and Zygmund boundedness theorem for singular integral operators, it formulates generalized Dirichlet a…
This paper extends the principle of monotonicity of the argument, previously used to differentiate majorization inequalities, from single-valued analytic functions to multivalued functions on the universal covering surface of a plane cut along intervals of the real axis. It defines an admissible cla…
This note studies the Cauchy problem for first order systems of linear partial differential equations with analytic coefficients and analytic initial data, focusing on convergence of a simple finite difference approximation. By extending the variables to a complex domain and using Cauchy estimates t…
This paper extends M. K. Fage’s theory of functions analytic with respect to an ordinary differential operator to functions of two variables analytic with respect to a second order hyperbolic operator. It defines infinite differentiability and analyticity relative to the operator, constructs inverse…
This note studies sets in metric spaces that are effectively distinct from all sets generated by a given delta s operation. It introduces the notion of one delta s operation embracing another and proves that effective distinction from all sets of the embracing operation implies effective distinction…
This paper studies how boundary smoothness and integrability properties are inherited by harmonic functions solving the Dirichlet and Neumann problems in a bounded three-dimensional domain with sufficiently smooth boundary. Using potential-theoretic methods, it extends earlier Hölder-type results of…
The paper develops improved estimates for Weyl sums associated with polynomials of degree \(n+1\), using a fundamental lemma based on Hölder’s inequality, solution counts for systems of power equations, and Vinogradov-type mean value estimates. It proves bounds for arbitrary Weyl sums when the leadi…
This paper studies stability, with respect to a complex parameter, of solutions to linear operator equations in a Banach space for analytic families of completely continuous operators. It defines stability points through strong convergence of regular resolvent solutions to a solution at a spectral p…
This paper addresses whether groups in which every abelian subgroup has only finitely many conjugates form a broader class than groups in which every subgroup has this property. Building on Neumann’s characterization of groups with finitely many conjugates of every subgroup, the argument reduces the…
The paper studies high-frequency asymptotics for eigenfunctions of the Helmholtz equation with Dirichlet boundary conditions in domains bounded by equidistant curves, including closed, finite, and infinite waveguide geometries. Using normal coordinates based on one boundary curve and a variational r…
The paper develops an asymptotic method for boundary value problems for quasilinear differential equations with a small parameter multiplying the highest derivative, using a second order ordinary equation as the principal example. Under positivity and smoothness assumptions and within a suitably def…
This note studies how the intrinsic smoothness of the metric of a convex surface in a space of constant curvature determines the smoothness of its extrinsic realization. It states that if the surface metric is k times differentiable, with k at least 4, and its Gaussian curvature is positive and grea…
