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
This paper studies generalized Cauchy problems for linear and quasilinear differential equations in a Banach space with time-dependent closed operators that may not admit classical solutions for all initial data. The authors construct an enlarged sequence space using invariant idempotent decompositi…
The paper studies geodesic fields of directions in spaces with affine connection and their relation to included systems of paths and groups of homotheties. It derives necessary and sufficient coordinate conditions for a space to contain several such fields, describes the resulting decomposition into…
This note states solvability results for the Cauchy problem for nonlinear and quasilinear parabolic systems in the sense of Petrovskii. Using fundamental matrices for linear parabolic systems and, for the nonlinear case, reduction to an equivalent quasilinear problem with successive approximations, …
This paper studies the relation between complete best approximation and partial best approximation for periodic functions of several variables in \(L_p\) spaces by trigonometric polynomials. It defines partial approximations in selected variables and proves inequalities bounding the complete best ap…
This paper studies the error of the arithmetic mean formula for multidimensional integration, including its use in Monte Carlo computation when the integration nodes are random. It compares uniform grids with random nodes, showing that in high dimensions standard uniform grids can have worse error o…
This note states an asymptotic expansion for the joint distribution of occupation counts in a finite nonhomogeneous Markov chain. Under uniform comparability of transition probabilities, a single essential class, and full rank, the probability of a given vector of visit counts, centered by its expec…
This paper studies simultaneous mean approximation of complex-valued boundary functions given on several rectifiable Jordan contours, in weighted Lebesgue-Stieltjes spaces. It characterizes when polynomial or rational systems are closed, relating this to logarithmic integrability conditions involvin…
This paper studies existence and uniqueness for several boundary value problems involving nonlinear ordinary differential equations and related systems. Using Chaplygin-type differential inequalities, derivative estimates, parameter continuation, compactness arguments, and the Leray-Schauder princip…
This paper studies global-in-time boundary value problems for nonlinear and quasilinear parabolic equations, including nonlinear boundary conditions in one space dimension and a second boundary value problem in several space dimensions. Using Rothe’s time-discretization method, together with auxilia…
This paper studies the behavior of solutions of a periodically perturbed system of differential equations near an isolated equilibrium of the unperturbed system when the linearized equations have one pair of purely imaginary characteristic roots and all remaining roots have negative real parts. By t…
This note constructs integral representations for functions that are operator-analytic with respect to an ordinary linear differential operator of order n. Building on a previously defined isomorphism between rings of operator-analytic functions, it studies the Cauchy problem for the partial differe…
This paper constructs a counterexample in dimension theory: a normal space whose small inductive dimension is one but which cannot be embedded in any one-dimensional bicompact space. The construction modifies a Lunc-type ordered product space, first building an auxiliary normal space with prescribed…
This note proves that every real continuous function on the n-dimensional unit cube, for n at least 2, can be represented as a finite sum of continuous functions of one variable applied to sums of fixed continuous one-variable functions of the coordinates. The construction first defines monotone aux…
This paper studies when hyperbolic systems of quasilinear equations can be represented by conservation laws, a form needed to define generalized solutions through integral relations. It formulates a criterion based on an associated overdetermined linear system and argues that systems with one or two…
This note studies convergence of Lagrange interpolation polynomials on the interval [-1,1] for triangular arrays of interpolation nodes, with emphasis on absolutely continuous functions and functions of bounded variation. Using known necessary and sufficient criteria involving bounded sums of fundam…
This paper formulates Cauchy and boundary value problems for a first order nonlinear conservation law with a source term in classes of bounded measurable, possibly discontinuous functions. Generalized solutions are defined by an integral identity together with a one sided regularity condition, and u…
This paper studies the Cauchy problem for a class of nonlinear equations in Banach spaces in which the operator is analytic in the independent variable and unknown function and linear in the time derivative. After reducing the problem by a local change of variables, the author analyzes a representat…
The paper addresses uniqueness for a one-dimensional Stefan problem with a one-phase initial state in a finite heat-conducting medium, under monotonicity and sign assumptions on the boundary and initial data and on the spatial derivatives of the temperature fields. The argument perturbs a given free…
The paper introduces a general construction of positive linear operators on continuous functions, defined from a sequence of analytic functions whose derivatives satisfy sign and asymptotic recurrence conditions. It proves uniform convergence on finite intervals by verifying convergence on the test …
This note studies periodic solutions of quasilinear differential equations with time delays and periodic coefficients. Using Lyapunov functionals and contraction arguments in a space of history functions, it gives sufficient conditions under which asymptotic stability of the zero solution of an asso…
The paper addresses the three-dimensional inverse problem for the Newtonian potential: determining a finite simply connected domain of constant density from its prescribed exterior potential. Using Cauchy-type integral formulas for potential-harmonic vector functions and their boundary limiting valu…
This paper studies extremal problems for differentiable functionals on classes of univalent functions, distinguishing extremal functions that optimize a real functional from boundary functions for vector-valued ranges of variation. It defines classes of weakly differentiable real and complex functio…
This paper studies equivalence of linear systems of partial differential equations with constant coefficients after reduction to first order in one distinguished variable. It defines equivalence by the existence of a nonsingular matrix differential operator transforming solutions of one system into …
This paper develops approximation methods for solving the transport equation in a finite plane layer when scattering is strongly anisotropic and standard spherical harmonic or small-angle methods are inadequate, especially at large angles. The solution is factored by a weight function chosen to capt…
This paper extends Kolmogorov’s theory of extrapolation for stationary processes to multidimensional homogeneous random fields with discrete and continuous arguments. It introduces direction-independent notions of regularity, nonsingularity, and singularity, proves decomposition and moving-average t…
This paper studies relations between moduli of smoothness of different orders for measurable functions on the whole real axis in the spaces Lp, 1 ≤ p ≤ ∞. The authors prove an integral inequality estimating a lower order modulus of smoothness in terms of a higher order modulus, derive consequences f…
This paper develops a local form of infinite divisibility for general stochastic processes, especially Markov processes that may be inhomogeneous in space and time. It defines right and left differentiability of families of distribution functions through local limits of characteristic functions and …
This paper studies the existence of solutions for the nonlinear bending problem of thin plates governed by the Kármán equations under clamped and related boundary conditions. The differential system is transformed into an integro-differential equation using the biharmonic Green function, and the Sch…
The paper studies analytic continuation and convergence properties of series in Faber polynomials associated with a bounded simply connected domain and its exterior conformal mapping. It establishes a correspondence between such Faber series and ordinary power series with the same coefficients, usin…
This note characterizes when two prescribed subsets of the real line can occur as the exact sets where the derivative of a finite real function is respectively equal to positive and negative infinity. It proves that this is necessary and sufficient precisely when both sets have measure zero and are …
This note studies linear interpolation for stationary processes with discrete time, extending Kolmogorov’s interpolability condition and related one-dimensional results to multidimensional and infinite-dimensional settings. It first formulates stationary processes in a coordinate-free Hilbert space …
The note proves a decomposition theorem for a random variable represented as the sum of independent Gaussian and Poisson components, generalizing results of Cramér and Raikov. It shows that any decomposition of such a law into two independent summands must itself split into corresponding Gaussian an…
This paper studies topological spaces whose weight, locally or globally, exceeds their cardinality, with emphasis on separation axioms and both regular and irregular infinite cardinals. It counts the class of T5 spaces of a given cardinality with larger weight, then constructs explicit examples usin…
The paper studies a special Chebyshev problem: the uniformly best approximation on [0,1] of a polynomial of degree n by polynomials of lower degree, reformulated as the construction of degree n polynomials with prescribed leading coefficients and minimal uniform deviation. Using the theory of class …
The paper addresses a question of N. N. Luzin concerning the measure of sets on which approximation errors attain their maximum, especially for best polynomial and trigonometric approximations. It constructs a continuous function on a closed interval and an infinite subsequence of degrees for which …
The paper studies Chebyshev best approximation of a continuous function on a closed subset of an interval by functions from an interpolation class, including linear and boundedly compact classes. It formulates the problem in a general interpolation setting, recalls uniqueness, and develops effective…
The paper computes matrix elements of irreducible unitary representations of the rotation group SO(n) and of the motion group of Euclidean space of dimension n minus 1. Using a parametrization generalizing Euler angles and an induction on n based on branching to SO(n minus 1), it constructs the repr…
This note extends Korovkin-type convergence criteria for linear positive operators from continuous functions of one variable to continuous functions on a closed bounded domain in two variables. It proves that uniform convergence of the operators on the four test functions 1, x, y, and x squared plus…
This paper studies finite difference methods for first boundary value problems for elliptic systems of second order linear partial differential equations with constant coefficients in multidimensional space. It constructs a fundamental matrix for the corresponding difference system by Fourier integr…
The paper studies a singularly perturbed system of differential equations whose slow equation also contains a rapidly varying argument. Under boundedness, Lipschitz, averaging, and uniform stability assumptions, it proves the existence and uniqueness, for sufficiently small positive parameter, of an…
The paper studies nonlinear second-order differential equations with slowly varying coefficients and small perturbation terms, focusing on oscillatory solutions over time intervals of order the reciprocal of the small parameter. Under sign and smoothness assumptions on the restoring force and pertur…
This paper proves embedding theorems for classes of real periodic functions of several variables that admit analytic continuation in strips and satisfy Hölder type boundary smoothness conditions. Using two approximation theorems of S. M. Nikol’skii and a lemma relating multivariate best trigonometri…
This paper studies the topological invariance of Pontryagin characteristic classes for smooth compact orientable manifolds, focusing on the reduced classes obtained from Hirzebruch, Thom relations between Pontryagin classes and the signature. It defines classes s4k as polynomial combinations of redu…
This paper establishes limit theorems for sums of functions of homogeneous Markov chains on general state spaces under a uniform geometric convergence condition to a stationary distribution. It proves a central limit theorem assuming only square integrability, extends convergence to stable laws unde…
This note studies a mixed initial boundary value problem for a parabolic system with constant coefficients in a domain bounded by a convex Lyapunov surface. Using Green functions previously constructed for the corresponding half-space problem, the solution is represented as a surface potential with …
This note outlines a proof of a theorem asserting that every real continuous function of three variables on the unit cube can be represented as a finite sum of continuous functions of two variables. Building on Kolmogorov’s representation using functions defined on a tree, the argument reduces the p…
This note refines Chunikhin’s factorization theorem for finite Pi-separable groups by addressing whether the factors may be chosen pairwise permutable. It defines Pi-closed subgroups and Pi-separable bases, then proves by induction on the group order that every finite Pi-separable group has such a b…
This paper proves a comparison and convexity property for complete Riemannian manifolds whose curvature is bounded below, first treating analytic metrics of strictly positive curvature and then passing to twice continuously differentiable metrics by approximation. The argument reduces local question…
