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 note characterizes paracompact spaces through projection spectra and perfect irreducible mappings. It defines regular and uniform spectra of simplicial complexes, proves that the spaces of regular uniform spectra are paracompact, and conversely constructs a complete regular uniform spectrum for…
The paper develops a general factorization theory for invertible matrix functions with entries in normed rings of continuous functions on a closed subset of the complex plane, under a rational approximation condition. It characterizes integer-valued multiplicative functionals on such matrix function…
This paper studies a general approximate method for linear problems in normed spaces, seeking finite linear combinations from an operator complete system that minimize the residual norm and converge to the best attainable approximation. The proposed method reduces the finite dimensional convex minim…
This note studies topological spaces with point-countable bases, especially the extent to which such bases imply metrizability or compactness properties. It proves that any bicompact T1 space whose base has bounded point multiplicity has base cardinality bounded by the same cardinal, yielding in par…
This paper studies embeddings of zero-dimensional compacta in Euclidean space, with emphasis on distinguishing tame embeddings from wild ones in dimensions at least three. It introduces the notion of a cellularly separated compactum and proves that any cellularly separated zero-dimensional compactum…
The paper develops an approach to uniqueness in inverse spectral problems for ordinary differential operators by relating unique determination to completeness of certain products of eigenfunctions, following and generalizing an observation of Borg. For first-order systems of vector functions with a …
The paper studies uniqueness and existence for constant coefficient partial differential equations in the whole space when the characteristic polynomial may have real zeros. It introduces thin sets relative to function spaces and uses Fourier transform support arguments to prove a uniqueness theorem…
The paper improves classical interpolation estimates for an n times differentiable function with n zeros by restricting attention to the interval between the first and last zero. It gives sharp constants for bounds on the function and its derivatives in terms of the maximum of the nth derivative, an…
This paper studies oscillation properties of eigenfunctions for third order boundary value problems with positive coefficient functions and a discrete spectrum. The problem is reduced to an integral equation with the Green’s function as kernel, and criteria are formulated for when this kernel is ord…
The paper studies a singularly perturbed system of differential equations near a family of closed orbits of the corresponding degenerate system. Using a transformation to separate slow variables, transverse deviations, and fast variables, and applying Bogolyubov’s method together with Lyapunov reduc…
This note addresses a conjecture arising in the use of Sobolev embedding theorems, namely that every bounded domain satisfying the cone condition can be expressed as a finite union of domains star-shaped with respect to balls. The proof establishes a compactness-type lemma: if a bounded domain is co…
The paper proves that any twofold continuous decomposition of a generalized homological cube must contain a singleton element, so a strictly twofold continuous decomposition is impossible. Arguing by contradiction, it analyzes the conjugacy relation of paired points, constructs a transfinite stratif…
This note studies harmonic functions in the unit disk and in the upper half-plane whose boundary values belong to an \(L_p\) space, estimating how far the harmonic extension deviates from its boundary function as the interior point approaches the boundary. For the disk, the deviation is bounded in t…
The paper studies boundary behavior of homeomorphic Q-quasiconformal mappings of an n-dimensional ball onto a domain, aiming at an analogue of Koebe’s theorem on attainable boundary points. Using modulus estimates for curve families, including lower bounds for curves joining connected sets in the ba…
This note studies asymptotic lines on regular surfaces in Euclidean three-space with negative Gaussian curvature that varies slowly relative to a constant value. It proves estimates generalizing the Chebyshev property known for constant negative curvature: in an asymptotic quadrilateral, the sums of…
This note studies the category of representations of the group of second order unimodular matrices over a finite field of odd characteristic, associated with its unipotent subgroup. Using induced representations from additive characters, it describes the corresponding intertwining rings and spaces, …
The paper studies the chromatic number of a finite undirected graph through orientations of its edges and Boolean powers of the resulting adjacency matrix. It proves that the chromatic number equals one more than the largest integer such that every orientation contains a directed path of that length…
This note extends work of Mineev on Diophantine equations with exponential terms to equations involving powers of a nonsingular integral matrix. It obtains an asymptotic formula, with a remainder term, for the number of solutions in a finite interval to a matrix Diophantine equation containing vecto…
This note studies general boundary value problems for properly elliptic systems in a smooth bounded multidimensional domain, allowing boundary operators whose coefficients are singular integral operators as well as ordinary differential operators. Using the Lopatinskii condition, the authors formula…
This paper studies convergence of projection methods for linear equations in Hilbert spaces, including Ritz, Galerkin, moments, and least squares methods, and relates their convergence to a geometric condition on pairs of finite-dimensional subspaces. An elementary proof is given that strong converg…
The paper establishes boundary growth estimates in the L2 metric for polyharmonic functions of arbitrary finite order in a disk, extending analogous results known for harmonic functions and second order elliptic equations. Using Fourier series representations of l-harmonic functions, coefficient tra…
This paper extends Katětov’s dimension equality theorem from compact spaces with zero-dimensional maps into the Hilbert cube to broader classes of Hausdorff spaces using the notion of decomposing mappings. It proves inequalities and equalities among small inductive dimension, covering dimension, lar…
This note studies the locality of approximation operators, asking how far the rate of convergence at a point is determined by the approximated function in a neighborhood of that point. It introduces a local characteristic for sequences of homogeneous operators and proves a general estimate separatin…
This paper studies billiard motion in an unbounded planar table bounded by the line y = 0 and a bell-shaped curve y = f(x), focusing on whether trajectories can be unbounded while repeatedly returning to the central axis. Using a phase space representation of successive intersections with the vertic…
This paper studies expansions in eigenfunctions for a non-self-adjoint operator generated by a system of second-order differential equations on the whole real axis with a complex matrix potential satisfying exponential integrability conditions. Using specially chosen fundamental matrix solutions, th…
This paper studies classes and sets of proper subgroups of finite groups with prescribed properties, extending earlier work on conjugate, isomorphic, and isoordic subgroup classes. It introduces a functional framework for assigning prime divisors to classes of subgroups and applies it to attainable,…
This paper studies the use of the least squares method for approximate solutions of nonlinear operator equations in Hilbert spaces. It establishes convergence of least squares approximations under density, monotonicity, and norm comparison assumptions, derives an error estimate for solvable equation…
The paper addresses the construction of sets of uniqueness failure for trigonometric series with exceptionally small Hausdorff size. It gives a Cantor-type construction of a perfect set and a continuous nondecreasing function, constant on complementary intervals, whose Fourier-Stieltjes transform te…
This paper studies local limit behavior for the densities of normalized sums of independent identically distributed random variables with zero mean and unit variance. It refines known conditions under which the integral distance between the density component of the normalized sum and the standard no…
This paper studies a boundary value problem for a system of ordinary differential equations in which a small parameter multiplies the highest derivative. It weakens earlier existence and uniqueness assumptions by restricting hypotheses on the right hand sides to a bounded neighborhood of the solutio…
This note proposes and studies three-dimensional analogues of the Tricomi problem for mixed-type equations, primarily the equation with coefficient changing sign across the plane z = 0 in domains bounded by characteristic cones and conical surfaces. It formulates basic and principal mixed boundary v…
The paper studies Green matrices for general boundary value problems for parabolic systems in a half-space under constant coefficients and parabolically homogeneous system and boundary operators. Using Fourier and Laplace transform representations and an algebraic solvability condition, it derives a…
The paper studies the size of the effective and ineffective domains of regular matrix summability methods, focusing on bounded divergent sequences. It proves that any regular matrix summing at least one bounded divergent sequence sums a continuum family of bounded sequences whose every finite nontri…
This note gives characterizations of B-completeness for Hausdorff topological linear spaces, with emphasis on ultrabarrelled and barrelled spaces. It formulates equivalent conditions in terms of openness of continuous or closed-graph linear mappings onto spaces of the same class, and continuity of c…
The paper defines a radical associated with a representation of a group by automorphisms of another group, using kernels of the induced irreducible actions on composition factors, and compares it with the locally stable radical. It gives model-theoretic and local criteria for stability conditions an…
The paper constructs a class of continuous homogeneous Markov processes on an open subset of Euclidean space, called Brownian motions with killing measure and speed measure, by applying killing via an additive functional and then a random time change to Wiener process. It formulates the construction…
This paper studies expansions in eigenfunctions and associated functions for ordinary linear differential operators of odd order on a finite interval, with boundary conditions that may be irregular. It introduces a class of boundary-value problems defined by asymptotic conditions on selected coeffic…
This paper studies relationships among zero-dimensional mappings, universal spaces, dimension theory, open mappings, and inverse spectra in general topology. It constructs bicompact universal spaces of prescribed weight and dimension for several classes of spaces, including bicompacta admitting zero…
The paper addresses the construction of Fourier summation methods that converge uniformly for all continuous periodic functions while retaining the best possible approximation order on smoothness classes characterized by derivatives satisfying Lipschitz conditions. It introduces a class of trigonome…
This note studies the classification up to isomorphism of two-dimensional formal abelian groups over an algebraically closed field of characteristic p greater than zero, using Dieudonné’s equivalence between formal abelian groups and modules over a complete topological ring. It reduces the problem t…
This note studies extinction and limiting behavior in continuous-time inhomogeneous branching processes, where particle reproduction probabilities depend on time and are described through a generating-function differential equation. It derives an integral representation for the generating function a…
This paper studies model representations for non-self-adjoint bounded operators of class Omega whose spectrum is real and whose non-Hermiticity has finite rank. It introduces generalized elements in a rigged Hilbert space constructed from a smooth function space transported by a unitary equivalence …
This note studies the structure of n-dimensional primitive parallelohedra of the first type, using Selling frames, circumscribed simplexes, and operations of affine transformation and stretching along zones of edges. It proves that any two such parallelohedra of the same dimension are related by the…
This paper proves two results in dimension theory concerning weakly and strongly infinite-dimensional spaces. The first shows that a continuous map from a weakly infinite-dimensional bicompactum onto a strongly infinite-dimensional bicompactum must have at least one fiber of cardinality not less tha…
The paper studies decision problems for finitely presented commutative semigroups, motivated by the contrast between undecidability in general groups and semigroups and the better behavior expected in the commutative case. It constructs an explicit algorithm for determining whether such a semigroup …
This paper derives an explicit formula for the Plancherel measure on Riemannian symmetric spaces of nonpositive curvature of the form G/U, where G is a connected semisimple Lie group with finite center and U a maximal compact subgroup. Using Harish-Chandra’s relation between the Plancherel density a…
This paper studies periodic subgroups of maximal solvable subgroups of the full linear group over an algebraically closed field of arbitrary characteristic. It proves, first for maximal irreducible solvable matrix groups and then in general, that all maximal periodic subgroups of such a maximal solv…
This paper studies the local behavior of trajectories near an isolated singular point of a system of differential equations using generalized Lyapunov functions. It refines earlier definitions by partitioning a neighborhood into domains separated by topological cones and relates the signs of a Lyapu…
The paper gives a general criterion for the existence of wave operators for pairs of self-adjoint operators in a Hilbert space, motivated by limitations of earlier trace-class perturbation results. It introduces a class of admissible real analytic functions of the operators and proves that, under a …
