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 invariant indecomposable measures for continuous one-parameter dynamical systems on compact phase spaces and relates them to indecomposable measures for individual time maps. It proves that, for any nonzero time, an indecomposable invariant measure of the flow can be represented a…
The paper studies closed subsets of Cantor cubes and their images, with emphasis on dyadic bicompacta and the role of neighborhood character, stratifications by coordinate layers, and associated skeletons. It develops auxiliary propositions relating stratifications of closed sets to bounds on neighb…
The paper studies a singularly perturbed Cauchy problem for a first-order differential equation in a real Banach space, where the nonlinear term admits a convergent Fréchet power expansion and the leading linear operator may be unbounded. It gives sufficient spectral and solvability conditions under…
The paper studies spectral decompositions for certain bounded non-self-adjoint operators in reflexive Banach spaces, focusing on operators with zero-dimensional spectrum and controlled resolvent growth near the spectrum. It constructs invariant subspaces by integrating the resolvent against suitable…
The paper extends index formulas based on the argument principle from analytic functions in plane domains to automorphic functions and mappings between domains on finite-sheeted Riemann surfaces. By uniformizing such mappings with automorphic functions, it derives a relation equating the boundary ro…
The paper studies eigenvalue problems for second order differential equations on the real line in which the spectral parameter enters nonlinearly and the coefficient may be complex, with emphasis on large values of a real parameter. Using asymptotic expansions in the complex plane, the authors relat…
This note studies when degeneracy of simple restricted Lie algebras over an algebraically closed field of characteristic p greater than 5 implies strong degeneracy, meaning the existence of a nonzero element whose adjoint square is zero. It proves that strong degeneracy follows under conditions invo…
This paper studies analytic continuation properties of the derivative of the spectral function for self-adjoint Sturm-Liouville operators on the half-line with boundary condition at the origin and potentials of the form q(x) = -x^alpha + p(x). It proves meromorphicity results for the unperturbed and…
This paper studies ranks of systems of open sets, including Nagata rank and related small, large, and local variants, and relates these notions to covering dimension. It gives characterizations of finite dimensionality for normal spaces, bicompacta, compacta, and metric spaces in terms of the existe…
The paper develops finite difference equations for the approximate solution of the Dirichlet problem for the Euler, Poisson, Darboux equation in axisymmetric coordinates. Extending a previously proposed construction based on local representations of solutions by special systems of functions satisfyi…
This paper studies the symmetry groups of frieze ornaments in real Euclidean space of dimension n+1, generalizing earlier results for four-dimensional friezes and Shubnikov’s concept of antisymmetry. It defines elementary sets, frieze ornaments, geometric equivalence of symmetries, rotations, and al…
The paper studies the closure of discrete direct products through a construction called the space of convergent sequences for a family of similar uniform spaces with distinguished base points. It establishes basic embedding, density, separation, compactness, local compactness, and completeness prope…
This paper derives large deviation estimates for two metric problems concerning incomplete systems of residues, extending questions arising from limit theorems of Davenport and Erdős and of Postnikov. For short sums of Legendre symbols over intervals, the argument uses even moment estimates together…
The paper studies expansions in root vectors for operators obtained by weakly perturbing a self-adjoint operator with discrete spectrum in a separable Hilbert space. Under conditions relating the perturbation to powers of the unperturbed operator and to the growth of the eigenvalues, it proves that …
This paper studies the stability of the absolutely continuous spectrum of a self-adjoint operator under symmetric perturbations, extending results of Kuroda on the existence of wave operators and the resulting unitary equivalence of absolutely continuous parts. It proves a generalized criterion in w…
The paper addresses the problem of explicitly constructing, for an arbitrary fixed real number lambda greater than 1, a real number theta such that the fractional parts of theta lambda^x are uniformly distributed. Extending beyond earlier constructions for integer bases and known special noninteger …
The paper studies nonlinear singular integral equations with a Cauchy kernel on a finite interval, focusing on bounded solutions in Hölder spaces under conditions that allow the kernel to grow arbitrarily fast with respect to the unknown function. Using estimates for Cauchy-type singular integrals a…
This paper studies nonstationary diffraction of a plane wave by conical obstacles and shows that, for the incident wave proportional to the minus one half power of the retarded time, the automodel solution inside the spherical front can be reduced to a Dirichlet problem for the Laplace equation. The…
This paper studies a specially constructed first order system of partial differential equations and uses it to analyze linear ordinary differential systems with quasiperiodic coefficients. It defines fundamental systems of solutions, introduces reducibility by Lyapunov type transformations, and exte…
This paper studies when locally normal groups can be embedded isomorphically in direct products of finite groups or in related product classes. It proves that a finitely approximable locally normal group with countable center embeds in a direct product of finite groups, using a lemma on locally norm…
The paper studies the justification of the Fourier method for a mixed initial boundary value problem for equations of the form Au plus the second time derivative of u equals f, where A is a formally self-adjoint uniformly elliptic operator of order 2m in a bounded domain. Using generalized eigenfunc…
This paper studies additive abstract set functions on measurable subsets of a domain in Euclidean space with values in a Banach space, focusing on normality, absolute continuity, translation continuity, and convolution operations in the spaces \(\Phi_p\), \(\overline{\Phi}_1\), and related Sobolev-t…
This paper studies extremal properties of meromorphic functions with prescribed principal parts in bounded finitely connected domains with analytic boundary, using special functions determined by boundary values on straight lines of fixed inclination. It defines exterior area for such mappings and p…
Golovin develops a framework for polyidentical relations in groups, generalizing ordinary verbal identities by allowing words whose variables range over distinct specified subgroups of a group. The paper defines polyverbal subgroups, equivalence of systems of polyidentities, neutral polywords, and t…
This paper studies a single-server queue in which customers arrive in random batches at renewal epochs, are served individually, and may experience an additional random start-up time when a batch finds the server idle. Under finite mean assumptions and the stability condition that the mean service r…
The note proves an existence theorem for a Frankl-type boundary-value problem for the Lavrent'ev-Bitsadze equation of mixed elliptic-hyperbolic type in a domain bounded by vertical half-lines, a smooth arc, and characteristics. The argument constructs a Green function using reflection and a Tricomi …
This paper characterizes strongly paracompact normal spaces in terms of their position inside the Stone-Cech compactification. It introduces the notion that a space is paracompactly situated in an extension when every neighborhood of the space contains a smaller paracompact neighborhood, and proves …
This note studies when the index of an elliptic boundary-value problem for a Petrovskii elliptic system in a bounded smooth domain is independent of the coefficients of the differential operator in the interior of the domain. Comparing two systems with the same boundary data near the boundary, the a…
The paper studies pairs of T-congruences in which corresponding rays have constant distance and constant angle, using a moving rectangular trihedron adapted to the congruence of common perpendiculars. By deriving and transforming the differential equations governing the focal abscissas, ray position…
The paper addresses the problem of determining whether the zero singular point of a planar continuous vector field is isolated and computing its Poincaré index when the field is represented by a finite Taylor expansion with a higher order remainder. It develops a finite algorithm based on successive…
This paper studies the unitary representation of a semisimple Lie group on \(L_2(G/\Gamma)\), where \(\Gamma\) is a discrete subgroup and the quotient need not be compact. It develops the method of horospheres to isolate a subspace \(L_2^0(G/\Gamma)\), consisting of square integrable functions whose…
This paper studies class numbers through finite segments of Euler products associated with Dedekind zeta-functions, congruence zeta-functions, and Hecke or Artin L-series. Using zero-free information, including the possible presence of a Siegel zero, it derives formulas expressing the class number o…
This note characterizes semigroups whose complete lattice of subsemigroups, with the empty set adjoined, has relative complements. Using a lattice-theoretic criterion for relative complementation of intervals, it proves that this property holds exactly for semigroups in which every element is idempo…
This note studies when Gaussian measures induced on function space by real processes with stationary Gaussian increments and zero mean are equivalent or mutually singular. It formulates sufficient conditions in terms of the asymptotic behavior of the spectral densities, especially for pairs whose de…
This paper studies periodic solutions and Lyapunov stability for systems of ordinary differential equations with periodic right-hand sides that preserve the nonnegative cone. Using the Poincare-Andronov operator and the theory of nonlinear positive and concave operators, it formulates growth and dec…
This paper studies the mixed initial boundary value problem for a hyperbolic equation whose elliptic spatial operator has discontinuous coefficients across internal interfaces. Using the Fourier method with eigenfunctions of the associated self-adjoint transmission problem, it proves uniqueness and,…
The paper studies the Dirichlet problem in the unit disk for a finite system of elliptic equations of the form \(A u_{xx} + 2B u_{xy} + C u_{yy} = 0\), extending an earlier two-equation case to arbitrary finite order under the same characteristic-root assumptions. It derives an explicit representati…
This note studies boundary correspondence for homeomorphic Q-quasiconformal mappings of a ball in N-dimensional Euclidean space. It introduces regular sequences of subdomains and boundary elements, proves that regular sequences in a ball contract to single boundary points, and shows that such sequen…
The paper studies Bernstein’s problem on weighted polynomial approximation on the real axis in the case where polynomials are not dense in the full weighted space of continuous functions. It introduces an extremal function defined over entire functions of zero degree and proves a necessary and suffi…
This note studies the uniqueness of extremal functions in sharp estimates for Taylor coefficients of bounded holomorphic functions of two complex variables. Using diagonal series representations, boundary values in Hardy class H1, and integral formulas for coefficients, it derives coefficient estima…
This note studies the sign of the Green’s function for a linear second order difference boundary value problem with zero endpoint conditions. After defining the associated Cauchy function and a notion of critical point, it shows that the usual Sturm type zero separation behavior for differential equ…
This paper extends known results relating growth indicators and zero distributions of entire functions of finite order and completely regular growth to subharmonic functions in multidimensional Euclidean space. It develops analytic properties of the spherical indicator, introduces subspherical funct…
This note studies inequalities and convexity descriptions for eigenvalues and singular values of sums and products of linear operators. Building on geometric majorization lemmas derived from convex hull arguments and the Krein-Milman theorem, it gives finite-dimensional results for singular values o…
This note studies simultaneous uniform approximation of functions and their derivatives by entire functions of bounded degree, focusing on uniformly almost-periodic functions whose Fourier exponents have bounded local density. It defines approximation constants comparing the errors for derivatives u…
This paper studies the structure of solution sets for nonlinear parabolic evolution equations and mixed boundary value problems, extending the Kneser Hukuhara connectedness principle from ordinary differential equations to parabolic settings. Using a topological connectedness theorem for fixed point…
This paper studies a one-phase generalized Stefan problem for a parabolic equation with nonlinear dependence on the unknown function, its spatial derivative, and the moving boundary and velocity. The problem is reformulated as a system of integral equations using Green’s functions for the heat equat…
This note describes the general form of solutions to homogeneous linear partial differential equations with constant coefficients in broad spaces of ordinary and generalized functions, including Gevrey-type spaces. Extending earlier formulations of the Ehrenpreis fundamental principle, it represents…
The paper studies the Cauchy problem for second order parabolic equations in Euclidean space whose coefficients may grow at infinity. It develops an operator theoretic approach, using a weighted transformation of the equation, nonpositive maximal operators in Hilbert space, and an analogue of essent…
This paper studies the analytic reducibility of ordinary differential equations in a neighborhood of an invariant torus filled with quasi-periodic trajectories. Assuming that the linear variational system with conditionally periodic coefficients has already been reduced to constant coefficients, the…
The paper studies perturbation determinants for pairs of operators in a separable Hilbert space whose perturbations, or resolvent differences, are nuclear, and relates these determinants to trace formulas. It establishes results for self-adjoint operators with nuclear difference, including an integr…
