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 gives probabilistic formulations and asymptotic estimates for two combinatorial optimization problems with random data: the Euclidean traveling salesman problem and the assignment problem. For independent random points in Euclidean space with density, it constructs lower and upper random e…
The paper studies when a second-order ordinary differential equation with two-point boundary data can be represented by a Massau nomogram, so that solutions are determined by collinearity relations on two scales and a point of constants. It proves a necessary and sufficient condition: the general so…
This paper extends Marchenko’s spectral expansion theory for non-self-adjoint singular second order differential equations from the half-line to the whole real line. For the equation with locally summable complex potential, the author uses transformation operators relating the fundamental solutions …
This paper studies extremal problems for analytic functions in the unit disk equipped with Orlicz and Luxemburg norms, extending known results for Hardy classes. It defines the corresponding analytic Orlicz classes, identifies them with boundary Orlicz spaces intersected with H1, and establishes com…
This paper derives index formulas for systems of two-dimensional singular integral equations on a smooth closed surface and for boundary value problems for systems of harmonic functions in a three-dimensional domain. For a normally solvable singular integral system with invertible symbol, the index …
The paper establishes a criterion for bounded solvability of a Cauchy, Goursat problem for linear partial differential equations in several variables with Banach-space-valued unknowns and a distinguished highest derivative term. Under compactness and weak variation at infinity assumptions on the ope…
The paper develops implicit finite difference schemes for nonstationary partial differential equations in which the main operator is split into lower dimensional, often one dimensional, factors. This construction is presented as a way to retain absolute stability while reducing the computational cos…
This paper studies invariants of finite undirected multigraphs with loops and parallel edges through deletion and contraction recurrences for normal edges. It defines polynomial functions satisfying these recurrences, establishes their invariance properties, multiplicative behavior, and special valu…
The paper studies isolated equilibrium states of analytic or sufficiently differentiable autonomous differential systems in n-dimensional space when the linearization has one zero characteristic root and all remaining roots have nonzero real parts. Using Lyapunov’s normal form, the analysis classifi…
The paper studies the sign behavior of the Green function for an n point linear boundary value problem for finite difference equations. Extending Mammana’s theory to difference equations, it proves that nonoscillation of the associated homogeneous equation is equivalent to a factorization of the dif…
This paper studies an inverse problem in radiative transfer: determining the scattering indicatrix of a medium from the asymptotic angular distribution of monochromatic radiation in a thick layer. For a class of nonnegative square-integrable indicatrices with positive absorption, the author analyzes…
This paper develops a method for constructing generalized discontinuous solutions for a system of two first order quasilinear hyperbolic conservation laws. Under structural assumptions expressed in Riemann invariants, including monotonicity, Hugoniot curve conditions, and shock admissibility inequal…
The paper studies estimation of an unknown probability density from independent observations by projecting the empirical measure onto finite-dimensional subspaces of a weighted Hilbert space, thereby generalizing the histogram method. It analyzes the tradeoff between approximation error and sampling…
This paper studies perfect measures and their relation to measurable partitions, Lebesgue spaces, subspaces, and regularity properties in topological settings. It proves that a complete measure is perfect exactly when every factor measure with respect to a measurable partition is a Lebesgue measure,…
This paper studies a recurrent vertex-edge function of graphs defined by deletion and contraction-type operations on the first ordered edge, with values in a ring generated by parameters. It gives necessary and sufficient algebraic conditions under which the function is independent of the chosen ord…
This paper studies when a system of exponential functions with complex exponents forms a Riesz basis in its closed linear span in an interval \(L^2(-\sigma,\sigma)\). It introduces the critical quantity \(\tau(\Lambda)\), defined through uniform minimality, and the class \(K\) of exponent sequences …
The paper studies inverse spectral problems for ordinary differential operators of order n at least 2 with bounded coefficient derivatives and boundary conditions defined by linear forms. It defines a spectral characteristic consisting of eigenvalues and norming constants for a family of boundary va…
This paper develops an algebraic theory of generalized analytic functions on closed Riemann surfaces of genus greater than two, for equations of the form U_{\bar z}=B(z)\overline{U}. Using a Cauchy kernel and the associated Fredholm integral equations, it formulates adjoint equations, solvability co…
This note extends several tools of representation theory from locally compact unimodular groups to ring groups, with emphasis on the compact case. It defines representations through the group algebra, studies the regular representation, introduces coefficients, characters, conjugates, and a generall…
This paper studies affine connections on even-dimensional manifolds endowed with an almost complex structure, focusing on conjugate and symmetric conjugate connections associated with a given symmetric affine connection. It introduces tensors measuring the relation between the original, conjugate, a…
The paper studies whether a linear operator assigning trigonometric polynomials of degree at most n can attain, on a whole function class, the same maximal error as best uniform approximation. For periodic classes defined by a concave modulus of continuity, the author proves that such a best linear …
The paper studies a one-parameter discontinuous point transformation of the real line into itself, motivated by problems in oscillation theory and automatic control, where a single jump discontinuity appears as the parameter becomes positive. It defines a notation for cycles generated by alternating…
This note continues Kurosh’s theory of radicals in groups by reformulating radicality axioms in terms of invariant, attainable, ascendant, and subinvariant subgroups. It gives criteria for the minimal radical class generated by a homomorphically closed class M, showing that a group belongs to this c…
This note develops an operational calculus for the third order operator obtained by iterating differentiation with multiplication by the independent variable, an operator associated with a special third order differential equation and generalized Bessel type functions. The construction defines suita…
This note addresses a Phragmen Lindelof type boundedness problem for harmonic functions in half-cylinders, in which the critical growth constant is related to geometric widths of the planar base domain. Building on earlier upper estimates involving the external width, it proves the complementary low…
This note proposes a unified definition for classes of Poisson-stable motions in metric dynamical systems, based on the dependence of a return-time bound on time and interval parameters. It identifies a new class, called pseudorecurrent motions, situates it between recurrent motions and two-sided Po…
This paper studies estimation of the damping and frequency parameters of a two-dimensional stationary Gaussian Markov process represented as a complex Ornstein-Uhlenbeck process. Using the likelihood with respect to a product of Lebesgue and Wiener measures, it derives sufficient statistics and maxi…
This paper studies the reduction of nonconstant regular solutions of linear elliptic differential equations in a bounded domain with excluded subdomains representing singularity nests. Using Green’s functions for an elliptic operator and its adjoint, it derives surface integral formulas that decompo…
This paper studies the embedding problem for finite degree algebraic number fields under the assumption that the relevant Galois group is a p-group. It analyzes how a solution may be constructed by successive p-steps through invariant subgroups, focusing on the obstruction to carrying out the r-th s…
This note studies the discrete spectrum of the Dirichlet Laplacian in three-dimensional domains that are asymptotically cylindrical, focusing on eigenvalues lying below the threshold given by the first transverse eigenvalue of the limiting cylinder. Using the splitting principle and Courant variatio…
This note establishes Wiman-Valiron type relations for entire transcendental functions of several complex variables at points where the maximum modulus is attained. Instead of using the central index, it introduces growth functions derived from the maximum modulus on circular, almost circular, and p…
The paper studies a three-dimensional analogue of the Beltrami equation, formulated as an elliptic first-order system for a four-component real vector with matrix coefficients satisfying a uniform bound. Using singular integral operators and estimates in Lebesgue and Hölder spaces, the equation is r…
This note improves the error term in Mertens’ asymptotic formula for the finite Euler product over primes. Using analytic estimates for the logarithmic derivative of a truncated Euler product together with I. M. Vinogradov’s zero-free region for the Riemann zeta function, the paper proves a more gen…
This note studies the distinction problem for Frommer normal domains of the second type associated with first order differential equations near a singular point, where the Hartman-Wintner theorem ensures existence of at least one curve tending to the singular point. For a class of equations whose ri…
The paper studies the regularization of products of generalized functions of causal type, a problem motivated by quantum electrodynamics and formulated for products involving linear combinations of vector variables and derivatives of such functions. The method replaces each generalized function by a…
The paper studies elliptic boundary-value problems for three-dimensional vector fields with axial symmetry, formulated in a meridian half-plane with prescribed source and vortex distributions and a general linear boundary condition. The problem is reduced to a generalized analytic equation with a Ri…
The paper develops a grid method for initial boundary value problems for higher order parabolic equations with separable spatial variables on a multidimensional rectangular domain. It proposes an alternating direction type difference scheme that reduces each time step to a sequence of one dimensiona…
This paper studies a boundary value problem for a system of first order differential equations in which a small parameter multiplies the derivative of one group of variables. Under smoothness and spectral separation assumptions for the linearization along the degenerate solution, it constructs match…
This paper develops an algebraic representation of semicontinuous multivalued mappings by means of generalized homomorphisms in partially ordered additive semigroups. It defines suitable semigroups of bounded integer valued lower and upper semicontinuous functions, introduces transformations preserv…
This note further analyzes the correspondence between excessive functions and additive functionals for homogeneous Markov processes. For a standard right-continuous Markov process, it proves that every finite excessive function can be decomposed into the sum of a regular harmonic component, a singul…
This note studies bounds for Dirichlet L-functions on the critical line near the real axis, specifically for nonprincipal characters modulo a prime p and |t| at most 1. Building on Linnik’s shortened functional equation and Burgess’s method for character sums, it proves an estimate for L(1/2+it, chi…
This paper addresses whether Freudenthal-type representations of compacta by polyhedral spectra extend to arbitrary bicompacta, especially with onto projections and prescribed dimension. It constructs two bicompacta, denoted AP and AP', as limits of transfinite spectra, and proves that neither is th…
The paper studies a compact completion of the countable set obtained by encoding each natural number as a binary fraction according to its divisibility by integers. Using the arithmetic of polyadic numbers, it defines a metric based on the first prime power at which two divisibility patterns differ …
This note studies boundary value problems for second order parabolic equations whose coefficients have first kind discontinuities across finitely many smooth surfaces. Using smoothing of the coefficients, partitions of unity, local coordinate flattening of discontinuity surfaces, a priori estimates,…
The paper studies approximation of periodic, possibly nondifferentiable functions by a class of positive linear operators defined through nonnegative trigonometric kernels, viewed as summability methods for Fourier series. It extends Korovkin type asymptotic results to these operators, giving necess…
The paper develops criteria for continuity and complete continuity of linear and nonlinear integral operators acting between spaces of measurable functions, including cases where the exponent may be below one. For linear operators, conditions on the kernel and its adjoint are combined with interpola…
This note proves uniqueness theorems for several boundary-value problems for equations of mixed type, motivated by Frankl’s formulation of transonic flow around a wedge and related problems for Chaplygin, Tricomi, and Lavrent’ev-Bitsadze type equations. The argument studies the location of possible …
This paper formulates averaging theorems for systems of differential equations with a small parameter in which the mean values may depend on the particular trajectory of the degenerate system used for averaging. Under detailed regularity, transversality, existence, and uniform averaging assumptions,…
This paper proposes a generalized framework for spectral theory of non-self-adjoint operators when invariant subspaces are complete but need not yield unconditionally convergent eigenvector expansions. It introduces generalized resolutions of the identity on rings of Borel sets, constructs associate…
This paper studies optimal control problems for processes governed by the one-dimensional heat equation with boundary or initial controls bounded in magnitude. It proves existence of controls minimizing terminal deviation functionals, analyzes conditions under which such controls are nonunique, and …
