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 studies the relation between topological completeness and order, or structural, completeness in normed and locally convex partially ordered linear spaces. It proves that Banach lattice-like structures with suitable projection properties are structurally complete, or conditionally sigma-com…
The paper studies one-sided boundary-value problems for analytic and piecewise analytic functions, in which boundary relations involve limiting values taken on only one side of a Lyapunov contour, possibly after an orientation-preserving or orientation-reversing transformation of the contour. It red…
This note proposes a formulation of dynamical systems without uniqueness as semigroups of multivalued mappings of a topological space, motivated by differential equations with multivalued or discontinuous right hand sides and by general topological dynamics. It defines the basic continuity and compo…
This paper studies the resolvent of the Schrödinger operator for a nonrelativistic three-particle system with pair interactions satisfying decay and Hölder-type regularity assumptions. Developing an integral-equation approach, it represents the full resolvent in terms of two-particle resolvents and …
This paper studies extremal problems for linear operators mapping continuous periodic functions to trigonometric polynomials while reproducing prescribed lower order polynomials. It characterizes operators of least norm in the classes considered, expresses their norms through a minimizing kernel, an…
The paper studies a boundary value problem proposed by S. L. Sobolev for a class of linear partial differential equations involving time derivatives of second order spatial operators in a bounded planar domain with smooth positively curved boundary. It constructs solutions satisfying the homogeneous…
This note constructs, for each integer base g at least 2, a real number alpha whose sequence of fractional parts {alpha g^x} is uniformly distributed with an improved discrepancy estimate. The construction follows Korobov’s method using normal periodic systems, repeating truncated systems a prescrib…
This paper studies estimation of the parameters of a stationary Gaussian Markov process observed continuously on a finite interval, focusing on the mean, variance, and correlation decay parameter, with the diffusion coefficient treated as exactly determined by a single realization. Using likelihood …
This note studies representability of commutative formal groups over an algebraically closed field of characteristic p, contrasting the commutative case with known results for noncommutative formal groups. It relates the local formal group structure of an abelian variety over a finite field to the p…
The paper studies when selected ordinary double points of a real plane algebraic curve can be varied by small perturbations of the curve while preserving the total configuration of simple singularities. It formulates variability in the parameter space of curves of fixed degree and relates it to line…
The paper constructs finite-dimensional difference models for problems of mathematical physics, motivated by Kolmogorov’s question of approximating the two-dimensional viscous incompressible Navier-Stokes equations while preserving an energy dissipation law. It defines discrete analogues of gradient…
This note proposes an axiomatic framework for Lipschitz spaces, intended to capture properties invariant under mappings satisfying a local Lipschitz condition. The construction uses filters on finite classes of pairs in a set, defines separated and strongly separated Lipschitz structures, and shows …
This paper studies the classification up to orientation preserving diffeomorphism of simply connected smooth manifolds of dimension at least five that are homotopy equivalent and have compatible stable normal bundles. Using Thom spaces of normal bundles, transversality, normal framings, and surgery …
This paper derives trace formulas for the Schrödinger operator in three-dimensional space with a smooth rapidly decreasing potential. It develops an asymptotic expansion for the resolvent kernel, relates the trace of the resolvent difference to the scattering operator and scattering amplitude, and u…
This paper studies local bifurcations of simple double points and cusps of real plane algebraic curves through the parameter space of curves of fixed degree. It formulates analytic elements in coefficient space describing curves with prescribed real or conjugate imaginary nodes and cusps, gives the …
This note treats a probabilistic problem in optimal control: estimating the probability that a Markov process in \(n\)-dimensional Euclidean space intersects a small moving surface during a prescribed time interval. Building on earlier work of Mishchenko and Pontryagin, it presents Kolmogorov’s simp…
This paper proves a uniform approximation theorem for generalized analytic functions satisfying first order equations of the form w_{\bar z}+A(z)w+B(z)\overline{w}=0 with coefficients in L_{p,2}, p>2. The argument reduces special cases to approximation of analytic functions by rational functions wit…
This paper studies analytic functions in the unit disk whose integral mean of order delta is bounded, deriving sharp estimates for their values, derivatives, and related extremal quantities. Using Cauchy integral formulas, Hölder and Schwarz inequalities, automorphisms of the disk, and known coeffic…
This paper studies the long-time behavior of the action as an adiabatic invariant for one-degree-of-freedom Hamiltonian systems whose analytic Hamiltonian depends slowly and periodically on time. It argues that, unlike the linear oscillator where parametric resonance can accumulate changes, a nonlin…
This note studies the fundamental equations for realizing a surface with a prescribed metric in Euclidean space, using semigeodesic coordinates to reduce the Gauss and Peterson-Codazzi relations to two quasilinear equations. For negative Gaussian curvature, the characteristic curves are identified w…
This paper studies continuous Hermitian-indefinite kernels with a finite number of negative squares that satisfy an invariance relation with respect to an ordinary differential expression. Using the associated Pontryagin space and self-adjoint extensions of the induced operator, it proves that after…
This note studies a two-point boundary-value problem for a first-order system of two ordinary differential equations under angular boundary conditions. Using polar coordinates and differential inequalities, it develops comparison theorems for angular functions of solutions and introduces classes cha…
The paper studies bifurcations in systems of ordinary differential equations depending on a parameter, focusing on the birth of periodic motions from trajectories that leave an equilibrium and return to it in n-dimensional space. It first treats the case of a saddle-node equilibrium with one zero ch…
This paper studies the error of summation methods for Fourier integrals in spaces \(L_p(-\infty,\infty)\), comparing it with best approximation by entire functions of bounded degree. It establishes lower and upper estimates for the deviation \(R_\lambda(f;\varphi)\) in terms of the approximation qua…
This paper develops an analogue of Herbrand’s theorem for a sequent formulation of the pure constructive, intuitionistic predicate calculus with multiple disjunctions. It introduces Skolem function systems, lexical examples, regular junctions of examples, and corresponding normality and regularity c…
This note extends Sobolev’s spaces of abstract additive set functions from bounded domains to spaces on all of Euclidean space and studies Fourier transforms in this setting. It defines the Banach spaces of such set functions, examines normality, translation continuity, density of finite functions, …
The paper studies boundary value problems for second order systems of partial differential equations of mixed type with symmetric matrix coefficients, hyperbolic in one half-plane and elliptic in the other. It formulates a mixed-domain problem with boundary data prescribed on part of the boundary an…
This paper establishes criteria for systems of analytic functions in a disc to form quasi-power bases in spaces of analytic functions. Using the representation of these spaces as projective limits of Banach spaces and applying Fredholm theory to associated linear operators, the authors extend earlie…
This note studies method of lines approximations for one-dimensional parabolic and hyperbolic boundary value problems whose coefficients and derivatives have finite jump discontinuities along fixed spatial lines. It constructs homogeneous differential-difference schemes on meshes aligned with the di…
This note studies the negative spectrum of the multidimensional Schrödinger operator Mh u = minus h Delta u minus P(x)u in L2(Rn), for n at least 3 and nonnegative locally bounded potential P. Using capacity estimates for condensers and closed sets, it formulates criteria for positivity inequalities…
The paper develops a general framework for monotone two-sided approximation methods for equations in partially ordered convergence groups, extending earlier treatments in conditionally complete ordered linear structures and topological groups. It defines partially ordered and semi-ordered convergenc…
The paper continues the study of systems of nonspecial subgroups of finite groups by introducing oriented subgroups, oriented Pi-systems, and indecomposable Pi-systems. It establishes existence results for oriented Pi-SC systems in nonspecial groups and examines how dispersiveness affects the possib…
This paper studies the construction of statistically similar regions and zonal statistics for one-parameter families of probability measures on Euclidean space. It identifies a broad class of distributions whose densities satisfy a linear differential equation in the parameter, with coefficients dep…
This paper studies a class of congruences of conics in three-dimensional projective space for which one focal surface degenerates to a point and two nondevelopable focal surfaces carry conjugate nets related by Laplace transformations. Using a canonical moving frame, it derives the differential form…
The paper studies inverse semigroups with zero and a finite number of idempotents, giving a structural description through finite ideal composition series whose factors are completely simple semigroups with finite identity defining matrix. It introduces a matrix of maps into semigroup algebras that,…
This note studies boundary value problems for second order elliptic equations whose coefficients are discontinuous across an interior hypersurface. Using Sobolev spaces adapted to the interface conditions, the authors formulate generalized solutions and prove a Gårding type inequality, which yields …
This note studies Beurling-type semigroups of real numbers divided into finitely many multiplicative classes, under uniform asymptotic counting assumptions with an unbounded class parameter. It proves a general theorem giving bounds for the existence, in every class, of a basic number in short multi…
This paper studies the discrete spectrum of the radial Schrödinger equation on the half-line with a centrifugal term and a potential whose behavior at infinity begins with Coulomb-type terms. Using variational characterization of the lowest eigenvalue, asymptotic analysis, and a spectral approximati…
The paper introduces and studies quasi-operator groups, or Ω-groups, generalizing Kontorovich’s R-groups by allowing operators from a principal ideal ring, and develops basic notions such as Ω-admissibility, Ω-isolation, ΩR-groups, and Ω-locally cyclic subgroups. It records extensions of standard re…
This paper studies embedding problems for several classes of algebras over a fixed field, including arbitrary nonassociative, commutative, anticommutative, and Lie algebras. It defines systems of algebraic equations over free products, introduces a notion of strong algebraic closedness based on cons…
This paper studies lattice coverings of n-dimensional Euclidean space by equal balls and focuses on the lattice constructed from a regular Selling frame, whose metric form is Voronoi’s principal form of the first type. Using Dirichlet regions, Selling parameters, and a related variational problem pr…
This paper studies the asymptotic distribution of eigenvalues for bilinear forms associated with higher order elliptic operators whose leading coefficients are weighted by a power of the distance to the boundary, producing boundary degeneration. Working in weighted Sobolev spaces and using estimates…
This paper studies uniqueness and bending of simply connected surfaces of strictly positive Gaussian curvature with smooth boundary under various boundary constraints. Using an index associated with a continuous field of directions along the boundary, it establishes criteria for when an isometric tr…
This note studies V. A. Steklov’s conjecture that positivity of the weight is necessary and sufficient for boundedness of an orthonormal polynomial system on an interval. Working first with polynomials orthonormal on the unit circle, the paper gives sufficient conditions, involving pointwise bounded…
This paper studies expansions in eigenfunctions for a non-self-adjoint system of differential equations of arbitrary even order on the half-axis in the space of vector functions. Under exponential decay assumptions on the matrix coefficients and regularity conditions on the boundary forms, it constr…
This note revisits Regge’s theorem on the analytic continuation of functions expanded in Legendre polynomials, where the coefficients are values of an analytic interpolating function in a half-plane. It argues that the theorem follows from the classical Le Roy-Lindelöf theorem on power series togeth…
An iterative finite difference method is proposed for the first boundary value problem for the Poisson equation, using the standard five point approximation on rectangular grids. The method alternates one dimensional implicit steps in the coordinate directions and is analyzed through the eigenfuncti…
The paper studies the asymptotic enumeration of primitive integer matrices of order three with prescribed determinant N, restricted after scaling to a fixed bounded domain in the group of unimodular matrices. It proves that, as N tends to infinity, the count is asymptotic to the Haar measure of the …
This paper studies nondegenerate congruences of parabolas in equiaffine geometry under assumptions on a distinguished focal surface. A canonical moving frame is constructed, yielding structure equations, invariants, the equation of the parabola, and the determination that the general congruence depe…
