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 convergence rate for the probability that normalized partial sums of independent bounded random variables remain between two Lipschitz boundary functions on the interval from 0 to 1. It proves that, under zero mean, unit variance, and a uniform boundedness assumption, this boun…
This paper studies locally bicompact solvable topological groups in relation to descending chain conditions on closed subgroups. It proves that such a group satisfies the minimality condition for all closed subgroups exactly when every closed abelian subgroup satisfies the corresponding minimality c…
This paper proves a mean-value theorem for solutions of a linear uniformly elliptic equation in an open multidimensional domain, under Lipschitz, more generally Hölder, regularity assumptions on the coefficients and with right-hand side in an \(L_p\) class. The argument constructs an averaged identi…
This paper develops local duality theorems for arbitrary subsets of an n-dimensional sphere. It defines local homology groups at a point using directed systems of compact subsets and neighborhoods, and defines corresponding Betti groups for complements by inverse limits, with coefficients in dual co…
This paper studies tangentially degenerate multidimensional surfaces in affine or projective space, defined by tangent planes depending on fewer parameters than the dimension of the surface. It analyzes parallel correspondences and Peterson transformations, then proves that every surface of dimensio…
This paper studies the realization of two-dimensional orientable metrized manifolds as surfaces in three-dimensional Euclidean space, extending earlier isometric embedding results for differentiable Riemannian metrics to metrics given intrinsically by distances between pairs of points. The main theo…
This paper studies the Riemann boundary value problem for analytic functions on a multiply connected Lyapunov contour when the coefficient is only measurable. The coefficient is assumed bounded away from zero and infinity and to have, locally at each contour point, argument oscillation less than a f…
The paper studies recurrent functions on the real line in relation to ergodicity, addressing the fact that general recurrent motions need not be strictly ergodic. It defines classes of recurrent functions determined by continuous generating functions satisfying a uniform vanishing mean condition for…
This paper studies when a finite metric space can be embedded isometrically into a unit cube with the Hamming metric, and how to determine all binary codes realizing a given distance matrix. It reformulates the nonlinear realization problem as an integer linear programming problem using characterist…
This paper develops a general construction for describing solutions of extremal problems for real monic polynomials least deviating from zero, especially when the solution has a prescribed number of points of maximum deviation. For a polynomial and bound, the author studies the associated set where …
The paper studies the first boundary-value problem for a quasilinear parabolic equation with a nonlinear term depending on the solution and with homogeneous boundary conditions. It applies the Fourier method using the eigenfunctions of an associated Sturm-Liouville problem, reducing the problem to a…
This paper describes closed densely defined restrictions of a self-adjoint operator with simple spectrum by reducing the problem to multiplication by the independent variable in a space \(L^2_\sigma\). It introduces an orthogonality operation on measurable functions and represents the domain of such…
This note studies Taylor coefficient estimates for holomorphic functions of several complex variables, extending Schur and Carathéodory type results from two variables to n variables. It introduces a special class of circular domains described by a parametric boundary representation, including domai…
The paper studies boundary value problems for second order elliptic and parabolic equations whose coefficients have jump discontinuities across smooth internal manifolds, with motivation from diffusion processes. Using approximation by equations with smoothed coefficients, together with Schauder est…
This note studies positive definite Riemannian spaces whose full groups of motions have dimensions close to the maximal possible value, with particular attention to gaps in the possible dimensions. Using known gap theorems, properties of isotropy subgroups, and semireducible decompositions of the me…
This note addresses Cohn-Vossen’s question on the existence of closed surfaces with more than one linearly independent infinitesimal bending. It constructs a regular closed surface of revolution by prescribing a piecewise meridian involving modified Bessel functions and matching conditions, then ide…
The paper studies the first homogeneous boundary-value problem for a hyperbolic equation arising from a generalized eigenvalue problem, specializing to the string vibration equation with parameter-dependent characteristic directions in an admissible planar domain. It introduces boundary automorphism…
This paper extends Mergelyan’s uniform approximation theorem from closed subsets of the complex plane to closed Riemann surfaces. It establishes necessary and sufficient conditions under which functions continuous on a closed set and analytic at its interior points can be uniformly approximated by r…
This note studies semigroups of almost identity transformations of an infinite set, focusing on congruence-like stable equivalences, endomorphisms, and related partial transformation semigroups. It defines equivalences determined by finite defect thresholds and normal divisors of the group of finita…
This paper examines the geometric meaning of the projective curvature tensor on a differentiable manifold with symmetric affine connection. Using the invariant hyperquadric associated with each local centro-projective space, it defines a natural connection by polar correspondence and compares its cu…
The paper studies the distribution of prime k-twins, pairs of primes of the form p and p plus 2k, with emphasis on gaps between consecutive such pairs. Combining an asymptotic formula obtained by Vinogradov’s method of trigonometric sums with estimates from Selberg’s sieve, it proves gap lower bound…
This note studies boundary behavior and trace problems for functions in weighted Sobolev-type classes, relating them to generalized Sobolev spaces of possibly fractional order. It establishes existence and regularity of boundary limits on subspaces for derivatives of functions with weighted highest …
This note derives topological index relations for analytic functions in a finitely connected Jordan domain when the functions may have finitely many algebraic or transcendental branch points and poles, so that their real and imaginary parts are generally multivalued. By analyzing local representatio…
Krylov studies generalized measures on the space of continuous paths associated with the higher order parabolic equation involving the operator of order 2q, extending questions analogous to Wiener measure. The paper defines the measure on cylindrical sets through the Green function, proves a Feynman…
This paper derives estimates for the Dirichlet problem for second order quasilinear equations with nonnegative coefficient matrix, under either Sobolev generalized second derivatives or classical twice differentiability. The argument is based on a lemma relating bounds on the equation, expressed thr…
The paper studies a one-dimensional free-boundary problem for the heat equation in a time-dependent interval, with prescribed values at the fixed and moving boundaries and a prescribed spatial derivative at the moving boundary. Under specified sign, monotonicity, and convexity assumptions on the bou…
This note proposes a natural definition of inductive dimension for proximity spaces, based on sets that free pairs of far sets, in response to Smirnov’s covering definition of proximity dimension. It proves general inequalities relating this invariant to proximity dimension and to classical inductiv…
The paper develops a parameter variation approach for numerically computing determinants of matrices whose entries depend smoothly on a parameter. It derives the differential identity for the determinant, expressing its derivative as the determinant times the trace of the product of the inverse matr…
This paper proves an a priori maximum estimate for a Dirichlet transmission problem for second order elliptic operators whose coefficients are discontinuous across an interior Lyapunov surface. The solution is assumed continuous across the interface, with a prescribed jump in conormal derivative and…
This note studies confidence estimation for prescribed linear functions of unknown parameters in systems of observation equations when the relative accuracies, or weights, of different groups of normally distributed observations are unknown. Using matrix least squares, Wald’s approach to the Behrens…
This note studies Dirichlet problems for several classes of second order quasilinear parabolic equations in two independent variables on curvilinear trapezoidal domains. It first proves a Hölder continuity estimate for sufficiently smooth solutions of a linear parabolic boundary value problem, then …
This note studies Peterson surfaces, defined as surfaces carrying conical nets and represented by sums of two curves in projective coordinates, with the aim of extending Lie’s theorem on translation surfaces. Using the known classification, up to collineation, of surfaces carrying two-parameter fami…
The paper studies analytic systems of ordinary differential equations whose right-hand sides depend explicitly and periodically on the independent argument, formulated through the construction of a one-parameter family of transformations interpolating between the identity and a given periodic analyt…
This note modifies Lehmer’s variant of the Lobachevsky, Graeffe method for the numerical solution of algebraic equations by replacing Lehmer’s auxiliary symmetric functions with functions that can be computed by the same recurrence program as the transformed coefficients. It derives transformation f…
This paper studies the Dirichlet problem in a half-space for the Beltrami equation with parameter range minus one less than mu less than one, formulated through finite weighted Dirichlet energy. It proves that a solution exists and is unique precisely when the boundary trace belongs to the fractiona…
This note identifies a new class of linear parabolic systems with time-dependent coefficients for which the Cauchy problem satisfies Petrovskii’s correctness condition. The class is defined by grouping unknowns according to derivative weights, requiring the principal part of the associated matrix to…
This paper continues the projective differential-geometric study of conjugate nets whose first or second axis congruences are parabolic. Using a moving projective frame adapted to the net and its Laplace transforms, it derives Pfaffian equations, expresses Darboux invariants, and formulates algebrai…
This paper studies the existence of bounded solutions on the half-axis for certain nonlinear differential systems with triangular principal part and perturbation terms. Using Perron-type conditions on comparison functions associated with the diagonal derivatives, it proves uniqueness under Lipschitz…
This paper develops for groups an analogue of the Baer and McCoy radical from associative ring theory, using commutators in place of multiplication. It defines prime normal divisors and prime groups, characterizes the existence of prime normal divisors by nonterminating commutator sequences, and rel…
The paper studies inhomogeneous multiple Gauss sums associated with integral quadratic and linear forms, including sums over arithmetic progressions modulo an auxiliary integer. It establishes structural formulas such as reduction to complete sums, multiplicativity over coprime moduli, invariance un…
This paper determines the linearizing central normal divisors and kernels of linear representations for noncompact real simple Lie groups. Using the structure of real forms via involutive automorphisms and integral lattices in Cartan subalgebras, it proves that the linearizing divisor of a simply co…
This note studies boundary-value problems for singularly perturbed systems in which a small positive parameter multiplies the highest derivative, extending earlier asymptotic methods from initial-value problems and second-order equations to more general systems. It constructs formal matched expansio…
This note studies a class of stable systems of linear difference equations and the reduction of their associated parameter-dependent matrices to simpler canonical forms. Using Fourier representation, analytic properties of eigenvalues, and local similarity transformations, it shows that under stated…
The paper studies a class of extremal problems for generalized polynomials in locally convex linear topological spaces, where the approximation error measured by a continuous symmetric convex functional is combined with a second convex functional of the coefficients. A dual extremal problem over con…
The paper presents a method for integrating exponential linear functions over regions defined by finite systems of linear inequalities, using contour integral representations of characteristic functions. By reducing the resulting multidimensional complex integrals through residue calculations, the a…
This note applies properties of envelopes of holomorphy to convolution equations in the space of tempered distributions, including linear differential equations with constant coefficients satisfying a specified nonvanishing condition in spacelike directions. By passing to Fourier transforms and usin…
This paper applies the parameter-variation method to the numerical inversion of matrices whose entries depend differentiably on a scalar parameter. Starting from a known inverse at an initial parameter value, the inverse matrix is obtained by integrating the differential equation dB/dλ = −B(dA/dλ)B,…
The paper studies a nonlinear boundary value problem for forced vibrations of a string, seeking a twice continuously differentiable solution that is periodic in time and satisfies fixed endpoint conditions. Extending the author’s earlier treatment for odd integral wave speeds, it reduces the problem…
The paper addresses the problem of justifying a double spectral representation for generalized functions of two variables, motivated by double dispersion relations in mathematical physics. It defines a complete countably normed space of test functions with specified differentiability, integrability,…
