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 when positive definite even linear functionals on spaces of entire test functions admit a unique representation by two measures, one associated with cosine kernels and the other with hyperbolic cosine kernels. By passing to the Fourier transform, the problem is reduced to uniquene…
This paper proves existence for a boundary value problem for the Blasius equation \(y''' + 2yy' = 0\) with matching conditions at the origin and prescribed limiting values of \(y'\) at positive and negative infinity. The argument develops qualitative properties of solutions, including nonvanishing a…
The paper studies a Hilbert boundary-value problem for analytic functions in a finite or infinite domain bounded by a smooth contour, with a boundary condition involving a homeomorphic involution of the contour. The problem is reduced to equivalent conjugation conditions and then to Fredholm integra…
This note studies relations between the real and imaginary Hermitian components of Volterra operators in Hilbert space, particularly their membership in Schatten classes and related compact operator ideals. Using an interpolation lemma for operator-valued holomorphic functions, triangular representa…
This paper studies the Riemann boundary value problem on Lyapunov contours for one or several pairs of analytic functions when the boundary coefficient is only measurable. Using functional analytic methods, it establishes Fredholm type results for scalar coefficients in a specified class, including …
This paper studies special pairs of T-congruences whose corresponding rays have equal focal distances and equal angles between their focal planes. Using a moving rectangular trihedron along the congruence of common perpendiculars, the author derives differential systems characterizing two types of s…
The paper studies planar differential systems that are small time-periodic perturbations of Hamiltonian systems with a center whose surrounding closed trajectories are bounded by separatrices through saddle points. For a fixed initial time, it formulates the problem of determining the set of initial…
This note studies the local relationship between a nonlinear differential system near a hyperbolic singular point and its linearization. Building on earlier topological equivalence results, it imposes a stronger smallness condition on the nonlinear term, expressed through a logarithmically weighted …
The paper introduces singular operators of arbitrary nonnegative order on compact smooth manifolds, unifying differential operators and singular integral operators within a common symbolic framework. It defines their principal symbols intrinsically on the nonzero tangent bundle, proves basic symboli…
The paper studies extremal problems for functions represented by integrals of nonnegative polynomials subject to several linear conditions on their coefficients, with attention to nonsymmetric intervals and cases including monotone behavior on a half-axis. It establishes structural restrictions on e…
This paper studies the Green’s function for an nth order linear ordinary differential equation with multipoint boundary conditions given by linear functionals of derivatives at prescribed points. Assuming the corresponding homogeneous problem has only the trivial solution, the author derives an expl…
This note addresses whether the completion by intersections or cuts of a Dedekind lattice with complements must itself be Dedekind. Using the lattice of subspaces of a Hilbert space, it studies the ordered set consisting of all finite-dimensional subspaces and their orthogonal complements, showing t…
This paper studies integral error functions of arbitrary real order, defined as solutions of a second order differential equation and represented by an integral for suitable indices. It derives series and asymptotic representations for positive and negative real arguments, treating separately positi…
This paper studies how membership of a periodic function in Nikol’skii’s classes can be characterized through its Fourier coefficients, rather than through best trigonometric approximation. Using the known equivalence between these classes and rates of best approximation, together with Hausdorff-You…
The paper develops projective differential geometry for an n-dimensional surface in a projective space of dimension 2n minus 1. Using canonization of a moving frame, it proves a general lemma for fixing components of a geometric object and applies it to define asymptotic directions and associated ca…
This note studies best approximation of functions on a bounded nonseparating continuum by finite linear combinations of elements of a basis of analytic functions. Building on Erokhin’s extension of Bernstein’s theorem and using the principal basis of the space of functions analytic in a surrounding …
This note establishes several Sylow type embedding theorems for finite groups, formulated in terms of sets of primes, Pi-subgroups, and Pi-Hall subgroups. It introduces a strong Pi-Sylow condition requiring conjugate embedding of subgroups of appropriate order into a given Pi-subgroup, and proves th…
The paper develops integral representations for functions holomorphic in bounded complete multicircular domains in several complex variables. Using biorthonormal systems on the distinguished boundary, finite complex measures, and moment conditions on auxiliary functions, it derives kernels that repr…
This paper studies integral transformations of homogeneous generalized functions in Euclidean space and the corresponding operators on functions defined on spaces of constant curvature. Using convolution operators, Fourier transforms, analytic continuation, and related transformations on elliptic an…
This note studies Weyl multipliers for unconditional almost everywhere convergence of series in the Haar orthonormal system. Building on earlier results that powers of logarithms with exponent greater than one are sufficient and those with exponent less than one are not, it proves a sharp criterion …
This paper formulates a discrete time problem of detecting a spontaneously arising change in the distribution of independent observations, where the unknown change time has a geometric prior distribution. It relates the expected number of false signals before the change to the probability of a prema…
This paper introduces two notions for the representation theory of complete completely regular rings, and by extension locally compact groups: isomorphism of representations, defined by equality of kernels or equivalently by equality of operator norms on all ring elements, and simple representations…
This paper studies the multidimensional Cauchy problem for the nonlinear parabolic equation governing nonstationary gas filtration in a porous medium. It introduces a generalized solution for bounded nonnegative initial data tending to a constant at infinity, proves uniqueness, and constructs soluti…
This note studies compact operators in the class defined by summability of singular numbers with weights \((2n-1)^{-1}\), and their role in triangular integral representations of Volterra operators in a separable Hilbert space. It proves that for every self-adjoint component in this class and every …
This note studies when perturbations of a complete system remain complete in a complete countably normed space represented as a projective limit of Banach spaces. Using weighted sequence spaces and operator arguments, it proves criteria for completeness under small matrix perturbations, triangular p…
This paper studies a nonlinear second order boundary value problem with a small parameter multiplying the highest derivative, motivated by the temperature field of a cooled gas turbine blade. The differential equation is formulated as an operator equation in a normed space, and Newton’s method is an…
The paper studies bases in spaces of abstract functions with values in a Banach space X, constructed from a Banach function space B and a basis in X. It defines the space B^X through approximation by step functions, establishes its basic integration and completeness properties, and formulates condit…
This note addresses the global isometric immersion of a two-dimensional Riemannian manifold homeomorphic to a sphere into a complete three-dimensional Riemannian space of nonpositive curvature. It improves an earlier curvature condition by proving that, when the ambient sectional curvatures do not e…
The note examines traveling-wave ordinary differential equations arising when discontinuities in quasilinear hyperbolic systems are regularized by viscous terms. Using a specific three-component hyperbolic system, it reformulates smeared shock profiles as trajectories orthogonal, with respect to a p…
The paper proves that for every complete orthogonal system in \(L^2[0,1]\) there exists an \(L^2\) function whose Fourier series can be rearranged so as to diverge almost everywhere. The argument introduces block unconditional bases, transfers a hypothetical unconditional convergence property betwee…
The paper studies ordinary differential equations in real Banach spaces, focusing on uniqueness for the Cauchy problem and nonlocal continuability of solutions. It introduces comparison functionals that may be Fréchet differentiable or semidifferentiable, and derives conditions under which estimates…
The paper presents new variants of Linnik’s dispersion method for binary additive problems of the forms involving a structured summand and a product term, with applications to equations containing primes, quadratic forms, and divisor functions. It describes the standard variance scheme, then extends…
This note proves existence theorems for time-periodic solutions of boundary-value problems without prescribed initial data for quasilinear parabolic equations. For one-dimensional equations with nonlinear lower-order terms, it treats Dirichlet, oblique derivative, and dynamic boundary conditions und…
The paper studies convergence of residuals for Bubnov-Galerkin and Ritz approximations to linear operator equations in a separable Hilbert space. It extends earlier results for positive self-adjoint operators with pure point spectrum by allowing coordinate systems formed from approximate eigen-eleme…
The paper determines exact upper bounds for best uniform approximation of periodic Hölder classes by trigonometric polynomials. Using reduction to polygonal functions, a comparison with Lipschitz classes, and Favard’s exact result for functions with bounded first derivative, it proves that for \(0<\…
This note extends an iterative minimal error method from linear operator equations to nonlinear equations in a Hilbert space. For a continuously Fréchet differentiable operator, it constructs successive approximations along the gradient of the residual functional, with a step chosen from an approxim…
This paper studies estimates for finite sums of primitive Dirichlet characters modulo composite odd prime powers and applies them to Dirichlet L-series in the critical strip. Using a decomposition of the modulus, expansions of indices modulo prime powers, and Vinogradov’s estimate for trigonometric …
The paper studies boundary value problems for the degenerate elliptic Beltrami operator \(B_k\) in domains adjacent to the axis, with emphasis on the \(E\) problem for \(k>1\) and its variational analogue. It constructs an \(E\)-Green function for a semicircle by using Weinstein’s fundamental soluti…
This note studies the regularization of integral equations with Cauchy kernel, including systems, in cases involving open contours or coefficients with discontinuities of the first kind. It shows that the same operator used for closed contours with continuous coefficients also provides left and righ…
The paper studies an inverse mixed boundary value problem for an analytic function in a domain whose boundary consists of several prescribed arcs and several unknown arcs, with boundary relations imposed on the former and prescribed values of the function on the latter. For polygonal prescribed arcs…
This paper studies nonnegative convex solutions of the Dirichlet problem for nonlinear elliptic equations involving the Monge-Ampère operator in a bounded convex planar domain with positively curved boundary. Using the normal mapping of convex functions, the authors define an associated solution ope…
This paper studies the extremum problem for the simplest variational functional on a class of curves that may have finitely many jump discontinuities, defining the functional by limiting approximations in which vertical segments are slightly inclined. It introduces a closure of broken-line approxima…
This paper proves global existence and uniqueness for plane nonstationary motions of an ideal incompressible fluid in a bounded domain, allowing vortical mass forces and without smallness assumptions on the data. The argument reformulates the Euler equations through a stream function, establishes a …
The paper studies when locally normal groups can be embedded isomorphically in direct products of finite groups, extending and qualifying earlier results of Chernikov and Hall. It constructs an example showing that, for groups of arbitrary cardinality, the factor group of a locally normal group by i…
This paper studies the reconstruction of a rapidly decreasing smooth function in complex, and analogously real, n-dimensional space from its integrals over all lines meeting a fixed curve. Using Fourier transforms, it reduces the problem to determining when associated data on the manifold of such li…
This paper formulates a general sequential decision problem for Markov processes with partially observed states, control-dependent transition laws, observation functions, admissibility constraints, and an additive loss criterion. Using the theory of conditional Markov processes, it derives a backwar…
This paper studies the asymptotic behavior, as a small parameter tends to zero, of the Green’s function for an ordinary linear differential operator whose highest order terms are multiplied by powers of the parameter. Under assumptions on the reduced boundary value problem and on the roots of the as…
This note studies the quickest detection of a change in a continuously observed Gaussian process whose drift switches at an unknown time, under constraints on the frequency or probability of false alarms. It formulates several versions of the problem, including Bayesian models with an exponential pr…
This paper develops an elimination method for linear programming problems formulated as systems of linear inequalities in a real linear space, allowing both non-strict and strict inequalities. It defines convolutions with respect to subspaces or sets of unknowns and proves consistency criteria: a sy…
This note gives internal characterizations of topologically complete spaces in the sense of E. Čech, where a completely regular space is complete if it is a G-delta subset of its Čech compactification. It introduces the notion of a diameter on a space, defines complete diameters through centered shr…
