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 extremal problems for mappings that are quasiconformal on average, defined by bounds on integrals involving the local characteristic, rather than by a uniform quasiconformality constant. Using variational arguments, it derives necessary extremality conditions for disk mappings wit…
The paper addresses the problem of describing all Hermitian positive extensions to the whole plane of a continuous Hermitian positive function initially given in a horizontal strip. It constructs spectral measures and associated canonical, or channel, positive-definite functions, proving an integral…
This note studies the representability of continuous functions of two variables by finite linear superpositions of the form involving fixed continuous coefficients, fixed continuously differentiable inner functions, and arbitrary one-variable outer functions. Using results of Vitushkin and auxiliary…
The paper addresses whether a complete orthonormal system of uniformly bounded functions can be a system of convergence, meaning that every square summable coefficient sequence yields an almost everywhere convergent orthogonal series. It constructs such a system on the unit interval by modifying Haa…
The paper studies multidimensional singular integral operators, including matrix operators, in spaces of test functions and generalized functions. It introduces a countably normed test function space and its dual, defines extensions of singular operators by adjointness, and proves normal solvability…
This note studies the loss of stability of stationary solutions and the emergence of limit cycles in a three-dimensional system modeling a damped rigid body under constant forcing, and in Galerkin approximations of the Navier-Stokes equations satisfying an energy-conservation condition. It gives suf…
The paper studies elliptic boundary value problems with nonhomogeneous boundary conditions for properly elliptic operators on bounded domains. It introduces Sobolev-type spaces with boundary trace norms adapted to low and negative smoothness, and proves a homeomorphism theorem for the operator mappi…
This paper studies a Hilbert-Poincare boundary-value problem for the Tricomi equation in a domain composed of an elliptic part above the degeneracy line and a hyperbolic part bounded by characteristics below it. The argument reduces the mixed-type problem, using the Tricomi problem and gluing condit…
The paper introduces partial topological products, a construction that generalizes Tychonoff products by attaching fibers only over specified open subsets of a base space. It defines the construction, establishes basic preservation and dimension properties, including conditions for compactness, regu…
This paper studies a mixed boundary value problem for a partial differential equation not solved with respect to the highest time derivative, with homogeneous Dirichlet conditions on a bounded planar domain. It introduces an associated spectral problem depending on a complex parameter and, for the c…
This paper studies when quotient images of metrizable spaces remain metrizable under special classes of mappings, including regular, uniform, bicompact, pseudo-open, monotone, and closed mappings. It introduces \(k_n\)-spaces and gives criteria showing, for example, that a regular quotient image of …
This paper studies a class of differential games in which the state evolves by analytic ordinary differential equations with two controls, and the objective is to reach a prescribed manifold in minimal time under an opposing control. Using Pontryagin-style adjoint variables and extremal trajectories…
The paper studies sequences of generalized Appell polynomials defined by the relation that the kth derivative of the nth polynomial equals the polynomial of degree n minus k. It gives necessary and sufficient integral moment conditions for such sequences, derives explicit forms of their generating f…
The paper addresses the Behrens-Fisher problem for two normal samples with unequal variances, focusing on the existence of nonrandomized homogeneous tests similar with respect to nuisance parameters. It proves that, for any prescribed level between 0 and 1 and sample sizes of different parity, there…
The paper studies extremal inequalities for moduli of smoothness of periodic functions whose pth derivative is bounded almost everywhere. Using an integral representation of such functions and an analysis of the signs of finite differences of the kernel, it proves that for each natural k not exceedi…
The paper studies solvability of the abstract Cauchy problem \(dx(t)/dt=Ax(t)\), \(x(0)=x_0\), for a linear operator in a Banach space. It introduces a local Laplace transform suitable for finite time intervals and for infinite intervals without growth restrictions, proves uniqueness and inversion r…
This paper studies spectral localization for normal operators in Hilbert space and extends earlier perturbation results and lemmas of Glazman. It establishes dimension and codimension criteria relating bounds on the difference of two normal operators to the number of spectral points of one operator …
The paper studies a linear dynamic programming problem, motivated by bottleneck problems, in which admissible controls are defined by polyhedral inequalities depending on the state and the state variables may have a fixed boundary. It formulates an augmented system and an adjoint construction analog…
The paper develops an algorithm for the finite Chebyshev approximation problem in Hilbert space, where one seeks a vector minimizing the maximum norm of deviations for a system of bounded linear operators. The method constructs successive approximations by identifying nearly maximal deviations, choo…
The paper proves uniqueness theorems for analytic and meromorphic functions in the unit disk belonging to refined Nevanlinna type classes defined by area growth conditions. Building on results of Carleson and integral representations of Dzhrbashyan, it shows that for functions in the classes \(T_\al…
This paper studies the inclined derivative problem for bounded solutions of the Poisson equation in a smooth plane domain when the boundary vector field is tangent at finitely many singular points. Using Freidlin’s construction, it relates the boundary value problem to a reflected Brownian motion st…
This paper studies tensor fields on compact homogeneous spaces that admit spherical models, extending earlier decompositions for tensor fields on spheres. It describes a general construction in which irreducible tensor spaces in an ambient Euclidean space are projected first to the sphere and then t…
This paper studies proper Riemannian spaces admitting a continuous group of motions whose isotropy group is reducible and decomposes with respect to two invariant orthogonal planes. Using adapted orthonormal frames, connection forms, and the invariance of the moving-frame equations under the station…
This note studies the existence of similar Fisher, Welch, Wald tests for comparing the means of two normal populations with unknown and unequal variances, allowing samples of arbitrary sizes. Using Wald’s representation of the critical region and the analytic continuation of the similarity equation …
The paper studies the limiting amplitude principle for abstract second order evolution equations in a Hilbert space and for elliptic operators in unbounded domains. It first gives sufficient spectral resolvent conditions under which the time harmonic response with zero initial data converges, or has…
This paper studies the size of defects of meromorphic functions in the plane in the sense of Nevanlinna theory, focusing on the supremum of the sum of square roots of positive deficiencies among functions of given lower order. Building on a theorem of Fuchs, the argument proves a new estimate for th…
This paper develops a local criterion for the existence of wave operators in abstract scattering theory for pairs of self-adjoint operators, defining strong and weak wave operators relative to a bounded Borel subset of the spectrum. It separates conditions ensuring weak existence, isometry, and comp…
The paper studies high-frequency asymptotics for the exterior Neumann problem for the Helmholtz equation describing diffraction of a cylindrical wave by a smooth finite convex cylinder, with attention to the geometrical shadow region. It proves an upper bound for the field of order k^{-1/2} exp[-c k…
This paper studies coverings of finite directed and undirected graphs by spherical neighborhoods of selected vertices, considering both vertex and edge coverage under graph metrics with positive arc or edge lengths. It proves that, for connected graphs, covering problems of this type can be reduced …
The paper studies entire functions of several complex variables of prescribed finite type that are positive on the real domain and belong to generalized Lebesgue spaces with mixed norms. It derives Nikolskii-type inequalities comparing mixed norms with different exponent vectors, including sharp con…
This paper generalizes M. Riesz’s maximal boundary theorem for Hardy class functions to functions in a domain that admit integral representations over a smooth boundary with kernels satisfying boundedness, regularity, and off-diagonal control conditions. Using ideas associated with Calderon and Zygm…
The paper studies the distribution of zeros of the Riemann zeta function and Dirichlet L-series near the line Re s = 1 by refining Linnik’s method of constructing sums that are large at zeros. Using estimates of I. M. Vinogradov, it partitions zeros of zeta up to height T into logarithmically many c…
This paper establishes two embedding results for weighted Sobolev-type spaces \(L_{p,b}^{(1)}(\Omega \times R_+)\) on cylinders over a half-line. Under integrability and connectivity assumptions on the weights, it proves the existence of an asymptotic constant for functions in the space and derives …
This paper studies the homogeneous Hilbert boundary value problem for a finite multiply connected planar domain and addresses its reduction to a Hilbert problem with a rational coefficient. Using harmonic measures, their conjugates on the covering surface, and solvability conditions for boundary rea…
This paper studies uniform convergence and error estimates for Fourier expansions of continuous and differentiable functions in orthonormal Legendre polynomials on the interval [-1,1]. Using a strengthened Jackson approximation theorem due to Timan, estimates for Legendre polynomial kernels, and the…
This note studies envelopes of holomorphy for semitube domains in several complex variables, extending earlier work that treated the case of one complex base variable. It defines locally normal semitube domains and proves that the envelope of holomorphy of any semitube domain is itself a locally nor…
This paper studies partial and full multiplication operations in ordered vector structures, focusing on when such operations can be represented as ordinary multiplication of continuous functions on the canonical space. It formulates axioms for partial multiplication, compares additional conditions u…
This note studies absolute summability almost everywhere of orthogonal and trigonometric series under Cesàro, Zygmund, and Riesz methods. It formulates conditions in terms of coefficient tails, dyadic block norms, monotonicity assumptions, and Weyl multipliers, extending and comparing earlier criter…
The paper studies Riemann integration within constructive analysis, using normal algorithms and constructive functions on the unit segment. It defines integral partitions, integral sums, regulators of integrability, and the Riemann integral constructively, then proves several nonexistence results: i…
This note characterizes Hausdorff spaces whose Boolean structures of canonical open, equivalently canonical closed, sets are isomorphic to a given complete Boolean structure. It first records that dense extensions preserve these structures and proves that closed, irreducible mappings satisfying a ne…
This paper characterizes the matrix correlation functions of a two-dimensional stationary, centered, normalized, nondegenerate Gaussian Markov process. Starting from positivity conditions for covariance matrices and the functional equations implied by the Markov property, the author reduces the prob…
This paper studies the location of singularities for Taylor-Dirichlet series of the form involving powers of the variable multiplied by exponential terms, under finite upper density conditions for the exponents counted with multiplicity. It introduces a condensation index adapted to multiplicities a…
This paper studies the classification of simply connected smooth manifolds with simply connected boundary, in dimensions greater than five with specified exceptions, that are homotopy equivalent to a fixed manifold and have equivalent stable normal bundles. Using Thom spaces, relative homotopy class…
The paper studies free products of associative calculi with an amalgamated subalphabet under group and isomorphism conditions, proving embedding and intersection properties for words belonging to the factor alphabets. Its main method introduces a combinatorial “analysis” of words using auxiliary let…
This note studies the first boundary-value problem in ellipsoidal domains for equations of the form Mu minus lambda Lu equals h, where M and L are homogeneous formally self-adjoint constant-coefficient differential operators of order 2s. Using weighted L2 spaces adapted to the ellipsoid and polynomi…
This note addresses the reconstruction of a category of correspondences from an arbitrary quasi-exact category, complementing earlier axiomatic work on correspondences over Abelian categories. It recalls the notions of an I-category, proper mappings, projections, injections, and quasi-exactness, the…
The paper studies a general boundary value problem with shift for a second order elliptic equation in a planar domain bounded by a Lyapunov contour, where the boundary homeomorphism has finite order. Using Vekua’s representation of solutions by boundary integrals, the problem is reduced to a singula…
The paper introduces quasi-nilpotent groups, defined as groups in which every finite set of elements generates a subinvariant subgroup, and studies their position among generalized nilpotent groups. It establishes closure properties, constructs the quasi-nilpotent radical as the subgroup generated b…
