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 note gives a necessary and sufficient condition for Riemann integrability of constructive functions on the segment from 0 to 1. The criterion characterizes integrability by boundedness together with a quantitative smallness condition on finite families of intervals on which the function has osc…
The paper studies the possible limiting behavior, in measure, of matrix summability means of trigonometric series for an arbitrary regular summation method whose defining matrix has finite rows. It proves that for any measurable functions satisfying a pointwise almost everywhere order relation, one …
This note generalizes the minimax principle for indecomposable nonnegative matrices to positive operators on ordered Banach spaces with a reproducing normal cone. It introduces semi-nonsupporting and strictly nonsupporting positive operators, uses a total subset of the dual cone, and formulates vari…
This note constructs a generalized Riemann-Liouville type operator determined by a weight function on the unit interval and studies its associated coefficient multipliers and kernel functions. It establishes positivity and boundary properties for the resulting series under monotonicity or limiting a…
This paper constructs a class of locally symmetric spaces of affine connection whose group generated by geodesic displacements is properly contained in a larger Lie transformation group. Using Lie algebras of transitive differential groups of order two, the authors associate such spaces with Jordan …
The behavior of solutions to differential equations containing angular coordinates is investigated. Dynamical systems defined by such equations are often referred to as phase systems. In the first part of the work, a third-order equation is studied. Using a specially constructed Lyapunov function, a…
This paper studies how large the class of bounded three-dimensional domains quasiconformally equivalent to a ball is among all bounded homeomorphic images of the unit ball. A Hausdorff-type metric is introduced on complements of such domains, and its relation to Carathéodory kernel convergence and t…
The paper formulates a stationary heat conduction problem motivated by crystallization of semiconductor melt droplets on substrates, considering a hemispherical body in perfect thermal contact with an infinite plane-parallel plate and subject to external heat transfer and imposed heat flux. Because …
The paper studies relative and absolute tensors over a complex vector space through their groups of invariance under changes of basis. It develops two lemmas on tensor concomitants: first, that a nonzero contravariant tensor has a nonzero concomitant of a canonical exterior product form, and second,…
The paper gives sufficient criteria for nonoscillation of nth order linear differential operators on a finite interval, where nonoscillation means that every nontrivial solution has at most n minus 1 zeros counted with multiplicity. It derives an improved inequality in terms of uniform bounds on the…
The paper studies generalized uniform spaces and identifies “correct” spaces as those satisfying separability and an intersection condition for neighborhoods, thereby retaining a usable proximity structure beyond Weil uniform spaces. It shows that merely separable uniform spaces have no complete obj…
The paper studies high-energy asymptotics for spectra of the three-dimensional Laplacian in a bounded domain with Robin boundary condition, focusing on how eigenvalues change when the boundary coefficient is varied. It first derives an expansion for the resolvent trace involving the volume, boundary…
The paper studies algorithmic problems for varieties of quasigroups and loops defined by additional identities, including word identity, isomorphism, embedding, and occurrence. It develops an embedding criterion for partial quasigroups via finite simple free extensions and identifies a condition und…
This paper studies extrema of the multidimensional lattice zeta function for lattices of fixed determinant, a problem motivated by Sobolev’s work on approximate computation of multidimensional integrals. Using Lagrange multiplier conditions, the authors introduce strongly critical lattices and final…
This paper studies finite-dimensional irreducible representations of complex semisimple Lie algebras, focusing on weight multiplicities, tensor product decompositions, and restrictions to semisimple subalgebras. Using the Weyl group and a formula of Brauer and Weyl, it derives recurrence relations f…
The paper develops topological properties of partially ordered dynamical systems in which the acting group is an arbitrary nontrivially partially ordered group, replacing earlier restrictions based on countable majorizing sequences by directedness where needed. It defines relative density, omega-lim…
For the third Painlevé equation, the nature of possible singular points of its solutions is investigated, the question regarding the number and residues of movable poles of the solutions is resolved, and necessary and sufficient conditions for the existence of rational solutions are specified. Bibli…
The paper studies a generalized Tricomi boundary value problem for Chaplygin’s mixed-type equation in a domain whose boundary includes elliptic and hyperbolic parts, with homogeneous data imposed on selected boundary arcs. It formulates generalized solutions in a Sobolev space through an integral id…
A number of theorems are proved on the topological structure of the phase portrait of the system of ordinary differential equations \begin{equation} \begin{aligned}\dot{x}&=y\\\dot{y}&=-g(x,y)\end{aligned}\biggr\}\tag{1}, \end{equation} which the author calls relaxation if: (I) the function $g(x,y)$…
This note studies the Cauchy problem for a one-dimensional parabolic equation on a finite interval with separated boundary conditions and a rapidly oscillating periodic coefficient. Under summability assumptions on the Fourier coefficients of the periodic term, the paper proves the existence, for su…
This paper considers the solution of certain boundary value problems for a two-dimensional elliptic equation with coefficients depending on two variables using the method of lines. The general solution to the system of differential equations of the method of lines is sought using the method proposed…
This note studies uniform approximation of functions regular on closed sets of the complex plane by interpolation polynomials with nodes equidistributed on level curves of the exterior conformal map. Using a lemma of Lebedev for univalent functions, it derives logarithmic estimates for the node poly…
This note announces results in set-theoretic topology obtained by combinatorial set-theoretic methods, especially partition relations, concerning cardinal bounds for discrete subspaces, density, and character in Hausdorff and related spaces. It improves earlier theorems of de Groot, Efimov, and Isbe…
This paper studies uniqueness for the Cauchy problem with zero initial data for general linear partial differential equations with constant coefficients in one spatial variable and time, restricting attention to solutions of normal exponential type in time. Using the Laplace transform in time, the p…
The paper studies the topological classification, up to isotopy in real projective three-space, of nonsingular real algebraic surfaces of degree four. It introduces a notation for surface components according to genus and the number of finite or infinite handles, defines surface types including conf…
The paper addresses the problem of K-continuability of polynomials, namely how to extend a given polynomial by adding higher-degree terms so that the roots of the resulting polynomial lie on the unit circle. It presents a simple algebraic construction based on transforming the polynomial, using Newt…
This bibliographic notice compiles recently published books and article collections relevant to differential equations, mathematical physics, functional analysis, stability theory, approximation theory, and related areas. The entries provide authors or editors, titles, publication locations and pres…
The paper studies a generalized Schwarz formula for the first-order elliptic equation ∂w/∂z̄ + b w̄ = 0 with constant nonzero coefficient, using a generalized Cauchy formula and the relation of the equation to the metaharmonic equation. For the upper half-plane, it derives an integral representation…
The paper studies functions represented by Dirichlet series that satisfy a pair of Riemann type functional equations, with specified meromorphic and decay conditions on the auxiliary factors. It proves a general shortened equation expressing the completed functions as sums of two integral Dirichlet …
The paper studies extremal quasiconformal self-mappings of the disk with a prescribed boundary correspondence, contrasting this problem with the classical case of finitely many prescribed boundary points where Teichmüller extremals are unique. It constructs and analyzes approximating extremal mappin…
The paper studies Diophantine properties of values of entire functions beyond Siegel’s class of E-functions, introducing a broader class of E*-functions with weakened growth and denominator conditions. Using a Thue, Siegel type construction of approximating polynomial forms and direct estimates at a…
This paper develops the notion of t-quasiconformal mappings with two triples of characteristics, extending a previous definition involving one triple and relating the elliptic case to Shabat’s quasiconformality. It defines mappings between rings of t-complex numbers, introduces appropriate forms of …
This paper studies degenerate quasilinear parabolic equations whose first order nonlinear part is subordinate to the degenerate second order operator in a probabilistic sense. Using Markov processes, Girsanov-type absolute continuity, and stochastic integral representations, it defines generalized s…
The work is devoted to a topical issue related to the practical calculation of electrostatic fields. One of the authors of this article previously introduced functions that allow for the exact satisfaction of boundary conditions for domains of practically arbitrary shape. These functions, while bein…
This paper develops properties of Orlicz classes and Orlicz spaces generated by variable N-functions on sigma-finite measure spaces. It introduces a generalized Delta2 prime condition, relates it to derivative inequalities for a variable N-function and its complementary function, and establishes den…
The paper studies tests of prescribed level for multidimensional polynomial hypotheses concerning the means and covariance matrices of several multivariate normal populations. It reformulates the problem in terms of sufficient statistics and exponential family parameters, reducing the characterizati…
The paper studies interpolation processes associated with node systems on the interval, focusing on Bernstein’s modified interpolation scheme and on an extended system of Chebyshev nodes that includes the endpoints. It addresses whether quasi-uniform distribution of nodes is sufficient for uniform c…
This note studies countably additive real set functions on Borel subsets of an n-dimensional cube that satisfy absolute continuity or translation continuity only in specified coordinate directions. It shows that, unlike the classical full-dimensional case, directional absolute continuity and directi…
The paper studies R. S. Phillips’s problem of extending an invariant dual pair of subspaces in a Hilbert space with an indefinite scalar product to a maximal invariant dual pair. For a commutative algebra generated by J-unitary operators, the author proves such an extension under power boundedness o…
This paper studies embedding problems for ordered and quasi-ordered semigroups, focusing on potential right divisibility, potential left invertibility of subsets, and embeddings into semigroups with one-sided invertibility. It introduces explicit compatibility conditions on a binary relation or subs…
This paper studies existence and conjugacy criteria for subgroups of finite groups whose order and index are not necessarily relatively prime. It introduces almost Sylow and separable divisors relative to a normal series, defines subgroup types with respect to such a series, and proves a main theore…
This note studies mean approximation on the boundary of a simply connected domain for analytic functions of class Ep, p greater than 1, under a smoothness condition on the boundary. It sharpens Al’per’s Jackson type inequality by deriving order-refined estimates relating best polynomial approximatio…
