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 a singular mixed type boundary value problem for an equation that is elliptic in one subdomain and hyperbolic in another, with Frankl and Tricomi type boundary data, a gluing condition across the line of type change, and a curvilinear jump condition. It develops representations for…
This paper estimates Cauchy integrals of bounded analytic functions in terms of the analytic capacity of the set of singularities, addressing a problem arising in approximation theory. It proves that for a function analytic in the unit disk outside a closed exceptional set and continuous on the boun…
This paper develops operator schemes for proving existence of solutions to classes of nonlinear equations in Banach spaces that model quasilinear problems in mechanics. Using Galerkin approximations, it establishes solvability theorems for stationary equations under ellipticity, orthogonality, and w…
The paper studies nonlocal solvability of initial boundary value problems for quasilinear hyperbolic partial differential equations in a bounded domain, with formally self-adjoint strongly elliptic operators of order 2m and boundary conditions satisfying the Shapiro-Lopatinskii condition. The proble…
The paper generalizes the Schaeffer-Duffin extremal problem for algebraic polynomials subject to prescribed bounds at n plus 1 points on an interval, replacing pointwise derivatives by an arbitrary finite linear functional. Using the Lagrange interpolation representation, it gives an explicit charac…
The paper studies locally perfect mappings between T1 spaces as a local analogue of perfect mappings and constructs, for any such map, a canonical perfect extension obtained by adjoining one point over each point where the original map fails to be perfect. It proves uniqueness and minimality propert…
The paper studies the limiting behavior of solutions to Cauchy problems for linear parabolic systems whose highest derivatives are multiplied by a small parameter, with emphasis on convergence to the corresponding hyperbolic limiting system as the parameter tends to zero. It establishes sufficient c…
In the peer-reviewed work, the following one-dimensional mixed problem is investigated: \begin{gather}\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}-\alpha\frac{\partial^3u}{\partial t\partial x^2}=\lambda F[t,x,U,U_x,U_t,U_{xx},U_{tx}],\tag{1}\label{1}\\U(t,0)=U(t,\pi)=0,\quad U(…
This paper corrects and refines a result of Bass on one-dimensional local commutative Noetherian reduced rings whose integral closure is finite, concerning when every indecomposable finitely generated torsion-free module is isomorphic to an ideal. The authors focus on the case where the integral clo…
Pontryagin extends earlier work on linear differential games for systems of the form dz/dt = Cz + u - v in a vector space of arbitrary dimension, with pursuing and evading controls drawn from closed bounded convex sets and termination on a closed convex set. The paper introduces operations on convex…
The paper considers an application of the theory of Panya’s special heat potential of a simple layer to a boundary value problem for a system of parabolic equations with discontinuous coefficients, arising in the study of the distribution of concentrations of substances involved in the vital process…
This note studies strictly cosingular bounded linear operators between Banach spaces and their relation to Fredholm type perturbation theory. Using duality, weakly closed subspaces of dual spaces, and compactness arguments, it proves equivalent characterizations of strict cosingularity in terms of t…
The paper considers the conditions for the existence and uniqueness of the solution to the specified problem, while simultaneously providing estimates for both the solution and its derivatives. The main results are Theorems $1$, $2$, $3$, and $4$. The periodic boundary value problem for third- and f…
This note studies almost periodicity and stability of bounded solutions of nonlinear ordinary differential systems using a generalized Lyapunov function depending on pairs of phase points. It introduces \(V\)-monotonicity and an associated \(A\)-property, proves their equivalence under bounded-domai…
This paper studies the Cauchy problem on a finite time strip for a first order in time linear equation with variable spatial coefficients of order n, under assumptions that the coefficients approach constants at spatial infinity and that the limiting constant coefficient equation is well posed in Pe…
This paper studies preservation and characterization properties of Hewitt \(Q\)-spaces, also called functionally closed spaces, in general topology. It proves that a perfect image of a normal countably paracompact \(Q\)-space is again normal, countably paracompact, and a \(Q\)-space, giving a partia…
This paper studies best approximation of elements in real and complex Banach spaces by elements of convex sets. It extends known duality relations and Rubinshtein’s criterion for best approximation from the real to the complex case, relates this criterion to Garkavi’s formulation using extreme point…
The paper studies generalized mean values of the support function of a convex body in n-dimensional Euclidean space, motivated in part by their role as sharp majorants for solutions of second-order elliptic equations with zero boundary values. It establishes basic monotonicity and convexity or conca…
This paper studies density estimates for zeros of Dirichlet L-functions, motivated by Bombieri’s refinement of Linnik’s large sieve method and its applications to primes in arithmetic progressions and additive number theory. It proves two strengthened average zero-density inequalities for primitive …
The paper studies boundary value problems for an ordinary differential equation of order n under Carathéodory assumptions on the right hand side. It establishes existence results for problems with initial conditions on derivatives up to order n minus 2 and an additional boundary condition at a termi…
The paper studies inductive and projective limits in categories of commutative topological groups, locally quasi-convex groups, and locally quasi-convex groups equipped with quasi-convex boundedness. It establishes existence and universal properties of strongest and weakest compatible topologies and…
The paper introduces theta spaces, defined by a weakened proximity relation on regular topological spaces, as a generalization of proximity spaces compatible with completely regular spaces. It establishes that each theta space determines a completely regular perfect irreducible preimage together wit…
This commemorative article surveys the life and scientific work of Evgenii Alekseevich Barbashin on the occasion of his fiftieth birthday. It traces his education, academic appointments, and role in building research groups in Sverdlovsk and Minsk, while emphasizing his contributions to qualitative …
The paper develops a framework for studying set-valued translations between topological spaces using generalized neighborhoods and a hierarchy of eight types of convergence for sequences of sets. It defines completeness, regularity, restrictions, inverse translations, and continuity of a given type,…
This note studies classes of functions that are quasi-analytic with respect to an ordinary linear differential operator with continuous coefficients, extending classical Denjoy-Carleman type classes through bounds on iterates of the operator. It gives sufficient conditions, expressed by convex regul…
This note studies duality operators for additive covariant functors in categories of abelian groups, especially finite, finitely generated, and arbitrary abelian groups. It introduces the functor \(T_{A,B}X=\operatorname{Hom}(\operatorname{Hom}(X,A),B)\), uses it to analyze reflexivity, and establis…
This paper studies when formal transformations that reduce analytic systems of ordinary differential equations near a singular point to normal form are convergent or necessarily divergent. It formulates two arithmetic and structural conditions on the eigenvalues and on the normal form, including a s…
This paper studies stability in the uniform metric for systems of linear difference equations with constant matrix coefficients and bounded initial data. Using the characteristic matrix obtained by Fourier transformation, it gives a necessary and sufficient condition in terms of boundedness, uniform…
A method is developed for obtaining uniform asymptotics of linear differential systems with a small parameter multiplying the derivative. The fundamental matrix is represented as a product of a diagonal exponential factor and a matrix having a finite limit as the parameter tends to zero, with the la…
The paper studies open finite-to-one continuous mappings in general topology, especially their effect on metrizability and covering properties. It proves that a regular p-space mapped openly and finite-to-one onto a metrizable space is metrizable, and that hereditary weak paracompactness, hereditary…
This commemorative article surveys the development of Soviet mathematics, especially the theory of differential equations and its applications, over the fifty years following the October Revolution. It argues that Soviet science transformed a formerly backward country into a major center of mathemat…
This note studies the spectral radius of positive operators on ordered Banach spaces with a reproducing normal cone, focusing on indecomposable or semi-non-supporting operators. It proves a limit formula expressing the spectral radius through scalar quantities of the form involving iterates of the o…
A quasilinear autonomous system with many degrees of freedom and delays is considered. Under the assumption that the generating system possesses a multi-frequency periodic regime, the solution of the system is constructed using the asymptotic method of N. M. Krylov and N. N. Bogolyubov. The possibil…
The paper studies the local structure of trajectories of a multidimensional smooth dynamical system near a homoclinic motion doubly asymptotic to a saddle periodic orbit. Using a Poincare map on a transverse section, stable and unstable manifolds, and a transversality assumption for their return int…
The paper studies the computation of saddle points for continuously differentiable concave-convex functions on Euclidean spaces and on convex bounded domains. It gives necessary, and under concave-convexity sufficient, stationarity conditions, then develops continuous dynamical systems whose traject…
This paper studies finite groups satisfying the QP condition, namely that any two distinct nonprimary maximal nilpotent subgroups of even order intersect trivially. It develops a centralizer criterion for such groups, proves heredity for subgroups and factor groups, and classifies solvable QP-groups…
