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 branching and small-solution structure for nonlinear analytic equations with completely continuous operators in complex Banach spaces. Using index results of Cronin and Krasnosel’skii’s criterion, it shows that bifurcation points of an analytic operator coincide with the character…
The paper studies a Cauchy problem for a higher order partial differential equation in one complex and one real variable, extending earlier work in which the highest order part had constant characteristic structure. For the third order case, the author analyzes the characteristic surfaces determined…
This note develops the algebraic theory of finite ring groups, focusing on homomorphisms, subgroups, quotient groups, and their behavior under duality. It defines subgroups via central projectors satisfying compatibility conditions, factor groups via invariant Neumann subrings, proves an analogue of…
This note studies the asymptotic growth of harmonic functions of three variables in unbounded domains contained in a rectangular half-cylinder. Building on an earlier result for half-cylinders, it proves a partial extension to arbitrary infinite three-dimensional domains whose boundary satisfies uni…
This paper develops a variational theory for boundary value problems in Sobolev type spaces where the boundary conditions contain spectral parameters and may include nonlinear terms. It formulates a principal problem for admissible integral forms on domains with decomposed boundaries, extends the se…
The paper proves uniqueness of generalized L2 solutions for basic boundary value problems of mathematical physics in arbitrary bounded connected domains, removing earlier smoothness assumptions on the boundary. The main argument is developed for the mixed problem for the wave equation with homogeneo…
For Gevrey classes \(C(n^{n\alpha})\) with \(\alpha>1\), the paper addresses a Carleman type interpolation problem: realizing prescribed derivative values at the origin under the corresponding growth condition. It constructs explicitly, by means of cutoff functions \(a_k(x)\), a Taylor like series w…
The paper studies four-point finite difference schemes on a hexagonal grid for approximating the planar Laplace operator, addressing the usual objection that their local approximation is only first order. It shows that, because leading local errors have alternating signs at neighboring grid points, …
This note studies uniform approximation of subsets of dynamic limit sets by semitrajectories in metric dynamical systems, extending earlier work on minimal omega-limit sets. It introduces psi-limit points, those uniformly approximated by a positive semitrajectory, and characterizes the corresponding…
This paper studies summability of orthogonal series in L2 by Euler methods and by the exponential Borel method, in relation to subsequence convergence methods. It introduces equivalence of summation methods in L2 and proves that all Euler methods with positive parameter, together with the Borel meth…
This note studies representations of abstract semigroups by binary relations on a set, extending earlier work on representations by transformations and partial transformations. It introduces the majorant extension of a binary relation to the power set, shows that this construction preserves the semi…
This paper studies stabilization as time tends to infinity for the Cauchy problem for a linear parabolic equation in several spatial variables with time-dependent coefficients. Using an explicit fundamental solution and Gaussian integral representation, it relates the limiting behavior of solutions …
This note develops a homotopy theory for functors on the category of pointed completely regular topological spaces, motivated by a justification of Eckmann-Hilton duality. It defines homotopy of functor maps, fibrations, cofibrations, fibers, cofibers, homotopy and cohomology groups of functors, and…
The paper studies boundary value problems for the Poisson equation in a rectangle, covering Dirichlet, Neumann, and mixed boundary conditions. It generalizes a regularity criterion for the Laplace equation by giving necessary and sufficient corner compatibility conditions for the solution to belong …
This paper studies the asymptotic behavior of convolution powers of probability measures on complex unimodular groups, especially beyond the symmetric case. Using principal series representations and associated integral kernels, it reduces questions about sets determined by eigenvalue inequalities t…
This paper studies linear operators from the space of continuous periodic functions into trigonometric polynomials of bounded order, without assuming that the operators preserve each Fourier mode diagonally. It constructs an associated convolution type operator determined by the diagonal coefficient…
The paper studies linear polynomial operators from the space of continuous periodic functions into trigonometric polynomials of bounded order, with particular attention to operators that commute with translation. It introduces an averaging construction that associates to any such operator a shift-co…
The paper studies when a normed linear lattice or ordered normed structure admits an equivalent monotone norm, thereby becoming a KN-lineal, KB-lineal, or KB-space. It establishes criteria in terms of properties of the positive cone, including normality, closedness, regularity or full regularity, to…
This note studies systems of rational functions orthonormal on the unit circle whose poles are prescribed by a sequence outside the unit disk, extending classical results for orthogonal polynomials obtained when all poles are at infinity. It constructs the systems from Malmquist rational functions w…
This note studies how order-theoretic properties of an ordered set are reflected in the semigroup of all its order-preserving endomorphisms, focusing on semisimplicity defined through two-sided stable equivalences. For a finite linearly ordered set, the paper describes the ideals of the endomorphism…
This note addresses A. I. Mal'cev's question on the relative elementarity of subalgebras and subspaces in Lie algebras, using first-order definability in the language of algebras with parameters. It proves that every subspace of a simple real compact Lie algebra, and likewise every subspace of a sim…
The paper studies bendings of bounded pieces of surfaces of positive Gaussian curvature under geometric boundary conditions. It reformulates the Gauss and Codazzi equations, in an isothermally conjugate parametrization, as a nonlinear boundary value problem for a complex function determined by the s…
This paper studies subdirect decompositions of semigroups and characterizes subdirectly indecomposable semigroups through stable equivalence relations. It proves that every such semigroup has at least two separating elements and a kernel, establishes restrictions on central idempotents, and derives …
This note studies a class of singular integral equations on a Lyapunov contour that include conjugation, Cauchy singular integrals, and a Carleman shift of the argument. The authors reduce the equation to an equivalent system of singular integral equations, formulate the adjoint problem, and derive …
This paper studies homogeneous convex cones and their automorphism groups through a class of finite-dimensional real matrix algebras with involution, called T-algebras. It gives a universal construction assigning to each T-algebra a cone of Hermitian elements represented as products of triangular el…
This paper studies differential properties of weak and strong generalized solutions of stable hypoelliptic linear differential equations with sufficiently smooth variable coefficients. It formulates stability and hypoellipticity conditions through associated polynomial inequalities and introduces Hi…
This note extends a previously established integral representation for regular functions in bounded complete doubly circular domains of two complex variables to meromorphic and related functions. It treats quotients whose denominators are either entire functions of the ratio w/z, arbitrary regular f…
This note addresses the construction of minimizing sequences for nonlinear variational problems, a point left open in general existence arguments based on convergence of such sequences. It proves that the Ritz method yields a minimizing sequence for a functional whose domain is linear, whose restric…
This note develops fractional step difference schemes for the periodic Cauchy problem for a multidimensional wave equation. Starting from an implicit finite difference approximation, the author constructs a factorized splitting scheme and a second related scheme, eliminates the auxiliary fractional …
This paper systematizes the study of inductively open and almost-open continuous mappings of topological spaces, defining these notions and establishing their basic permanence properties under subspaces, composition, products, and open covers. It proves representation theorems showing that broad cla…
This paper studies first boundary value problems for two classes of second order linear elliptic systems in a planar domain whose boundary includes a segment on which the equations degenerate parabolically. It introduces weighted Sobolev-type spaces and negative norms adapted to the degeneracy, then…
This note studies generalized regularly monotone functions associated with a nondecreasing sequence of exponents and their relation to expansions in quasi-power series. It defines the classes R, T, AT, and AC, compares their inclusions, and gives necessary and sufficient conditions for representatio…
This paper develops a ring-theoretic framework for studying one-sided invertibility in normed rings and applies it to operator equations, Toeplitz-type systems, and singular integral equations. It establishes criteria for left, right, and two-sided invertibility of elements generated by an element w…
This paper studies the approximation of periodic functions in \(L_p\) by linear summation processes applied to their Fourier series, with errors compared to best trigonometric approximation. It proves general estimates for arbitrary triangular summability matrices, including analogues of Lebesgue-ty…
This paper studies oscillation and nonoscillation of solutions to higher order ordinary differential equations of the form \(u^{(m)}+F(u^2,t)u=0\), where \(F\) is nonnegative and monotone in its first argument. Using sign properties of derivatives of nonoscillatory solutions, the author classifies s…
This paper studies restrictions on entire functions whose exponentials can serve as characteristic functions of probability laws, motivated by a question of Yu. V. Linnik concerning transcendental entire functions of at most minimal type of order one. Using refined growth theory for entire functions…
The paper studies a complex differential equation equivalent to the potentiality and incompressibility conditions for an axisymmetric vector field in cylindrical coordinates, with singular coefficients on the symmetry axis. It constructs unique kernels for a generalized Cauchy formula in the meridia…
This note studies the long time behavior of nonhomogeneous diffusion processes in Euclidean space whose transition densities are Green’s functions for a pair of adjoint parabolic equations. Under a dissipativity condition on the coefficients, ensuring that the distribution does not spread to infinit…
The paper introduces the notion of computable invariants for equivalence relations on constructive objects and studies their limitations for words, associative calculi, inverse calculi, and higher-dimensional polyhedra. It defines transformation relations for associative and inverse calculi and prov…
This note addresses time-optimal control problems in which Filippov’s existence condition may fail, so that an ordinary optimal control need not exist although minimizing trajectories may converge to a limiting motion. It introduces sliding optimal regimes as limits of rapidly switching admissible c…
This paper develops a projective differential theory for curves in n-dimensional projective space by associating a curve with a central conical surface and a doubled fibered space. It constructs differential invariants of least possible order, affine connection objects, a natural frame, and Frenet-t…
This paper develops a general theory of linear filters defined by convolution with a transition function, distinguishing stable filters from a broader class of weakly stable filters characterized by an energy condition for rectangular impulses. It formulates three problems concerning the realization…
This paper studies principal directions of an m-dimensional surface in Euclidean space through the infinitesimal displacement of its tangent plane. It defines directions that are principal relative to a given tangent direction, derives their determining equations from the second fundamental form, an…
This paper studies a one-dimensional freezing, or Stefan, problem with a moving phase boundary and an arbitrary prescribed temperature at a fixed boundary. Using a change to coordinates attached to the moving front and the two-sided Laplace transform, it represents the temperature field by Poisson-t…
This paper studies relaxation oscillations in singularly perturbed systems of two first-order differential equations, focusing on periodic solutions close to discontinuous limiting cycles composed of slow and fast motions. Building on earlier matched asymptotic constructions, it refines local expans…
This note studies extension of functions from anisotropic Sobolev spaces on a two-dimensional bounded convex domain to the whole plane, with preservation of an a priori norm estimate. For functions in \(W_{(x,y),2}^{(m,n)}(Q)\), with \(m<n\), satisfying vanishing boundary conditions in the \(x\) dir…
This note studies a free-boundary mixed problem for two parabolic equations whose coefficients are discontinuous across an initially unknown moving interface, motivated by hydraulic engineering problems involving injection of binding liquids into porous rock. The problem, known as Verigin’s problem,…
