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 the Tricomi boundary value problem for a second order mixed type equation with lower order terms, after reducing the equation to a form without a first derivative in the degeneracy variable. Under specified regularity, sign, and boundary assumptions on the coefficients, the domain,…
This paper studies best approximation of continuous and analytic functions by algebraic and trigonometric polynomials subject to homogeneous linear constraints on their coefficients, extending problems originating with Markov. It first derives general inequalities in a normed linear space relating c…
The paper studies convergence and error bounds for lattice cubature formulas applied to periodic functions on a torus in the Sobolev space \(L_2^{(m)}\). It shows that, among formulas with the prescribed lattice nodes, the minimal norm of the error functional is obtained when all coefficients are eq…
This note examines whether interpolation results known for Chebyshev nodes extend to more general quasi-uniformly distributed nodes on the interval [-1,1]. Using a node system formed by adjoining the endpoints to Chebyshev nodes, it proves that Lagrange interpolation of the function |x| diverges at …
The paper extends a general method for constrained extremum problems from linear approximation to higher order variations in Banach spaces. It formulates admissible and forbidden cones for first and second variations, derives corresponding Euler equations through separation conditions in the adjoint…
The paper studies the regularized trace of the differential operator d n/dx n plus a smooth potential q(x) on the interval [0,1], under regular boundary conditions identical to those for the unperturbed operator and with zero mean potential. Extending earlier trace formulas known mainly for second o…
The paper studies infinite systems of linear inequalities over real linear spaces and formulates a notion of polyhedral closure for their dual cones, extending Minkowski’s finite theorem on consequences of linear inequalities. It proves that a consistent system is finitely determined, in the sense t…
The paper develops a general framework for difference schemes approximating abstract Cauchy problems with possibly unbounded, time-dependent operators in Banach and Hilbert spaces. Instead of placing the discrete solution in the original space, it introduces a sequence of approximating spaces with p…
The paper studies asymptotic solutions on the half-line for ordinary linear differential equations of order n with a small parameter, and for a related class of even order quasi-differential equations. Under hypotheses on coefficient limits, separation of characteristic roots, and summability of der…
This paper studies Poincare’s problem on periodic solutions of nonautonomous differential systems with analytic right hand sides in the resonant case, focusing on solutions branching from a periodic solution of the generating equation. The authors reduce the existence and enumeration problem to a fi…
The paper treats a special integrable case of the Riemann boundary value problem for several piecewise analytic functions with jumps on a contour decomposed into parts, where the coefficient matrix is diagonal on one part and cyclic off diagonal on the other. By introducing canonical scalar factors,…
The paper studies when a structural isomorphism, or projection, between groups is induced by an actual group isomorphism, a property that does not hold in general. It proves an approximation theorem: if a group is approximable, via a strict filter of normal subgroups, by a class of groups whose proj…
The paper studies semigroups of full transformations whose elements have rank at most two and whose images collectively cover the underlying set, with at least one rank one transformation. It gives intrinsic algebraic criteria for a semigroup to be isomorphic to one in this class, using relations de…
This note addresses the role of normality in regular convex partitions of Euclidean space, particularly in relation to Delone’s finiteness theorem for stereohedra. It constructs four infinite series of regular but nonnormal partitions of three-dimensional space into congruent brick-like parallelepip…
This paper constructs optimal quadrature formulas for classes of functions on the unit interval whose even order derivative is bounded in the uniform, \(L_1\), or \(L_2\) norm. The formulas use function derivatives up to order \(r-2\), are exact for all polynomials of degree \(r-1\), and are obtaine…
The paper introduces singular linear operators on scales of Banach spaces, defined by bounded action between smaller spaces with a norm growing at most like the inverse loss of scale parameter. Using successive approximations, it proves a local existence and uniqueness theorem for the abstract Cauch…
The paper develops a numerical method for minimizing a convex Fréchet differentiable functional over a bounded convex feasible set in a Hilbert space defined by convex inequality constraints. The proposed feasible direction algorithm chooses each descent direction by solving a finite-dimensional qua…
The paper develops a systematic theory of double operator Stieltjes integrals of the form involving two spectral resolutions, a bounded operator, and a scalar kernel, viewed as transformations on ideals of compact operators in a Hilbert space. It defines these integrals first in the Hilbert Schmidt …
This note proves a generalization of Kolmogorov’s theorem on the persistence of conditionally periodic motions under small analytic perturbations of a Hamiltonian. For Hamiltonians depending on transverse variables and action-angle variables, under specified nondegeneracy and nonresonance conditions…
This paper studies the convergence of a splitting method for a finite-difference approximation of the plane-parallel radiative transfer equation with isotropic scattering and prescribed inflow boundary data. The transfer operator is decomposed into a differential part and a scattering-absorption par…
This note proves a regularity assertion for singular integral equations of normal type in Euclidean space, addressing a hypothesis of I. N. Vekua on when solutions inherit the smoothness class of the right hand side. For singular operators of class \(C_\alpha^\infty\) acting on \(L_p(E_n)\), the pap…
This paper formulates an additivity principle for constructing economical locally one-dimensional difference schemes for abstract Cauchy problems in a Banach space, where the main operator is represented as a sum of simpler one-dimensional operators. It interprets the method as an approximate factor…
This note studies continuous decompositions of metric spaces into closed sets and their application to closed images of metric spaces. It proves that, except for a sigma-discrete subfamily, the elements of such a decomposition are compact and have empty interior, using a convergence lemma for closed…
The note studies estimates for holomorphic functions of two complex variables in bounded complete bicircular and circular domains, with analogous extensions indicated for more variables. Using reductions to one-variable functions along complex lines, it proves sharp bounds for diagonal Taylor sums a…
The paper studies the classification of orbits in the dual of the Lie algebra of the group of upper unitriangular matrices under the representation dual to the adjoint action, motivated by Kirillov’s correspondence between such orbits and irreducible unitary representations of nilpotent Lie groups. …
This note addresses the inverse problem of determining characteristics of a single-server queueing system with waiting from observations of its departure process, for a Poisson input flow and independent identically distributed service times. It derives relations between the Laplace transforms of th…
This paper develops an analogue of the Plemelj-Privalov theorem for Cauchy type singular integrals on closed rectifiable Jordan curves that may be nonsmooth, assuming a metric arc condition controlled by a function beta. It introduces generalized Hölder spaces defined by moduli of continuity, derive…
The paper studies scattering operators for pairs of unitary groups in Hilbert spaces under a generalized Lax and Phillips framework, without requiring the incoming and outgoing subspaces to be orthogonal or cyclic in the whole space. It defines wave and scattering operators, represents their suboper…
This note studies the determinant of the general rational solution of the matrix equation AX = XB for two similar integer matrices A and B, using their quasi-natural normal form and the elementary divisors over the rational field. It derives explicit forms for the commuting solutions and gives produ…
The note compares two definitions of cohomological dimension of a topological space with coefficients in an Abelian group: Aleksandrov’s definition via nonvanishing relative cohomology and Okuyama’s definition via epimorphic restriction maps to closed subsets. It proves that these definitions coinci…
This paper studies high energy asymptotics for a one dimensional scattering problem governed by a second order differential equation with a real potential function tending to negative limits at infinity. Under analyticity and simple zero assumptions on the coefficient, it derives asymptotic formulas…
This paper studies a nonlinear singular integral equation with a shift on a finite interval, under Lipschitz-type and modulus-of-continuity assumptions on the shift function and kernel. Building on previously established existence and uniqueness in a Hölder-type class for sufficiently small paramete…
The paper develops a framework for abstract N-almost-periodic functions with values in a Banach space and proves approximation and uniqueness results via Fourier-Bohr type coefficients. It applies this framework to nonstationary abstract Cauchy problems with almost-periodic coefficients, giving cond…
The paper studies decompositions of infinitely divisible probability laws without a Gaussian component, focusing on whether membership in the class of laws whose components are all infinitely divisible requires a finite or countable Poisson spectrum. It gives a negative answer by identifying two cla…
This paper studies the stability of grid, or net, methods for elliptic boundary value problems under small perturbations of the discrete operator, rather than only perturbations of the right-hand side. Using a variational construction of the discrete Dirichlet problem, Friedrichs extension, and Kant…
This note studies completeness of systems of eigen and associated elements for polynomial operator pencils built from a completely continuous operator in a Hilbert space. It derives explicit resolvent expansions for an operator with a Riesz type basis of root elements and uses estimates on rays avoi…
