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 time-periodic solutions of boundary-value problems without initial conditions for second-order parabolic equations. For Dirichlet problems with time-independent elliptic part, the solution is expanded in a Fourier series in time, reducing the problem to elliptic boundary-value syst…
The paper develops a generalized Frommer method for studying first order differential equations whose coefficients need not be analytic, focusing on characteristics entering the origin from the right and on the smallness order of solutions vanishing there. It introduces comparison notions for orders…
The paper studies the long time behavior of solutions to a one dimensional reaction diffusion Cauchy problem arising in combustion theory, under structural assumptions on the nonlinear term and on the initial data. Using maximum principles, comparison arguments, Bernstein type estimates, and auxilia…
This paper studies coefficient estimates for analytic functions of two complex variables in bounded complete bicircular domains and in bicylinders, under the condition that no product of two function values equals one. Using Temlyakov’s integral representation and boundary value arguments for an ass…
The paper constructs and analyzes an iterative method for solving finite-difference systems that approximate self-adjoint elliptic boundary value problems of order 2m on a square. It first establishes that the chosen difference approximation preserves self-adjointness and positivity, then compares t…
This note studies spectral densities of stationary Gaussian processes under two dependence weakening conditions: strong mixing and a stronger conditional probability condition. It shows that the latter condition is equivalent to eventual independence of the past and future sigma algebras, yielding a…
The paper studies how smoothness classes defined by moduli of smoothness can be characterized through local piecewise-polynomial approximation, addressing gaps between direct and inverse theorems for global algebraic or trigonometric approximation. It constructs linear local interpolation processes …
This note characterizes continuous linear functionals on the space of functions analytic in a complete semicircular domain in two complex variables. Using Hartogs expansions and a reduction to finitely many bicylinders, it shows that any such functional can be represented as a series of contour inte…
This note treats the remaining binary case in the additive problem of representing integers as sums of squares of prime numbers. Using a sieve argument together with the prime number theorem in arithmetic progressions, it derives an asymptotic formula for the number of integers up to x representable…
This paper develops the method of indexials for studying subgroups of finite groups, extending earlier existence theorems in this area. It introduces regular indexials, extensions of indexials, and a measure of solvability, then relates these notions to the structure and solvability measure of corre…
This note studies Chebyshev sets in Banach spaces, focusing on when uniqueness of nearest points implies stronger geometric structure. Using a fixed point argument based on Schauder’s principle, it proves that every boundedly compact Chebyshev set in an arbitrary Banach space is a sun. It then shows…
This note develops criteria for embedding first order Sobolev type spaces on arbitrary open subsets of Euclidean space into spaces of continuous functions, using the notion of p-conductivity and p-capacity of conductors. After defining conductivity and establishing basic variational, monotonicity, a…
The paper formulates new minimax extremal problems motivated by mathematical cartography, where one seeks boundary or initial conditions for partial differential equations that make a selected unknown function deviate as little as possible from zero in a prescribed domain. After contrasting variatio…
This note studies extremal norm problems for linear polynomial operators on the space of continuous periodic functions, especially operators that reproduce derivatives or prescribed convolutions on trigonometric polynomials of bounded order. It determines the exact minimal norm for operators reprodu…
This note studies separatrices of plane dynamical systems with continuous right hand sides, uniqueness of solutions, and isolated finite singular points, using the one point compactification of the plane. It reformulates Markus’s notion of a separatrix in terms of nonordinary semitrajectories, orbit…
This paper studies value distribution of meromorphic functions whose zeros and poles are separated by angular sectors, using Nevanlinna-theoretic quantities measuring the combined deficiency of zeros and poles. It proves that such angular separation forces a positive lower bound for the deficiency u…
This paper studies bases of Boolean functions under Post’s completeness criterion, focusing on “simple bases,” in which no member can be replaced after identification of variables by functions of fewer variables while preserving completeness. It first observes that the total number of bases is infin…
This paper extends Volkonskii’s correspondence between homogeneous additive functionals of Markov processes and excessive functions. For a standard homogeneous Markov process, it introduces a regularity condition on bounded measurable excessive functions, formulated through convergence along monoton…
The paper introduces the notion of a unitary pair of bounded linear operators in a Hilbert space as a generalization of a unitary operator, characterized by relations involving one operator, its adjoint, and a completing second operator. It establishes elementary structural properties of such pairs,…
This paper presents several iterative algorithms for the complete eigenvalue problem for real nonsingular matrices with eigenvalues of distinct moduli. The methods construct sequences of triangular matrices by multiplying auxiliary matrices by orthogonal transformations, yielding convergence estimat…
The paper studies iterative methods for solving nonlinear operator equations in Banach and Hilbert spaces when the linearized Newton equations cannot be solved exactly. It formulates a general scheme in which each Newton or modified Newton step is replaced by an approximate solver for the correspond…
This paper studies geodesic mappings between Riemannian spaces and introduces an involutive transformation, called the Gamma transformation, which constructs from any pair of Riemannian spaces with common geodesics a new pair having the same property. The transformation is expressed in terms of the …
This note studies deviations between sets in metric and normed spaces arising in approximation theory, beginning with finite-dimensional geometric models in the uniform metric. It derives exact formulas for the distance from one polyhedral class to another and transfers these formulas to classes of …
The paper studies singular integral equations on a Lyapunov contour involving an orientation-preserving involutive transformation of the contour, together with the special case in which this transformation is the identity. Under modulus and compatibility conditions on the coefficients, the equations…
This paper studies hypersurfaces in four-dimensional non-Euclidean spaces of arbitrary index, formulated projectively by means of a Cayley-Klein absolute and analyzed with moving frames and exterior forms. It defines first- and second-order fundamental geometric objects for a hypersurface and proves…
This paper studies linear systems of differential equations whose coefficients are quasiperiodic functions with a common frequency basis. The method embeds the original system into a system in several periodic variables and uses the resulting periodicity to define a characteristic equation, under an…
This paper generalizes Lindemann’s theorem from the exponential function to a class of transcendental Siegel E-functions satisfying first order linear differential equations with polynomial coefficients. Using earlier algebraic independence criteria for E-functions, together with lemmas on the algeb…
This note studies homotopy-theoretic properties of locally trivial fiber spaces, with emphasis on higher obstructions to extending cross-sections and on operations with fibrations over a common base. Using Postnikov systems, it gives criteria under which truncated fibrations become products and deri…
This note studies an optimal pursuit problem for two controlled points in an n-dimensional phase space, where the pursuer seeks to minimize the capture time and the evader seeks to maximize it. Under the additional assumption that the pursuer’s dynamics are linear and nondegenerate and that its cont…
The paper proves an analogue of the Fortet-Kac theorem for normalized sums of the form \(\sum_{k=0}^{h-1} f(ag^k/p)\), where \(f\) is a bounded periodic real function of mean zero, \(g\) is fixed, \(p\) is coprime to \(g\), and \(h\) grows logarithmically with \(p\). Using the method of moments, the…
This note proves a periodicity theorem for the cohomology of the group of norm one units in a maximal order of a finite-dimensional division algebra over the rational numbers. Using Grothendieck’s theory of equivariant sheaves and the associated spectral sequences for a group action, the argument re…
This paper studies elliptic second order equations whose lower order coefficients have regular singularities of order one and two at finitely many points, including possible boundary points and infinity. It introduces weighted Banach spaces and establishes norm estimates, compactness criteria, and F…
The paper revisits M. A. Lavrent’ev’s notion of a derived system associated with a nonlinear first-order system of partial differential equations, formulated through characteristic quantities of the local mapping. It gives a simpler proof, with a refinement, of Lavrent’ev’s theorem relating positivi…
This note addresses the fundamental problem of non-Riemannian geometry for two-dimensional manifolds with symmetric affine connection, namely the conditions under which such a space is reducible to Weyl or Riemannian geometry. It classifies binary affine-connection spaces by the Weierstrass characte…
The paper studies the asymptotic power of the weighted Cramer von Mises type statistic omega squared for testing a simple distributional hypothesis against local alternatives of order n to the minus one half. It derives the limiting distribution under such alternatives as a quadratic functional of a…
This note develops a direct method for proving convergence of certain difference and differential-difference schemes without invoking existence or uniqueness theorems for the limiting differential problem. The argument uses one-sided a priori estimates and comparison of solutions on successively ref…
This paper generalizes the multidimensional Bochner theorem for positive definite functions to positive definite generalized kernels associated with systems of differential, and more general, operators. Using Hilbert space scales, generalized eigenvector expansions, and spectral measures for self-ad…
This paper strengthens earlier regularity results for bounded generalized solutions of quasilinear elliptic equations in divergence form and for Euler equations of variational integrals with natural growth in the gradient. Under reduced smoothness assumptions on the coefficients, together with coerc…
This paper studies spaces with affine connection that admit simply transitive or Abelian groups of affine collineations, with particular attention to torsion-free connections and their extensions. It derives the general form of a torsion-free affine connection admitting a simply transitive group of …
The paper studies spaces of functions analytic in bounded complete circular domains in two complex variables, more specifically \((p,q)\)-circular domains containing the origin. It constructs polynomial bases homogeneous with respect to \(w^{1/p}\) and \(z^{1/q}\), proves a convergence criterion for…
This paper gives a sufficient criterion for embedding certain monotone images of three-dimensional Euclidean space in four-dimensional Euclidean space. It considers continuous decompositions of Euclidean 3-space into points and smooth continua whose nondegenerate elements have zero-dimensional compa…
The paper extends a parameter variation method for approximating eigenvalues and eigenvectors of matrices to the case of complex eigenvalues of real parameter dependent matrices. By differentiating the characteristic equation with respect to the parameter, it derives differential equations for the r…
The paper extends earlier results on parabolic equations to Banach spaces for time dependent unbounded operators whose fractional powers satisfy uniform domain and continuity conditions. It proves existence of an evolution operator for the homogeneous problem, including semigroup composition, differ…
The paper studies norm and pointwise inequalities for entire functions of finite exponential degree in several variables, extending Bernstein type estimates and Nikol’skii inequalities. It derives a refined embedding inequality between Lp norms for classes of entire functions with prescribed degrees…
This note presents an exact method for evaluating singular and regular integrals with Cauchy-type kernels on the interval from minus one to one, of forms arising in continuum mechanics. The method introduces an analytic function in the unit disk, real on the real axis, and uses its expansion togethe…
This paper studies stability and asymptotic stability of solutions of second order ordinary differential equations, with emphasis on linear equations with variable coefficients. It first proves comparison theorems and derives amplitude estimates for solutions, then applies these estimates to the lin…
This note generalizes a theorem of Eichler on the remainder term in representation numbers associated with positive definite quaternary quadratic forms. For a theta series with a rational characteristic satisfying a level congruence, the author decomposes it into Eisenstein and cusp parts and studie…
This paper studies a continuous analogue of polynomials orthogonal on an arc of the unit circle, formulated through families of entire functions that provide isometric transforms of L2 functions on the half-line. For a spectral measure supported on the real axis with the interval (-1, 1) removed, th…
This paper studies local inequalities for orthonormal polynomials on the unit circle, relating positivity of the derivative of the orthogonality distribution, growth bounds for the Christoffel kernel, and pointwise boundedness of the polynomials. It proves that, under a local regularity condition, a…
The paper studies expansions in eigenfunctions for a nonselfadjoint second order system of differential equations on the half-line in the space of vector-valued square integrable functions, with a matrix potential and a boundary condition at the origin. Using matrix solutions with prescribed asympto…
