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 introduces a normed space of completely additive set functions on the Borel sets of a metric compact space, with a norm defined through the metric rather than total variation. It identifies the dual of the zero-mass subspace with Lipschitz functions modulo constants, extends the construct…
This paper studies intrinsic rigidity for several classes of convex surfaces in Lobachevsky space. It defines caps, generalized horospherical caps, and acute infinite convex surfaces, then proves that under bounded specific curvature and stated boundary or asymptotic conditions, an isometric convex …
This paper studies uniform convergence of eigenfunction expansions for the equation Δu + λu = 0 in arbitrary domains of even dimension, under homogeneous boundary conditions of the first, second, or third kind, when terms are summed by increasing eigenvalues. It proves that the usual smoothness assu…
This paper addresses the nomographic problem of determining when an equation of the form z = F(x,y) can be represented by a Soreau determinant and thus solved by an aligned-points nomogram. Assuming sufficient differentiability and nonvanishing first partial derivatives, it derives differential cond…
The paper studies linear elliptic partial differential equations in which a small parameter multiplies the highest derivatives, under homogeneous first boundary-value conditions. For even-order operators satisfying positivity, ellipticity, and characteristic root assumptions, it analyzes how solutio…
This paper studies the stability of periodic solutions in quasilinear autonomous systems with many degrees of freedom when the associated linear system has a multiple zero root and may have multiple purely imaginary roots, while the remaining roots have negative stability exponents after the chosen …
This paper studies boundary value problems for a second-order elliptic equation that degenerates on part of the boundary, with analytic lower-order coefficients and nonpositive zeroth-order term. It introduces an auxiliary singular weight describing the behavior of solutions near the degeneracy set …
This note extends Sobolev embedding theorems to abstract functions of sets in the space Ψp, defined as the closure of step measurable functions and characterized by absolute continuity and continuity under shifts. It defines integrals of such set functions against Lp′ kernels, proves continuity resu…
This note studies Lyapunov stability of the trivial solution for systems parabolic in the sense of I. G. Petrovskii, including systems with time-dependent coefficients in a half-space. Using estimates for the Green matrix, it gives sufficient conditions for stability and asymptotic stability in weig…
This paper studies a finite difference approximation for a boundary value eigenvalue problem involving a system of ordinary differential equations with piecewise discontinuous coefficients and matching conditions at interior points. Under symmetry, positivity, smoothness, and equal mesh size assumpt…
This paper proves embedding results for function spaces on a bounded plane domain whose metric degenerates at an interior point. It defines completions of smooth functions vanishing near the boundary and the singular point under weighted quadratic forms involving first, and then second, generalized …
This note addresses whether an asymptotically stable periodic solution of a nonlinear system persists, in a suitable sense, under small periodic perturbations. For a system with continuous periodic right hand side and a small parameter, the argument reduces the unperturbed solution to the origin, us…
This paper studies multidimensional surfaces in Euclidean and non-Euclidean spaces whose tangent spaces decompose into completely isotropic, pairwise weakly conjugate directions. Using the moving frame method and Cartan exterior forms, it derives restrictions on the first normal plane and proves tha…
This note studies the large argument behavior of solutions to a nonlinear third order boundary value problem arising in boundary layer theory, with parameters beta at least zero and positive limiting slope k. The authors transform the problem by using the dependent variable as the independent variab…
This paper studies the curvature tensor of spaces with a symmetric almost symplectic connection and derives additional identities specific to this setting. It characterizes spaces whose holonomy algebra elements associated with elementary cycles lie in the symplectic algebra, showing their equivalen…
This paper studies representations of natural numbers in the form n equals p plus a power of a fixed integer a, where p is prime and the exponent is nonnegative. Using a counting function for such representations and Romanov’s identity relating its second moment to prime differences and differences …
This note establishes a general dimension estimate for spaces of automorphic forms associated with certain discrete groups acting on bounded domains in several complex variables. It introduces Siegel domains of the first and second kinds, describes their relation to irreducible bounded symmetric dom…
The paper studies summation of analytic functions in the classes defined by bounded higher derivatives in the unit disk, extending earlier results of Stechkin on Taylor sums and Fejér means. It proves a representation theorem for a broad class of regular triangular Toeplitz summation methods, using …
This paper establishes criteria under which systems of analytic functions of the form \(z^n\varphi_n(z)\) constitute a basis for holomorphic functions in a disk or related simply connected domain. The authors express the factors through analytic logarithms, derive coefficient recursions for formal e…
This paper studies the Dirichlet problem for polyharmonic functions in the unit disk and relates the smoothness of the solution to the smoothness of the prescribed boundary values and their normal derivatives. It proves a theorem asserting that if the boundary functions belong to suitable Nikol’skii…
This paper derives analytic sufficient conditions for stability, semistability, and instability of a limit cycle of the differential equation dy/dx = P(x,y)/Q(x,y), assuming sufficient smoothness of P and Q. By introducing normal coordinates near a closed integral curve and studying the displacement…
This note studies spectral properties of semibounded self-adjoint elliptic differential operators on the whole space, including strongly elliptic systems with bounded smooth coefficients. Using estimates for the Green function of the associated parabolic Cauchy problem, it proves an \(L^2\) bound fo…
This paper studies a finite difference method for a mixed initial boundary value problem for equations of S. L. Sobolev type, involving a second time derivative applied to an elliptic spatial operator. A grid analogue is constructed, and energy estimates are derived to prove weak convergence of the …
This paper develops an abstract notion of Lyapunov norm on a linear set, defined by order-valued homogeneity and ultrametric-type subadditivity conditions. It establishes basic properties of such norms in finite-dimensional subspaces, including the existence of a specially adapted basis whose linear…
This note computes matrix elements of irreducible unitary representations of the three-dimensional Euclidean motion group using an integral method, complementing earlier infinitesimal calculations. The authors express the translation matrix elements through integrals of rotation-matrix functions, de…
The paper studies the spectral effect of adding a continuous potential perturbation tending to zero at infinity to a closed differential operator of Schrödinger type in \(L_2\) over Euclidean space. It proves that, for every point in the resolvent set of the unperturbed operator except possibly a co…
The paper studies how the largest characteristic exponent of a linear nonautonomous differential system can change under small nonlinear perturbations satisfying a Lipschitz bound. It defines a quantity Omega from bounds on the fundamental matrix of the unperturbed system and proves that, for suffic…
This paper studies oscillation and nonoscillation criteria for solutions of the second order linear equation y'' + p(x)y = 0 on a half-line. Using Riccati-type inequalities involving auxiliary differentiable functions r(x), it derives several sufficient conditions for nonoscillation and oscillation,…
This paper determines the range of the functional f(z0)/F(zeta0) for pairs of non-overlapping simply connected domains, where f maps the unit disk onto a domain containing 0 and F maps the exterior disk onto a domain containing infinity. Using Goluzin’s variational method, the author derives extrema…
This note studies groups in which every conjugacy class is finite and gives structural criteria for such groups in terms of locally normal and torsion-free central components. It proves that a torsion-free group whose quotient by its center is locally finite must be abelian, and uses this with Dietz…
This note studies a mixed initial boundary value problem for a second order hyperbolic integro-differential equation with measurable elliptic spatial coefficients, lower order terms, and integral terms involving the unknown function and its time derivative. Using expansion in generalized eigenfuncti…
This paper studies local representation of solutions to the Euler Poisson Darboux equation near the symmetry axis, extending a known integral representation involving an analytic function of one complex variable. For domains adjacent to an interval of the axis and satisfying a vertical convexity con…
This paper studies boundary-value problems for elliptic systems of differential equations in the plane, including higher-order systems with nonlocal boundary terms. The problem is reduced, using Sobolev’s integral identity, to a first-order elliptic system with an integral term, then analyzed throug…
This paper extends results of Hardy, Ingham, and Pólya on mean moduli of analytic functions in a finite strip, removing the assumption of boundary continuity. It studies classes defined by harmonic majorants of subharmonic functions and by bounded integral means, proves boundary value and factorizat…
This paper defines and studies spaces of symmetric almost symplectic connection on even dimensional differentiable manifolds equipped with a nondegenerate skew-symmetric tensor. It derives the affine connection from the tensor together with a symmetric geometric object satisfying a specified transfo…
This note proves asymptotic uniformity for the distribution of integral points on the four-dimensional sphere defined by a sum of four squares equal to an odd integer. Building on Jacobi’s formula and a refinement of Kloosterman’s method, it estimates exponential sums over the sphere and uses Fourie…
This note proves a local limit theorem for sums of integer-valued variables forming a nonhomogeneous Markov chain with countably many possible states. Under a uniform minorization condition, linear growth of the variance, bounded moments of order at least three, and an aperiodicity condition express…
This paper derives an integral-form solution for a mixed initial-boundary value problem for a coupled system of two parabolic differential equations arising in heat and mass transfer. The method extends the unknown functions evenly across the coordinate axes, applies a double Fourier transform on a …
This note establishes local limit theorems for large deviations of sums of independent random variables, where the normalized deviation tends to infinity but remains \(o(\sqrt n)\). Using a systematic saddle point argument, it derives asymptotic formulas for densities in the non-identically distribu…
This paper develops the axiomatic theory of radicals of associative rings in the framework of Kurosh and Amitsur. It studies radicals whose radical rings are closed under ideals, introduces complementary and dual radicals, and characterizes special classes of rings that define upper radicals, includ…
The paper studies a Riemann type boundary value problem for first order elliptic systems reducible to the generalized analytic equation involving the conjugate derivative of a complex function. Using Vekua’s correspondence between regular solutions and analytic functions, together with an analogue o…
This paper develops number-theoretic quadrature formulas for approximating multiple integrals of periodic functions over the unit cube. It constructs deterministic sampling points from fractional parts of polynomial residues modulo primes or prime squares, and proves error bounds using estimates for…
This paper studies spectral properties of Volterra integral operators and their role in inverse problems for differential equations. It gives sufficient smoothness and nondegeneracy conditions on a Volterra kernel under which the corresponding operator is linearly equivalent to the double integratio…
This paper studies convergence of approximate methods for differential equations in Banach spaces with unbounded linear operators and bounded nonlinear terms. It establishes conditions under which solutions of equations with bounded approximating operators converge uniformly to the corresponding sol…
This note studies the location of extremal error, or alternation, points for polynomials of best uniform approximation to a continuous function on the interval [-1,1]. Motivated by the computational efficiency of the mesh version of the Remez method, it derives bounds for these points under the assu…
The paper studies two classes of infinite systems of linear algebraic equations with convolution-type coefficients, drawing an analogy with integral equations on the whole line and half-line. It introduces Laurent and generalized transforms for two-sided sequences, proves convolution and analytic-co…
This note studies uniqueness properties of real functions of several variables that are continuous in each variable, in connection with the Sierpiński and Tolstov theorem that such functions of two variables are determined by their values on an everywhere dense set. It shows by example that an analo…
This paper studies the computation of the smallest eigenvalue of a real symmetric positive integral-equation kernel using traces of iterated kernels. It reformulates the Fredholm determinant trace expansion through the series for the ratio of the determinant to its derivative, derives positivity and…
This paper studies conjugacy and intersections among several classes of triangular sequence transformations, especially Hausdorff, Voronoi, Riesz, Cesàro, Euler, and analytic transformations. It formulates criteria connecting conjugate Hausdorff transformations through delta transformations, absolut…
