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 how the algebraic notion of generation can be extended to abstract classes of first order models, focusing on classes in which intersections of submodels yield natural generated submodels. It introduces pseudoaxiomatizable classes and proves that, for such classes with natural gene…
This paper studies completeness and basis properties in the Hilbert space \(L_2\) for systems of functions that are close to known complete systems. It proves a general operator criterion: an invertible bounded linear transformation preserves completeness and basis properties, then applies it to per…
This note studies when continuous minimizers of regular nonparametric double integrals in the calculus of variations satisfy a local Lipschitz condition, a property needed to obtain higher differentiability and analyticity from known regularity theorems. The paper imposes convexity and asymptotic gr…
The paper studies sequences of analytic functions in the unit disk that satisfy the Khinchin and Ostrowski hypotheses, namely a uniform logarithmic integral bound and convergence of angular boundary values on a set of positive measure. Using a previous subsequence extension theorem together with res…
This paper extends the theory of potential-harmonic vector functions from three-dimensional space to n-dimensional space. Using results of V. K. Ivanov, it derives an analogue of the Cauchy formula and applies it to relate the support function of the convex hull of the singularities of a harmonic fu…
The paper studies semi-reducible Riemannian spaces, whose metric can be written as a sum of an independent principal metric and a conformally scaled additional metric. It gives a geometric characterization in terms of two mutually orthogonal foliations, one totally geodesic and the other umbilical w…
This note extends the classification of completely irreducible linear representations from the proper Lorentz group to the full Lorentz group. Using the group ring of the full group and the known representations of the associated proper group, it formulates the additional reflection operator conditi…
This paper studies reducibility for a class of two-dimensional linear systems of differential equations with quasiperiodic coefficients, a problem complicated by small divisors and by the behavior of indefinite integrals of almost periodic functions. It introduces corresponding majorant series to es…
This paper studies obstruction classes for extending section surfaces in a pair of Serre fiber spaces arranged as a double fibration over a simply connected simplicial complex. Given two section surfaces over an r-skeleton that agree on the preceding skeleton, it compares the obstruction cohomology …
The paper addresses the problem of deciding when two algebraic fields of degree n, given by irreducible monic equations, are identical. It introduces sequences of lattice points associated with the embeddings of a field and with regions defined by bounded conjugate coordinates, and gives a computati…
This paper studies the convergence rate of the method of orthogonal projections for the first boundary-value problem for elliptic equations of polyharmonic type with constant coefficients. It constructs an orthonormal polynomial system associated with solutions of a factored differential operator, p…
This paper studies a singular Volterra type integral equation in two variables arising from a heat exchange problem for bodies in thermal contact. Using the Fourier transform of generalized functions in the sense of Schwartz, the equation is reduced to a convolution equation in the transformed varia…
This paper develops a field theory of local hypercones in an n-dimensional space for dimensions at least four, extending earlier work on local conical surfaces and their applications to variational problems and first-order partial differential equations. It treats pseudoregular central hypercones th…
This note studies inductive and projective limits of locally convex spaces whose connecting maps are completely continuous, extending classes introduced by Sebastião e Silva that include many function spaces used in analysis. It proves that inductive limits of regular sequences of locally convex spa…
This note studies Tauberian questions for generalized Fourier, or Bochner-Stieltjes, transforms associated with functions of locally bounded variation whose growth is controlled by a parameter n. It asks what asymptotic information about the spectral function can be inferred from differentiability p…
The paper applies Kantorovich’s general theory of approximate methods to the perturbative determination of eigenvalues and eigenvectors of completely continuous operators in related normed spaces. By reformulating the normalized eigenvalue problem as a nonlinear functional equation, it derives condi…
This note proposes a finite set construction from which the usual scalar product emerges as a limiting notion. It defines components, grains, symmetric grains, superposition, and a combinatorial measure of closeness between grains, then considers structures with a fixed number of elements per compon…
The paper studies the Cauchy problem for a nonlinear parabolic equation of the form u_t equals the second spatial derivative of a function of time, space, and u, including equations of nonstationary filtration that may degenerate when the solution vanishes. It defines a generalized solution through …
This paper studies sharp radius bounds under which normalized univalent holomorphic functions in the unit disk map subdisks to convex, starlike, or generalized starlike domains. Extending results of Nevanlinna, Grunsky, and Goluzin, it derives bounds for disks with arbitrary Euclidean or non-Euclide…
This note studies the inverse scattering problem on the half-line for a system of second-order differential equations with a Hermitian matrix potential satisfying a first-moment integrability condition and Dirichlet boundary condition at the origin. Using a direct Marchenko-type approach, it derives…
This paper studies the maximal number of limit cycles for a planar differential equation whose nonlinear terms are homogeneous polynomials of degree n and whose origin is a singular point of the second group. By reducing the equation through linear and polar transformations, expanding the solution i…
This paper examines why Chaplygin’s inequality theorem for a single first-order differential equation does not directly extend to systems of first-order differential equations. After giving a counterexample, it formulates additional conditions on comparison functions under standard continuity and Li…
This paper studies linear systems of equations in total differentials with coefficient matrices depending separately on two parameters and satisfying a commutativity condition, with emphasis on periodic coefficients and stability of the zero solution. It establishes properties of integral matrices, …
This note studies bounded solutions on a semi-infinite interval for an inhomogeneous convolution-type integral equation with symmetric kernel, extending earlier treatments that required stronger integrability and decay assumptions. Under square-integrability conditions on the kernel and free term, a…
This note studies a finite difference method for the nonlinear Goursat problem \(u_{xy}=f(x,y,u,u_x,u_y)\) with prescribed data on the coordinate axes, allowing a general right hand side under continuity and Lipschitz assumptions. The authors construct a bilinear interpolating approximate solution f…
This paper studies the Cauchy problem for a second order parabolic equation with variable coefficients in the whole space, allowing solutions with rapid growth at infinity. Using a weighted Hilbert space determined by a function related to the drift coefficients, the operator is shown to be symmetri…
The paper studies iterative solution of nonlinear functional equations in complete linear spaces normed by semi-ordered spaces, extending Newton and Chebyshev methods through a higher-order process interpreted as a method of tangent parabolas. Using a majorant equation, it proves that existence and …
This paper develops Frommer’s method for studying characteristics of analytic differential equations near a singular point when possible real tangents occur. It defines the order and measure of curvature of characteristics entering the origin, introduces a polygonal diagram constructed from exponent…
The paper studies evolutionary systems of linear partial differential equations with constant coefficients and shows how such systems can be transformed into scalar equations or independently integrated subsystems. Using invariant factors and polynomial similarity transformations of the coefficient …
This paper develops sharp boundary inequalities for derivatives of analytic, possibly multivalued functions of finite degree in plane domains obtained by removing a perfect subset of the real axis. Using conformal mappings of the upper half-plane onto slit domains of several types, the authors const…
This note studies boundary value problems for eigenvalues and eigenfunctions of even order ordinary differential equations in which a small positive parameter multiplies the highest derivative. Using asymptotic representations of fundamental solutions, including boundary layer terms, it derives expa…
The paper studies the biharmonic Dirichlet type problem in the unit disk with prescribed boundary values for the function and its radial derivative, relating Sobolev regularity of the solution to Nikol’skii type smoothness classes of the boundary data. Using Fourier expansions of biharmonic function…
This paper develops extensions of spaces of Banach-valued abstract functions associated with integration, starting from Bochner’s construction and replacing point functions by additive set functions. Sobolev introduces broader norms of the type Phi p, shows that completion may require ideal elements…
This note studies converse embedding theorems in the limiting case not covered by a theorem of S. M. Nikol’skii, where the smoothness parameter on the embedded subspace is zero and is interpreted as membership in an Lp space. It constructs an extension of a function given on an m-dimensional subspac…
This paper studies linear systems of partial differential equations with constant coefficients and the reduction of their Cauchy problems to systems of normal type. It defines the reduced order through the growth of the real parts of characteristic roots and proves a formula expressing this order as…
This paper develops a method for reducing systems of linear difference and differential equations with variable coefficients to diagonal forms with summable or integrable remainders, extending earlier approaches to asymptotic analysis. The construction uses a sequence of matrix transformations deter…
The paper studies formal power series solutions of nonlinear integral equations whose kernels are continuous and analytic in the unknown function and parameter. It focuses on the difficult case in which one is an eigenvalue of the associated linear integral operator, and introduces a stabilization c…
The paper presents an asymptotic solution of the one-dimensional unsteady equations for an ideal gas with spherical symmetry, expressed in terms of characteristic variables. The pressure, density, velocity, and integrating factors are expanded in series in inverse powers of radius with logarithmic t…
This paper derives asymptotic representations for angular spheroidal functions with azimuthal index m = 1 in the large parameter regime. Using a comparison equation method, the spheroidal differential equation is transformed to an equation with degenerate hypergeometric solutions, chosen to preserve…
This paper proposes a finite difference method for numerically integrating the one dimensional heat equation with homogeneous boundary conditions. The method alternates two one sided implicit difference sweeps, which can be implemented explicitly because the associated matrices are bidiagonal, and i…
The paper develops a theory of functions analytic with respect to an ordinary linear differential operator with continuous coefficients on an interval. It defines infinite operator differentiability and operator analyticity through factorial growth estimates, constructs an operator basis analogous t…
This paper develops an entropy theory for stochastic processes with general, possibly nonstationary state spaces and densities relative to product measures. It defines time-dependent process entropy, relates its existence to Cesàro summability of conditional entropies, and gives conditions under whi…
This note proposes a method for constructing stable finite difference schemes for Cauchy problems for multidimensional hyperbolic systems by composing schemes for associated one-dimensional subsystems. The authors define a common weighted norm and show that if each one-dimensional scheme is locally …
This note studies descriptive set theoretic properties of several derived delta s operations with rigid bases, focusing on points classified by the number and topological structure of chains in a reduced base that determine them. It defines first, second, third, and fourth type points, using uncount…
This paper treats a plane elasticity boundary value problem for a finite simply connected isotropic homogeneous domain, where the normal displacement and tangential stress are prescribed on a smooth boundary. Using complex potentials and specially chosen contour integral representations, it reduces …
This note proves a refined local limit theorem for sums of independent, non-identically distributed integer-valued random variables. Assuming finite absolute moments of order 2 plus delta, a Lyapunov-type fraction, and an aperiodicity condition expressed through the lattice probabilities, it establi…
The paper studies convergence classes for interpolation series associated with entire functions defined by generalized moment functionals. It formulates criteria, based on limiting functions derived from the moment kernels and on the nearest zero of those functions, that determine the exact class in…
