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 modules of families of curves and hypersurfaces in an n-dimensional Euclidean domain with two distinguished boundary continua, together with the associated conformal capacity. Using a potential defined from a nonnegative metric and a coarea-type argument, it proves an integral ine…
This paper develops a geometric framework for the space of mutually absolutely continuous probability distributions on a measurable space. It embeds probability measures in a cone of positive measures, uses Radon-Nikodym derivatives to define tangent and dual structures, and introduces a flat affine…
The paper studies quadrature formulas for integration on a finite interval when accuracy is controlled by comparing two formulas using partly shared nodes. It defines the cost and algebraic accuracy of individual formulas and pairs, proves a lower bound relating the cost of a pair to its accuracy, a…
This paper studies fundamental matrices used to represent solutions of homogeneous boundary value problems for general constant coefficient parabolic systems in a half space. Under Petrovskii parabolicity, homogeneity, and an algebraic complementing condition, the argument analyzes the Fourier-Lapla…
This paper studies the Cauchy problem for a higher order differential operator that factors into powers of wave operators with distinct propagation speeds. The authors derive formulas expressing the solution in terms of spherical means of the initial data, first for the strictly hyperbolic case and …
The paper studies the high energy asymptotic behavior of the trace of the spectral function for a self-adjoint second order elliptic differential operator in Euclidean space with uniformly elliptic coefficients and nonnegative potential. Since known pointwise asymptotics for the spectral function ar…
This note studies the scalar product of Hecke Z-functions attached to Größencharaktere of two distinct imaginary quadratic fields, expressed as a Dirichlet series over pairs of integral divisors with equal norms. It proves regular continuation of this function into a half-plane slightly to the left …
The paper studies nonhomogeneous linear equations of infinite order with constant coefficients in generalized derivatives, seeking analytic or entire solutions under conditions on the coefficient sequence defining the derivative and on the characteristic function. It reformulates the equation as an …
This note studies angular limit values at a prescribed point of a simple rectifiable plane arc for Cauchy type integrals whose densities satisfy local estimates relative to a bounded nonnegative lower semicontinuous function. It introduces geometric measure quantities describing how the curve and th…
The paper studies the long-time behavior of solutions to first boundary-value problems with zero boundary data for certain degenerate quasilinear parabolic equations, including one-dimensional nonstationary filtration type equations and a multidimensional analogue. Assuming existence of regularized …
The paper studies a class of non-self-adjoint boundary-value problems in which the spectral parameter appears both in the differential equation and in the boundary condition, although the corresponding fixed-parameter operators and boundary conditions are self-adjoint. Using an abstract Hilbert spac…
This paper studies analytic mappings of bounded domains in complex Euclidean space through the variational characterization of the Bergman function. It defines a class of mappings normalized by the modulus of their Jacobian at a point and proves that the reciprocal infimum of the squared integral of…
The paper studies convolution type integral equations on the half line with integrable kernel and right hand side, under the condition that the Fourier transform satisfies \(1-K(t)\neq 0\). By extending the equation to the whole line and applying Fourier transforms, the problem is reduced to a Wiene…
This paper studies the topological analogue of the Baer radical for associative Hausdorff topological rings, defining it by transfinite iteration from closures of sums of topologically nilpotent ideals. It establishes general characterizations and inclusion properties, including that the radical is …
This paper studies the steady state of elastic hereditary systems governed by Volterra integral equations whose kernels may have forms that make closed form solution impractical. It proves a theorem giving a direct limiting solution for equations with positive input and kernel when the integral of t…
This note studies spaces of sequences with terms in a locally convex space as functorial constructions, extending earlier work on Banach spaces to categories of separated locally convex spaces, especially nuclear Frechet spaces. Starting from a perfect sequence space with a normal topologizing syste…
This paper studies multiple completeness of systems of eigen and associated elements for compact operator pencils that are rational functions of a complex parameter in a separable Hilbert space. It develops growth estimates for resolvents near infinity and near finite singular points, using a Phragm…
This paper proves a symmetrization principle for functions regular in multiply connected planar domains bounded by finitely many Jordan curves, extending Hayman’s principle and a generalization by Abe and Kobori. Using Lindelöf’s principle, it establishes a lower bound for the inner radius of the im…
This paper studies the Riemann boundary-value problem on a domain with boundary interval extending to infinity in the case where the coefficient has infinite positive index, modeled by an argument growing as a Hölder perturbation of a positive multiple of t to the power rho, with 0 < rho < 1/2. A ca…
The paper studies boundedness and stability of solutions to linear partial difference equations with values in a complex Banach space on an unbounded multidimensional domain, under natural boundary conditions. It formulates necessary and sufficient stability criteria first for constant operator coef…
This paper studies the spectral multiplicity of self-adjoint operators in L2 generated by formally self-adjoint ordinary differential expressions of arbitrary even order, allowing one or both endpoints of the interval to be singular. Using properties of solutions of the equation l[y] = λy on a fixed…
This paper studies stochastic differential equations in a separable Hilbert space driven by a Wiener random measure, with a linear evolution operator and nonlinear drift and diffusion terms. Under boundedness, Lipschitz, and differentiability assumptions, it establishes differentiability of the solu…
This note proves the real case of K. Mahler’s hypothesis on the measure of the set of real S-numbers, establishing that the supremum of the exponents theta_n equals 1 for all n. Building on a previous argument for complex numbers, it develops estimates for integer irreducible polynomials of fixed he…
This paper studies whether locally nilpotent torsion-free groups are determined by the lattice structure of their subgroups, and how structural isomorphisms relate to mappings of group elements. Building on known results for abelian, nilpotent, and metabelian groups, it proves that a nonabelian loca…
This paper studies the inverse spectral problem for a singular Sturm-Liouville equation on the half-line with locally summable real potential and two different boundary conditions at the origin. For a class of potentials characterized by specified asymptotic and separation properties of the spectral…
This paper studies hypothesis testing with nuisance parameters in exponential families, focusing on hypotheses expressed as polynomial relations among the natural parameters. It restricts attention to randomized similar tests based on sufficient statistics and considers optimality against simple or …
The paper studies additive structure under small doubling, especially finite sets of integers K for which the sumset 2K has size less than C times the size of K. It proves that such a set is contained in the homomorphic image of the lattice points of a convex set in a bounded-dimensional integer lat…
The paper studies the first boundary value problem for the nonstationary Navier-Stokes equations by projecting the system onto spaces of solenoidal functions and treating the resulting evolution equation in the Banach space setting. It establishes resolvent estimates for the Stokes operator in \(H_q…
This note studies a general mixed initial-boundary value problem in a rectangle for a two-dimensional integro-differential equation of arbitrary order, including as a special case mixed problems for general hyperbolic equations. Under smoothness assumptions, compatibility conditions at the corner po…
The paper applies the method of fractional powers of operators to the Navier-Stokes equations in a bounded domain, formulated as an integral equation in the Hilbert space of solenoidal square-integrable vector fields. It establishes estimates relating fractional powers of the Stokes operator and the…
The paper studies Fredholm integral equations with kernels smooth in one variable and applies the resulting spectral estimates to linear differential boundary-value problems. It proves that the Fredholm determinant and resolvent numerator are entire functions of order at most 1 divided by the smooth…
The paper studies the spectral structure of non-self-adjoint differential operators obtained by relatively small lower-order perturbations of self-adjoint, and more generally normal, operators in Hilbert space. Using compactness assumptions on powers of the perturbed resolvent and analytic Fredholm …
The paper studies mean square sums of Fourier coefficients of a parabolic form when the indices are restricted to an arithmetic progression modulo a prime. Using a modification of Rankin’s method, the authors construct an associated Dirichlet series, analyze its pole and functional behavior, and red…
The paper studies the construction of irreducible polynomials over finite fields, motivated in part by applications to linear coding theory. It defines an operator transforming polynomials by Frobenius powers and proves a divisibility lemma, then uses it to establish that certain irreducible factors…
The paper formulates criteria for the existence of periodic and globally bounded solutions of ordinary differential systems with periodic right hand sides, using the method of guiding functions and topological fixed point arguments. It gives conditions involving a guiding function of nonzero index, …
This paper studies when a one-to-one continuous map from a topological space onto a metric space forces the domain to be metrizable or the map to be a homeomorphism. Using Bing’s metrization criterion, it proves that a locally connected, peripherally bicompact space condensed onto a metric space is …
This paper studies periodic groups expressible as uniform products of their p-subgroups, a form of subgroup factorization in which cyclic subgroups from distinct factors are pairwise permutable. It gives structural criteria for groups decomposable into uniform products of Sylow p-subgroups, characte…
This note gives an elementary proof of the existence of universal compact Hausdorff spaces of prescribed weight and finite covering dimension. For every cardinal weight and every nonnegative integer dimension, it constructs an n-dimensional bicompactum of that weight containing homeomorphic images o…
This note studies linear difference equations with constant coefficients on the integer lattice, including homogeneous equations, equations with a point source, and equations with a general right-hand side. Using the characteristic trigonometric polynomial, the authors identify a zero-free complex s…
The paper develops a finite-difference grid method for second-order strongly elliptic equations, motivated by the need for convergence estimates that do not require continuous fourth derivatives of the solution. It constructs grid equations variationally by averaging the coefficients of the differen…
This paper develops the theory of scales of Banach spaces, focusing on minimal scales and their interpolation properties. It defines regular and reflexive continuous normal scales, proves that maximal scales constructed from normally embedded endpoint spaces are regular, and shows that a minimal sca…
This note examines the Fisher, Welch, Wald test for equality of the means of two normal samples when variances are unknown and possibly unequal, focusing on whether a nonrandomized similar test of the usual boundary form can exist. Building on earlier nonexistence results under differentiability and…
This paper develops one-sided versions of Chebyshev-type probability inequalities that require assumptions only on one tail of a distribution rather than on moments over the whole real line. It proves a general bound for probabilities of the form P(X ≥ t) and P(X ≤ -t) using monotone nonnegative fun…
This paper studies the first boundary-value problem for two-dimensional Monge-Ampere equations in a convex domain, seeking solutions regular up to the boundary. It introduces boundary-dependent geometric quantities, lower and upper twisting of the prescribed boundary curve, and uses them to formulat…
This note studies symmetric Banach spaces of measurable functions on the unit interval, defined by rearrangement invariance and monotonicity with respect to absolute value. It characterizes the possible fundamental functions of such spaces, proves continuous embeddings between every symmetric space …
This paper studies involuted semigroups representable by semigroups of complete binary relations, with multiplication and inversion of relations, and their ordered analogues under inclusion. It gives a necessary and sufficient condition for an ordered involuted semigroup to be represented by complet…
This paper studies regularity of proximity spaces, understood as possession of a greatest compatible uniform structure, and shows that not every proximity space is regular. It introduces a strong Cartesian product for proximity spaces, compares it with the earlier weak product, and derives criteria …
The paper studies the high frequency asymptotics of eigenvalues of the Laplace operator in an m-dimensional polyhedron with either Dirichlet or Neumann boundary conditions. It proves that the standard Weyl remainder for a piecewise smooth domain can be sharpened in the polyhedral case from \(O(k^{m-…
This note extends Radon-type potential theory for irregular domains in three-dimensional space from double-layer to single-layer potentials and applies it to Dirichlet and Neumann boundary problems. Under a bounded-variation condition on the solid angle, it defines interior and exterior boundary flu…
The paper studies majorants for the kth derivative of algebraic polynomials of degree at most n, comparing the classical Markov majorant under a uniform bound on the interval with a discrete majorant defined by bounds at n plus 1 interpolation nodes. It proves an exact formula for the discrete major…
