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 the relation between Nevanlinna growth and the growth of a meromorphic function on a fixed ray, extending earlier inequalities for entire functions. Using a Green function representation in a sector and integral estimates for boundary values and poles, it proves that if a meromorp…
The paper proposes a general framework intended to unify ordinary topological spaces, proximity spaces, and uniform spaces through families of set-valued mappings defined relative to specified collections of subsets. It formulates axioms for a “topology in the broad sense,” defines bases, comparison…
The paper studies the approximation of mixed boundary-value problems for second-order parabolic and hyperbolic equations by Cauchy problems posed in the whole space with coefficients depending on a small parameter. The coefficients are extended outside the original domain with prescribed powers of t…
This note develops a theory of singular integral operators and equations on closed Lyapunov manifolds in Lipschitz spaces, extending earlier multidimensional results obtained under stronger smoothness assumptions. It defines singular operators on manifolds via local coordinate representations, intro…
This note studies internal extensions of incomplete Archimedean planes and spaces satisfying selected Hilbert axioms, focusing on relations between real and ideal elements without increasing dimension. It establishes properties of real and ideal circles and spheres, including the nonexistence of rea…
This paper studies coercivity estimates for abstract parabolic Cauchy problems in Banach spaces generated by strongly continuous semigroups. It proves that, in weighted Hölder-type spaces and their higher-order analogues, such coercivity is equivalent to strong positivity of the operator, characteri…
The paper develops estimates for the spectral radius of bounded linear operators, motivated by the difficulty of computing the spectral radius from powers of the operator and by the crudeness of norm estimates. Using an order-theoretic theorem for positive operators dominated with respect to normal …
This paper studies a nonlinear singular integral equation with Hilbert kernel in the generalized Hölder-type space \(H_k(\varphi)\). It establishes auxiliary compactness, convergence, and boundedness properties for this function space and for the associated singular integral operator, then proves th…
The paper proposes a statistical formulation of well-posedness for problems of mathematical physics whose initial or boundary data are obtained with experimental error and are treated as realizations of random processes. Focusing on the Cauchy problem for the Laplace equation in a strip, it derives …
This paper develops a unified axiomatic foundation for geometries with free mobility whose metric may be positive definite, alternating, or degenerate, using points, lines, order, incidence, motion, and a distinguished class of postulated lines. It introduces variable postulates governing homogeneit…
The paper studies integral transformations in the complex plane with kernels built from Mittag-Leffler type functions, extending Fourier-Plancherel and Paley-Wiener theory to sets formed by finitely many nonoverlapping rays and angular domains with a common vertex. It defines weighted square-integra…
This paper studies analytic functions in the unit disk belonging to the area integral class H′p and compares this class with the classical Hardy classes Hp. It proves several inclusion and noninclusion results involving derivatives, including conditions under which f′ in H′1 implies f in H1, when me…
The paper studies a modified Riemann-Hilbert boundary value problem for a first-order elliptic system that degenerates on a segment of the boundary. Rewriting the system in complex form, it derives solvability and uniqueness results according to the parameter governing the degeneration, the index of…
The paper develops a method for determining Green’s functions for boundary-value problems of the heat-conduction equation on a line segment whose endpoints move uniformly. By transforming to a coordinate system moving with one boundary, applying Laplace transforms and the Riemann-Mellin inversion fo…
This paper studies stability of sequences of linear computational problems in Banach spaces under perturbations of both the operator and the right hand side. It gives necessary and sufficient conditions for stability in terms of uniform boundedness of the inverse operators and of the quantities obta…
This paper generalizes P. S. Alexandrov’s theorem on one-point bicompactification to non-bicompact T1 spaces using the notion of a noncontractible bicompact extension. It constructs a space by adjoining a single point and defining neighborhoods of that point as complements of closed bicompact subset…
This paper proposes a modified small-parameter method for solving the Boltzmann kinetic equation, motivated by Poincaré’s treatment of auxiliary variables in asymptotic expansions. The distribution function is expanded while its dependence on density, velocity, pressure, and a rescaled time is used …
This paper presents a successive approximation method for finding a best approximating polynomial, understood as an element of a finite-dimensional span in a normed space. The method constructs a sequence of auxiliary minimax problems involving finitely many norming functionals, each solvable by lin…
The paper extends Lax-type convergence theorems for stable difference schemes to broader classes of nonlinear evolution equations in Banach spaces, including equations with a linear principal part and quasilinear equations. It formulates abstract consistency and stability conditions for quotient-spa…
The paper studies Fourier series of continuous functions with respect to the Haar system, focusing on conditions for absolute convergence of Haar Fourier coefficients and the sharpness of such conditions. It establishes criteria involving moduli of continuity and best approximation by Haar polynomia…
The paper establishes Cauchy-type integral representations for analytic functions in domains bounded by smooth or Lyapunov contours, with densities modified by a prescribed Hölder continuous function of given index. Using solvability results for Riemann boundary value problems, including versions wi…
The paper studies solvability of Cauchy problems for linear and nonlinear evolution equations of arbitrary order in a Banach space. Using semigroup methods, it first establishes a representation and differentiability result for first-order equations generated by semigroups of specified classes, then…
The paper addresses the extension of algebraic homotopy methods beyond polyhedra by proposing universal homotopy groups for arbitrary subcategories of pointed normal spaces. It formulates a system of axioms for a functor to groups, including a Whitehead-type property, compatibility with ordinary hom…
This paper studies analogues of classical horospheres in Grassmann manifolds associated with non-Euclidean projective spaces of index l, focusing on the case where infinitely distant elements represented by generators of the absolute exist. Horospheres are introduced as limits of geodesic spheres wh…
The paper studies an approximate multiple-collocation method for boundary-value problems for linear ordinary differential equations with analytic coefficients depending on a complex parameter. The solution is expanded in functions satisfying the boundary conditions, and the coefficients are determin…
The paper studies recovery of an analytic function from the values at a point of its successive generalized derivatives in the sense of Gelfond, generated by a fixed analytic function. It first recalls a uniqueness result for points inside a disk determined by the nearest zero of the generating func…
The paper studies finitely presented groups whose defining relators satisfy a small cancellation condition: overlaps between distinct noninverse relators have length less than one sixth of a relator. It proves strengthened Greendlinger type lemmas for ordinary and circular words, introducing configu…
This paper studies when a real equation of the form t3 = f(t1, t2) can be represented by a nomogram of the second kind with a rectilinear t3 scale. Using the associated function M and the Saint-Robert function, it reduces nomographability to solvability of Gronwall’s differential equation and derive…
This paper studies a multi-index transportation problem with axial sums, formulated as the minimization of a linear objective over a nonnegative array with prescribed one-dimensional marginal sums. It establishes necessary and sufficient consistency conditions for feasibility, gives a constructive b…
This note extends properties of multiple power series to multiple Hartogs series in bounded complete multiple Hartogs domains. It establishes convergence criteria and coefficient estimates using the quantities defined by suprema of monomials over the domain, then proves isomorphisms between spaces o…
The paper studies a class of ultraparabolic second-order equations in which diffusion acts only in part of the variables while first-order terms couple these variables to the remaining ones. Under nondegeneracy conditions on the coupling matrix and bounded smoothness assumptions on the coefficients,…
This note proves a limiting amplitude principle for exterior boundary value problems for the three-dimensional wave equation with a time-harmonic forcing term, posed outside a smooth star-shaped obstacle. The argument treats Dirichlet, Neumann, and Robin boundary conditions, reducing the time-depend…
This paper studies weakly dense subspaces of dual Banach spaces whose associated norm on the original space is not equivalent to the given norm, termed subspaces of characteristic zero. It proves that if a Banach space is isomorphic to a Cartesian product with a nonreflexive factor, then its dual co…
This paper studies a special case of the Behrens-Fisher problem concerning the existence of nonrandomized similar tests, with respect to the unknown variances and common mean, that depend only on the sufficient statistics from two normal samples. By transforming these statistics to two variables on …
The paper studies an elliptic first order system in four real variables interpreted through quaternionic notation as an analogue of the Cauchy, Riemann equations. Using a quaternionic form of the Gauss, Ostrogradsky formula and the fundamental solution of the four dimensional Laplacian, it derives C…
The paper studies approximation methods for singular solutions of the Chaplygin equation near the degenerate line and along characteristic boundaries. It reformulates the problem through an auxiliary equation, constructs Riemann integral kernels from boundary data, and develops iterative expansions …
This paper develops a spatial analogue of the length and area method used in the theory of plane conformal and quasiconformal mappings, based on transformations of a three-dimensional Dirichlet-type integral. For continuously differentiable topological mappings in Euclidean three-space with bounded …
This note proves several completeness theorems for root subspaces of completely continuous operators in a separable Hilbert space, using resolvent estimates and growth arguments for entire functions. It establishes criteria in terms of singular numbers, including results for operators with nonnegati…
The paper establishes an \(L_p\) inequality for trigonometric polynomials that yields S. N. Bernstein’s theorem as a special case. Using two summation and integral representation lemmas, it derives a basic norm estimate for an operator defined by convolution with an auxiliary trigonometric polynomia…
The paper studies quasiconformal mappings between simply connected domains in n-dimensional space that are closest to conformal mappings in the sense of minimizing the distortion constant relative to conformal capacity. It defines “best extremal” mappings through equality in the capacity distortion …
This paper studies nonnegative harmonic functions in a smooth plane domain satisfying an oblique derivative boundary condition, with possible singular behavior allowed at exceptional boundary points where the normal component of the vector field changes sign. Using an extension of Martin’s method fo…
The paper defines and studies the space of relative topology, obtained from a topological space by taking components of elements of a base, as a topological invariant generalizing the Mazurkiewicz and Urysohn space of relative metric. It establishes basic preservation and characterization results, i…
This note studies weighted norm estimates for entire functions of finite exponential type on lines parallel to the real axis, under a polynomial growth condition on the weight function. Using an auxiliary factor involving the sine kernel and Boas-type interpolation, the authors derive bounds for sym…
The paper studies the homogeneous Dirichlet problem in a bounded multiply connected plane domain for an elliptic system of second-order differential equations with variable matrix coefficients. It constructs a Levi function and uses Green’s formula to represent solutions, then reduces the boundary-v…
This paper studies smooth codimension one foliations on compact oriented manifolds, focusing on the structure of connected components defined by transverse accessibility. It classifies possible components, introduces a partially ordered invariant of a foliation, and develops tools based on closed tr…
This paper studies closures of classes of Hausdorff topological spaces under omega-mappings, defined by the ability to refine inverse images of an open cover through a continuous map into another space. It introduces the notion of a class omega-generating a space and records general closure properti…
The paper classifies semisimple Lie algebras over a p-adic field by reducing the problem to absolutely simple forms over finite extensions and applying root-system methods, including Satake’s description of forms. It proves the existence of a maximal nilpotent subalgebra over an unramified extension…
This paper studies automorphisms of planar groups acting orientation preservingly on cellular decompositions of the plane with bicompact fundamental domain, a class including fundamental groups of orientable closed surfaces. It gives an algebraic description of such groups and proves that every auto…
The paper studies an approximate solution of the Dirichlet problem for the Laplace equation in the unit multidimensional cube with continuous boundary data, focusing on computation at an interior point. It represents the solution through the normal derivative of the Green function, derives a conveni…
The paper studies the large time behavior of solutions to one dimensional boundary value problems for a quasilinear parabolic equation with uniformly positive dependence on the spatial derivative term. Using comparison arguments, auxiliary monotone solutions, compactness, and passage to stationary l…
