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 how the rate of uniform approximation of a function by algebraic or trigonometric rational functions controls global regularity properties expressed through generalized variation, generalized absolute continuity, and Orlicz space moduli. Using estimates for the Phi-variation and O…
The paper studies the first boundary-value problem for a class of differential equations and systems in function spaces more general than weighted or unweighted Sobolev spaces, whose polynorms include both derivatives and differential expressions. It formulates geometric and weight conditions on pos…
The paper studies the spectral and scattering theory of a three-dimensional Schrödinger operator for spinor wave functions that includes a spin-orbit interaction term, as used in the optical model of the nucleus. Under decay and regularity assumptions on the scalar potential and spin-orbit coefficie…
This paper studies conjugate functions associated with periodic summable functions and the regularity of integral transforms built from them. For even one variable functions, it establishes continuity and uniform convergence results for transforms defined through the conjugate function, including a …
This note studies mixed initial-boundary value problems in a cylindrical domain for general first-order hyperbolic systems whose coefficients need be Hermitian only on the lateral boundary. Under generalized Petrovskii hyperbolicity, a noncharacteristic boundary condition, and Friedrichs-type positi…
The paper studies infinitesimal bendings of surfaces of revolution with positive curvature when the pole is a conical or parabolic singular point. It develops a reduction of a first order generalized Cauchy, Riemann type system with singular coefficients to a second order elliptic equation, then app…
The paper studies statistical characterization of linear types of distributions under transformations of location and scale, focusing on symmetric stable laws. It proves that the linear type generated by a symmetric stable distribution belongs to the union of the classes characterized by invariant s…
This paper studies asymptotic properties of solutions, spectra, and eigenfunctions for one-dimensional singular differential systems of the form y' equals mu A(x)y under structural and regularity assumptions on the matrix coefficient at infinity. It proves a fundamental matrix asymptotic expansion f…
The paper develops an integral representation for sufficiently smooth functions of several variables using mixed finite differences and derivatives indexed by subsets of coordinate directions, extending a representation associated with V. P. Il’in in a special case. It introduces and compares severa…
The paper studies embedding theorems for weighted Sobolev type spaces of functions defined on unbounded Euclidean domains, including half-spaces and traces on lower-dimensional hyperplanes. It defines appropriate weighted norms, including fractional-order variants, establishes several trace and embe…
This paper studies Gaussian probability measures on the space of continuous linear functionals over a real separable countably Hilbert space. It characterizes the possible mean and covariance functionals, showing that they arise from a continuous linear form and a positive nuclear operator with resp…
This paper studies finite groups whose Sylow 2-subgroups have a specified presentation and relates them to earlier classification results of Gorenstein and Walter. It proves that if the centralizer of a distinguished involution in such a group is soluble, then the group has one of three described st…
This paper studies when metrizability is preserved under quotient monotone mappings in set-theoretic topology. After showing that pseudo-open bicompact images of metric spaces can be represented as pseudo-open, bicompact, monotone images of another metric space, it proves the main theorem: a quotien…
This paper studies topological properties of function spaces arising in the variational theory of closed geodesics, focusing on spaces of unoriented loops and unoriented closed paths on Riemannian manifolds diffeomorphic to spheres. Using a grading of homology groups by critical values of the length…
This note studies how structural relations among maximal subgroups of a finite group constrain its normal structure, especially nilpotency, solvability, and supersolvability. It proves that quasireachability or permutability conditions on first through fourth terms of maximal series force strong res…
The paper proves a local existence theorem for a smooth solution of a mixed initial boundary value problem for a quasilinear system modeling aspects of short-range weather forecasting in a domain unbounded in the horizontal variables. The solution is constructed by the method of fractional steps, re…
This paper develops a structural approach to dimension by first defining dimension for partially ordered sets in terms of chains of filters, then applying this notion to basic lattices of closed sets in topological spaces. It proves that zero-dimensional distributive lattices with zero and unit are …
The paper studies bounded linear operators in Hilbert spaces equipped with an indefinite metric, focusing on plus-operators, \(J\)-noncontracting operators, and their adjoints. It develops an elementary theorem on Hermitian sesquilinear forms and applies it to show when plus-operators are collinear …
This paper formulates and analyzes three linearized inverse problems for hyperbolic equations arising from wave propagation. The first concerns recovery of a refractive coefficient from boundary travel times, and in a special background medium it is reduced to determining a perturbation from its int…
This note studies closed subalgebras of the algebra of continuous complex functions on a compact Hausdorff space, focusing on antisymmetry, weak analyticity, and partitions associated with such algebras. It introduces antisymmetric measures and sets of weak analyticity, proves reconstruction criteri…
This note studies how structural and embedding properties of selected subgroups determine the structure of finite groups. It formulates a series of classification results for groups whose maximal, higher maximal, or maximal solvable subgroups satisfy restrictions such as being minimal nonnilpotent, …
This paper studies extremal norm problems for linear polynomial operations on translation-invariant spaces of periodic functions, especially continuous and integrable periodic functions. For convolution-type operations determined on trigonometric polynomials of order at most n by a kernel, the paper…
This paper studies when a premeasure defined on cylindrical sets in a real linear space can be extended to a countably additive measure without assuming a topology on the space. It proves that, when the chosen linear functionals separate points, such an extension exists exactly when the image of the…
This paper studies spaces representable as limits of inverse spectra whose terms are metric spaces, extending earlier work on spectral decomposability. It introduces notions of extremal spectra and uniform extremal spectra, then proves that the completion of a uniform space is the limit of a unique,…
This paper develops the notion of hyperscales of ideal Banach function structures within the setting of measurable functions ordered almost everywhere. It defines hyperscales by a logarithmic convexity type inequality, establishes existence and properties of maximal hyperscales, and proves interpola…
This note studies skew fields of fractions associated with universal enveloping algebras of Lie algebras over a field of characteristic zero, motivated by noncommutative rings arising in analysis. It introduces a dimension invariant for arbitrary fields over a base field, proves that filtered algebr…
This paper studies spaces of analytic functions in complete multiple Hartogs domains, with emphasis on domains whose projections may be unbounded. Using Hartogs series expansions, it establishes coefficient estimates, convergence criteria, and uniform convergence consequences for bounded analytic fu…
This paper studies lower bounds for the diameter of finite strongly connected directed graphs in terms of the number of vertices and the cyclomatic number. Building on a known radius inequality, it proves that for any such graph with cyclomatic number at least two, the product of the diameter and th…
This note establishes criteria for completeness of systems of root vectors of completely continuous linear operators in a Banach space equipped with an additional weaker Hilbert norm. It extends Hilbert space completeness results to spaces with two norms, proving completeness theorems for perturbed …
The paper develops a general framework for recursive hierarchies of length up to the least nonconstructive ordinal in an arbitrary space, using set-theoretic operations, bases, and effectively controlled numberings. It introduces standard operators on enumerated families of sets, defines recursive h…
This paper determines the exact radius of circular univalence for a meromorphic subclass of the class Phi consisting of finite sums of principal parts with prescribed argument relations among coefficients and poles. Using a sharp lemma on positivity of real parts for products of powers, together wit…
The paper studies weighted Sobolev spaces on a bounded Lipschitz domain, where the weight depends on the distance to a smooth manifold that may lie on or inside the boundary. It formulates trace and zero boundary conditions according to whether a certain integral determined by the weight converges, …
This note studies whether the range conclusion in the Riesz-Thorin interpolation theorem can be sharpened from an ordinary Lebesgue space to a smaller rearrangement-invariant space. Using Lorentz-type spaces defined by decreasing rearrangements, the authors prove an interpolation theorem for operato…
The note studies quasiconformal mappings in three-dimensional Euclidean space, with emphasis on distortion estimates for self-mappings of the unit ball and on extremal mappings of domains with edges. Using modulus estimates for ring domains and comparisons with planar extremal mappings, it derives H…
The paper studies closed primary ideals in the convolution algebra of integrable functions on the positive half-line, using Fourier transforms on the closed lower half-plane and invariance under right shifts. It describes three cases: interior points yield a discrete chain of ideals defined by vanis…
This note studies the classification of completely irreducible representations of a connected semisimple complex Lie group in arbitrary complete locally convex spaces. It introduces notions of complete irreducibility and weak equivalence suitable for nonunitary representations, relates them to the c…
This paper studies stability of normal solvability and of the index for closed extensions of general partial differential operators with variable coefficients in a bounded domain. Using Hilbert space decompositions of domains between the minimal and maximal operators, it gives criteria under which s…
This paper presents two finite-difference schemes for the initial-boundary value problem for the incompressible Navier-Stokes equations in a bounded three-dimensional domain. The authors formulate an implicit grid method with discrete solenoidality, boundary and initial conditions, prove layerwise u…
The paper studies stability conditions for singularly perturbed systems with slow and fast variables, motivated by resonance problems in nonlinear oscillations. After shifting a nearby equilibrium, the authors reduce the problem to a linear system with a small parameter and nonlinear perturbations w…
This paper addresses Severi’s question whether a complex algebraic surface with vanishing first homology and geometric genus zero, or more strongly a simply connected surface with geometric genus zero, must be rational. Using the theory of principal homogeneous spaces over elliptic fibrations and re…
This note proposes a method for studying a nonlinear singular integral equation with Cauchy-type kernel in a weighted Hölder class introduced by Guseinov. It establishes a series of functional inequalities relating weighted Hölder norms and weighted \(L_p\) norms, then uses them to show that the ass…
