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 note develops a method for constructing resolvents of symmetric real integral kernels by uniformly convergent bilinear series. Starting from a representation of a positive continuous kernel as an integral product, it builds auxiliary functions through Gram determinant formulas and proves unifor…
The paper investigates the relation between the Routh-Hurwitz stability criterion and determinant criteria arising from Markov’s theory of continued fractions for real characteristic polynomials. By factoring Hurwitz matrices into triangular coefficient matrices and matrices built from Markov parame…
The paper studies approximation of functions with prescribed smoothness on the exterior of an interval and on a half-line, extending earlier results on polynomial and entire-function approximation. It proves a direct theorem for approximation on the set outside the interval by entire functions of bo…
This note introduces a class of parabolic systems in which different spatial variables may have different highest differentiation orders, extending Petrovsky parabolic systems as the special case of equal orders. It defines such systems through a spectral negativity condition with generalized homoge…
The paper studies the Green function for the Cauchy problem for Petrovsky-correct equations and systems in two variables, including cases with coefficients depending on time. It derives asymptotic formulas as t tends to zero and x tends to infinity, with corresponding formulas also applying for fixe…
The paper studies mixed boundary value and singular Goursat problems for a hyperbolic equation with singular coefficient, depending on two parameters. It derives integral transformation formulas connecting solutions corresponding to different parameter values and different boundary data, including k…
The paper studies affine connections induced by a principal relative scalar on a locally projective manifold and on its associated centro-projective spaces. It derives the curvature and Ricci tensors of the connection determined by the scalar, then characterizes when the corresponding connection in …
The paper examines summability of orthogonal Fourier series in \(L^2\) by linear methods, motivated by known results that Cesàro summability almost everywhere is characterized by convergence of a dyadic subsequence of partial sums. It asks whether an analogous characterization can hold for arbitrary…
The paper studies Lie transformation groups preserving a linear second order partial differential equation in more than one independent variable. It derives infinitesimal determining equations, separates the always present subgroup generated by scaling and adding solutions, and shows that, apart fro…
This note develops the Radon transform of rapidly decreasing functions on real and complex affine spaces, emphasizing its geometric role and its usefulness beyond the ordinary Fourier transform. It states inversion formulas, including a complex case formula involving integration over representatives…
The paper develops a method for embedding groups into complete groups, where every equation of the form x^n = g is solvable, while preserving selected structural properties. Using diagonal embeddings into transformation groups and adjoining roots of chosen elements, it proves that any group can be e…
This paper develops radical theory for weakly associative nonassociative rings, a class defined by a containment condition on ideals generated inside nested subrings and including associative rings. It proves extension and restriction results for ideals and establishes that supernilpotent and subide…
The paper studies the representation of solutions of linear operator differential equations in a Hilbert space by means of continual integrals over paths in the spectrum of an auxiliary self-adjoint operator. It develops a framework of generalized and basic elements, uses generalized eigen-elements …
This note proves a formula for the second obstruction to extending a section of a skew product whose fiber is sufficiently aspherical and simple in the relevant dimensions. Using Boltyansky’s formula for comparing second obstructions and the Serre spectral sequence, it defines a cohomology class ass…
This paper studies the Schwarz alternating method for the stress formulation of linear elasticity on a domain formed by two partially overlapping subdomains. Using Sobolev’s variational approach, it constructs successive stress fields satisfying equilibrium and boundary tractions on alternating subd…
This paper develops a numerical method for boundary value problems for elliptic partial differential equations by deriving explicit summation formulas for finite difference operators on rectangular grids. It gives general solution representations for finite difference analogues of the Helmholtz or P…
The paper develops a Stieltjes integral for functions on a compact real interval with values in a K-space, using order uniform continuity rather than norm continuity. For an integrand taking values in a K-space and an integrator of bounded variation with values in the space of regular order-continuo…
This paper studies ordered Banach spaces through regular and completely regular cones, defined by norm convergence of monotone sequences under order or norm boundedness assumptions. It establishes implications among complete regularity, regularity, and normality, gives criteria for normality using o…
The paper studies the planar Dirichlet problem for a second-order elliptic equation with real analytic coefficients in a simply connected domain. Using a complete system of particular solutions of the adjoint equation, derived from Vekua’s representation, it expresses the unknown normal derivative o…
This paper studies bounded non-self-adjoint operators in a separable Hilbert space, especially dissipative and completely continuous operators whose imaginary parts are trace class. Using infinite determinants associated with trace-class perturbations, it establishes contractivity properties of char…
This paper completes the decomposition problem for tensor products of irreducible unitary representations of the proper Lorentz group by treating the case in which both factors belong to the complementary series. Using Hilbert space realizations by generalized functions and Fourier transforms, the a…
This paper studies embedding properties of fractional Sobolev classes defined by difference norms of derivatives of noninteger order. It proves a main embedding theorem showing that, under specified relations among dimension, integrability exponents, and smoothness, a function in \(W_p^r(R_n)\) belo…
The paper proves an existence theorem for periodic solutions of a nonlinear first order ordinary differential equation in a Hilbert space under positivity, compactness, and bounded periodic forcing assumptions. Using a Galerkin approximation, energy estimates, and Brouwer’s fixed point theorem, the …
This paper studies singularities on the axis of convergence of generalized Dirichlet series whose exponent sequence has gaps bounded below and contains an almost regular subsequence. Building on results of Pólya and Agmon, it proves that under suitable hypotheses simple poles on the axis must be dis…
The paper introduces a notion of rotation for weakly continuous vector fields of the form x minus F(x) in a real separable Hilbert space, using Leray’s full index on weakly compact domains such as generalized balls, cylinders, and hyperbolic domains. It establishes basic properties of this rotation,…
The paper studies the spectral relationship between two operators associated with a class of variable-coefficient differential systems of S. L. Sobolev type on a bounded smooth domain. One operator acts on a Hilbert space of solenoidal vector fields and is generated by the system, while the other is…
The paper studies transitive spectra of finite complexes with simplicial onto projections and their limit spaces, addressing Aleksandrov’s problem of relating such spectra to bicompacta. It introduces essential simplices, threads, Hausdorff separation, separating subspectra, and extremal spectra, pr…
This note studies how invariance of a differentiable function under a group action can yield lower bounds for stationary values that remain stable under small, not necessarily invariant, perturbations. Using critical values defined by weak homotopy changes in sublevel sets, it relates a function on …
This note generalizes the Wiman, Valiron theorem to entire transcendental functions of several complex variables by considering maximum modulus on hypersurfaces defined by sums of powers of the coordinate moduli. Using the homogeneous decomposition of the power series and the central index of an ass…
Pinsker studies measure-preserving dynamical systems in Lebesgue spaces through the relation between entropy, factor systems, and Kolmogorov regularity or singularity. The note defines completely positive entropy as positivity of entropy for every nontrivial factor system, introduces generating suba…
The paper studies Fourier expansions in the principal vectors, including eigenvectors and associated vectors, of completely continuous non-self-adjoint operators in a Hilbert space, where ordinary convergence may fail even under completeness. It defines an Abel-type summability method adapted to cha…
This paper develops comparison principles for second-order linear differential equations with summable coefficients on a finite interval. Using the logarithmic derivative transformation to Riccati equations, it proves conditions under which nonvanishing of one solution and integral inequalities betw…
The paper studies Kolmogorov n-dimensional widths of subsets of Banach spaces, with emphasis on classical classes of periodic, analytic, harmonic, and smooth functions in the uniform metric. It proves a general lower-bound theorem: if an n plus 1 dimensional section of a class contains a scaled sect…
This paper studies locally finite groups satisfying minimality conditions on subgroup chains detected by elements whose orders involve specified primes, with particular attention to groups satisfying p-minimality for every prime. It develops several criteria for the Pi-minimality condition, relating…
Boltyanskii and Postnikov propose an axiomatic formulation of cohomology groups for pointed topological spaces that avoids relative groups and therefore dispenses with the excision axiom. The note defines admissible categories, homotopy, cofibrations, and connecting homomorphisms, then states three …
The paper studies optimal coefficients for multidimensional quadrature formulas on classes of periodic functions whose Fourier coefficients have prescribed decay. It gives methods for computing coefficients of the form 1, a, ..., a^{s-1}, including a criterion based on minimizing an auxiliary functi…
This note studies best weighted polynomial approximation on the real line for continuous functions satisfying a weighted vanishing condition at infinity, focusing on the Cauchy kernel \(1/(x-a)\) with nonreal pole. For weights with regularly decreasing logarithm, represented through a monotone funct…
This paper studies the large-index asymptotic behavior of normalized eigenfunctions for a Sturm-Liouville operator on the interval with Dirichlet boundary conditions, treating the potential term as a perturbation of the second derivative operator. Under smoothness and endpoint assumptions on the pot…
This paper studies how sectional curvature pinching constrains the topology of complete even-dimensional Riemannian manifolds. Building on results of Rauch and Klingenberg, it proves that if the curvature satisfies 0 < L/4 < K <= L at every point and in every two-dimensional direction, then the mani…
The paper derives a Lagrange-Sylvester type formula for a symmetric second-rank tensor function depending on two symmetric tensors that cannot be simultaneously reduced to canonical form, under the assumption that one tensor has three distinct eigenvalues. The argument represents the function as a l…
This paper announces results on variational integrals with prescribed boundary values and on first boundary value problems for general quasilinear elliptic equations in several independent variables. Under specified ellipticity, growth, smoothness, and boundary regularity assumptions, it derives a p…
This note studies the behavior under differentiation of entire and meromorphic functions whose zeros, and in the meromorphic case poles, remain sufficiently close to prescribed boundary rays, with particular attention to functions whose zeros are close to the real axis. Using Nevanlinna’s angular ch…
This note extends Mikhlin’s theory of multidimensional singular integral equations in Hilbert spaces by applying methods from the theory of normed commutative rings. For the two-dimensional case, it constructs a norm-closed ring of singular integral operators modulo compact operators, identifies its…
The paper studies how left generalized rings of quotients of an associative ring are related when they are formed with respect to two multiplicatively closed systems of nonzero elements, one containing the other. It analyzes the induced system of elements in the smaller quotient ring, proves that ce…
This note studies the Dirichlet problem for the nonlinear elliptic equation Δu = u² in a bounded domain, motivated by questions from transonic gas motion. It proves existence and uniqueness of small solutions by a contraction mapping argument applied to the associated Green function integral equatio…
This paper studies asymptotic properties of polynomials orthogonal on a fixed arc of the unit circle with respect to a nonnegative weight, reformulating the problem through a conformal map from the cut plane to the unit disk. It constructs a special class of explicitly representable orthogonal polyn…
The paper develops an invariant formulation of Lie differentiation for fields of geometric objects associated with analytic transformation groups and their normal prolongations. It shows that the differential equations defining a field, together with prolongation and envelope operations, suffice to …
This paper studies structural and model theoretic properties of free solvable groups, defined as quotients of free groups by terms of the derived series. Using a theorem of Auslander and Lyndon, it proves restrictions on commuting elements, shows that free solvable groups are R-groups, and establish…
