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 Cauchy type singular integrals on closed rectifiable Jordan curves with tangent at every point, deriving estimates for the modulus of continuity of the integral in terms of the modulus of the density and geometric conditions on the curve. It introduces classes of functions defined …
The paper studies asymptotic representations of solutions to first order linear differential systems with a large real parameter when the characteristic equation has multiple elementary divisors. It develops a construction for a Jordan block of multiplicity m, showing how fractional powers of the pa…
This note studies spectral multiplicity and continuity phenomena for ergodic automorphisms, especially interval exchanges and finite group skew products over rotations. It proves that for an interval exchange satisfying a generating condition, the spectral multiplicity is bounded by the number of ex…
This note proves that all separable Banach spaces are homeomorphic, answering a question attributed to Fréchet and Banach. The argument reduces the problem, using the Bessaga and Pełczyński theorem, to Banach spaces with bases, then constructs a homeomorphism to Hilbert space by encoding points on t…
The paper studies uniqueness and boundary formulation for elliptic operators that may degenerate, using generalized solutions interpreted through the associated Markov processes. It refines the Dirichlet problem in bounded domains by adding boundary data on an additional set determined by passable c…
The paper studies the rate at which normalized convolutions of a distribution in the domain of normal attraction converge uniformly to a stable law. Using tail characterizations of normal attraction and an Esseen smoothing inequality, it derives bounds in terms of auxiliary functions measuring the r…
The paper studies additional conditions on interpolation nodes that can yield positive convergence results despite the Bernstein and Faber obstruction for arbitrary continuous functions. It introduces monotonicity and regularity of node matrices, possibly with weights, and proves criteria reducing m…
This letter provides corrections to the author’s earlier article on tensor products of C*-algebras, amending several displayed norm inequalities, tensor product notations, and statements concerning kernels and quotient constructions. It also adds two substantive remarks reflecting subsequent develop…
This note studies the moment problem in quantum field theory through a Hilbert space construction generated by positive functionals on sequences of test functions. It introduces quasianalytic functionals defined by a growth sequence satisfying Carleman type quasianalyticity conditions, and applies u…
The paper studies infinitesimal bendings of a positively curved piece of a surface of revolution bounded by a parallel, with the aim of estimating the cardinality of nonrigid sleeve constraints. It reformulates the bending equations as a Beltrami-type system and reduces the associated scalar equatio…
The paper develops generalized length and area relations for plane mappings with generalized first partial derivatives and finite Dirichlet integral. Using an extension of Fubini’s theorem based on level sets of the distance to a closed set, it derives integral inequalities relating the lengths of i…
This note extends results of Erdős and Turán on fine and coarse convergence of Lagrange interpolation processes from the case of Lipschitz classes with \(0\beta\), the paper establishes threshold results: uniform convergence for all such node matrices when \(\alpha>\beta\), existence of convergent p…
This note studies the asymptotic probability that an n by m random matrix over GF(2), with independent but not necessarily identically distributed Boolean entries, has full row rank. Assuming all entry probabilities are bounded between delta and 1 minus delta, it proves that for m/n below an explici…
This paper studies when a topological ring becomes a division ring after completion. It proves that the completion of a topological ring contains an identity and makes every element of the original ring invertible if and only if the ring has no closed one-sided ideals and no generalized zero divisor…
The paper gives a constructive characterization of a class of nonperiodic functions in \(L_2[-1,1]\) whose best algebraic polynomial approximation decreases as \(n^{-(s+\gamma)}\), with \(01/2\), then the associated Legendre coefficient series is absolutely convergent.
This note studies real canonical linear differential systems with periodic coefficients whose Hamiltonian is nonnegative, focusing on stable systems and their associated positively directed symplectic curves. Using a spectral representation of the matriciant through the eigenvalues and eigenvectors …
This paper studies subspaces of L infinity invariant under the shift operator, using strong operator topology and a bounded almost everywhere convergence notion, together with related weighted approximation problems by analytic polynomials. It proves a classification of such closed invariant subspac…
This paper studies groups of similarity symmetry in Euclidean space, focusing on the fundamental property that every transformation in such a group fixes each singular point of the group. After recalling the decomposition of a similarity transformation into a homothety and a motion, the author prove…
This paper proves an existence theorem for asymptotic geodesics on compact oriented two-dimensional Riemannian manifolds not homeomorphic to the sphere. For any point and any free homotopy class of closed curves, the argument uses the universal covering surface, properties of minimal arcs, and monot…
This paper studies functional completeness for the class of functions definable in Smetanich’s three-valued logic, corresponding to Jaśkowski’s first matrix. It characterizes this class as the intersection of two preservation classes, equivalently by an identity involving double negation, and shows …
The paper studies how the derivative relation for Jacobi orthogonal polynomials changes when the Jacobi weight is multiplied by a positive Lipschitz factor. For polynomials orthonormal with respect to \((1-x)^\alpha(1+x)^\beta q(x)\), with \(\alpha,\beta \geq -1/2\), it proves that the derivative is…
This bibliographic notice surveys recently published mathematical books and collected volumes available in 1965, with emphasis on differential equations, mathematical physics, operator theory, numerical methods, and related areas of analysis. It lists monographs, textbooks, translated works, proceed…
The paper studies integral representations for holomorphic functions of several complex variables that retain a feature of the one-variable Cauchy formula, namely kernels with first-degree denominators or one-variable Cauchy integrals. It first proves reconstruction formulas for functions holomorphi…
The paper studies self-similar traveling wave solutions with discontinuities for a scalar quasilinear equation and for equations describing water flow in an inclined channel. It defines stability under the addition of small dissipation and proves that, for a symmetric source term with a single sign …
This note studies the existence of completely recurrent solutions of nonautonomous differential equations in a Banach space. It develops characterizations of completely recurrent mappings through a shift dynamical system and uses these properties to prove criteria for equations of the form dx/dt = f…
This paper studies homeomorphic mappings of domains in three-dimensional Euclidean space that preserve angles only for rays issuing from each point, a weaker condition than uniform preservation of angles for arbitrary curves. It proves that any such mapping is a Möbius transformation on the domain. …
The paper studies nonlinear systems of ordinary differential equations near a singular point by comparing them with their linear part, under smallness conditions on the nonlinear term expressed through a Lipschitz function. It proves the existence of local homeomorphisms that relate stable solutions…
This paper studies infinite groups defined by restrictions on their infinite subgroups, especially groups in which all infinite abelian subgroups are invariant and locally finite groups in which no infinite proper subgroup coincides with its normalizer. It establishes structural results for these cl…
The note examines whether linear parabolic equations with merely continuous leading coefficients necessarily possess classical solutions, bounded adjoint solutions, or solutions with bounded derivatives in the self-adjoint case. It constructs a one-dimensional uniformly parabolic equation whose coef…
The paper develops a theory of resolvent matrix functions for simple closed Hermitian operators in Hilbert space with equal deficiency indices, allowing the index to be infinite. Using a representation subspace, projector functions, and an associated operator function, it establishes a compact ident…
This publication is a compiled bibliography of recent journal articles in differential equations, mathematical physics, integral equations, and numerical methods, with particular emphasis on Soviet mathematical literature from 1965 and early 1966. The entries are organized by subject area and list a…
This paper studies the global asymptotic behavior of phase trajectories for quasilinear differential equations with delayed arguments and small nonlinear perturbations. It formulates the phase space for such delay systems, compares the associated period mapping with that of an auxiliary ordinary dif…
This paper studies shortened functional equations for general Dirichlet series whose completed forms satisfy a gamma-factor functional equation. It proves a main lemma giving an identity between weighted sums over the two Dirichlet series and residues, under explicit analytic and growth conditions o…
This paper studies integral rings associated with a finite group, principally the integral character ring and the integral group ring over the ring of integers of a finite extension of the rationals. It proves that finite order units in the character ring are precisely roots of unity times linear ch…
This note studies approximation of positive bounded measures on separated uniform spaces by finite molecular measures within the dual scheme of Katětov, Raikov, and Pták. It characterizes when positive elements in the completion of the space generated by points can be represented as measures or Dani…
This paper studies elliptic boundary value problems for systems in which a complex parameter appears only in the boundary conditions, while the differential equations themselves are parameter independent. Under ellipticity, solvability assumptions for the Dirichlet problem, and a local or global con…
The paper studies zero sets of solutions to completely solvable multidimensional second order linear differential equations with real continuous coefficients. It introduces zero-manifolds and an associated mapping from the domain into a unit sphere, using local diffeomorphism and inverse mapping arg…
This paper studies a boundary value problem for the mixed type equation y(y minus 1)u_xx plus u_yy equals 0 in a domain containing both parabolic degeneration lines y equals 0 and y equals 1. The author formulates a regularity class allowing prescribed singular behavior at selected boundary and char…
