Showing 50 of 5847 papers in Mathematics

ASYMPTOTIC REPRESENTATIONS OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS IN THE CASE OF MULTIPLE ELEMENTARY DIVISORS OF THE CHARACTERISTIC EQUATION

N. N. Moiseev
1966 SovietRxiv: ru-196601.14506

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…

ON THE SPECTRUM OF ERGODIC AUTOMORPHISMS

V. I. Oseledets
1966 SovietRxiv: ru-196601.13967

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…

TOPOLOGICAL EQUIVALENCE

M. I. Kadets
1966 SovietRxiv: ru-196601.13866

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…

ON THE RATE OF CONVERGENCE

Yu. P. Studnev
1966 SovietRxiv: ru-196601.13261

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 MONOTONICITY PRINCIPLE IN INTERPOLATION THEORY

D. L. Berman
1966 SovietRxiv: ru-196601.13191

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…

LETTER TO THE EDITOR

Unknown
1966 SovietRxiv: ru-196601.13029

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…

QUASIANALYTIC FUNCTIONALS IN QUANTUM FIELD THEORY

V. P. Gachok
1966 SovietRxiv: ru-196601.12925

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…

ESTIMATE OF THE CARDINALITY OF THE SET OF NONRIGID SLEEVE CONNECTIONS FOR SURFACES OF REVOLUTION

V. T. Fomenko
1966 SovietRxiv: ru-196601.12860

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…

RELATIONS OF THE TYPE OF THE “LENGTH AND AREA PRINCIPLE”

B. P. Kufarev
1966 SovietRxiv: ru-196601.12850

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…

ON THE RANK OF MATRICES WITH RANDOM BOOLEAN ELEMENTS

Unknown
1966 SovietRxiv: ru-196601.12478

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…

INVERTIBILITY IN TOPOLOGICAL RINGS

V. A. Andrunakievich, V. I. Arnautov
1966 SovietRxiv: ru-196601.11589

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…

ON THE THEORY OF CANONICAL SYSTEMS OF DIFFERENTIAL EQUATIONS OF POSITIVE TYPE WITH PERIODIC COEFFICIENTS

P. A. Shvartsman
1966 SovietRxiv: ru-196601.10890

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 …

ON SPATIAL GROUPS OF SIMILARITY SYMMETRY

A. M. Zamorzaev
1966 SovietRxiv: ru-196601.09544

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…

A CRITERION OF FUNCTIONAL COMPLETENESS IN THE LOGIC CORRESPONDING TO JAŚKOWSKI’S FIRST MATRIX

M. F. Raţă
1966 SovietRxiv: ru-196601.09258

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 …

New Books

Unknown
1966 SovietRxiv: ru-196601.08619

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…

ON SELF-SIMILARLY STABLE SOLUTIONS OF THE TRAVELING-WAVE TYPE FOR CERTAIN QUASILINEAR EQUATIONS, INCLUDING THE EQUATIONS OF WATER FLOW IN AN INCLINED CHANNEL

É. B. Bykhovskii
1966 SovietRxiv: ru-196601.08188

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 …

RECURRENT SOLUTIONS OF DIFFERENTIAL EQUATIONS

B. A. Shcherbakov
1966 SovietRxiv: ru-196601.08148

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…

ON PARABOLIC EQUATIONS WITH CONTINUOUS COEFFICIENTS

Unknown
1966 SovietRxiv: ru-196601.07720

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…

Bibliography of Journal Articles

A. R. Shakun
1966 SovietRxiv: ru-196601.07131

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…

ON THE GLOBAL BEHAVIOR OF PHASE TRAJECTORIES OF QUASILINEAR DIFFERENTIAL EQUATIONS WITH DELAYED ARGUMENTS

Yu. I. Neimark, L. Z. Fishman
1966 SovietRxiv: ru-196601.06616

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…

ON FUNCTIONAL EQUATIONS OF DIRICHLET FUNCTIONS

A. F. Lavrik
1966 SovietRxiv: ru-196601.06351

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…

ON SOME INTEGRAL RINGS ASSOCIATED WITH A FINITE GROUP

A. I. Saksonov
1966 SovietRxiv: ru-196601.05951

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…

LIMITS OF POSITIVE MOLECULAR MEASURES IN CERTAIN UNIFORM SPACES

I. A. Berezanskii
1966 SovietRxiv: ru-196601.05940

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…