Showing 50 of 5847 papers in Mathematics

Osvald DEMUTH (Osvald DEMUTH)

Unknown
1967 SovietRxiv: ru-196701.55298

This note gives a necessary and sufficient condition for Riemann integrability of constructive functions on the segment from 0 to 1. The criterion characterizes integrability by boundedness together with a quantitative smallness condition on finite families of intervals on which the function has osc…

Generalized Minimax Principle for Indecomposable Operators

Unknown
1967 SovietRxiv: ru-196701.54593

This note generalizes the minimax principle for indecomposable nonnegative matrices to positive operators on ordered Banach spaces with a reproducing normal cone. It introduces semi-nonsupporting and strictly nonsupporting positive operators, uses a total subset of the dual cone, and formulates vari…

ONE CLASS OF SYMMETRIC SPACES WITH AN EXTENDABLE GROUP OF MOTIONS AND A GENERALIZATION OF THE POINCARÉ MODEL

I. L. Kantor, A. I. Sirota, A. S. Solodovnikov
1967 SovietRxiv: ru-196701.54113

This paper constructs a class of locally symmetric spaces of affine connection whose group generated by geodesic displacements is properly contained in a larger Lie transformation group. Using Lie algebras of transitive differential groups of order two, the authors associate such spaces with Jordan …

ON THE RICHNESS OF THE CLASS OF QUASICONFORMAL MAPPINGS OF DOMAINS IN THREE-DIMENSIONAL EUCLIDEAN SPACE

A. P. Kopylov
1967 SovietRxiv: ru-196701.53819

This paper studies how large the class of bounded three-dimensional domains quasiconformally equivalent to a ball is among all bounded homeomorphic images of the unit ball. A Hausdorff-type metric is introduced on complements of such domains, and its relation to Carathéodory kernel convergence and t…

ON A PROBLEM OF STATIONARY HEAT CONDUCTION

V. S. RAVIN
1967 SovietRxiv: ru-196701.53607

The paper formulates a stationary heat conduction problem motivated by crystallization of semiconductor melt droplets on substrates, considering a hemispherical body in perfect thermal contact with an infinite plane-parallel plate and subject to external heat transfer and imposed heat flux. Because …

CORRECT SPACES

V. A. Efremovich, A. G. Mordkovich, V. Yu. Sandberg
1967 SovietRxiv: ru-196701.53026

The paper studies generalized uniform spaces and identifies “correct” spaces as those satisfying separability and an intersection condition for neighborhoods, thereby retaining a usable proximity structure beyond Weil uniform spaces. It shows that merely separable uniform spaces have no complete obj…

SOME ASYMPTOTIC FORMULAS FOR THE SPECTRA OF THE THIRD BOUNDARY-VALUE PROBLEM RELATED TO VARIATION OF THE FUNCTION ENTERING THE BOUNDARY CONDITION

S. I. Grinberg
1967 SovietRxiv: ru-196701.52845

The paper studies high-energy asymptotics for spectra of the three-dimensional Laplacian in a bounded domain with Robin boundary condition, focusing on how eigenvalues change when the boundary coefficient is varied. It first derives an expansion for the resolvent trace involving the volume, boundary…

ON ALGORITHMIC PROBLEMS FOR SOME CLASSES OF QUASIGROUPS

A. A. Gvaramiya, M. M. Glukhov
1967 SovietRxiv: ru-196701.52727

The paper studies algorithmic problems for varieties of quasigroups and loops defined by additional identities, including word identity, isomorphism, embedding, and occurrence. It develops an embedding criterion for partial quasigroups via finite simple free extensions and identifies a condition und…

ON THE THEORY OF EXTREMA OF A MULTIDIMENSIONAL $\zeta$-FUNCTION

B. N. Delone, S. S. Ryshkov
1967 SovietRxiv: ru-196701.52640

This paper studies extrema of the multidimensional lattice zeta function for lattices of fixed determinant, a problem motivated by Sobolev’s work on approximate computation of multidimensional integrals. Using Lagrange multiplier conditions, the authors introduce strongly critical lattices and final…

ON THE MULTIPLICITIES OF WEIGHTS OF REPRESENTATIONS

A. U. Klimyk
1967 SovietRxiv: ru-196701.52572

This paper studies finite-dimensional irreducible representations of complex semisimple Lie algebras, focusing on weight multiplicities, tensor product decompositions, and restrictions to semisimple subalgebras. Using the Weyl group and a formula of Brauer and Weyl, it derives recurrence relations f…

TOPOLOGICAL PROPERTIES

Unknown
1967 SovietRxiv: ru-196701.52487

The paper develops topological properties of partially ordered dynamical systems in which the acting group is an arbitrary nontrivially partially ordered group, replacing earlier restrictions based on countable majorizing sequences by directedness where needed. It defines relative density, omega-lim…

On the theory of Painlevé's third equation

N. A. Lukashevich
1967 SovietRxiv: ru-196701.52442

For the third Painlevé equation, the nature of possible singular points of its solutions is investigated, the question regarding the number and residues of movable poles of the solutions is resolved, and necessary and sufficient conditions for the existence of rational solutions are specified. Bibli…

ON THE GENERALIZED TRICOMI PROBLEM

V. P. Mikhailov
1967 SovietRxiv: ru-196701.52319

The paper studies a generalized Tricomi boundary value problem for Chaplygin’s mixed-type equation in a domain whose boundary includes elliptic and hyperbolic parts, with homogeneous data imposed on selected boundary arcs. It formulates generalized solutions in a Sobolev space through an integral id…

A Parabolic-Type Equation with a Periodic Coefficient

G. Ya. Lyubarskii
1967 SovietRxiv: ru-196701.51463

This note studies the Cauchy problem for a one-dimensional parabolic equation on a finite interval with separated boundary conditions and a rapidly oscillating periodic coefficient. Under summability assumptions on the Fourier coefficients of the periodic term, the paper proves the existence, for su…

ON THE INTERPOLATION OF FUNCTIONS REGULAR ON CLOSED SETS

V. A. Baranova
1967 SovietRxiv: ru-196701.51160

This note studies uniform approximation of functions regular on closed sets of the complex plane by interpolation polynomials with nodes equidistributed on level curves of the exterior conformal map. Using a lemma of Lebedev for univalent functions, it derives logarithmic estimates for the node poly…

Some Results in Set-Theoretic Topology

Unknown
1967 SovietRxiv: ru-196701.51058

This note announces results in set-theoretic topology obtained by combinatorial set-theoretic methods, especially partition relations, concerning cardinal bounds for discrete subspaces, density, and character in Hausdorff and related spaces. It improves earlier theorems of de Groot, Efimov, and Isbe…

ON THE CAUCHY PROBLEM FOR GENERAL LINEAR EQUATIONS

V. M. Borok
1967 SovietRxiv: ru-196701.51033

This paper studies uniqueness for the Cauchy problem with zero initial data for general linear partial differential equations with constant coefficients in one spatial variable and time, restricting attention to solutions of normal exponential type in time. Using the Laplace transform in time, the p…

$K$-extendability of polynomials

Unknown
1967 SovietRxiv: ru-196701.50623

The paper addresses the problem of K-continuability of polynomials, namely how to extend a given polynomial by adding higher-degree terms so that the roots of the resulting polynomial lie on the unit circle. It presents a simple algebraic construction based on transforming the polynomial, using Newt…

New books

A. R. Shakun
1967 SovietRxiv: ru-196701.50572

This bibliographic notice compiles recently published books and article collections relevant to differential equations, mathematical physics, functional analysis, stability theory, approximation theory, and related areas. The entries provide authors or editors, titles, publication locations and pres…

ON ONE CLASS OF DEGENERATING QUASILINEAR EQUATIONS

M. I. Freidlin
1967 SovietRxiv: ru-196701.49095

This paper studies degenerate quasilinear parabolic equations whose first order nonlinear part is subordinate to the degenerate second order operator in a probabilistic sense. Using Markov processes, Girsanov-type absolute continuity, and stochastic integral representations, it defines generalized s…

The solution of a boundary value problem by the method of$R$-functions

A. P. Volkov, V. F. Kravchenko, G. P. Man'ko, V. L. Rvachev
1967 SovietRxiv: ru-196701.48839

The work is devoted to a topical issue related to the practical calculation of electrostatic fields. One of the authors of this article previously introduced functions that allow for the exact satisfaction of boundary conditions for domains of practically arbitrary shape. These functions, while bein…

ON TESTING A MULTIDIMENSIONAL POLYNOMIAL HYPOTHESIS

V. P. Palamodov
1967 SovietRxiv: ru-196701.48608

The paper studies tests of prescribed level for multidimensional polynomial hypotheses concerning the means and covariance matrices of several multivariate normal populations. It reformulates the problem in terms of sufficient statistics and exponential family parameters, reducing the characterizati…

INVESTIGATION OF INTERPOLATION PROCESSES CONSTRUCTED FOR AN EXTENDED SYSTEM OF P. L. CHEBYSHEV NODES

D. L. Berman
1967 SovietRxiv: ru-196701.48501

The paper studies interpolation processes associated with node systems on the interval, focusing on Bernstein’s modified interpolation scheme and on an extended system of Chebyshev nodes that includes the endpoints. It addresses whether quasi-uniform distribution of nodes is sufficient for uniform c…

ON ADDITIVE FUNCTIONS OF SETS CONTINUOUS IN A DIRECTION

Yu. I. Gil'derman
1967 SovietRxiv: ru-196701.48340

This note studies countably additive real set functions on Borel subsets of an n-dimensional cube that satisfy absolute continuity or translation continuity only in specified coordinate directions. It shows that, unlike the classical full-dimensional case, directional absolute continuity and directi…

EXTENSION OF DUAL SUBSPACES

Unknown
1967 SovietRxiv: ru-196701.48280

The paper studies R. S. Phillips’s problem of extending an invariant dual pair of subspaces in a Hilbert space with an indefinite scalar product to a maximal invariant dual pair. For a commutative algebra generated by J-unitary operators, the author proves such an extension under power boundedness o…

ON SOME EMBEDDINGS OF ORDERED SEMIGROUPS

È. G. Shutov
1967 SovietRxiv: ru-196701.47755

This paper studies embedding problems for ordered and quasi-ordered semigroups, focusing on potential right divisibility, potential left invertibility of subsets, and embeddings into semigroups with one-sided invertibility. It introduces explicit compatibility conditions on a binary relation or subs…

ON SEPARABLE DIVISORS OF THE ORDER OF A GROUP

S. A. Chunikhin
1967 SovietRxiv: ru-196701.47719

This paper studies existence and conjugacy criteria for subgroups of finite groups whose order and index are not necessarily relatively prime. It introduces almost Sylow and separable divisors relative to a normal series, defines subgroup types with respect to such a series, and proves a main theore…