Mathematics › Mathematics ×

Showing 50 of 5847 papers in Mathematics

On the Problem of Gluing Two Semicircles

D. B. POTYAGAILO
1961 SovietRxiv: ru-196101.20468

The paper studies the type problem for Riemann surfaces associated with gluing two half-disks, reformulated in terms of gluing two half-strips by a prescribed boundary homeomorphism. It constructs a class of simply connected Riemann surfaces with first-order algebraic branch points, decomposed into …

Higher approximations in averaging

Unknown
1961 SovietRxiv: ru-196101.20269

This paper studies higher order averaging for singularly perturbed systems with slow variables and fast degenerate motion whose trajectories admit uniform mean values. It formulates a second approximation averaged system, constructed through characteristic equations and auxiliary correction function…

Modules over a $K$-space

S. N. Slugin
1961 SovietRxiv: ru-196101.20185

This paper develops a theory of modules over a \(K\)-space with unit, treating the \(K\)-space as a generalized scalar ring and using suitable notions of quotient, convergence, norm, and scalar product. It defines generalized \(M_Z\)-modules, normed \(B_Z\)-modules, and inner product \(H_Z\)-modules…

On a Representation of a Tensor Function

V. D. BONDAR
1961 SovietRxiv: ru-196101.20132

The paper develops a representation of tensor functions by extending the Pfaffian form representation of vector fields. Using canonical forms of Pfaffian forms, it derives general formulas for vector components in n-dimensional space and applies them to tensor functions viewed as vectors in the spac…

On the regularity of convex surfaces with a regular metric in Lobachevsky space

Corresponding Member of the Academy of Sciences of the USSR A. V. POGORELOV
1961 SovietRxiv: ru-196101.20072

This note studies the regularity of convex surfaces in Lobachevsky space determined by the regularity of their intrinsic metric, without imposing the previously used assumption of positive Gaussian curvature. It states that if a convex surface has a regular metric and Gaussian curvature greater than…

The Galois group of a local field

HELMUT KOCH
1961 SovietRxiv: ru-196101.19084

The paper studies the structure of Galois groups associated with local fields, focusing first on regular finite extensions of the p-adic numbers and on maximal normal p-extensions over a finite regular extension without higher ramification. It gives an explicit presentation of the resulting Galois g…

Approximation of Functions by Polynomials with Integer Coefficients

The article considers certain questions in the theory of approximation of functions by polynomials
1961 SovietRxiv: ru-196101.18702

The paper studies uniform and integral approximation of real functions by algebraic polynomials with integer coefficients on intervals of length less than 4, emphasizing the arithmetic restrictions that distinguish this problem from ordinary polynomial approximation. It establishes direct approximat…

ON THE BEHAVIOR OF CORRECTIONS IN SOME METHODS FOR APPROXIMATE COMPUTATION OF THE BOUNDS OF THE SPECTRUM OF A SELF-ADJOINT OPERATOR

Unknown
1961 SovietRxiv: ru-196101.18413

The paper studies how correction vectors arising in iterative methods for approximating spectral bounds of a bounded positive self-adjoint operator can provide additional spectral information. It defines extremal, strongly minimizing, strongly maximizing, and biextremal sequences in terms of the Ray…

Criterion for the Unicellularity of Volterra Operators

M. S. BRODSKII
1961 SovietRxiv: ru-196101.17506

The paper establishes a criterion for when a simple Volterra operator in a separable Hilbert space is unicellular, meaning that its invariant subspaces are totally ordered by inclusion. It develops the criterion through the characteristic operator function associated with the imaginary part of the o…

Semi-Euclidean and Semi-Non-Euclidean Spaces

===========
1961 SovietRxiv: ru-196101.16822

This paper develops a general theory of semieuclidean and semineuclidean spaces, extending earlier work that treated only special cases. It defines these spaces by systems of scalar products with prescribed signatures, introduces distances, angles, hyperspheres, absolute cones and planes, and descri…

On the Level Lines of a Solution to an Elliptic Equation

Let us consider the equation:
1961 SovietRxiv: ru-196101.16576

The paper studies level sets of bounded solutions to a uniformly elliptic second order linear equation in an infinite strip, under regularity and boundedness assumptions on the coefficients. It proves that two proper components of the zero level set, both extending to infinity without meeting the ho…

Radicals in Group Theory

Unknown
1961 SovietRxiv: ru-196101.16144

This note proposes the axiomatic notion of a radical as a means of organizing numerous group classes related to abelian, finite, soluble, and generalized soluble groups. It formulates radical and semisimple classes of groups through closure and series conditions, describes minimal radical and semisi…

ON THE SOLUTION OF SYSTEMS OF DIFFERENCE EQUATIONS

Unknown
1961 SovietRxiv: ru-196101.15981

This paper addresses the direct solution of large block systems of linear algebraic difference equations arising from grid methods for partial differential equations, with boundary conditions represented at the first and last grid layers. It proposes a combined sweep and pivoting elimination procedu…

On nonholonomic $W$-congruences

Unknown
1961 SovietRxiv: ru-196101.15478

This note develops a nonholonomic analogue of W congruences within the equiaffine theory of linear complexes. Using semicanonical and canonical moving frames, it derives invariant conditions under which a nonholonomic congruence has corresponding asymptotic lines on its nonholonomic focal surfaces, …

In my article (V. F. Zhdanovich, “Asymptotic expansions of eigenvalues of a boundary-value problem with a parameter”), published in *DAN*, vol. 135, no. 6, 1960, Theorem 3 in the formulation given in the article is incorrect. Since Theorem 4 partially relies on Theorem 3, Theorem 4 is not always true. Theorem 4 remains true if one additionally requires that representation (13) hold. In addition, in the formulation of Theorem 4, instead of the word “products” (p. 1321, line 8 from the top), one should read “derivatives.”

V. F. Zhdanovich
1961 SovietRxiv: ru-196101.15315

On the Quasianalytic Continuation of Analytic Functions

A. A. GONCHAR
1961 SovietRxiv: ru-196101.14998

The paper studies when limits of rational functions with prescribed poles near a continuum determine a unique quasianalytic continuation across domains separated from that continuum. It proves geometric convergence criteria, expressed through level curves of the conformal map of the exterior of the …

Homotopy Duality for a Space with an Operator Group

A. S. SCHWARZ
1961 SovietRxiv: ru-196101.14835

This note generalizes Spanier and Whitehead homotopic duality to spaces equipped with a fixed point free action of a topological group. It defines stable classes of equivariant mappings by iterated joins with a chosen equivariant sphere-like space, introduces an equivariant duality operator on finit…

ON INFINITE-DIMENSIONAL HOMOGENEOUS SPACES

E. G. SKLYARENKO
1961 SovietRxiv: ru-196101.13723

The note studies how homogeneity assumptions influence the dimension theory of locally bicompact infinite-dimensional spaces. It first observes that a metrizable locally bicompact doubly homogeneous infinite-dimensional space cannot have transfinite dimension omega, under the stated definition. The …

ON THE GEOMETRY OF CONES IN A BANACH SPACE

Unknown
1961 SovietRxiv: ru-196101.13601

The paper studies geometric properties of pairs of cones in a real Banach space, extending classical notions of normal, generating, nonflattening, and regular cones to the setting of a subcone ordered by a larger cone. It proves the equivalence of two definitions of relative normality, gives a chara…

DIMITAR SKORDEV

Unknown
1961 SovietRxiv: ru-196101.13239

This paper studies locally convex real linear spaces ordered by a convex cone under compactness, positivity, and independence assumptions on quasi-indecomposable vectors. It defines a ring of order-bounded linear operators and identifies it with the ring of continuous real functions on the compact s…

On the Theory of Orthogonal Polynomials on Several Intervals

N. I. AKHIEZER and Yu. Ya. TOMCHUK
1961 SovietRxiv: ru-196101.13223

The paper studies monic polynomials orthogonal on a finite system of intervals with respect to weights involving a positive function, extending earlier work on the associated hyperelliptic Riemann surface. Using Abelian integrals, the authors give a parametric representation for auxiliary functions …

On a New Numerical Scheme of an Algorithm for Chebyshev Approximation of an Inconsistent System of Linear Equations and a System of Linear Inequalities

S. I. ZUKHOVITSKII
1961 SovietRxiv: ru-196101.12858

The paper presents a simplified numerical scheme for a previously developed finite monotone algorithm for Chebyshev approximation of inconsistent systems of linear equations. Keeping the geometric structure of the earlier method, it reformulates the computations through Jordan eliminations analogous…

On Some Homogeneous Boundary Value Problems for the Vibrating String Equation

E. A. ARUTYUNYAN, A. G. GYULMISARYAN, and S. G. OVSEPYAN
1961 SovietRxiv: ru-196101.12828

This paper studies eigenvalue boundary problems for the hyperbolic equation of string vibrations, replacing the usual homogeneous boundary condition by conditions involving a constant coefficient differential operator, possibly of arbitrary finite order. For the unit disk, the authors relate these p…

Solution of a system of quasilinear equations in divergence form under periodic boundary conditions

M. I. VISHIK
1961 SovietRxiv: ru-196101.12512

This note studies systems of quasilinear elliptic equations in divergence form on an n-dimensional torus under periodic boundary conditions. Using a Galerkin approximation with trigonometric basis functions and a topological lemma for finite nonlinear systems, it establishes existence of weak soluti…

Various Types of Invariant Systems of the Simplest Structure

Unknown
1961 SovietRxiv: ru-196101.12416

This paper extends the study of invariant first-order differential systems expressed through exterior differentiation and its metric adjoint beyond previously treated elliptic and hyperbolic cases. It constructs parabolic, semi-degenerate parabolic, and intermediate systems on covariants, relates th…

ON THE EXISTENCE OF PERIODIC SOLUTIONS IN CERTAIN NONLINEAR SYSTEMS

Consider the system of differential equations
1961 SovietRxiv: ru-196101.12221

The paper gives sufficient conditions for the existence of a periodic solution in a nonlinear nonautonomous system of differential equations with a constant linear part and a continuous time-periodic perturbation satisfying uniqueness. It considers the Poincare transformation over one period and com…

On Infinite-Dimensional Spaces

Unknown
1961 SovietRxiv: ru-196101.11465

This note studies weakly infinite-dimensional spaces and transfinite dimension in dimension theory. It extends Hurewicz-type theorems on dimension-lowering mappings to weakly infinite-dimensional bicompact and strongly paracompact spaces, proving criteria under which a space or the domain of a close…

MINIMAX PROBLEMS IN THE THEORY OF DIFFUSION PROCESSES

Unknown
1961 SovietRxiv: ru-196101.11025

The paper studies two-person minimax games associated with diffusion processes whose drift is modified by competing vector fields subject to local convex constraints. For payoffs given by the expected boundary value plus an additive running functional, the argument connects the value of the game to …

On the Approximate Solution of Volterra Equations of the Second Kind by the Method of Iterations

Yu. N. SHAKHOV
1961 SovietRxiv: ru-196101.10824

The paper studies approximate solution of linear Volterra integral equations of the second kind with smooth kernels and free terms. It adapts Ryaben’kii interpolation formulas based on number theoretic grids, first proving an interpolation error estimate for functions with bounded derivatives of ord…

On the densities of hyperimmune sets

E. A. PAVLOVA
1961 SovietRxiv: ru-196101.10624

The paper studies Medvedev’s density relation on subsets of the natural numbers, with emphasis on hyperimmune sets, whose densities are below that of the full set of natural numbers. It characterizes the induced partially ordered structure of density degrees, introduces rarefied and weakly rarefied …

The Problem of Best Chebyshev Approximation in a Complex Domain with Additional Conditions on the Coefficients of the Approximating Polynomial

E. G. GOLSHTEIN
1961 SovietRxiv: ru-196101.10455

This note studies a complex analogue of the Chebyshev problem for best uniform approximation of continuous functions on a compact set by generalized polynomials whose complex coefficients satisfy linear equality constraints and convex-domain inequality constraints. Under a regularity condition ensur…