Showing 50 of 5847 papers in Mathematics

Densely embedded ideals of semigroups

Unknown
1960 SovietRxiv: ru-196001.76493

This note studies densely embedded ideals in abstract semigroups, extending earlier characterizations related to transformation semigroups. Using right and left shifts and their linked pairs, it constructs for a semigroup without equiacting elements a canonical semigroup in which the original semigr…

On the stability of the Ritz method

Unknown
1960 SovietRxiv: ru-196001.75502

This note studies the numerical stability of the Ritz method for solving equations with positive definite operators in Hilbert spaces, focusing on how the choice of coordinate system affects the behavior of the coefficients as the number of terms increases. It reviews reliable coordinate systems, re…

On the index of boundary value problems for a system of harmonic functions with three independent variables

A. I. VOLPERT
1960 SovietRxiv: ru-196001.75411

This paper studies the index of boundary value problems for systems of harmonic functions in a three dimensional convex domain with elliptic first order boundary operators. It associates the problem with elliptic first order systems on the boundary surface, defines a characteristic through a bundle …

On the Problem of Isomorphism of Structures

Unknown
1960 SovietRxiv: ru-196001.74972

The paper addresses the isomorphism problem for finitely defined structures by relating them to free extensions of finite structuroids. It defines irreducible tabular systems of relations, finitely free extensions, bases of finite structuroids, and removable elements, then proves that every finite s…

Maximum coefficients of multiple correlation

O. V. SARMANOV and V. K. ZAKHAROV
1960 SovietRxiv: ru-196001.74511

This paper extends the notion of the maximal correlation coefficient from two random variables to multiple correlation among random variables with a joint density. It defines maximal correlation between random vectors formed from nonintersecting subspaces through an extremal bilinear functional, rel…

On the Adams spectral sequence

Unknown
1960 SovietRxiv: ru-196001.74112

This note studies the limiting term and filtration structure of the Adams spectral sequence modulo a fixed prime. It introduces p-spaces and p-systems, proves the existence and uniqueness, up to singular homotopy type, of a maximal p-system, and uses this construction to define a natural filtration …

Intrinsic Correlation Functions and Their Applications in the Theory of Stationary Markov Processes

O. V. SARMANOV
1960 SovietRxiv: ru-196001.73418

The paper introduces maximal and intrinsic correlation functions for stationary real processes and applies them to stationary Markov processes whose two-dimensional densities are symmetric and square-integrable in a specified sense. It shows that such a density defines a continuous Markov process pr…

On the Stability of Periodic Motions

T. N. TRIBELEVA
1960 SovietRxiv: ru-196001.73330

This paper studies the stability of periodic motions in autonomous differential systems and in a special class of nonlinear canonical systems. It extends a theorem of Andronov and Witt to families of periodic solutions whose period depends on parameters, using variational equations, characteristic r…

Stable Situations in Coalition Games

N. N. VOROBYEV
1960 SovietRxiv: ru-196001.73012

This note develops a variant of the theory of coalition games in which coalitions have nondivisible payoffs and mixed behavior is represented through consistent families of measures and systems of random transitions. It introduces internal consistent measures, Markovian extensions, realizable transi…

RANGE OF VALUES OF THE FUNCTIONAL

Unknown
1960 SovietRxiv: ru-196001.72619

The paper studies ranges of logarithmic functionals involving values and derivatives of bounded univalent functions in the unit disk. Using Kufarev’s method, it derives parametric equations for the boundaries of these ranges in three settings: functions with prescribed modulus at a fixed point, the …

Estimates of Resolvents of Singular Elliptic Operators

Unknown
1960 SovietRxiv: ru-196001.71737

This note studies resolvent estimates for a class of singular elliptic matrix differential operators on Euclidean space, with strongly negative principal symbol and a confining matrix potential whose eigenvalues tend to negative infinity at a prescribed rate. Using estimates for the Green function o…

ON LOCAL THEOREMS FOR LARGE DEVIATIONS

Unknown
1960 SovietRxiv: ru-196001.71461

This paper establishes local large deviation theorems for sums of independent random variables beyond the classical Cramér exponential moment condition. Using methods associated with Linnik, it gives uniform asymptotic formulas for the densities, and for lattice probabilities, of normalized sums in …

On the $\varepsilon$-entropy of some classes of functions

S. Ya. AL′PER
1960 SovietRxiv: ru-196001.70569

This paper studies the epsilon entropy of several classes of complex functions under smoothness and growth restrictions. For analytic functions in a bounded simply connected domain, entropy estimates are obtained in terms of the boundary regularity and Hölder smoothness of derivatives, using Kolmogo…

On a nonlinear boundary value problem of Riemann type

Unknown
1960 SovietRxiv: ru-196001.70357

The paper studies a nonlinear Riemann type boundary value problem for analytic functions, in which the nth power of the interior boundary value is related linearly to the exterior boundary value and a given Hölder continuous term. By substituting the nth power of the interior function, the problem i…

On stationary sequences forming a basis

Yu. A. ROZANOV
1960 SovietRxiv: ru-196001.70259

This paper studies when the coordinate values of a multidimensional stationary random sequence form a basis in the Hilbert space generated by the process, with emphasis on representations relevant to linear prediction. Using the spectral density matrix, it gives necessary and sufficient conditions f…

On an Interpolation Theorem in Operator Theory

S. G. KREIN
1960 SovietRxiv: ru-196001.70199

This paper formulates a general interpolation theorem for operators acting between Banach spaces organized into analytic scales, defined through parameter-dependent analytic operator families and logarithmically convex norms. It develops examples including scales generated by fractional powers of po…

On the Riemann Problem on Closed Riemann Surfaces

Unknown
1960 SovietRxiv: ru-196001.69500

This note studies homogeneous and nonhomogeneous Riemann boundary value problems on closed Riemann surfaces, together with conjugate problems formulated for analytic differentials. Using the Riemann Roch theorem, it gives dimension counts for the solution space in terms of the index and genus, estab…

Conformal Theory of Two-Parameter Families of Spheres

R. M. GEIDELMAN
1960 SovietRxiv: ru-196001.69236

This paper develops a conformal differential geometry of two-parameter families of spheres in three-dimensional conformal space using Cartan moving frames and exterior forms. It identifies fundamental geometric objects of first, second, and third order, proves that the third-order object determines …

On Homogeneous Difference Schemes of High Order of Accuracy

Unknown
1960 SovietRxiv: ru-196001.68944

The paper develops exact and high-order homogeneous three-point conservative difference schemes for one-dimensional boundary-value problems of the first, second, and third kinds for a second-order linear differential equation with variable coefficients. The construction uses local template functions…

On subsemigroups of free semigroups

L. N. SHEVRIN
1960 SovietRxiv: ru-196001.68341

This note studies when a subsemigroup of a free semigroup is itself free, allowing free semigroups that include both group-like generators with formal inverses and purely semigroup generators. After establishing basic properties concerning kernels, pure parts, bases, and cancellation, it introduces …

Theorems on an Implicit Abstract Analytic Function

Unknown
1960 SovietRxiv: ru-196001.67746

This paper develops implicit function theorems for analytic mappings between complex Banach spaces, using the representation of such mappings by homogeneous power series and a majorant series method. After establishing comparison lemmas for analytic functions and scalar majorants, it proves existenc…

New Limit Theorems for Sums of Independent Random Variables

Corresponding Member of the Academy of Sciences of the USSR Yu. V. LINNIK
1960 SovietRxiv: ru-196001.67588

This note studies large deviation behavior for normalized sums of independent identically distributed random variables beyond the range covered by the classical central limit theorem. It defines zones of normal convergence and gives necessary and sufficient conditions, in terms of exponential moment…

On the Spectrum of an Operator and the Dirichlet Problem for the Equation $\square^2u+4\frac{\partial^2}{\partial t^2}\square u+2\frac{\partial^4u}{\partial t^4}=f(x,y,z,t)$

Unknown
1960 SovietRxiv: ru-196001.67097

This paper studies spectral properties of operators associated with elliptic and hyperbolic fourth order equations in a four dimensional ball, formulated in Hilbert spaces defined by boundary compatible Sobolev type scalar products. It proves that the operator obtained from the inverse biharmonic op…

On the Problem of Identity in Associative Systems of a Special Type

1.** An associative system of a special kind, given by generators
1960 SovietRxiv: ru-196001.66608

The paper studies the identity problem for finitely presented associative systems whose defining relations have a special uniform form, in particular systems generated by relations of fixed word length. It proves that if the identity problem is decidable for all groups with a given number of nontriv…

Integral Representations

A. A. Temlyakov
1960 SovietRxiv: ru-196001.66315

The paper extends Temlyakov’s integral representation theory for analytic functions in bicircular domains of two complex variables to cases where parts of the boundary may be analytic hypersurfaces and the Levi determinant vanishes on boundary portions. By redefining the radius functions with condit…

On a Special Integral Equation with Shift

G. S. LITVINCHUK
1960 SovietRxiv: ru-196001.66210

This paper studies a singular integral equation on a closed Lyapunov contour whose Cauchy kernel contains a shift mapping the contour onto itself with reversed orientation. Under Carleman-type conditions on the shift and coefficients, the equation is transformed via the Sokhotski formulas into a bou…

On the Embeddability of Semigroups in Groups

Unknown
1960 SovietRxiv: ru-196001.65829

This note studies when finitely presented semigroups with cancellation can be represented inside more general associative systems or groups. It gives an explicit embedding construction showing that every finitely presented semigroup with two-sided cancellation embeds in a finitely presented associat…

Multidimensional moment problem

Unknown
1960 SovietRxiv: ru-196001.65480

This note studies multidimensional moment problems through positive-definite functionals on nuclear algebras of sequences and formal power series. Using an integral representation scheme for nuclear spaces, it proves representation theorems by positive measures on the real line, Euclidean spaces, an…

On the Asymptotic Behavior of Solutions of Multidimensional Systems of Ordinary Differential Equations with a Higher-Order Singular Point

A. A. SHESTAKOV
1960 SovietRxiv: ru-196001.65215

The paper studies the asymptotic behavior near a higher order singular point for analytic multidimensional systems of ordinary differential equations whose right hand sides have no constant or linear terms. Using a supporting hyperplane construction for the exponent sets, it extracts a quasihomogene…

On the Coincidence of the Dimensions $\operatorname{ind}G$ and $\dim G$ for Locally Bicompact Groups

A. ARKHANGEL’SKII
1960 SovietRxiv: ru-196001.64278

This note studies dimension theory for locally bicompact topological groups, extending known results for bicompact groups. It proves first that every locally bicompact group is strongly paracompact, by exhibiting an open and closed subgroup as a countable union of bicompact sets and applying Smirnov…