Mathematics › Mathematics ×

Showing 50 of 5847 papers in Mathematics

ON EXISTENCE THEOREMS IN THE CALCULUS OF VARIATIONS

G. P. Ivanova
1966 SovietRxiv: ru-196601.04110

This note formulates an existence theorem for time-optimal control processes under a compactness condition on trajectories and a convexity condition on sets determined by the maximizers of the Hamiltonian. The proof embeds the original controlled system into a convexified system, applies the known F…

On solutions in generalized functions of ordinary differential equations with polynomial coefficients

F. S. Aliev
1966 SovietRxiv: ru-196601.03756

This note studies ordinary differential equations with polynomial coefficients that are not of Fuchs type, focusing on solutions in spaces of generalized functions that permit regularization of exponential singularities. For equations of a specified form with an isolated singularity at zero, it anal…

EMBEDDING THEOREMS FOR SPACES WITH MIXED NORM

Unknown
1966 SovietRxiv: ru-196601.03357

This paper studies embedding theorems for function spaces with mixed norms, focusing on removing earlier monotonicity restrictions on the norm parameters. It defines the relevant mixed norm and Sobolev-type spaces, proves ordering and interpolation lemmas, and establishes a general boundedness theor…

ON THE TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF VALUES OF \(E\)-FUNCTIONS THAT ARE SOLUTIONS OF A LINEAR DIFFERENTIAL EQUATION OF THIRD ORDER

V. A. Oleinikov
1966 SovietRxiv: ru-196601.03284

The paper develops a method for proving algebraic independence of values of E-functions satisfying linear differential equations, with particular attention to homogeneous equations of third order. It introduces a criterion of differential reducibility for algebraic differential equations, expressed …

ON ABSOLUTE AND UNCONDITIONAL CONVERGENCE

P. L. Ul'yanov
1966 SovietRxiv: ru-196601.02285

This note studies absolute and unconditional convergence of Fourier series with respect to the Haar system, emphasizing distinctions between pointwise absolute convergence, absolute convergence of coefficients, and almost-everywhere absolute convergence. It gives sufficient conditions in terms of in…

ON A CLASS OF DISCRETE GROUPS OF LOBACHEVSKY SPACE HAVING AN INFINITE FUNDAMENTAL DOMAIN OF FINITE MEASURE

V. S. Makarov
1966 SovietRxiv: ru-196601.01742

The note constructs infinite families of discrete groups acting on three-dimensional Lobachevsky space whose fundamental domains are noncompact but have finite volume. The construction begins with polyhedra associated to fine square decompositions of a horosphere, chooses dihedral angles of the form…

On Singular Points of Topological Embeddings of Manifolds and the Union of Locally Flat Cells

A. V. Chernavskii
1966 SovietRxiv: ru-196601.01660

This note studies singular points of topological embeddings of manifolds in Euclidean space and the local flatness of unions of locally flat cells. It proves that, in dimensions \(n \ge 5\), singular interior points are removable except in codimension two, where local flatness is characterized by th…

Bibliography of Journal Articles

Unknown
1966 SovietRxiv: ru-196601.01514

This bibliographic survey records recent journal literature on differential equations, primarily from Soviet and Eastern European mathematical publications of 1965 and early 1966. The entries are organized under ordinary differential equations and cover qualitative theory, stability, asymptotic meth…

ON THE INVARIANT COMPLEMENTABILITY OF SOME SUBSPACES GENERATED BY A LINEAR OPERATOR

M. A. Gol'dman, E. M. Levich
1966 SovietRxiv: ru-196601.01110

This paper studies when the subspace of null elements of a linear operator on a vector space admits an invariant complement. It proves several sufficient conditions, including bounded height of null elements, finite-dimensionality of the null subspace, stabilization conditions on kernels intersected…

ON THE NORMAL STRUCTURE OF FINITE GROUPS

L. A. Shemetkov
1966 SovietRxiv: ru-196601.00975

This note studies the normal structure of finite groups through systems of cyclic chief factors, with particular attention to groups whose chief factors have cyclic Sylow p-subgroups. Using auxiliary results from modular representation theory, it gives criteria involving the Frattini subgroup, gener…

THE INTEGRAL FUNCTIONAL AND ITS NORM

V. A. Gusev
1966 SovietRxiv: ru-196601.00743

The paper studies integral functionals on algebraic polynomials generated by moment segments of nondecreasing functions on the unit interval, extending a problem concerning the functional with moments 1, xi/2, xi squared/3, and so on. Using determinant criteria for absolutely monotone segments and r…

On Solving the Kinetic Transport Equation by the Splitting Method

Corresponding Member of the Academy of Sciences of the USSR G. I. Marchuk, U. M. Sultangazin
1965 SovietRxiv: ru-196501.99992

This paper studies the stationary one-velocity kinetic transport equation with isotropic scattering in a bounded convex domain and proposes a splitting method for its solution. The authors formulate the boundary-value problem in an operator setting, define a class of generalized solutions in an \(L_…

ON A GENERALIZATION OF THE CONCEPT OF A LIE ALGEBRA

A. Blokh
1965 SovietRxiv: ru-196501.99895

The paper introduces left, right, and two-sided D-algebras as distributive algebras satisfying differential identities that generalize the Lie algebra identity while also encompassing structures equivalent to modules over Lie algebras. It proves that the quotient of a left D-algebra by its left cent…

SOME RELATIONS BETWEEN THE BEST POWER APPROXIMATION OF ANALYTIC FUNCTIONS AND THEIR EXPANSION COEFFICIENTS

Sh. R. Mamedov
1965 SovietRxiv: ru-196501.95288

This paper studies relations between the best polynomial approximation of analytic functions of several variables and the coefficients of their orthogonal expansions. Using mean square approximation in a cube with weight, the author proves lemmas identifying generalized Fourier coefficients as optim…

Some Boundary Value Problems for Systems of Second-Order Elliptic-Type Equations in the Plane

N. E. TOVMASYAN
1965 SovietRxiv: ru-196501.94706

This paper studies a boundary value problem for systems of second order elliptic equations in a finite multiply connected plane domain with smooth boundary and a first order linear boundary condition. Using a Green formula and a matrix fundamental type representation, the problem is reduced to an eq…

Boundary Values of Functions from Weighted Classes

Yu. S. Nikol'skii
1965 SovietRxiv: ru-196501.94347

The paper studies traces and boundary values for weighted Sobolev-type classes of functions in a half-space, with weights satisfying monotonicity and doubling-type conditions. It defines corresponding fractional weighted spaces on the boundary and proves direct trace embeddings, inverse extension em…

On the expansion in eigenfunctions of a non-self-adjoint boundary value problem for a differential equation with a singularity at zero

M. G. GASYMOV
1965 SovietRxiv: ru-196501.94241

This paper studies a non-self-adjoint boundary value problem on the half-axis for a second order differential equation with the singular term l(l+1)/x2 at the origin and a complex locally summable potential. It refines transformation-operator representations for the regular solution, proving differe…

On multiple completeness and convergence of multiple expansions in the system of eigenvectors and associated vectors of an operator pencil

A. S. MARKUS
1965 SovietRxiv: ru-196501.94157

This note studies multiple completeness and multiple expansions for systems of eigenvectors and associated vectors of polynomial operator pencils in Banach and Hilbert spaces. By reducing higher degree pencils to linear pencils on product spaces and applying known results on compact and Schatten typ…

On series close to Dirichlet series

B. S. BRONSTEIN
1965 SovietRxiv: ru-196501.94079

This paper introduces and studies “D-series,” a class of series close to Dirichlet series whose basis functions have prescribed exponential asymptotics in a bounded domain and whose boundary of convergence contains a vertical segment. After reducing the general case by a linear change of variable, t…