Vol 229 (2023)
Статьи
3-11
On bounded difference operators with involution
Abstract
In this paper, we considers difference operators of a special type (with involution) whose infinite matrix has two nonzero diagonals. We introduce the notion of an abstract involution operator and examine its such as invertibility, spectrum, and commutability condition. Also, we discuss the problem of whether the original operator and its inverse belong to special operator classes.
12-21
Necessary and sufficient conditions for the stability of systems of ordinary differential equations
Abstract
In this paper, we develop an approach to the analysis of the Lyapunov stability for systems of ordinary differential equations based on stability conditions in the multiplicative form. Under additional restrictions, various versions of stability conditions are obtained based on the behavior of the right-hand side of the system.
22-32
New identities from enumeration of graphs
Abstract
In this paper, three new combinatorial identities related to the enumeration of labeled connected graphs with a given number of endpoints are presented. We give a proof of these identities independent of the enumeration of graphs. For one of the identities, a course of the proof based on formulas for enumerating graphs is outlined.
33-36
Solutions of some systems of functional equations related to complex, double, and dual numbers
Abstract
In this paper, we solve the problem on the embedding of three two-metric, phenomenologically symmetric geometries of two sets of rank (3, 2) related to complex, double, and dual numbers, into a two-metric, phenomenologically symmetric geometry of two sets of rank (4, 2) determined by a functions of two points . The problem is reduced to the search for nondegeenerate solutions of three special systems of functional equations immediately related to complex, double, and dual numbers.
37-46
Relationships between the best uniform polynomial approximations of functions and their even and odd prolongations
Abstract
In this paper, we study the relationships between the best uniform polynomial approximations of a continuous function on an interval and its even and odd prolongations. We consider examples that demonstrate the accuracy of the results obtained. Similar issues are also discussed for rational approximations.
47-52
Structure of the essential spectrum and discrete spectrum of the energy operator of four-electron systems in the impurity Hubbard model. The third triplet state
Abstract
The structure of the essential spectrum and the discrete spectrum of the energy operator of four-electron systems in the Hubbard impurity model for the third triplet state of the system are examined. The following statements are proved. (a) The essential spectrum of the third triplet is the union of three segments and the discrete spectrum of the third triplet is empty. (b) The essential spectrum of the third triplet is the union of eight segments and the discrete spectrum of the third triplet consists of three eigenvalues. (c) The essential spectrum of the third triplet is the union of sixteen segments and the discrete spectrum of the third triplet consists of eleven eigenvalues.
53-82
Generalized mixed problem for the simplest wave equation and its applications
Abstract
In this paper, we present results for generalized homogeneous and inhomogeneous mixed problems for the wave equation based on the operation of integrating a divergent series of a formal solution using the method of separation of variables. A solution to the generalized mixed problem for an inhomogeneous equation is found under the assumption that the function characterizing the inhomogeneity is locally summable. As an application, a mixed problem with nonzero potential is considered.
83-89
Tensor invariants of geodesic, potential and dissipative systems. III. Systems on tangents bundles of four-dimensional manifolds
Abstract
In this paper, we present tensor invariants (first integrals and differential forms) for dynamical systems on the tangent bundles of smooth n-dimensional manifolds separately for and for any finite
The first part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 227 (2023), pp. 100–128.
The second part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 228 (2023), pp. 92–118.
90-119
Optimization of thermal processes in a nonlocal problem with a redefinition function under an integral condition
Abstract
In this paper, we examine the weak generalized solvability of an inverse optimization problem for the heat equation with a nonlocal boundary condition and a nonlinear target performance. We formulate necessary optimality conditions and reduce the search for a control function to a functional integral equation.
120-130