Published in Russian Mathematics
For the Gellerstedt equation with a singular coefficient in some mixed domain, when the ellipticity boundary coincides with the segment of the Oy axis and the normal curve of the equation, a problem with the Bitsadze–Samarskii conditions on the elliptic boundary and on the degeneration line is studied. The well-posedness of the formulated problem i...
Published in Russian Mathematics
A Kaczmarz method is presented for solving a class of fuzzy linear systems of equations with crisp coefficient matrix and fuzzy right-hand side. The iterative scheme is established and the convergence theorem is provided. Numerical examples show that the method is effective.
Published in Russian Mathematics
We consider the properties of systems of functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Phi_1$\end{document} orthogonal with respect to a discrete-continuous...
Published in Russian Mathematics
For a differential-difference equation with a positive fundamental solution we obtain exponential stability conditions with exact estimates of the exponent and the coefficient of the exponential decay. These estimates are expressed in terms of the largest of two possible real roots of the characteristic function. We prove that one can obtain exact ...
Published in Russian Mathematics
The structures of partially ordered sets of degrees of negative and positive representability of linear orders are studied. The focus is on the negative representability of linear orders and orders with endomorphisms. In particular, for these structures, we established the existence of incomparable, maximal, and minimal degrees, infinite chains and...
Published in Russian Mathematics
We study five-dimensional pseudo-Riemannian h-spaces \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{221}$\end{document} of type \documentclass[12pt]{minimal} \usepac...
Published in Russian Mathematics
In the paper, we consider a boundary value problem for a second order functional-differential equation with sufficiently general linear homogeneous boundary conditions. On the basis of the theory of semi-ordered spaces and with the help of special topological methods, we prove the existence of a unique positive solution to the problem.
Published in Russian Mathematics
The paper deals with the canonical deformed group of diffeomorphisms with a given length scale which describes the motion of single scales in a Riemannian space. This allows to measure the lengths of arbitrary curves implementing the length principle which was laid by B. Riemann at the foundation of geometry. We present a method of univocal extensi...
Published in Russian Mathematics
Formulas are obtained for calculating the curvatures of an implicitly defined curve in n-dimensional Euclidean space. For these curves, Beltrami's theorem is generalized, which was proved by Beltrami in the case of three-dimensional space.
Published in Russian Mathematics
A linear boundary-value problem for a system of integro-differential equations with weakly singular kernels is considered. Questions of the unique solvability and the construction of algorithms for finding solution to the considered problem are studied. Conditions for the solvability of the boundary-value problem for a system of integro-differentia...
