Published in Doklady Mathematics
The ray statement of the inverse problem of determining three unknown variable coefficients in the linear acoustic equation is studied. These coefficients are assumed to differ from given constants only inside some bounded domain. There are point pulse sources and acoustic receivers on the boundary of this domain. Acoustic signals are measured by a...
Published in Doklady Mathematics
A mathematical model is proposed that not only generates various scenarios of development, but also forms specific management measures aimed at suppressing the pandemic and restoring economic growth. The developed model of the mutual influence of the pandemic and the economy is not only a tool for effective and adequate forecasting, but is also cap...
Published in Doklady Mathematics
AbstractIn the present paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three specific axioms for corresponding defining relations that provide the small cancellation properties of the obtained ring. We show that th...
Published in Doklady Mathematics
AbstractAbstract integro-differential equations that are operator models of viscoelasticity problems are studied. The kernels of the integral operators can be specified as sums of decreasing exponentials or sums of Rabotnov functions with positive coefficients, which are widely used in viscoelasticity theory. A method is described whereby the origi...
Published in Doklady Mathematics
AbstractWe consider the eigenvalue problem for a two-dimensional Laplace operator with mixed boundary conditions (Zaremba problem), which (presumably) has a smooth solution inside the domain. Calculations show that the operator –Δ has a negative eigenvalue, i.e., it is not positive definite.
Published in Doklady Mathematics
AbstractIn this paper, a number of generalizations of the known characterization of Gaussian transition operators is obtained.
Published in Doklady Mathematics
AbstractA k-spectrum is a set of all positive α such that the random binomial graph \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G(n,{{n}^{{ - \alpha }}})$$\end{docu...
Published in Doklady Mathematics
AbstractFor systems of nonlinear equations, we propose a new version of the Gauss–Newton method based on the idea of using an upper bound for the residual norm of the system and a quadratic regularization term. The global convergence of the method is proved. Under natural assumptions, global linear convergence is established. The method uses an ada...
Published in Doklady Mathematics
AbstractThe asymptotic behavior of systems with Coulomb friction represented as Lagrange’s equations of the second kind is investigated. Lyapunov’s direct method is used in combination with the method of limiting equations, which goes back to the works by G.R. Sell (1967) and Z. Artstein (1977, 1978) on topological dynamics of nonautonomous systems...
Published in Doklady Mathematics
AbstractIn this paper, we construct three new periodic ultradiscrete plane transformations. Two such transformations were previously known.
