http://journals.rudn.ru/CMFD/issue/feedContemporary Mathematics. Fundamental Directions2020-03-02T20:10:23+03:00Скубачевский Александр Леонидовичskub@lector.ruOpen Journal Systems<p><strong>Editor-in-Chief: Revaz Valerianovich Gamkrelidze,</strong> Academician of the Russian Academy of Sciences, Professor, Doctor of Physical and Mathematical Sciences, Steklov Mathematical Institute, Russian Academy of Sciences, Russian Federation</p> <p><strong>ISSN: </strong>2413-3639 (print) 1573-8795 (online)</p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Founded in</strong> 2003 г. <span class="tlid-translation translation" lang="en"><strong>Publication frequency</strong>:</span> quarterly</p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Indexation</strong>: Russian Index of Science Citation, <a href="http://www.mathnet.ru/php/journal.phtml?jrnid=cmfd&wshow=details&option_lang=eng" target="_blank" rel="noopener noreferrer">mathnet.ru,</a> <a href="http://scholar.google.ru/">Google Scholar</a>, Lens, Microsoft Academic, Research4Life</p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Open Access</strong>: Open Access. </p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Publisher</strong>: <a href="http://eng.rudn.ru/" target="_blank" rel="noopener noreferrer">Peoples’ Friendship University of Russia (RUDN University)</a></p> <p> </p> <p>The English version is published by "Springer Science+Business Media, Inc." (USA) in the series "Journal of Mathematical Sciences." ISSN: 1072-3374 (print version) ISSN: 1573-8795 (electronic version)<br /><br /></p>http://journals.rudn.ru/CMFD/article/view/23049On One Damping Problem for a Nonstationary Control System with Aftereffect2020-03-02T20:06:57+03:00A. S. Adkhamovaami_adhamova@mail.ruA. L. Skubachevskiiskublector@gmail.com<p>We consider a control system described by the system of differential-difference equations of neutral type with variable matrix coefficients and several delays. We establish the relation between the variational problem for the nonlocal functional describing the multidimensional control system with delays and the corresponding boundary-value problem for the system of differential-difference equations. We prove the existence and uniqueness of the generalized solution of this boundary-value problem.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23050Translational Rectilinear Motion of a Solid Body Carrying a Movable Inner Mass2020-03-02T20:07:23+03:00B. S. Bardinbsbardin@yandex.ruA. S. Paneva.s.panev@gmail.com<p>We consider the motion of the mechanical system consisting of the case (a solid body) and the inner mass (a material point). The inner mass circulates inside the case on a circle centered at the center of mass of the case. We suppose that absolute value of the velocity of circular motion of the inner mass is constant. The case moves translationally and rectilinearly on a flat horizontal surface with forces of viscous friction and dry Coulomb friction on it. The inner mass moves in vertical plane. We perform the full qualitative investigation of the dynamics of this system. We prove that there always exist a unique motion of the case with periodic velocity. We study all possible types of such a periodic motion. We establish that for any initial velocity, the case either reaches the periodic mode of motion in a finite time or asymptotically approaches to it depending on the parameters of the problem.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23051On Asymptotics of the Density of States for Hypoelliptic Almost Periodic Systems2020-03-02T19:58:16+03:00V. I. Bezyaevvbezyaev@mail.ru<p>In this paper, we find the asymptotics of integrated density of states with remainder estimate for hypoelliptic systems with almost periodic (a.p.) coefficients. We use the approximate spectral projector method for matrix a.p. operators with continuous spectrum.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23052Absence of Solutions for Some Nonhomogeneous Elliptic Inequalities2020-03-02T20:07:49+03:00E. I. Galakhovgalakhov@rambler.ruO. A. Salievaolga.a.salieva@gmail.com<p>By means of the modified method of test functions, we obtain sufficient conditions of absence of nontrivial solutions for some classes of semilinear elliptic inequalities of higher order and quasilinear elliptic inequalities containing nonhomogeneous terms (independent of the unknown function).</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23053Boundary-Value Problems for Differential-Difference Equations with Incommeasurable Shifts of Arguments Reducible to Nonlocal Problems2020-03-02T20:08:11+03:00E. P. Ivanovaelpaliv@yandex.ru<p>We consider boundary-value problems for differential-difference equations containing incommeasurable shifts of arguments in higher-order terms. We prove that in the case of finite orbits of boundary points generated by the set of shifts of the difference operator, the original problem is reduced to the boundary-value problem for differential equation with nonlocal boundary conditions.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23054Application of Contemporary Proof of the Sforza Formula to Computation of Volumes of Hyperbolic Tetrahedra of Special Kind2020-03-02T20:08:33+03:00V. A. Krasnovkrasnov_va@rudn.university<p>In this paper, we use the contemporary proof (by Abrosimov and Mednykh) of the Sforza formula for volume of an arbitrary non-Euclidean tetrahedron to derive new formulas that express volumes of hyperbolic tetrahedra of special kind (orthoschemes and tetrahedra with the symmetry group S 4) via dihedral angles.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23055Strongly Elliptic Differential-Difference Equations with Mixed Boundary Conditions in a Cylindric Domain2020-03-02T20:08:55+03:00V. V. Liikovikalijko@gmail.comA. L. Skubachevskiiskub@lector.ru<p>We consider strongly elliptic differential-difference equations with mixed boundary conditions in a cylindrical domain. We establish the connection between such problems and nonlocal mixed problems for strongly elliptic differential equations, and prove the uniqueness of solutions.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23056Smoothness of Generalized Solutions of the Second and Third Boundary-Value Problems for Strongly Elliptic Differential-Difference Equations2020-03-02T20:04:35+03:00D. A. Neverovadneverova@gmail.com<p>In this paper, we investigate qualitative properties of solutions of boundary-value problems for strongly elliptic differential-difference equations. Earlier results establish the existence of generalized solutions of these problems. It was proved that smoothness of such solutions is preserved in some subdomains but can be violated on their boundaries even for infinitely smooth function on the right-hand side. For differential-difference equations on a segment with continuous right-hand sides and boundary conditions of the first, second, or the third kind, earlier we had obtained conditions on the coefficients of difference operators under which there is a classical solution of the problem that coincides with its generalized solution. Also, for the Dirichlet problem for strongly elliptic differential-difference equations, the necessary and sufficient conditions for smoothness of the generalized solution in Holder spaces on the boundaries between subdomains were obtained. The smoothness of solutions inside some subdomains except for ε-neighborhoods of angular points was established earlier as well. However, the problem of smoothness of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations remained uninvestigated. In this paper, we use approximation of the differential operator by finite-difference operators in order to increase the smoothness of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations in the scale of Sobolev spaces inside subdomains. We prove the corresponding theorem.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23057On the Algebra of Operators Corresponding to the Union of Smooth Submanifolds2020-03-02T20:10:23+03:00D. A. Poluektovadarya.loshhenova.90@bk.ruA. Yu. Savinantonsavin@mail.ruB. Yu. Sterninantonsavin@mail.ru<p>For a pair of smooth transversally intersecting submanifolds in some enveloping smooth manifold, we study the algebra generated by pseudodifferential operators and (co)boundary operators corresponding to submanifolds. We establish that such an algebra has 18 types of generating elements. For operators from this algebra, we define the concept of symbol and obtain the composition formula.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directionshttp://journals.rudn.ru/CMFD/article/view/23058On Initial-Boundary Value Problem on Semiaxis for Generalized Kawahara Equation2020-03-02T20:05:50+03:00A. V. Faminskiiafaminskii@sci.pfu.edu.ruE. V. Martynove.martynov@inbox.ru<p>In this paper, we consider initial-boundary value problem on semiaxis for generalized Kawahara equation with higher-order nonlinearity. We obtain the result on existence and uniqueness of the global solution. Also, if the equation contains the absorbing term vanishing at infinity, we prove that the solution decays at large time values.</p>2019-12-15T00:00:00+03:00Copyright (c) 2020 Contemporary Mathematics. Fundamental Directions