Russian Universities Reports. Mathematics
Journal “Russian Universities Reports. Mathematics” is a peer-reviewed scientific and theoretical journal, where articles on mathematics and its applications with new mathematical results and reviews highlighting modern condition of current problems of mathematics are published. The journal is intended for a wide range of specialists in the field of mathematics, as well as for research scholars and students applying mathematical methods in the natural sciences, technics, economics, humanities.
The main scopes of the journal are: prompt publication of new original mathematical results of theoretical and applied importance; informing about the directions of research in various branches of mathematics, about modern mathematical problems; promoting the development of applications of mathematical methods and results.
It is published since June 14, 1996. Until May 27, 2019, the journal was published under the name “Tambov University Reports. Series: Natural and Technical Sciences” (ISSN 1810-0198).
The establisher, publisher, editorial office of the journal is FSBEI of HE “Derzhavin Tambov State University” (33 Internatsionalnaya St., Tambov 392000, Tambov Region, Russian Federation, tel. +7(4752)72-34-40, e-mail: post@tsutmb.ru).
The publication is registered by the Federal Service for Supervision of Communications, Information Technology and Mass Media (Roskomnadzor), extract from the register of registered mass media (register entry dated July 3, 2019 ПИ no. ФС77-76133).
ISSN 2686-9667 (Print). ISSN 2782-3342 (Online).
The journal is a member of the partnership: “Committee on the Ethics of Scientific Publications” and the professional community “Association of Science Editors and Publishers (ASEP)”, CrossRef (DOI of the journal: 10.20310/2686-9667).
Publication frequency is 4 issues per year (March, June, September, December).
Edition is 1000 copies.
Distribution territory of the journal: Russian Federation and foreign countries. The journal is distributed through subscription, at conferences, exhibitions, in the editorial office and partner universities.
General instruction on formation and publishing the scientific and theoretical journal is implemented by the editorial board with the editor-in-chief.
Editor-in-chief of the journal – Doctor of Physics and Mathematics, Professor, Director of Research Institute of Mathematics, Physics and Informatics of Derzhavin Tambov State University Evgeny Semenovich Zhukovskiy.
Themes of the journal. The journal publishes articles on various areas and branches of mathematics (algebra and logic, geometry and topology, functional analysis, differential equations, optimization and control, probability theory and mathematical statistics, computational methods, etc.), its applications.
Scientific works are published in three main types:
– review articles reflecting the current state of research in a certain mathematical direction;
– original articles describing the results of the research of specific mathematical problems, containing complete proofs of the results obtained by the author;
– short messages which present the results of the research of specific mathematical problems, containing precise formulations without complete proofs.
The journal also publishes the proceedings of mathematical conferences organized by the university, pee-reviews, personalia and informational materials about mathematical life of the university.
The authors of the journal are Russian and foreign scholars. Editorial office accepts manuscripts in Russian or English languages.
It is possible to get acquainted with the requirements to the arrangement of the materials in the sections “Rules of scientific articles sending, reviewing and publishing” and “Rules for authors”.
Publications in journal are made on non-commercial basis. The editorial office does not take payment from the authors for preparation, placement and printing of materials.
Indexing
The journal is indexed in the database of the Russian Science Citation Index (RSCI), included in the RSCI core collection, indexed in the Russian Science Citation Index (RSCI) database on the Web of Science platform, Scopus.
The journal is included in the "White list", List of peer-reviewed scientific publications recommended by the Higher Attestation Commission (HAC) (Q1) – a group of scientific specialties according to the HAC Nomenclature: 01.01.00 – mathematics.
The journal is also included in Zentralblatt MATH (“Central Journal on Mathematics”) – reviewing mathematical journal established by the Publisher “Springer” and electronic database “ZBMATH – The database Zentralblatt MATH”; Norwegian Register of Scientific Journals, Series and First Level Publishers (NSD); Math-Net.Ru – all-Russian portal of scientific information on mathematics, physics, information technology and related sciences; Reviewing journal and Databases of VINITI of the Russian Academy of Sciences; the International database of Scientific Literature SciLIT; one of the biggest International bibliographic databases “Ulrich’s Periodicals Directory” of American publisher Bowker (containing and describing the world flow of periodicals in all thematic areas).
Free full-text network versions of the issues of scientific and theoretical journal “Russian Universities Reports. Mathematics”, abstracts and keywords for all scientific articles and reviews can be found in open access on Russian and English languages at platforms of Scientific Electronic Library eLIBRARY , Electronic Library “CyberLeninka” and on the All-Russian mathematical portal Math-Net.Ru.
Copyright
Authors retain the copyright without restrictions. When re-publishing materials, the author undertakes to give a reference to the previously published articles in the journal “Russian Universities Reports. Mathematics”.
“Russian Universities Reports. Mathematics” provides Open Access to full-text issues.
Plagiarism policy
In the editorial office of the journal “Russian Universities Reports. Mathematics” all articles submitted for consideration are checked in the Antiplagiat system.
Editorial office and publisher address: 33 Internatsionalnaya St., Tambov 392000, Tambov Region, Derzhavin Tambov State University
Contact telephone of editorial office: +7(4752)72-34-34 ext. 0440.
E-mail of editorial office: zukovskys@mail.ru; ilina@tsutmb.ru
Editorial board, Editor-in-Chief of the journal Dr. Prof. Evgeny S. Zhukovskiy.
Current Issue
Vol 30, No 152 (2025)
Original articles
On coincidence points in $(q_1, q_2)$-quasimetric space
Abstract
In this paper, we present a theorem on a coincidence point of mappings which extends the Arutyunov theorem. The original version of the Arutyunov theorem guaranteed the existence of a coincidence point for two mappings acting in metric spaces, one of which is $\alpha$-covering and the other is $\beta$-Lipschitz, where $\alpha > \beta.$ This theorem was then extended to mappings acting in $(q_1, q_2)$-quasimetric spaces. In this paper, the problem of the existence of a coincidence point is solved for mappings acting from a $(q_1, q_2)$-quasimetric space to a set equipped with a distance satisfying only the identity condition (the distance vanishes if and only if the points coincide). Under conditions similar to those of the Arutyunov theorem, the existence of a coincidence point is proved. In addition, the questions of convergence of sequences of coincidence points of mappings $\psi_n, \varphi_n$ to the coincidence point $\xi$ of mappings $\psi, \varphi$ are investigated under the convergences $\psi_n(\xi)\to \psi(\xi),$ $\varphi_n(\xi)\to \varphi(\xi).$
309-321
On the control problem for a pseudo-parabolic equation with involution in a bounded domain
Abstract
This paper considers a control problem for a pseudo-parabolic equation with an involution operator in a bounded domain. A generalized solution to the corresponding initial boundary value problem is obtained. By introducing an additional integral condition, the control problem is reduced to a Volterra integral equation of the first kind. To show that the integral equation has a solution, some estimates are obtained for the kernel of this integral equation. The existence of a solution to the integral equation is shown using the Laplace transform method and the admissibility of the control function is proved.
Keywords: pseudo-parabolic equation, Volterra integral equation, admissible control, initial boundary value problem, Laplace transform, weight function
322-337
Recurrence theorems for dynamical systems in a sequentially compact topological space with invariant Lebesgue measure
Abstract
A property is presented that characterizes quite fully the interrelation of motions of a dynamical system $g^t$ defined in a Hausdorff sequentially compact topological space $\Gamma.$ It is noted that in the space $\Gamma$ with an invariant (with respect to $g^t$) Lebesgue measure $\mu,$ a direct analogue of the Poincare--Caratheodory recurrence theorem for sets is valid. In addition, it is shown that if $\bar{\mathcal{M}}$ is the closure of the union $\mathcal{M}$ of all minimal sets of the space $\Gamma,$ then $\mu\bar{\mathcal{M}}=\mu\Gamma,$ and through each point $p\notin\mathcal{M}$ there passes a motion $f(t,p)$ that is both positively and negatively asymptotic with respect to the compact minimal sets $\Omega_p\subset\mathcal{M}$ and $\mathrm{A}_p\subset\mathcal{M}.$ If $\Gamma$ satisfies the second axiom of countability, then $\mu\mathcal{M}=\mu\Gamma,$ i.~e. in $\Gamma,$ there is an important addition to the Poincare-Caratheodory theorem on the points recurrence.
338-345
Globalized piecewise Levenberg–Marquardt method with a procedure for avoiding convergence to nonstationary points
Abstract
The modern version of the Levenberg–Marquardt method for constrained equations possess strong properties of local superlinear convergence, allowing for possibly nonisolated solutions and possibly nonsmooth equations. A related globally convergent variant of the algorithm for the piecewise-smooth case, based on linesearch for the squared Euclidian norm residual, has recently been developed. Global convergence of this algorithm to stationary points for some active smooth selections has been shown, and examples demonstrate that no any stronger global convergence properties can be established for this algorithm without further modifications. In this paper, we develop such a modification of the globalized piecewise Levenberg–Marquardt method, that avoids undesirable accumulation points, thus achieving the intended property of B-stationarity of accumulation points for the problem of minimization of the squared Euclidian norm residual of the original equation over the constraint set. The construction consists of identifying smooth selections active at potential accumulation points by means of an appropriate error bound for an active smooth selection employed at the current iteration, and then switching to a more promising identified selection when needed. Global convergence to B-stationary points and asymptotic superlinear convergence rate are established, the latter again relying on an appropriate error bound property, but this time for the solutions of the original constrained equation.
346-360
Integral representation of the solution of the initial value problem for the wave equation on a geometric graph without boundary vertices
Abstract
We study the initial value problem $u(x,0)=\varphi(x),$ $u_t(x,0)=0$ for the wave equation $u_{xx}(x,t)=u_{tt}(x,t)$ for $x\in\Gamma\setminus J$ and $t>0,$ where $\Gamma$ is a geometric graph (according to Yu. V. Pokornyi) with straight-line edges and without boundary vertices ($\partial\Gamma=\varnothing$), $J$ is the set of all internal vertices of $\Gamma,$ and the function $\varphi$ is given; the transmission conditions that close the problem are, in addition to the continuity of the function $u(\,\cdot\,,t)$ at the interior vertices, the smoothness conditions for it, the essence of which is that for each $t\geqslant0$ at each interior vertex $a\in J$ the sum of the right derivatives of the function $u(\,\cdot\,,t)$ in all admissible directions is 0. It is proved that if $G^\ast$ is a generalized Green's function (according to M. G. Zavgorodniy, 2019) for the boundary value problem $-y''(x)=f(x),$ $x\in\Gamma\setminus J,$ under smooth transmission conditions (here $y$ is the desired function, continuous at the points of $J,$ and $f$ is a given function, uniformly continuous on each edge of $\Gamma$), then the classical solution $u$ of the initial value problem is representable in form:
where $\langle\varphi\rangle$ is the average of $\varphi$ over $\Gamma,$ and $g^\ast(x,t,s)=[\mathcal C(t)G^\ast(\,\cdot\,,s)](x),$ where, in turn, $\mathcal C$ is an operator function finitely described only through the metric and topological characteristics of $\Gamma.$ The approach to obtaining this representation of $u$ is similar to the approach implemented by the author earlier (2006) in the case where $\partial\Gamma\ne\varnothing$ and Dirichlet conditions are imposed at the points of $\partial\Gamma.$
361-381
Solution of the Cauchy problem for a degenerate second order differential equation in a Banach space
Abstract
This article is devoted to the study of the Cauchy problem for a second-order differential equation with a non-invertible operator at the highest derivative, as a result of which, the solution exists not for every initial value. This operator is Fredholm with a zero index. The cascade splitting method is used to solve the problem. This method splits the equation and conditions into the corresponding equation and conditions in subspaces of smaller dimensions. The case of invertibility of some operator constructed by using the operator coefficients of the equation is investigated. The conditions under which a solution to the problem exists and is unique are determined; it is found in the analytical form.
382-391
Attraction sets in abstract attainability problems and their representations in terms of ultrafilters
Abstract
Abstract problems about attainability in topological space (TS) under constraints of asymptotic nature (CAN) realized by nonempty family of sets in the space of usual solutions (controls) are considered. As analog of the attainability set defined by image of the target operator (TO) with values in TS, attraction set (AS) in classes of filters or directednesses of usual solutions is considered. Questions connected with the AS dependence under cange in the family of sets of usual solutions generating CAN are investigated. The special attention is paid to the case when this family is a filter (every AS is either generated by a filter used as CAN or is empty set). At the same time, AS under CAN generated by ultrafilters (u/f) that is by maximal filter under unrestrictive conditions on TS and TO there is a singleton, which allows to enter attraction operator which, in the case of regular TS, is continuous under equipment of the set of all ultrafilters on the set of usual solutions with Stone topology. On this basis, it is possible to give a practically exhaustive representation of constructions connected with AS in a regular TS in the class of u/f with their natural factorization based on TO. A whole range of obtained properties extend to the case of TO with values in a Hausdorff TS. Some questions connected with topology weakening of the space in which AS is realized are investigated.
392-424