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.
Current Issue
Vol 30, No 150 (2025)
Original articles
On dynamic reconstruction of a disturbances in distributed parameter systems
Abstract
The problem of dynamic reconstruction of disturbances acting on a nonlinear system composed of two coupled parabolic-type equations is under consideration. Assuming that a solution of the system is measured (with errors) at discrete times, an algorithm for solving the problem is proposed. The algorithm, based on the principles of feedback control theory, is shown to be robust with respect to informational noises and computational inaccuracies. An estimate of the convergence rate of the algorithm is provided.
97-109
Proof of Brouwer's conjecture (BC) for all graphs with number of vertices $n>n_0$ assuming that BC holds for $n\leq n_0$ for some $n_0 \leq 10^{24}$
Abstract
Abstract. In the article, the authors consider the problem of constructing an upper bound for the sum of the maximal eigenvalues of Laplacian of a graph. The article is devoted to proving the Brouwer conjecture, which states that the sum of the -maximal eigenvalues of Laplacian of a graph does not exceed the number of edges of the graph plus \( (t + 1)t⁄2 \). Note that we prove the validity of the general Brouwer conjecture under the assumption that the conjecture is valid for a finite number of graphs with the number of vertices less than \( 10^{24 } \), i.e., a complete proof of the conjecture is reduced to establishing its validity for a finite number of graphs. The proof of this conjecture attracts the interest of a large number of specialists. There are a number of results for special graphs and a proof of the conjecture for almost all random graphs. The proof we are considering uses an inductive method that has some peculiarities. The original method involves constructing various estimates for the eigenvalues of Laplacian of a graph which is used to construct the induction step. Several variants of the method are considered depending on the values of the coordinates of the eigenvectors of the Laplacian. The well-known fact of equivalence of the validity of the Brouwer conjecture for the graph itself and the complement of the graph is used.
110-127
Pólya groups and fields in some real biquadratic number fields
Abstract
Let K be a number field and \( O_K \) be its ring of integers. Let \( Π_q (K) \) be the product of all prime ideals of \( O_K \) with absolute norm q. The Pólya group of a number field is the subgroup of the class group of K generated by the classes of \( Π_q (K) \). K is a Pólya field if and only if the ideals \( Π_q (K) \) are principal. In this paper, we follow the work that we have done in [S. EL Madrari, “On the Pólya fields of some real biquadratic fields”, Matematicki Vesnik, online 05.09.2024] where we studied the Pólya groups and fields in a particulare cases. Here, we will give the Pólya groups of \( K=Q(√(d_1 ),√(d_2 )) \) such that \( d_1=lm_1 \) and \( d_2=lm_2 \) are square-free integers with \( l>1 \) and \( gcd(m_1;m_2)=1 \) and the prime 2 is not totally ramified in \( K⁄Q \). And then, we characterize the Pólya fields of the real biquadratic fields K.
128-143
On the structure of the kernel of the Schwarz problem in an ellipse in the general case
Abstract
The paper calculates the structure of the kernel and co-kernel of the Schwartz problem for $J$-analytic functions defined in the ellipse $D$ with a boundary $\Gamma.$ The Schwartz problem consists in finding a $J$-analytic function in the ellipse $D$ by the known value of its real part on $\Gamma. $ In paragraphs 1 and 2 the problem is formulated and its solution for a~special right part is studied. Paragraph 3 contains the necessary information from one paper by A.\,P.~Soldatov. Paragraph 4 constructs the solution of the Schwarz union problem for the special right-hand side. On the basis of these results, paragraph 5 calculates the kernel and the co-kernel of the Schwartz problem. The model of their calculation is briefly described at the beginning of the fifth paragraph. Then in the theorems \ref{th5.1}--\ref{th5.6} this scheme is implemented. Here the notions of theoretical and algorithmic solvability of the special Schwarz problem introduced by the author are used. The method of mathematical induction is used as well. It is shown that the kernel and co-kernel of the Schwarz problem in an ellipse consist only of vector polynomials. The paper describes the structure of the kernel and co-kernel in terms of the ranks of some real matrices depending on the matrix $J$ and the ellipse $\Gamma.$ The paper concludes with an example of calculating the kernel of the Schwarz problem in an ellipse for a two-dimensional matrix $J$ with multiple eigenvalue.
144-159
Characterizations of geometric tripotents in strongly facially symmetric spaces
Abstract
The concept of a geometric tripotent is one of the key concepts in the theory of strongly facially symmetric spaces. This paper studies the properties of geometric tripotents. We establish necessary and sufficient conditions under which a norm-one element of the dual space (real or complex) of a strongly facially symmetric space is a geometric tripotent. We prove that two geometric tripotents in such a space are mutually orthogonal if and only if both their sum and difference have norm one. Furthermore, we show that the set of extreme points of the unit ball coincides with the set of maximal geometric tripotents in the dual of a strongly facially symmetric space. Finally, we examine the relationship between M-orthogonality and ordinary orthogonality in the dual of a complex strongly facially symmetric space, providing a geometric characterization of geometric tripotents.
160-169
On the asymptotic behavior of solutions of nonautonomous differential inclusions with a set of several Lyapunov functions
Abstract
or non-autonomous differential inclusions, the issues of attraction and asymptotic behavior of solutions are considered. The basis of the research is the development of the method of limit differential equations in combination with the direct Lyapunov method with several Lyapunov functions. This makes it possible to more accurately localize and determine the structure of \( ω \)-limit sets of solutions. The main problems of the research are the absence of properties of the invariance type of \( ω \)-limit sets of non-autonomous systems and the construction of limit differential relations. They are solved using limit differential inclusions constructed using shifts (translations) of the main differential inclusions. The results have the form of generalizations of the LaSalle invariance principle and provide preliminary information on the limit behavior of solutions. A set of additional Lyapunov functions allows one to refine this behavior and to single out those points from the set of zeros of the derivative of the main Lyapunov function that obviously do not belong to the \( ω \)-limit sets. The results are illustrated by the example of a linear oscillator with dry friction.
170-182
Two parameter $C_{0}$-semigroups of linear operators on locally convex spaces
Abstract
The purpose of this paper is to study two parameter (resp. $n$-parameter) expo\-nen\-tial\-ly equicontinuous $C_{0}$-semigroups of continuous linear operators on sequentially complete locally convex Hausdorff spaces. In particular, we demonstrate the Hille--Yosida theorem for two parameter (resp. $n$-parameter) exponentially equicontinuous $C_{0}$-semigroups of continuous linear operators on sequentially complete locally convex Hausdorff spaces. Moreover, the $n$-parameter $C_{0}$-semigroups of continuous linear operators on Banach spaces are studied.
183-204