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 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 29, No 148 (2024)
Articles
On impulse control problems arising in automatization of pests control in greenhouses
Abstract
The paper proposes a mathematical model based on a continuous dynamic system that formalizes the interaction of populations of a greenhouse agricultural insect pest and an entomophage acting as an agent of environmental control of the pest population in the framework of the concept of integrated pest management paradigm. The model parameters are identified based on experimental data obtained in laboratory conditions for the greenhouse system “cucumber — spider mite — acariphage mite”. For the proposed system, an impulse control problem that corresponds to the implementation of the pest population control using an entomophage is formulated, and the issues of the existence of solutions and their continuous dependence on control are investigated. Based on the studied control system, the issues of constructing cost-effective control strategies that allow implementing the mathematical software for automated pest control systems in greenhouses are discussed.
381-390
On the recalculation of ellipsoids in estimating the error of the implicit Stormer method for a second-order linear differential equation
Abstract
In the paper, a new method is proposed for constructing an error estimate for the numerical solution of the Cauchy problem for a second-order differential equation obtained using the implicit Stormer method. Unlike the previously proposed methods, it allows one to take into account the signs of small terms when recalculating ellipsoids containing the exact solution in the case of implicit multistep numerical method. This leads to a more accurate estimation of the error of the numerical solution and the applicability of the ellipsoid method over large intervals. A numerical experiment is presented demonstrating the effectiveness of the proposed method for obtaining a guaranteed error estimate of the implicit Stormer method.
391-400
Accelerating convergence of Newton-type methods
Abstract
We consider the simplest extrapolation procedure, specifically doubling the step, intended for acceleration of convergence of Newton-type methods to singular solutions of smooth nonlinear equations. We demonstrate that the acceleration effect of this procedure can be different for different Newton-type methods. For linear-quadratic equations we provide theoretical results yielding quantitative estimates of the potential effect of extrapolation for the Newton method, for the Levenberg–Marquardt method, and for the recently proposed LP-Newton method, in some sense explaining the observed difference. Theoretical analysis relies on interpretation of these methods as a perturbed Newton method with the appropriate estimates of perturbations, as well as on sharp results yielding a quantitative characterization of a step of such perturbed method, and its local convergence at a linear rate to singular solutions satisfying the 2-regularity condition in a direction from the null space of the first derivative. Furthermore, we perform numerical experiments with globalized versions of the algorithms in question, equipped with choosing the stepsize parameter, on two sets of test problems. Experimental observations confirm the theoretical results, and also demonstrate that in cases when the equation contains nonlinear and nonquadratic terms, the effect of extrapolation is evened out.
401-424
Decomposition of modules over generalized Dickson algebras
Abstract
The article is devoted to modules over generalized Dickson algebras. These algebras are nonassociative and generally can be nonalternative. They compose an important class of algebras and an area in mathematics. Left, right and two-sided modules over generalized Dickson algebras are studied. Their structure and submodules are investigated. Bimodules with involution are scrutinized over generalized Dickson algebras with involution. Such bimodules have specific features caused by involution. Minimal submodules and decomposition of modules are investigated. In particular, cyclic submodules are studied.
425-439
A compact scheme for solving a superdiffusion equation
Abstract
A superdiffusion equation with Riesz fractional derivatives with respect to space with several delay variables is considered. The problem is discretized. For this purpose, an analog of the Crank–Nicolson difference method with piecewise linear interpolation to account for the effect of variable delay and with extrapolation by continuation is constructed in time so that the implicitness of the method becomes finite-dimensional. An analog of a compact scheme with a special replacement of Riesz fractional derivatives by fractional central differences is constructed in space. As a result, the method is reduced to solving a system of linear algebraic equations with symmetric and positive-definite main matrix at each time step. The order of smallness with respect to the discretization time-steps and space-steps h of the residual of the method without interpolation and with interpolation is studied; it is equal to . The main result consists in proving that the method converges with the order in the energy and compact norm of the layered error vector. The results of test examples for superdiffusion equations with constant and variable delay are presented. The computable orders of convergence for each discretization step in the examples turned out to be close to the theoretically obtained orders of convergence for the corresponding discretization steps.
440-454
Regularization of classical optimality conditions
Abstract
The regularization of classical optimality conditions (COCs) — the Lagrange principle (LP) and the Pontryagin maximum principle (PMP) — in a convex optimal control problem with a strongly convex objective functional and with pointwise state constraints of the equality and inequality type is considered. The control system is defined by a linear functional-operator equation of the second kind of general form in the space the main operator of the right-hand side of the equation is assumed to be quasi-nilpotent. Obtaining regularized COCs is based on the dual regularization method. The main purpose of regularized LP and PMP is stable generation of minimizing approximate solutions (MASs) in the sense of J. Warga. Regularized COCs: 1) are formulated as existence theorems of MASs in the original problem with simultaneous constructive representation of these solutions; 2) are expressed in terms of regular classical Lagrange and Hamilton–Pontryagin functions; 3) “overcome” the ill-posedness properties of the COCs and provide regularizing algorithms for solving optimization problems. The article continues a series of works by the authors on the regularization of the COCs for a number of canonical problems of optimal control of linear distributed systems of the Volterra type. As an application of the “abstract results” obtained in the work, the final part considers the regularization of the COCs in a specific optimization problem with pointwise state constraints of the equality and inequality type for a control system with delay.
455-484
ρ–F contraction fixed point theorem
Abstract
In this paper, we study the question of conditions for the existence and uniqueness of a fixed point of a mapping over a complete metric space. We first discuss the concepts of F-contraction and -contraction in fixed point theory. These concepts, developed respectively by Wardowski and Piri with Kumam, have catalyzed significant research in various metric spaces. We then propose a generalization of these concepts, -contraction and -contraction, and demonstrate its effectiveness in ensuring the existence and uniqueness of fixed points. This new approach provides greater flexibility by including a function that modulates the contraction, extending the applicability of F- and -contractions. We conclude the paper with an example of a mapping that is a -contraction and a -contraction, respectively, and has a unique fixed point. However, this mapping does not satisfy the conditions of Wardowski and the conditions of Piri and Kumam.
485-493
On λ-commuting and left (right) pseudospectrum and left (right) condition pseudospectrum of continuous linear operators on ultrametric Banach spaces
Abstract
In this paper, we demonstrate some spectral properties of the -commuting of continuous linear operators on ultrametric Banach spaces and we introduce and study the operator equations and We give some properties of these operator equations. Some illustrative examples are provided. On the other hand, we introduce and study the left (right) pseudospectrum and the left (right) condition pseudospectrum of continuous linear operators on ultrametric Banach spaces. We prove that the left pseudospectra associated with various are nested sets and the intersection of all the left pseudospectra is the left spectrum. We give a relationship between the left (right) pseudospectrum and the left (right) condition pseudospectrum. Moreover, many results are proved concerning the left (right) pseudospectrum and the left (right) condition pseudospectrum of continuous linear operators on ultrametric Banach spaces.
494-516