Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
«Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory» («Progress in Science and Technology. Contemporary Mathematics and Its Applications. Thematic Surveys») is a scientific peer-reviewed journal published since 1995 by the Department of Scientific Information in Fundamental and Applied Mathematics of the Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences (VINITI RAS).
The journal publishes research and review articles on all areas of modern mathematics: algebra, topology, number theory, mathematical logic, differential geometry, functional analysis, probability theory, real and complex analysis, asymptotic methods, ordinary differential equations and partial equations derivatives, mathematical physics, as well as on applied aspects of mathematics and its applications in the natural and technical sciences.
Russian version of the journal is published in the online electronic form on the websites of VINITI RAS, the All-Russian Mathematical Portal MathNet.ru, and in the Electronic Scientific Library eLibrary.ru (see links above).
All issues of the journal are abstracted and indexed by the following databases: “Referativnyi Zhurnal “Matematika” (VINITI RAS), RSCI (eLibrary), Mathematical Reviews. All issues of the journal are fully translated into English by Springer Nature in Journal of Mathematical Sciences, which is abstracted in the SCOPUS database.
Media registration certificate: ЭЛ № ФС 77 - 82877 от 25.02.2022
Editor-in-Chief
Gamkrelidze Revaz V., Academician of RAS, Doctor of Sc., Professor
Frequency / access
12 issues per year/ Open
Current Issue
Vol 236 (2024)
Статьи
On strong solutions of a B-elliptic boundary-value problem and its difference approximation
Abstract
In this work, a finite-difference scheme for a boundary-value problem for a B-elliptic equation is constructed. The convergence is examined in the Kipriyanov weight space. An integral balance relation for the exact solution of the original problem is obtained by using Steklov averaging operators. A five-point difference scheme and an a priori estimate for the error are obtained.
3-12
On functioning of resource networks
Abstract
Resource networks are dynamic graph models introduced by O. P. Kuznetsov and L. Yu. Zhilyakova. These models are based on their functioning rules. The paper proposes a general approach to determining the functioning of resource networks, which consists of specifying a priority function on arcs of the resource network. Such a function determines the rules for the functioning of the resource network. Kuznetsov–Zhilyakova resource networks are a special case of resource networks with priorities on the arcs, where all arcs have the same priorities. We show by examples that resource networks of the same topology with different priority functions operates differently. Criteria for the emergence of stationary functioning of a resource network with priorities on arcs are obtained; the main criterion is the condition of flow balance. Also, we propose a more general extension of the concept of a resource network, namely, the definition of a resource network with dynamic priorities on arcs. In this case, the priority function specified on the network arcs is a function of discrete time in which the network operates.
13-21
A contribution of the generalized bochner technique to the geometry of complete minimal submanifolds
Abstract
In this paper, based on methods of the Bochner technique, which is an important part of the geometric analysis, we establish conditions under which minimal and stable minimal submanifolds in Riemannian manifolds are characterized as totally geodesic submanifolds.
22-30
Structure of the essential spectrum and the discrete spectrum of the energy operator of six-electron systems in the Hubbard model. Fourth triplet state
Abstract
In this paper, we analyze the energy operator of six-electron systems within the framework of the Hubbard model and examine the structure of the essential spectrum and the discrete spectrum of the system in the fourth triplet state. We prove that in the one- and two-dimensional cases, the essential spectrum of the six-electron fourth triplet state operator is the union of seven segments, whereas the discrete spectrum contains at most one eigenvalue. In the three-dimensional case, the following situations can occur: (a) the essential spectrum of the operator is the union of seven segments and the discrete spectrum contains at most one eigenvalue; (b) the essential spectrum is the union of four segments and the discrete spectrum is empty; (c) the essential spectrum is the union of two segments and the discrete spectrum is empty; (d) the essential spectrum consists of a single segment and the discrete spectrum is empty. We found conditions under which each of these situations occurs.
31-48
Splitting transformation for a linear nonstationary singularly perturbed system with constant delay in the equation for the slow variable
Abstract
A method of splitting with respect to rates in change of variables is developed for a linear nonstationary singularly perturbed system with constant delay in the equation for slow variables. The splitting method is based on an algebraic approach, namely, the immersion of the system with delay into a family of systems with an extended state space, and a nonlocal change of variables. The existence is proved and the asymptotics of the Lyapunov transformation is constructed, which generalizes the splitting Chang transformation to systems with delay and performs a complete splitting of a two-rate system with constant delay into two independent subsystems of lower dimensions than the original system: separately for the fast and slow variables. We prove that the split system is algebraically and asymptotically equivalent to the original system in the extended state space. The asymptotics is constructed and the action of asymptotic approximations of the splitting transform is examined.
49-71
Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. I. Third-order systems
Abstract
Abstract. In this paper, we present new examples of integrable dynamical systems of the third order that are homogeneous in part of the variables. In these systems, subsystems on the tangent bundles of two-dimensional manifolds can be distinguished. In the cases considered, the force field is partitioned into an internal (conservative) part and an external part. The external force introduced by a certain unimodular transformation has alternate dissipation; it is a generalization of fields examined earlier. Complete sets of first integrals and invariant differential forms are presented.
72-88