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 228 (2023)
Articles
3-9
Dirichlet problem on the semiaxis for the abstract Euler–Poisson–Darboux equation containing powers of the group generator
Abstract
For the abstract Euler–Poisson–Darboux equation containing powers of an unbounded operator, sufficient conditions for the unique solvability of the Dirichlet problem on the semiaxis are obtained.
10-19
The influence of competition on the dynamics of macroeconomic systems
Abstract
The problem of interaction (competition) of two identical macroeconomic systems is studied in the case where the dynamics of each of them is modeled by the well-known Keynes system of differential equations. It is shown that this problem can be interpreted as the problem of synchronization of two self-oscillating systems. The analysis is based on the method of integral manifolds and Poincaré method of normal forms. We prove that three types of oscillations arise in the problem: completely synchronous self-oscillations, antiphase oscillations, and asymmetric oscillations. For all solutions, their stability is examined and asymptotic formulas are obtained.
20-31
On the type of delta-subharmonic functions of generalized refined order
Abstract
In function theory, the Lindelöf theorem on zeros of entire functions is well known: A given sequence is the set of zeros of an entire function of finite order ϱ > 0 and normal type if and only if for noninteger ϱ, it has a finite upper density at this order, and for integer ϱ, it possesses, in addition, a certain asymptotic symmetry. In this paper, we give a review of recent results relating to the extension of Lindelḟ theorem to the case of entire functions that are analytic in the half-plane and meromorphic and subharmonic functions in the complex plane and half-plane whose is determined by the generalized refined order. Similar statements are proved for delta-subharmonic functions in the complex plane. The resulting criteria are formulated in terms of the Riesz measure functions.
32-51
Recovery of the Laplace–Bessel operator of a function by the spectrum, which is specified not everywhere
Abstract
In this paper, we present results related to the problem of the best recovery of a fractional power of the B-elliptic Laplace–Bessel operator of a smooth function from its Fourier–Bessel transform, which is known exactly or approximately on a certain convex set. The cases of primary estimates in L₂γ and L∞ are considered.
52-57
Spontaneous clustering in Markov chains IV. Clustering in turbulent environments
Abstract
In the fourth part of the review, we discuss mathematical models of clustering that describe the behavior of impurity particles (markers, tags, etc.) in a turbulent environment. Along with the classical approach (Smoluchowski, Richardson), we describe statistical models used in computer modeling of processes (the Neyman–Scott and Metropolis models and Markov chains). Some aspects of the processes of local accumulation and gravitational sedimentation of particles in a turbulent environment are discussed. The last section is devoted to the concept of a representative sample, which is important in natural and numerical experiments.
The first part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. "— 2023. "— 220. "— P. 125–144.
The second part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. "— 2023. "— 221. "— P. 128–147.
The third part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. "— 2023. "— 222. "— P. 115–133.
58-84
On optimal linear regression for fuzzy random variables
Abstract
In this paper, we construct an optimal linear regression of fuzzy random variables whose coefficients are similar to the case of “ordinary” random variables. We prove under certain conditions, the optimal regression has a maximum correlation coefficient with the predicted fuzzy random value.
85-91
Tensor invariants of geodesic, potential and dissipative systems. II. Systems on tangents bundles of three-dimensional manifolds
Abstract
In this paper, we present tensor invariants (first integrals and differential forms) for dynamical systems on the tangent bundles of smooth n -dimensional manifolds separately for n = 1, n = 2, n = 3, n = 4, and for any finite n. We demonstrate the connection between the existence of these invariants and the presence of a full set of first integrals that are necessary for integrating geodesic, potential, and dissipative systems. The force fields acting in systems considered make them dissipative (with alternating dissipation).
The first part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 227 (2023), pp. 100–128.
92-118