Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ

The article presents an analysis of instabilities known from previous works in a two-dimensional mathematical model of plasma configuration equilibrium using the example of a toroidal magnetic trap “Galatea–Belt” straightened into a cylinder and possessing plane symmetry. It is established that the previously observed large values of the two-dimensional velocity of disturbances in the plane of the cylinder cross-section arise on the periphery of the configuration near its conventional boundary, do not grow with time, and are due to arbitrarily small values of density, which is not determined by the idealized model of strict equilibrium. By varying the density, it is possible to influence stability. Three-dimensional (corrugated along the axis of the cylinder) disturbances grow with time in accordance with the traditional Lyapunov instability. Calculations allow us to determine the dependence of its quantitative characteristics on the problem parameters.

In this paper we develop a method to study Horn classes of Kripke frames from a probabilistic perspective. We consider the uniform distribution on the set of all

The paper is devoted to the method of numerical beamforming for processing spatio-temporal data obtained from supercomputer simulation of aeroacoustics problems, in order to localize a distributed acoustic source formed by interaction of turbulent flow and an aircraft or its elements in flight mode, and to determine its amplitude-frequency characteristics. Mathematically, the proposed method is based on solving the inverse problem of restoring the right-hand side in the Helmholtz equation for sources of monopole and dipole types. Compared to an analogue intended for the analysis of experimental measurements, the new method has significant advantages and allows generalization to the case of correlated sources. In the paper, the capabilities of the method are demonstrated by solving the problem of identifying an acoustic source that is generated by an upswept aircraft wing with deployed high-lift devices in landing mode.

The paper gives a theoretical and numerical justification of the bias with the

The article proposes a new exact quadratic algorithm in complexity that solves the problem of the shortest transformation (“alignment”) of one loaded tree into another, taking into account arbitrary prices of operations on trees. Three operations are considered: adding vertex deletions to an edge or root of a tree and shifting a subtree with deletions.

Consider sequences of integers

Digital technologies are known to have high potential for economic growth, to promote social and political communications. They are platforms for the implementation of new business ideas. New digital phenomenon ”— the information business ”— is investigated in the article. How does information business affect the economy and society? This question determines the main topic for discussion. The following methods were used in the article: system analysis, content analysis, sociological survey, comparative analysis, cluster analysis, fuzzy logic methods, mathematical modeling. The purpose of the article is to determine the relationship and spread of new digital technologies and phenomena in the socio-economic and political spheres of Russia. There are such results as recommendations on the transformation of socio-economic relations, modeling and state regulation of processes in the information environment in the article. At the same time, mathematical methods for studying the tasks are proposed.