IKBFU's Vestnik

2012 Issue №4

Mathematical model of transportation of relativistic electronic beams. Analogy to the equations of gas dynamics

Abstract

Analytical comparison of hyperbolic system consists of four equations for moments of the distribution function of relativistic electron beam (REB), the modeling transportation processes in the gas environment and the equations of gas dynamics of ideal polytropic gas was carried out. The found analogy between these models allowed to specify mathematical statement of a problem for REB and to facilitate a choice of edge conditions of the task.

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Mathematical simulation in road-building

Abstract

Mathematical models for an estimation of quality of road-building materials are considered. The mathematical model of the modern asphalt-concrete factory with several asphalt-mixing installations is constructed. The technique of definition of reliability of work of a factory on release asphalt-concrete mixes is given.

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Fundamental-group connections, induced by composite clothing of family of centered planes in projective space

Abstract

This paper continues the cycle of works dealing with connections on a smooth family of centered planes in projective space. It is shown that composite clothing of such a family induces three-parameter bunch of bundles of fundamental-group connections. One induced connection is allocated from each of this bundles. Coincidence conditions of the received connections and geometrical interpretation of the linear sub connections is given.

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The technical neural system for mobile robots

Abstract

The concept of the technical neural system for mobile robots is described. Mathematical description and the algorithm of learning are provided. A brief description of a subject domain is given and a feature of the problem is explained. The ways of application of the theory to mobile ropotics are specified. The future design of the theory is provided.

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Neuro-iterative method for reconstruction of distributed physical fields

Abstract

In this paper call attention to the neuro-iterative reconstruction algorithm based on the mathematical model of the measuring system. It combines the positive features of artificial neural networks and algebraic methods. Numerical simulation shows the characteristics of the reconstruction of influene for distributed physical fields.

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The problem of complex meaning nonlinear equation in quotiend derivatives

Abstract

Several ways of finding of the exact solutions inherent in the equations with soliton like solutions were applied to the given equation. In particular the presence of property of Penleve in the equation was conducted, solutions in the form of numbers of Lorana, exact solutions in the form of running waves and solutions received by the method of Hiroty were found.

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