In the present work we consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous Riemann

The diagonal acts and biacts over right or left invariant semigroups are considered. It is proved that the diagonal right act (S x S)_S of such semigroup S is not finitely generated in case of invariant right or left invariant semigroup.Moreover, it is proved that this statement is wrong in case of biacts_s(S x S)_S .Besides an example is constructed where S is an infinite right simple (and therefore right invariant) right cancellative semigroup and the biacts_s(S x S)_S is cyclic.

Equation trajectory relativistic particles (in particular, quanta) received within the specific model of the dispersion relation between the energy and momentum. Revealed a complete analogy with the equations for classical particles (obtained from the variational principle of mechanics) and rays (derived from Fermat's principle). We formulate the problem of further development of the tasks associated with a particular form of the potential energy of the quantum.

A theory of dyes orientation in the field of a light wave is proposed. The energy of dye molecules’ interaction with the magnetic field of laser radiation is determined. The orientation of the dye molecules is shown to depend on their interaction with electric field of radiation.

According to common point of view, the temperature dependence С(Т) of the lattice heat capacity of solid bodies in the temperature range T → 0 should have a region corresponding to the so-called Debye limiting law С(Т) ~ T3. This law should be obeyed regardless of the atomic (molecular) structure and type of chemical bonding in solid bodies. This paper shows that this is true, if it is assumed that the frequency spectrum of the investigated body is continuous and varies in the range of 0 ≤ ω ≤ ω max (model of infinite wavelength spectrum of the crystal), and the exponent of its dimensions varies in the range of 1 ≤ df ≤ 3. This model has been successfully applied during the past century studying of macroscopic bodies, but it is practically useless for clusters and nanostructures. In the general case, i.e. outside this range, when df < 1 or df > 3, and with finite of the both sides spectrum, the temperature change of the lattice heat capacity has a different nature.

Formulas for calculating the time of complete evaporation of aerosol droplets by integrating the equations obtained for the initial and final limits the rate of change of the radius of the aerosol droplets. The numerical analysis of these formulas by considering the process of unsteady evaporation of single droplets of water into the air. Lists features found simplify formulas depending on the initial size of the evaporating water droplets.

The research results of the structure of the porous silicon film, formed by electrochemical etching method on the textured surface of the monocrystalline silicon substrate are presented. It has been established that, treatment of the porous silicon film in an aqueous solution of HF, promotes formation of developed surface. The investigated film consists of layers with different silicon crystallite size and chemical composition.

The theory of two-dimensional filtering liquid and gas flows in curved seams constant and variable thickness plays a crucial role in the design of oil and gas development. Great contribution to the development of this theory has made a Doctor of Physics and Mathematics, Professor Olga Golubeva, a long time headed the Department of Theoretical Physics in MOPI them. N.K. Krupskaya and created hydrodynamic theory school in twodimensional flows of liquids and gases in cooperation with numerous pupils. Presented to the anniversary date of the birth of 19 July 1915 Professor Golubeva O.V. article contains the results is the continuity of the development of approaches Golubeva O. V. to the modeling of two-dimensional seepage flows. Specifically, the paper is devoted two-dimensional mathematical models of linear filtering liquid and gas in curved seams of varying thickness, where impenetrable sole and top which can be defined as a coordinate surfaces such as same orthogonal curvilinear coordinate system.

The results of modelling of the mechanical oscillations which can take place in a suspension system of the autonomous vehicle-like robot are presented in this paper. If the robot has computer-vision stabilized platform, it's movements can interact with vehicle's suspension. To ensure stability of the robot computer simulation of the system were performed. Dependencies allowing to select safe operation modes of the robot are calculated basing on the numerical solution of differential equations. Thus, there is a possibility to control the fluctuations arising from the interaction between the platform and mechanical components of the computer vision system and to avoid a situation of overturning the platform.

The article raises the plane-parallel boundary value problem of the battery performed well in anisotropic - homogeneous soil, for the case when the permeability tensor is not symmetric and simulated circuit power line. In this case, a system of equations describing the operation of the battery wells. The paper studied the effect of soil anisotropy on the battery discharge wells. Studied the contribution of a single well in the overall production rate of the battery wells.

This paper discusses the cognitive component of the research competence of future teachers of mathematics and examines levels rigor of mathematical knowledge in the study of mathematical disciplines in order to develop the cognitive component of research competence, discloses a technique for working pre- feeder according to severity level of educational material. These selected levels rigor are illustrated by possible approaches to the construction of the complex numbers as an extension of the field of real numbers.

For the design of display products for technique of special purpose thin-film electroluminescent investigation of indicators is an important task. Of particular interest is investigation of lighting characteristics. In this paper we consider one of the ways to determine the brightness based on the use of computational tools. Currently thin-film electroluminescent indicators are the most promising, since high brightness, reliability, wide viewing angle and speed. For determining the parameters of thin-film structures that have used different systems of equations. Evaluate the resulting brightness, as well as design parameters influencing the result is an important task in the design of new products.