Research dielectric function for collisional plasmas with any degree of degeneracy of electronic gas is carried out. By special limiting transition the dielectric function of Maxwell plasmas is received. Research and comparison of longitudinal dielectric functions of quantum and classical Maxwell collisional plasmas is resulted.

Author continues construction of the theory of nonstationary diffusiophoresis of large non-volatile solid spherical particle in a viscous gas medium. The solution of diffusion problem is carried out. This problem is divided into stationary and strictly nonstationary parts. Final formula for determining stationary diffusiophoresis velocity component of the particle was obtained. For determining nonstationary diffusiophoresis velocity component of this particle corresponding formula in the space of Laplace images was obtained.

In the boundary phase between liquid and gas at low temperatures clusters of particles are formed. Dimer is the simplest cluster. Formation of dimer of argon at threefold collisions is considered. Plots of gathered statisticians for a case of dimer’s formation are provided. The technique of use of results in the solution of gas flow problems at low temperatures by Monte-Carlo methods is offered.

The author formulated the principles of the cumulative quantum mechanics (CQM). CQM describes: 1) unlimited cumulation of symmetric ψ_n__½- electron function of the de Broglie waves (with a spectrum E_n__½ ~±(n-½)^±2) captured potentials in spherical and cylindrical hollow cavities, 2) the polarization quantum-dimensional effects, 3) the Vysikaylo’s split of the quantum level with principal quantum number п into two sublevels (with ψ_n and with ψ_n__½) with the splitting energy ΔE_n__½,n ~ n-¼ in the case of the barrier, and with ΔE_n__½,n =13.56-(n-¼)/ε²(n-1/2)²n² [eV] for the potential well with U(r)~1/εr); and 4) spectra of the transitions between states with different symmetry of ψ-functions (ψ_n→ψ_n__1/2) in the superlattices of standing excitons in IV group crystals, B-doped.

It is shown that many-particle interactions should be taken into account to describe physical properties and phase transitions in condensed systems. The model of effective pair interactions is suitable only for qualitative estimation of real systems properties. The concept of effective pair interactions and ways to calculate them are discussed.

The statistical two-step multiboson algorithm as applied to a U(1) model of fermions on the four-dimensional space-time lattice is considered. It is shown that introduction of the second field accept-reject step leads to increase of performance of the algorithm.

Scattering cross section of small metal spherical-shaped particle in the field of a plane electromagnetic wave was calculated under the dipole approximation. The radius of the particle is assumed to be small comparing with the skin depth, the fact allowed us to neglect the skin effect. The calculations are performed in terms of kinetic approach with an arbitrary ratio between the mean free path of electrons and the particle radius. Type of carrier - surface interaction mechanism considered is fully diffuse reflection. It is shown that at certain angles of scattering magnetic dipole scattering is the dominant.

The analytical method of investigating the structure of shock wave front with nonequilibrium translational chemical reaction is considered. The method is based on elliptic bimodal approximation of the function of the molecules distribution in connection with the analysis of the barrier chemical processes rates.

The article is devoted to the problems of automating the drafting of thin film electroluminescent indicators, as elements of electronic means. Envisaged are the principles, aspects, means, of developing CAD systems of thin film electroluminescent indicators and their structures. The results of executing the research will improve the algorithms, and create a new program allowing to automate the design and technology of thin-film electroluminescent indicator elements.

For strongly collision range of frequencies (ω > υ_en) heterogeneous weakly ionized plasma in the limiting cases of large ((K_n V_te)² >ωυ_en ) and small ((K_n V_te)²< ωυ_en electronic diffusion coefficients of drift oscillation spectra on the basis of the solution of the kinetic equation by Grad.

For a strongly non-uniform frequency region of weakly ionized plasma in the limiting cases of large and small electronic diffusion coefficients obtained spectra of drift oscillations on the basis of the solution of the kinetic equation by Grad.

The results of investigations of superhydrophobic, hydrophobic and ordinary surfaces in the artificial icing conditions are generalized. The availability of the superhydrophobic coatings for anti-icing systems is demonstrated. The effect of the superhydrophobic surface self-cleaning from ice in the flow conditions is considered. The simple mathematical model was developed illustrating dependences tendencies of hydrothermodynamic parameters of different formations on solid surface (film, rivulet, droplet) from the flow velocity and contact angle.

In this paper we investigate the question of equiconvergence on T^N = [-π,π)^N expansions in multiple trigonometric series and Fourier integral functions f ∈ L₁(T^N) и g ∈ L₁(R^N), Р>1, N≥2, g(x)=f(x) на T^N = [-π,π)^N.

The paper formulates the basic principles of module-rating system of education in the University goals and objectives pursued by this system. Provides development of the training course "Analytic geometry" based on a modular system.