The formalism for the description of vector paraxial light beams is extended to Gaussian-like with non-homogeneous polarization, including the general TM and TE modes. Simple expressions for polarization and the energy flux density of an electromagnetic field of such beams are discovered. The carried-out graphic modeling of polarizing and power properties of vector Gaussian-like TM beams confirms and calculations supplements analytical.

Keywords: paraxial beams, vector beams, Gaussian-like beams, polarizable properties, energy properties, TE modes, TM modes, non-homogeneous polarization.

S.S. Girgel – Faculty of Physics and Information Technology, F. Skorina Gomel State University

In the framework of thermodynamic method the properties of non-ideal gas are considered in the paper, using the Ishikawa – Chung – Lu equations of state. The parameters of the equation are expressed by characteristics of critical state and reduced form of the equation is found as well. Analytical relations are derived for physical parameters, entropy, and thermodynamic potentials of gas. The Joule-Thomson process is considered, the shape of the inversion curve of the sign of the effect in the reduced variables is determined. Expressions for the parameters of the equation are found ensuring the coincidence of the argon inversion curve with the experimental results.

Keywords: non-ideal gas, critical parameters, Ishikawa – Chung – Lu equation of state, reduced variables, Joule – Thomson process, inversion curve, critical compressibility coefficient.

E.A. Dey – Faculty of Physics and Information Technology, F. Skorina Gomel State University

G.Yu. Tyumenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

The theory of formation of photodeflection signal in the dense layer of chiral and achiral carbon nanotubes by irradiation of polarized modes of Bessel light beams was investigated. For the first time the solution of the heat equation was obtained using integral transforms Fourier – Bessel and Laplace for a three-layer medium, which is irradiated with light polarization modes Bessel beams with an intensity distribution in space.

Keywords: photothermal transformation, photodeflection spectroscopy, chiral carbon nanotubes, Bessel light beam, energy dissipation, Bessel function, heat equation, Fourier – Bessel transformation, angle of photodeflection.

G.S. Mityurich – Faculty of Physics and Information Technology, F. Skorina Gomel State University

E.V. Lebedeva – Belarusian Trade and Economics University of Consumer Cooperatives, Gomel

A.N. Serdyukov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Microhardness, modulus of elasticity, internal mechanical stresses, tribotechnical properties of chromium and titanium-doped carbon coatings are determined. It is shown that doping with carbide-forming metals of carbon coatings allows preserving high microhardness, leads to a decrease in internal stresses in 1.2 ... 3.2 times, decays high strengths of the adhesive compound (its maximum value is recorded with chromium alloying) and reduces in more than 2 times Coefficient of friction in comparison with single-component carbon coatings.

Keywords: carbon coatings, doped, titanium, chromium, microhardness, internal stress, coefficient of friction.

D.G. Piliptsou – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.V. Rogachev – F. Skorina Gomel State University

A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Xiaohong Jiang – Nanjing University of Science and Technology

N.N. Fedosenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Experimental studies on the laser polishing of quartz glass with the help of a full-order first-order phase-effect experiment of the PFE 2ⁿ type with a two-level variation of the factors are carried out. A regression model of polishing of quartz glass by laser radiation is calculated taking into account the calculated significant factors using the analysis of variance.

Keywords: laser treatment, full factor experiment, quartz glass.

E.B. Shershnev – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Y.V. Nikitjuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University

S.I. Sokolov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.E. Shershnev – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Matrix-functions that arise when solving systems of differential equations with Delta-shaped coefficients are investigated. The process of reducing the matrix-function is considered depending on two variables to the normal form by means of the matrix functions G and T such that their elements belong to a ring wide then the ring containing elements of . The explicit form of the main term of expansion in the case of matrices of dimension 2 is found explicitly. The cases of resonance for systems with delta-coefficients are revealed.

Keywords: matrix-function, normalized form, resonance, ring, main term of expansion.

A.B. Antonevich – Belarusian State University, Minsk

Ì.G. Kot – A.S. Pushkin Brest State University

A simple model to study the effect of properties of thin coatings on the characteristics of elastic waveguide is considered. It was established that the choice of the elastic properties of the coatings can increase or decrease the phase velocity of shear waves.

Keywords: elastic waveguide, thin coating, phase velocity, shear waves.

Mels V.Belubekyan – Doctor of Mechanics, Professor, Main scientific researcher, Institute of Mechanics of NAS of Armenia

Gagik Ohanyan – Institute of Mechanics of NAS of Armenia

Karen Ghazaryan – Institute of Mechanics of NAS of Armenia

V.V. Mozharovsky – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

N.A. Maryina – Belarusian State University of Transport, Gomel

The structure of a subgroup equal to the intersection of kernels non-nilpotent maximal A-admissible -subgroups that do not contain Fitting subgroup is considered. The influence of the corresponding generalized Frattini subgroup on the structure of the group itself was found.

Keywords: finite group, abnormal subgroup, Fitting subgroup.

R.V. Borodich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

E.N. Borodich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

M.V. Selkin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

n-Multiply -local (totally -local) Fitting classes having a Stone lattice of n-multiply -local (totally -local) Fitting subclasses are described.

Keywords: Fitting class, complete lattice of Fitting classes, atom of lattice, distributive lattice, lattice with complements, pseudocomplement, Boolean lattice, Stone lattice.

N.N. Vorob'ev – P.M. Masherov Vitebsk State University

A.I. Titova – P.M. Masherov Vitebsk State University

The problem of symmetric bending of a three-layer elastic plate with a compressible filler asymmetrical in thickness is ñonsidered. Kirchhoff's hypotheses are accepted for thin bearing layers. In a relatively thick aggregate, the transverse shear, radial displacements and deflection, which vary linearly in thickness are taken into account. The differential equations of equilibrium in the effort are obtained using the Lagrange variational method. The setting of the boundary value problem in the displacements is given in the cylindrical coordinate system.

Keywords: circular three-layer plate, elasticity, compressible filler.

Yu.V. Zakharchuk – Belarusian State University of Transport, Gomel

For a GWP-formation the L.A. Shemetkov’s theorem on the complementability of -residual of finite group is developed.

Keywords: finite group, formation, residual, complement, GWP-formation.

S.F. Kamornikov – F. Skorina Gomel State University

O.L. Shemetkova – Plekhanov Russian University of Economics, Moscow

An inverse problem for the elliptic equation of the second order with periodical boundary conditions is investigated. The definition of a classical solution of the problem is introduced. The essence of the problem is that together with the solution it is required to determine the unknown coefficient. The problem is considered in a rectangular domain. To investigate the solvability of the inverse problem, the conversion from the original problem to the some direct auxiliary problem with trivial boundary conditions is realized. Using the principle of condensed mappings, the existence and uniqueness of the solution of the auxiliary problem are proved. The existence and uniqueness of the classical solution of the original problem are also proved.

Keywords: inverse boundary value problem, elliptic equation, Fourier method, classical solution.

Y.T. Mehraliev – Baku State University

N.A. Heydarzade – Baku State University

The relationships between some numerical characteristics of the members and factors of the upper and lower central series in groups and Lie algebras are investigated.

Keywords: Schur’s theorem, Baer’s theorem, special rank, section p-rank, upper (lower) central series of Lie algebra.

A.A. Pypka – Oles Honchar Dnipro National University

Let be a non-empty class of finite groups. A complete lattice of formations is said to be -separable if for every term of signature -formations and every group exists -groups such that In particular, if is the class of all finite groups then the lattice of formations is said to be -separable or, briefly, separable. It is proved that the lattice of all -closed totally -saturated formations is -separable for any subgroup functor .

Keywords: formation of finite groups, -closed formation, totally -saturated formation, lattice of formations, -separated lattice of formations.

V.G. Safonov – Belarusian State University, Minsk

I.N. Safonova – Belarusian State University, Minsk

Let G be a finite group. Let be a partition of the set of all primes and n an integer. We write A set of subgroups of G is said to be a complete Hall -set of G if every member of is a Hall -subgroup of G for some and contains exact one Hall -subgroup of G for every A subgroup A of G is called a -Hall subgroup of G if We say that a subgroup A of G is -subnormally embedded in G if A is a -Hall subgroup of some -subnormal subgroup of G.

Keywords: finite group, -subnormal subgroup, -permutable subgroup, -Hall subgroup, -subnormally embedded subgroup.

D.A. Sinitsa – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

A.N. Skiba – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

W. Guo – University of Science and Technology of China, Hefei

Chi Zhang – University of Science and Technology of China, Hefei

A new approach to modeling of technological processes of systems in the form of a sequence of connected physical states of objects is considered. These objects are changed under the influence of external forces, which are determined after some time intervals. This period of time includes several calculated states. If the established criteria aren’t met, an additional impact is produced. It simulates control stimulus in order to return the model system to the zone of normal execution of the operation. The calculated states that have passed the test are visualized in the corresponding 3D model.

Keywords: modeling, dynamics, adaptive algorithms, technical systems, physical processes.

A.K. Golovnich – Belarusian State University of Transport, Gomel

A step-by-step succession of activities implemented in the course of simulation experiments which allows to give up performing natural experiments is suggested.

Keywords: simulation experiment, natural experiment, local area network.

Î.Ì. Demidenko – F. Sñorina Gomel State University

The architecture of software Toolkit for secure LAN node by gathering and analyzing information about components of computers and the modes of its functioning article is discussed.

Keywords: automated workplace (AWP), Windows Management Instrumentation (WMI), ODBC, SQL Server, LAN.

A.I. Kucharau – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.V. Varuyeu – Faculty of Physics and Information Technology, F. Skorina Gomel State University

O.M. Demidenko – F. Skorina Gomel State University

V.D. Liauchuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University

The Web-services developed by the authors, with the help of which it is possible to increase the efficiency of the road police service in Gomel are considered.

Keywords: web-application, web-services, road police service, efficiency.

S.S. Sudakov – Belarusian State University of Transport, Gomel

S.A. Azemsha – Belarusian State University of Transport, Gomel

S.F. Maslovich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

V.N. Halushko – Belarusian State University of Transport, Gomel