The amplitude of the interaction of the electromagnetic field with structural microparticles was defined on the basis of the gauge invariance approaches and the solutions of the electodynamics' equations using covariant method of the Green function. This amplitude is presented in terms of the electric and magnetic polarizations of compound system using no multipole expansion. In the framework of this approach the Lagrangian of the interaction of electromagnetic field with compound system and the Compton scattering amplitude were obtained taking into account electric and magnetic polarizabilities of the spin-1/2 particles.

Keywords: gauge invariance approaches; Green function; electric, magnetic and spin polarizabilities; Compton scattering amplitude.

Maksimenko N.V. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

This paper analyzes characteristic dislocation mechanisms of metallic (nickel) surface layer destruction under friction. The authors define the effective role of slipping strips of material, doubles, large angle borders of block and crystalline structure disorientation in the formation of uniformity rupture.

Keywords: effective slipping zones (areas), shear deformation, cellular structure, zone stratification, transcrystalline and inter-crystalline destruction.

Pinchuk V.G. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Korotkevich S.V. – RUP Gomelenergo, Gomel, Belarus

Bobovich S.O. – RUP Gomelenergo, Gomel, Belarus

The peculiarities of the influence on morphology and molecular orientation of polytetrafluoroethylene coatings formed from active gas phase and filled with nanosized metal particles of different nature are observed. Metal doping was established to result in the formation of disperse structures and influence on the character of molecules orientation of polymer matrix. Moreover, the boundary coating-substrate interlayer characterized by macro molecules orientation parallel to the substrate surface has significantly small thickness in comparison with single-component coating. Regularities of the molecular structure transformation in the process of composite layers growth are defined.

Keywords: morphology, molecular structure, composite coating, polytetrafluoroethylene, metal nanoparticles.

Rogachev A.A. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Yarmolenko M.A. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Rogachou A.V. – Rector of F. Skorina Gomel State University, Gomel, Belarus

The method of determination of fuel and condensation components in Chernobyl radioactive sediments is described. It is based on the investigation of statistic behavior of radionuclid pair radioactivity.

Keywords: caesium, radioactivity , radionuclid , radioactive sediments.

Rudak E.А. – Institute of Physics NAS RB , Minsk, Belarus

Maksimenko N.V. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Andreev V.V. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Yachnik O.I. – Institute of Physics NAS RB , Minsk, Belarus

Research of interaction of electromagnetic radiation of the UHF (ultra high frequency) range with the bi-dimensional lattice consisting of mutually orthogonal pairs of helices, containing left-handed and right-handed one-turn or double-turn helical elements with precalculated optimum parameters is carried out. The obtained artificial structures possess equally significant dielectric and magnetic properties and compensated chirality. The purpose of the research is demonstration of the possibility to use such structures for creation of weak reflecting coatings.

Keywords: nonreflecting coatings, composite media, chirality, the electric dipole moment, the magnetic moment.

Semchenko I.V. – Prorector of F. Skorina Gomel State University, Gomel, Belarus

Khakhomov S.A. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Samofalov A.L. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

The electrodynamical equations for continuous medium in strong gravitational field are constructed. The influence of gravitation on propagation of electromagnetic waves in the medium with Faraday effect is considered. The received solutions for non-uniform electromagnetic waves allow to model the propagation of electromagnetic radiation in the matter of neutron stars.

Keywords: gravitational interaction, electromagnetic waves.

Serdyukov A.N. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Yegorov A.N. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Let be some subgroup property and n is a natural number. A formation is called _n-recognizable if contains each group G having n -subgroups belonging . In the paper an original method, based on the concept of T-models for study _n-recognizable formations is proposed.

Keywords: finite group, local formation, local screen, T-model, _n-recognition.

Vasilyev A.F. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Vasilyeva T.I. – Belarusion State University of Transport, Gomel, Belarus

We consider the exponential network with two independent Poisson enter flows of customer batches: general and additional. The customers of additional flow arrive in empty nodes. The batches required for the service move to other nodes with possible change of size or leave the network according to some irreducible Markov matrix. The batches which don't achieve the required size are served but after the service is done they leave the network. The criterion of existence of stationary distribution in the form of the product of geometric distributions is established.

Keywords: queueing networks, bathes of customers, stationary distribution, geometric distribution, product form, quasireversi-bility.

Malinkovsky Yu.V. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated by operators which arised in the calculus is given, and the inequality of moments for such operators in the one-dimensional case is proved.

Keywords: semigroup of operators, semigroup generator, functional calculus, Bernstein function.

Mirotin A.R. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Let be some -closed -saturated formation, be the formation of all soluble groups. Then denotes the lattice of all -closed -saturated formations such that . A length of the lattice is called a soluble -defect of the -closed -saturated formation . The description of reducible -closed -saturated formations of finite groups with a soluble -defect 2 is obtained.

Keywords: formation of finite groups, -saturated formation, defect of a formation, lattice of formations, -closed formation.

Safonov V.G. – Ministry of Education of Republic of Belarus, Minsk, Belarus

Safonova I.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Asymptotic behavior of Pade table rows for Markov functions (z) generated by Borelean power-type measures is found. This enabled us to find sharp decreasing orders of the best approximations of (z) by rational functions with fixed number of poles. The obtained theorems supplement the known results of A.A. Gonchar, T. Ganelius, H. Stahl, D. Braess, A.A. Pekarskii, E.A. Rovba dealing with research of approximating properties of Markov functions.

Keywords: Markov function, Pade approximants, rational approximations, polynomial approximations, best approximations in the uniform norm.

Starovoitov A.P. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Labych Yu.A. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The successful implementation of a typical actual Internet-project is described in the paper. Approved technology of communication provides a quick exchange of knowledge, comprehensive, qualitayive elaboration of ideas, methods and solutions. The proposed project is considered by the authors as a model for the formation of inter-regional scientific information space, which is the priority directions of the development of the state system of scientific and technical information of the Republic of Belarus.

Keywords: interregional scientific information space, the Internet project, a portal, a model of interaction, overcoming the effects of the Chernobyl disaster.

Liauchuk V.D. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Demidenko O.M. – Prorector of F. Skorina Gomel State University, Gomel, Belarus

Liauchuk A.A. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

The problem of calculation and experimental determination of stresses and displacements of composite pipes under hydrostatic pressure is considered. Based on previously obtained theoretical relations and algorithms, the program module of finite-element calculation of stress-strained state of pipe which assumed as hollow cylindrical body with heterogenious structure, has been developed. Experimental part of study includes mechanical tests of cylindrical pipes made of reinforced materials. Using developed software, the influence of reinforcing fibers on the stress concentration has been studied.

Keywords: composite pipes, reinforcement, stress-strain state, finite element method, mechanical tests.

Mozharovsky V.V. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Marjin S.A. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Marjina S.A. – Belarusion State University of Transport, Gomel, Belarus

Shilko S.V. – V.A. Belyi Metal-Polymer Research Institute National Academy of Sciences of Belarus, Gomel, Belarus

Kuhorev L.P. – V.A. Belyi Metal-Polymer Research Institute National Academy of Sciences of Belarus, Gomel, Belarus