The option of relativistic-invariant definition of spin polarizability on the basis of covariant creation of the induced dipolar moments and phenomenological effective Lagrangian interactions of an electromagnetic field with these moments is offered.

Keywords: polarizability, Lagrangian, Compton scattering.

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

O.M. Deryuzhkova – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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

The expression defining the mass of the spherical dustlike shell with regard to the gravitational defect is obtained. It is shown that the mass of a spherical dustlike shell increases with its radius. In the limiting case, the mass tends to the value of free, not connected with gravitational interaction of mass.

Keywords: theory of gravitation, dustlike spherical shell, gravitational mass defect.

N.A. Akhramenko – Belarusian State University of Transport, Gomel, Belarus

L.M. Bulauko – Belarusian State University of Transport, Gomel, Belarus

Experimental results obtained for a single helical radiator, as well as for the system of helical elements similar to the directional antenna Yagi – Uda are presented. These results suggest that for a helical antenna with optimized parameters, it is possible to obtain an effective lateral radiation and design of the directional antenna based on such helical elements. However, it is necessary to optimize the system parameters of helical elements forming an antenna for higher directivity and polarization of the radiation required.

Keywords: antenna, polarization, double-turn helix, ellipticity coefficient.

S.D. Barsukov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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

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

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

T.A. Dzerzhauskaya – F. Skorina Gomel State University, Gomel, Belarus

A.P. Slobozhanyuk – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

A.E. Krasnok – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

P.A. Belov – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

The complex scaling method is applied to the non-relativistic and relativistic two-particle equations in the momentum representation for resonance sates finding. The comparison of the resonance states spectra obtained in the momentum representation with the similar results obtained in the coordinate representation for the Schrodinger equation and in the relativistic configurational representation for the two-particle relativistic equations is carried out. A good agreement of the results obtained in different representations is shown.

Keywords: relativistic two-body equations, complex scaling method, resonance states, momentum representation, relativistic configuration representation.

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

M.S. Danilchenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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

The method of preparation of suspensions based on nano-sized particles of fumed silica is described. The process and results of chemical-mechanical polishing of silicon wafers carried out in industrial environments are investigated. Recommendations on the use of polishing compositions in the chemical-mechanical polishing are making. When using the polishing suspensions SPS-81M and SPS-55M in the process of single-crystal silicon wafer CMP, high structural perfection and atomic smoothness of the surface roughness are achieved at the level of tenths of a nanometer.

Keywords: chemical-mechanical polishing, fumed silica, nanosized particles, surface, roughness.

Ya.À. Kosenok – F. Skorina Gomel State University, Gomel, Belarus

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

O.I. Tyulenkova – F. Skorina Gomel State University, Gomel, Belarus

V.G. Denisman – «Kamerton» subsidiary of JSC «INTEGRAL», Pinsk, Belarus

Relativistic theory of the Cox’s scalar not point-like particle with intrinsic structure is developed in the presence of external electromag-netic and gravitational fields; the latter is described by pseudo-Riemannian space-time geometry. It is shown that the generalized Proca-like tensor system of equations of the first order contains non minimal interaction terms through electromagnetic tensor and Ricci tensor . Generalized scalar equation of the Klein – Fock – Gordon type turns out to be much more complicated than the ordinary wave equation.

Keywords: spin zero, intrinsic structure, Cox’s particle, generalized wave equation, Riemannian space.

E.M. Ovsiyuk – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

O.V. Veko – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

K.V. Kazmerchuk – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

The data of the influence of the impurity Nb, La and annealing temperature on the structural characteristics of the layers SrBi₂(Ta_õÌå_1-õ)₂O₉ are discussed. As research methods the atomic force microscopy and X-ray diffraction method were used.

Keywords: sol-gel method, ferroelectric sol, heat treatment, SBT-film perovskite, X-ray diffraction method, method of atomic force microscopy.

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

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

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

V.V. Kolos – JSC «INTEGRAL», Minsk, Belarus

A.S. Turtsevych – JSC «INTEGRAL», Minsk, Belarus

The results of theoretical research of the optimization process of readout mixed transmission holograms formed in the -cut Bi₁₂TiO₂₀ photorefractive piezoelectric crystal are presented. It is shown that in comparison with the case of pure phase holograms, traditionally regarded in photorefractive crystals, additional accounting of the amplitude component of the holographic grating leads to a qualitative and quantitative changes in the orientation dependence of the polarization-optimized values of the diffraction efficiency of holograms recorded in this crystal.

Keywords: diffraction efficiency, phase grating, amplitude grating, mixed hologram, photorefractive piezocrystal, BTO.

V.V. Shepelevich – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

A.V. Makarevich – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

S.M. Shandarov – Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia

Let H be a subgroup of a group G. We say that H has P-property in G if is a p-number for any pd-chief factor L/K of G. Using this property of subgroups, some new criterions of p-nilpotency of groups are obtained.

Keywords: finite group, p-nilpotent group, P-property of subgroup.

Baojun Li – College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China

Aming Liu – College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China

The class of all finite groups with Sylow -subnormal subgroups is considered. The condition of saturation of this class is investigated, as well as the local screen in solvable case is established.

Keywords: finite group, Sylow subgroup, -subnormal subgroup, saturated formation, local formation.

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

It is proved that the derived p-length of the p-solvable group G in which the Sylow p-subgroup has order is at most and if then

Keywords: finite group, p-solvable group, Sylow subgroup, derived p-length.

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

The existence of hyperradical formations which are not hereditary is established.

Keywords: formation, hyperradical formation, superradical formation, finite group.

S.F. Kamornikov – Gomel Branch of International University «MITSO», Gomel, Belarus

The convex Semi-Infinite Programming (SIP) problems with polyhedral index sets are considered. For these problems a finite algorithm for determination of immobile indixes and their immobility orders along the feasible directions is described and justified. An example illustrating the application of the algorithm is provided.

Keywords: semi-infinite programming, convex programming, immobile index, immobility order, cone of feasible directions, extreme ray.

M.V. Kulahina – Institute of Mathematics of National Academy of Sciences of Belarus, Minsk, Belarus

The problem of the computation of the left inverse of a linear combination of values of the resolvent of a closed operator in a Banach space is solved. Several unsolved problems are formulated.

Keywords: closed operator, left inverse of an operator, resolvent, Banach space, functional calculus, Markov function.

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

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

A system describing the motion of four bodies under the action of gravity is considered. By elementary algebraic manipulations a simple system consisting of non-linear differential equations, each of which has a second order is selected. For each simplified system there are sets of constants of interparticle interaction, in which the general solution is meromorphic.

Keywords: movement of four bodies, constant interaction, Painleve property, meromorphic function.

A.T. Sazonava – Y. Kupala Grodno State University, Grodno, Belarus

The solvability of the finite group in which any Sylow subgroup is either -subnormal or abnormal, was proved.

Keywords: Sylow subgroup, simple non-abelian group, -subnormal subgroup, abnormal subgroup.

V.N. Tyutyanov – Gomel Branch of International University, Gomel, Belarus

T.V. Tihonenko – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

Sag of RIT-piles on condition of linear and nonlinear deformation of soil taking into account and without consolidation of the soil basis in the field of explosion is investigated.

Keywords: pile-RIT, camouflage broadening, soils, mathematical model, computer simulation.

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

Problem of effective technology of modeling of the creation of the so-called active system (AS) is considered. The active system differs from other systems by its source of organization which is internally independent and has the ability to change structure and parameters of functioning of the system based on its own needs. As alternative to the traditional method-oriented approach to technological designing of AS-models the basic circuit of problem-oriented technology of modeling is offered. The peculiarity of this technology is that the interaction and development of the formed models of the desired AS-operation are provided due to the introduction of the block of conceptual modeling and special research functioning. The new approaches to simulate experiment (SE) are considered at design AS model-ing. At the heart of the proposed technologies of SE is the operational and process way of formalization and technique of AS research. The practical use of the proposed technology is interpreted by the problem of modeling activities of the production unit.

Keywords: active system, problem-oriented technologies of modeling, conceptual modeling, target functioning, intellectual system.

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

N.B. Osipenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus