Mean-square radii and electromagnetic form factors of light mesons are obtained in the framework of Poincare covariant quark model based on the point form of relativistic Hamiltonian dynamics. Calculations are performed with the use of the requirement of self-consistent description of electroweak properties and masses of pseudoscalar and vector mesons.

Keywords: meson, quark model, electromagnetic form factor, leptonic decay constant.

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

Krutov A.F. – Department of Physics, Samara State University, Samara, Russia

The simple formalism for the description of the vector paraxial light beams of general type is offered. Simple expressions for the energy flux density of the electromagnetic field S of the vector light beams with the homogeneous polarization are discovered. It is discovered that paraxial circular polarized light beams are spread independently, and their streams of energy are parted and they are also independent.

Keywords: paraxial beams, vector beams, light beams, polarizable properties, energy properties, polarization.

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

Features of laser excitation of the pulses of surface acoustic Rayleigh waves in solid state bodies through a prism by a source of radiation of the round form are investigated. It is shown, that at increase in the azimuth angle there is increase in the amplitude and reduction of duration of the ultrasound pulse; at increase in the angle of the prism inclination the amplitude of the acoustic pulse decreases, and the duration increases. It is established, that at increase in the radius of an aperture of the round form the pulse amplitude increases and the duration decreases; with the increase in the factor of absorption of a hypersound the pulse amplitude decreases, and the duration increases.

Keywords: acoustic pulse, surface acoustic wave, solid state body, hypersound absorption.

Gudelev V.G. – B.I. Stepanov Institute of Physics NASB, Minsk, Belarus

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

Matveeva A.G. – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

The procedure for constructing of stationary perturbation theory for the Schrodinger equation and corrections to the energy spectrum and corresponding wave functions is implemented in case of the potential, represented in the form of a series in powers of a small parameter (potential-series). The application of the obtained scheme for the anharmonic oscillator is examined as a physical example.

Keywords: stationary perturbation theory, Schrodinger equation, wave function, energy spectrum, potential, correction, anharmonic oscillator.

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

Korsun L.D. – Department of Automation and Information Systems, P. Sukhoi State Technical University, Gomel, Belarus

The paper presents the results of research of the process of cutting of fragile nonmetallic materials by the influence of the directed stream of hot air and coolant. The finite element method was used to decide the problems of thermo elasticity. The features of spatial localization of thermo elastic fields are defined and the mechanism of dividing crack formation is revealed.

Keywords: hot air jet, glass, crack.

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

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

The change of morphology and molecular structure of surface layers of polyimide-fluoropolymer film after low-frequency glow discharge plasma treatment by the method of infrared spectroscopy and atomic force microscopy is determined. In case polyimide layer treatment occur mainly layer-by-layer etching and formed layers have cyclic variations of polar and disperse fraction of surface energy. The etching of molecules aligned primary parallel to the surface of a substrate in case fluoropolymer layer treatment is shown.

Keywords: low-frequency glow discharge plasma, polyimide-fluoropolymer film, infrared spectroscopy, molecular orientation, Kelvin mode of scanning probe microscopy.

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

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

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

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

All groups considered are finite. Let be a set of non-empty subclasses of a class of groups such that for all distinct . We write to denote the collection of all groups of the form , where for some . We proved the following theorem.
Theorem. Let where is a formation. Then is n-multiply -saturated formation if and only if is n-multiply -saturated for all  

Keywords: formation of finite groups, complemented subformation, direct decomposition of a class of groups, -local satellite, n-multiply -saturated formation.

Vorob’ev N.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Mekhovich A.P. – Department of Mathematics, P.M. Masherov Vitebsk State University, Vitebsk, Belarus

The transposed vector-matrices are defined and studied in this paper.

Keywords: matrix, vector-matrix, ring, field, semigroups, n-ary group.

Gal’mak A.M. – Department of Economic, Mogilev State University of Food Technologies, Mogilev, Belarus

Let G be a finite group, A a subgroup of G. Then we say that A is generalized quasinormal in G if A either covers or avoids every maximal pair (K,H) of G. We say that A is m-supplemented in G if G has a subgroup T and a generalized quasinormal subgroup C such that G=AT and Based on these concepts new characterizations of finite p-supersoluble and supersoluble groups are obtained.

Keywords: maximal pair, generalized quasinormal subgroup, m-supplemented subgroup, p-supersoluble group, supersoluble group.

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

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

The following theorem is proved.
Theorem. If in a non-identity finite group G every primitive subgroup has a prime power index, then G=[ D] H, where D and H are Hall nilpotent subgroups of G and D coincides with the -residual of G.

Keywords: primitive subgroups, finite group, soluble group, supersoluble group, nilpotent group.

Kosenok N.S. – Gomel Branch of International Institute of Labor and Social Relations, Gomel

New criteria of semiabelian of n-ary groups expressed in terms of the properties of vectors G are determined.

Keywords: symmetrical points, parallelogram G, semiabelian n-ary group, vector G.

Kulazhenko Yu.I. – Vice Rector of F. Skorina Gomel State University, Gomel, Belarus

The paper is concerned with the description of the asymptotic behaviour of parabolic sequences of the elements of Pade-Chebyshev table for some continuous functions represented by Chebyshev series. The asymptotic form of the best rational approximations for such functions is determined.

Keywords: best approximations in the uniform norm, Pade–Chebyshev approximant, trigonometric Pade approximant, rational approximation, the accurate constants of rational approximation.

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

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

We consider Hilbert transformation of vector-valued functions on the group of p-adic integers Z_p taking values in Banach space X, and square-integrable in Bochner sense. If Hilbert transformation with is a bounded operator, then Banach space X is an UMD space.

Keywords: Hilbert transformation, UMD space, p-adic numbers, Fourier transformation.

Sidoryk H.G. – Mechanics-Ìathematical Department, Belarusian State University, Minsk, Belarus

Let G be a finite group, X – some non-empty subset of the group G. The subgroup H of group G is identified -supplemented in G if there exists a subgroup B such that G=HB and for any maximal subgroup of H there is such that and The p-supersolvability of a finite group with -supplemented Sylow p-subgroup for initial importance of the number p are obtained. New conditions of the supersolvability finite groups is received.

Keywords: finite group, Sylow subgroup, -supplemented subgroup, supersolvable group, p-supersolvable group.

Shnyparkov À.V. – Gomel Engineering Institute of the Ministry for Emergency Situations of the Republic of Belarus, Gomel

The paper presents one of the ways of decision of the problem of perfection of the resource-saving technology in industrial and civil construction. Materials of the original researches are considered on the basis of concepts of the system approach, modern computer technologies and the developed methods of decision of boundary problems of the nonlinear theory of elasticity.

Keywords: nonlinear systems, deformable solid bodies, construction, methods, means and technology of optimization.

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