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

The internal symmetries of massless and massive Dirac equations in space-time 2+1 are investigated. It is shown that the massless Dirac equation has 12-parameter symmetry group which as a subgroup contains 10-parameter group Lee SO(3,2). The massive equation has the symmetry group SO(2,2).

Keywords: internal symmetry, Dirac field, generators, group, invariance.

Andrusevich P.P. – Department of Physics, Belarusian State University, Minsk, Belarus

Pletyukhov V.A. – Department of Physics, Brest State University, Brest, Belarus

Strazhev V.I. – Department of Physics, Belarusian State University, Minsk, Belarus

Local spatial spectra of Bessel beams fragments limited by the radial-shifted circular diaphragms have been investigated. It has been shown theoretically and experimentally that in case when circular diaphragm is placed on the axis of zero-order Bessel beam or includes its central maximum, the spectrum of such Bessel beam fragment is annular. When shifting the diaphragm behind the limits of the axial maximum, the spectrum takes the form of an arc. It has been established that the detected properties of spatial spectra occur independently of the technique and optical scheme of Bessel beams formation.

Keywords: Bessel light beam, local spatial spectrum, annular and arc spectra.

Belyi V.N. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Kazak N.S. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Khilo N.À. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Ropot P.I. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Vasilyev R.Yu. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

In this paper the capabilities of two plasma-assisted techniques (laser ablation and electrical discharges in liquids) for fabrication of gadolinium silicide nanoparticles have been investigated. The composition, morphology and magnetic properties of the particles formed under various experimental conditions have been analyzed. The synthesized Gd-Si particles exhibit the superparamagnetic behavior promising for application in the method of magnetic hyperthermia treatment.

Keywords: nanoparticles, laser ablation in liquid, electrical discharge in liquid, laser-induced modification.

Burakov V.S. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Tarasenko N.V. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Butsen A.V. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Nedelko M.I. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Nevar A.A. – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

The possibilities of the use of double-pulse laser atomic-emission spectroscopy for quantitative analysis with submicron resolution of brass, bronze and Ti-Zr-coatings have been examined. A new method to control the radiation flux density on the sample surface has been proposed. This method allows to change the thickness of evaporated substance layer from 0,1 up to 5 micrometer. It has been found that the heating of the sample during deposition of the coating leads to a heterogeneous distribution of elements due to the thermo diffusion.

Keywords: laser ablation, double laser pulses, laser plasma, laser atomic emission spectroscopy, layer wise quantitative analysis, functional coating.

Voropay E.S. – Department of Physics, Belarusian State University, Minsk, Belarus

Ermalitskaia K.F. – Department of Physics, Belarusian State University, Minsk, Belarus

Zajogin A.P. – Department of Physics, Belarusian State University, Minsk, Belarus

Structures formation’s process model is proposed. Physicotechnological processes at influence of electromagnetic forces and their applications in various areas of modern science and technics are described and proved. Various materials forms and parameters are investigated on the basis of mathematical model.

Keywords: formation of thin-film structures, electromagnetic effects of the plasma formation of thin-film structures, electromagnetic effects of plasma.

Dostanko A.P. – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

Grinchik N.N. – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

Spresov I.N. – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

New expressions for physical structured functions of the inelastic lepton-hadron scattering which contain a dependence on a target mass and are in agreement with the spectral property, are obtained. We demonstrate that target mass corrections to structure functions calculated by using the new method noticeably differ from the standard Georgi-Politzer method, as well as from the Steffens-Melnitchouk approach.

Keywords: inelastic lepton-hadron scattering, structure function, target mass corrections.

Lashkevich V.I. – International Center for Advanced Studies, P. Sukhoi Gomel State Technical University, Gomel, Belarus

Solovtsova Î.Ð. – International Center for Advanced Studies, P. Sukhoi Gomel State Technical University, Gomel, Belarus

Two models for the process of formation of micro- and nanostructures are proposed. The differences between the two models are shown. Various forms and material parameters in the course of action are studied on the basis of mathematical models.

Keywords: formation of thin-film structures, electromagnetic effects of the plasma formation of thin-film structures, electromagnetic effects of plasma.

Spresov I.N. – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

In this report we discuss the new concept of “optimal metamaterials” for interactions with electromagnetic waves. In these materials the inclusion shape is chosen so that the particles have the maximum possible energy in the field of a given plane electromagnetic wave propagating or decaying inside the composite medium composed of these particles. It appears that the optimal particles are bianisotropic, and the “optimal material” for interactions with plane linearly polarized evanescent waves is the omega material, while for propagating waves it is a certain nonreciprocal material.

Keywords: metamaterial, electromagnetic waves, composite medium, interactions, omega material.

Tretyakov S.A. – Aalto University School of Electrical Engineering, Finland

The structure of a finite soluble group with two inconjugate selfnormalizable maximal subgroups belonging to the local subformation of the formation of all metanilpotent groups is studied.

Keywords: finite group, soluble group, maximal subgroup, inconjugate subgroups, local formation, formation of all metanilpotent groups.

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

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

Keywords: vector-matrice, determinant, vector-determinant, n-ary group.

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

A new characterization of generalized analytic functions in sense of Arens-Singer is given in the case of maximal semigroups. It is shown that this result can be applied to approximation problems.

Keywords: algebra of generalized analytic functions, semigroup of semicharacters, Shilov boundary, approximation.

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

Romanova M.A. – Polesskiy State University, Pinsk, Belarus

This work is devoted to the study of finite groups factorizable by formation subgroups.

Keywords: group, formation, coradical, generalized subnormal subgroup, index, subgroup Frattini.

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

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

In the article a brief description of the researches based on scientific ideas of academician F.I. Fedorov and executed in the field of research of optical activity of transparent and absorbing crystals in the Institute of Crystallography of the Russian Academy of Sciences is given. Results of study of polarizing characteristics of eigen waves uniaxial and biaxial crystals depending on the thickness of a crystal layer, temperature and other parameters are presented. In the article the information about devices and the methods of research developed and used in the Institute of Crystallography of the Russian Academy of Sciences for obtaining the information about optical properties of crystals (about components of gyration tensor, parameters of refraction, value of circular anisotropy, circular dichroism, etc., as optical active crystals, and not showing gyrotropy, in various phase conditions) is presented. The polarizing characteristics of the radiation passed through a crystal layer or reflected by it and calculated with the application of methods of computer modelling on the basis of the theoretical relations corresponding to variations of accuracy approximation are described. The article is added to the extensive list of the scientific works used for preparation of the manuscript.

Keywords: F.I. Fedorov's scientific ideas, covariant methods, transparent and absorbing crystals, uniaxial and biaxial crystals, refraction, absorption, optical activity, specific rotation, circular birefringence, circular dichroism, gyration tensor, dispersion, eigen waves, azimuth of polarization, ellipticity, reflection coefficient, spectropolarimeter, dichrograph, spectrophotometric setup, theoretical calculations, an experimental research, computer modelling.

Konstantinova A.F. – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia

The influence of works of F.I. Fedorov and his scientific school on the progress in the optics of photorefractive crystals is considered. It is shown that the covariant methods created by F.I. Fedorov promoted the elaboration of the strict theory of the photorefractive effect in crystals. Special attention is given to the development of holography on the base of photorefractive crystals in Belarus.

Keywords: piezoelectric effect, photoelasticity, piezocrystal, gyrotropy, diffraction efficiency.

Shepelevich V.V. – Chief of the Theoretical Physics Department and the Laboratory of Coherent Otptics & Holography I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus