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Edition address:
F. Sorina Gomel State University
Sovetskaya Str., 104, 246019, Gomel,
Republic of Belarus

Phones:
+375 (232) 51-00-77
+375 (232) 51-03-21
+375 (29) 678-62-50

E-mail:
pfmt*gsu.by

Website:
http://pfmt.gsu.by

MATERIALS: 3 (24) 2015


PHYSICS

Girgel S.S. Beams of Kummer without the Gaussian apodization with transferable terminating power

The new solutions of the parabolic equation featuring paraxial light beams are offered. Such beams are featured by Kummer functions of complex argument with two free parameters without a Gaussian. Restrictions on these parameters, at which beams of Kummer transfer terminating power and are physically realized, are discovered.

Keywords: paraxial beams, beams of Kummer, square integrability.

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

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Kolyadko Zh.V., Shepelevich V.V., Davydovskaya V.V. Propagation of singular beams in a cubic optically active photorefractive crystal

The features of the propagation of singular beams with various signs of the topological charge in a cubic optically active photorefractive crystal of cut, to which an external electric field is applied, are investigated. The dependence of the angle of rotation of the sin-gular beam on value of external electric field applied to the crystal and sign of unit topological charge of the beam is analyzed. It is shown how the optical activity affects the distribution of singular beam in the crystal.

Keywords: singular beam, photorefractive crystal, optical activity.

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

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

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

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Matuk E.V., Gaida L.S., Guzatov D.V. The movement of the metal nanoparticles near the surface of the air bubble in the liquid by the radiation pressure force

The effect of laser radiation pressure on the metal nanoparticles located near an air bubble in water is experimentally investigated. The reasons of the observed movement of nanoparticles along a bubble surface are discussed.

Keywords: light pressure of laser radiation, metal nanoparticles.

E.V. Matuk – Y. Kupala Grodno State University, Grodno, Belarus

L.S. Gaida – Y. Kupala Grodno State University, Grodno, Belarus

D.V. Guzatov – Y. Kupala Grodno State University, Grodno, Belarus

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Ovsiyuk .. Electromagnetic field in the Majorana Oppenheimer formalism in the anti de Sitter Universe

Exact solutions with spherical symmetry of the Maxwell equations in the oscillating anti de Sitter Universe are constructed. 3-Dimensional complex formalism by Majorana Oppenheimer, generalized to pseudo-Riemannian space-time models in accordance with the tetrad method, is applied. The established dependence of the constructed solutions on the time variable leads to independence of the Pointing vector on time. This means that the change in time of the anti de Sitter geometry cannot be seen by measuring the energy flow density.

Keywords: Maxwell's equations, tetrad formalism, anti de Sitter Universe, non-static coordinates, complex formalism of the Majorana Oppenheime, exact solutionsr.

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

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Rudenkov A.S. Influence of metal concentration on the phase composition, structure and properties of carbon-metal coating

The morphological features, phase composition, microhardness and tribological properties of composite carbon coatings formed by co-precipitation of carbon plasma streams of pulsed cathodic arc discharge and flows of atoms of the metal ions (Cr, Ti, Cu) generated by magnetron sputtering, and their dependence on the power source sputtering are determined. It is shown that such layers are characterized by high density and order of sp2-clusters and low roughness. The hardness increases and the wear rate of counterbody decreases with in-creasing the power of magnetron.

Keywords: carbon coatings, sp2-clusters, alloying, magnetron, phase composition, morphology, roughness, hardness, friction, wear.

A.S. Rudenkov – F. Scorina Gomel State University, Gomel, Belarus

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Staskov N.I., Parashkov S.O., Shylov A.V., Krekoten N.A. Analytical solution of the inverse problem of a spectrophotometer absorbing layer on an absorbing substrate with a dielectric layer

On the example of a two-layer structure of a semiconductor insulator semiconductor the possibility of an analytical determination of the optical parameters and thickness of the upper layer on the reflection spectrum envelope at normal incidence of light is considered. It is very difficult to calculate these functions even in the case of absence of the transition zones between the layers. Mismatching enve-lopes calculated and measured reflection coefficients in certain areas of the spectra indicates the presence of inhomogeneous surface and transition zones in real structures pSi SiO2 cSi.

Keywords: bilayer structure, optical spectra, envelopes extrema, transition layers, pSi SiO2 cSi.

N.I. Staskov – .A. Kuleshov Mogilev State University, Mogilev, Belarus

S.O. Parashkov – .A. Kuleshov Mogilev State University, Mogilev, Belarus

A.V. Shylov – .A. Kuleshov Mogilev State University, Mogilev, Belarus

N.A. Krekoten – JSC INTEGRAL, Minsk, Belarus

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Yurevich Yu.V., Yurevich V.A. Modulation of optical radiation in case of thin film reflection of dense resonant medium

The possibility of temporal modulation of quasi-continuous radiation in the reflection of thin film of dense resonant medium is theoretically defined for the relative weakness of the relaxation processes. Resonant conversion of the light field in the reflection mode coherent interaction can be used to form the optical signals in ultrafast interaction processes of light radiation with thin layers.

Keywords: resonant reflection, thin optical films, dense resonant medium, dipole-dipolar interaction.

Yu.V. Yurevich – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

V.A. Yurevich – Mogilev State University of Food Technologies, Mogilev, Belarus

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MATHEMATICS

Belokon L.M. On the problem of intersections of the maximal -subgroups of finite groups

Let be a nonempty formation, some set of prime numbers. The theorems reflecting the general regularities on intersections of maximal subgroups of a finite group mutually simple with numbers from indexes including statements on the intersections and are received.

Keywords: formations of finite groups, subgroup m-functor, intersections of maximal -subgroups in a finite group.

L.M. Belokon – Mogilev State University of Food Technologies, Mogilev, Belarus

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Belokursky M.S. Erugins problem on the existence of irregular solutions in one case of the linear system with nonzero mean of periodic coefficient

The necessary and sufficient conditions under which linear periodic differential system has strongly irregular periodic solutions were obtained.

Keywords: strongly irregular periodic solution, linear differential system, periodic coefficient.

M.S. Belokursky – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

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Borodich R.V., Bykov S.N. On operator generalization of Frattini subgroup

The behavior of normal subgroups in generalized Frattini extension is studied.

Keywords: formation, normal subgroups, Sylow p-subgroup, group of operators.

R.V. Borodich – F. Scorina Gomel State University, Gomel, Belarus

S.N. Bykov – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

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Kamornikov S.F. Solvable NT-functors

The problem of characterization of all hereditary regular transitive subgroup functors is solved. It is proved that any natural transitive subgroup functor is -subnormal for some primitive class .

Keywords: finite solvable group, primitive group, subgroup functor, natural transitive subgroup functor (NT-functor), formation.

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

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Mironenko V.V. On periodic solutions of differential equation with linear-fractional right-hand part

The conditions of existence of periodic solutions of differential equation with linear-fractional right-hand side are given.

Keywords: differential equation, reflecting function, Poincare mapping, linear-fractional function, periodic solution.

V.V. Mironenko – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

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Sazonova A.T. On the results of the study of simplified systems in the problem of motion of four bodies in a plane

The system describing the motion of four bodies in a plane is considered. The method of the small parameter of a simplified system consisting of nonlinear differential equations, each of which has a second order is determined. For these systems, a set of interparticle interaction constants in which all its solutions of the system are meromorphic functions is specified.

Keywords: motion of four bodies in a plane, interaction constant, simple system, meromorphic function.

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

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Skiba A.N. On -properties of finite groups II

Let G be a finite group, some partition of the set of all primes and a subset of the set . A set of subgroups of G is said to be a complete Hall -set of G if contains exact one Hall -subgroup of G for every such that We say also that G is: -full if G possess a complete Hall -set; a -full group of Sylow type if for each every subgroup E of G is a -group, that is, E has a Hall -subgroup H and every -subgroup of E is contained in some conjugate of In this paper we study properties of finite -full groups. The work continues the research of the paper [1].

Keywords: finite group, -full group, -soluble group, -nilpotent group, -quasinilpotent group.

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

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Starovoitov A.P., Kechko E.P. On localization of the zeroes Hermite Pade approximants to the exponential functions

The upper estimates are determined for modules of the zeros of Hermite polynomials (Hermite Pade approximation type I) of the exponential system where are arbitrary complex numbers. The proven statements complement and generalize known results about the behavior of the zeros of Hermite polynomials for exponential system by E. Saff and R. Varga, H. Stahl, F. Wielonsky.

Keywords: exponential system, Hermite polynomials, Hermite Pade approximation, zeros of Pade approximation.

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

E.P. Kechko – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

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INFORMATION SCIENCE

Bykhoutsev V.E., Prokopenko D.V., Curganova L.A. Calculation of piles-CIT on the first limiting condition

The limiting bearing ability of a pile-cit in the nonlinear-deformed soil basis, taking into account ground consolidation in zone running-impulse processing is considered.

Keywords: pile-cit, mathematical model, limiting bearing ability.

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

D.V. Prokopenko – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

L.A. Curganova – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

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Zhdanov O.N., Sokolov A.V. Algorithm of construction of optimal according to criterion of zero correlation non-binary S-boxes

This paper considers the construction of cryptographic S-boxes of the length which are optimal from the point of view of the ab-sence of correlation between the output and input vectors. Constructed sets of S-boxes can be recommended for upgrading of the existing block symmetric ciphers, as well as for the synthesis of new high-speed encryption algorithms based on the principles of multi-valued logic.

Keywords: S-box, matrix of correlation coefficients, Kim scheme.

O.N. Zhdanov – M.F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, Russia

A.V. Sokolov – Odessa National Polytechnic University, Odessa, Ukraine

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Maslovich S.F., Gorbach A.B., Halushko V.N., Drobov A.V. Web-application electrical calculations

The idea of creating software is considered. With this software, one can automate the calculations for determining the rational schemes and designs of electrical networks, determine the electrical load, loss of power and loss of supply, reactive power compensation, maintain the required voltage quality, quantity and variety of power transformers.

Keywords: software tools, web-application, power supply, power consumption, circuitry.

S.F. Maslovich – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

A.B. Gorbach – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

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

A.V. Drobov – Gomel State Technical College, Gomel, Belarus

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