
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N1 (14) 2013
PHYSICS
Balmakov A.P., Semchenko I.V., Khakhomov S.A., Nagatsu M. Microwave circular polarizer based on bifilar helical particles
In this paper, we describe practical realization of a new type of circular polarizer based on metallic doublestranded (ds) array particles, operating under normal to the helix axis wave propagation. The latter is the key distinction of this array from a number of analogous operating under propagation along the helix axis. Theoretical foundation of dshelices polarization selectivity is given for a wave propagation perpendicular to the helix’s axis. A computer model is created to study electrodynamic properties of arrays of helices, which confirms the circular polarizer feasibility for a microwave wavelength region.
Keywords: helix, array, polarization, metamaterial.
A.P. Balmakov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
I.V. Semchenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
S.A. Khakhomov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
M. Nagatsu – Shizuoka University, Hamamatsu, Japan
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Veko O.V., Ovsiyuk E.M., Red’kov V.M. Jones 4spinors for the partially polarized light
The known grouptheory based description of constructing of 4tensors based on the second rank 4spinor permits to introduce definition for Jones 4spinor of a partially polarized light and relates this object with Stokes 4vector and Stokes antisymmetric 4tensor. It provides us with extension of the known attitude to the problem when only Jones 2spinors relevant to a completely polarized light are used.
Keywords: polarization optics, Jones 4spinors, Stokes parameters.
O.V. Veko – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus
E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus
V.M. Red’kov – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
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Girgel S.S. KummerGaussian scalar astigmatic threedimensional light beams
The formalism for the description of paraxial 3D Gaussianlike light KummerGaussian beams by a simple astigmatism is offered. Conditions of their physical realizability are formulated. New types of KummerGaussian beams are found. Such beams are presented by Gaussian product on Kummer function of a complex argument and a nonnegative integer index n.
Keywords: paraxial beams, HermiteGaussian beams, KummerGaussian beams, Gaussianlike beams.
S.S. Girgel – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Grishechkin Yu.A., Kapshai V.N. Relativistic bound state problem for twoparticle systems with energy dependent one boson exchange potential
Numerical solutions of quantum field theory equations describing bound sstates of two scalar particles with equal masses are found in the case of oneboson exchange potential dependent on the system energy. The mass of the scalar exchange boson is chosen to be equal to zero. The constants of scalar particleantiparticle system decay into two photons are calculated based on obtained solutions.
Keywords: relativistic twoparticle equations, oneboson exchange potential, wave functions, bound states, normalization condition, energy eigenvalues, decay constant.
Yu.A. Grishechkin – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
V.N. Kapshai – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Zalesski V.B., Kravchenko V.M., Leonova T.R., Polikanin A.M., Zaretskaya E.P., Petrosyan S.G., Kechiantz A.M. CIGS solar cells with efficiency 10,1% on perlite galssceramic substrates
For the first time thin film solar cells with CuInGaSe_{2} absorber layer were formed on a specially designed nonconductive ceramic substrates on the basis of pearlite to produce photovoltaic devices fully integrated into building constructions. This glass ceramic satisfies the physical demands of the substrate material as well as the requirements of cost reduction of solar cells production. This paper presents preliminary results which show that these type solar cells with the efficiency higher than 10 % may be designed.
Keywords: thin films, CIGS, solar cells, glass ceramic.
V.B. Zalesski – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
V.M. Kravchenko – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
T.R. Leonova – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
A.M. Polikanin – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
E.P. Zaretskaya – Scientific and Practical Materials Research Centre of NAS Belarus, Minsk, Belarus
S.G. Petrosyan – Institute of Radiophysics and Electronics, NAS RA Ashtarak, Armenia
A.M. Kechiantz – Institute of Radiophysics and Electronics, NAS RA Ashtarak, Armenia
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Tsyrelchuk I.N., Khoroshko V.V., Gremenok V.F., Mishuto V.A. The optical properties of thin films of solid solutions CU_{X}In_{X}Zn_{22X}Se_{2}, obtained by a twostage selenization
This paper discusses the results of studies in the temperature range of 80 and 300 K absorption spectra and photoluminescence spectra of thin films of Zn_{22X}Cu_{X}In_{X}Se2 with the concentration of zinc atoms 0–10 at.%. Polycrystalline films of ptype conductivity were obtained on glass substrates by a twostage selenization base layers ZnSe / (Cu + In) under an inert atmosphere. The authors established the character of the width of the band gap and photoluminescence spectra of the concentration of zinc atoms.
Keywords: thin film, twostage selenization, absorption coefficient, photoluminescence, band gap.
I.N. Tsyrelchuk – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
V.V. Khoroshko – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
V.F. Gremenok – Institute of Solid State and Semiconductor Physics of NAS Belarus, Minsk, Belarus
V.A. Mishuto – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
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Zhubo Liu, Rogachåv A.A., Yarmolenko M.A., Jiang X.H., Rogachåv A.V., Gorbachev D.L. Influence of assisting laser radiation at electronbeam dispersion on the molecular structure of polyethylenesilver nanocomposite coatings
The paper deals with the study of the molecular structure and morphology of polyethylenesilver nanocomposite coatings. Polyethylenesilver nanocomposite coatings were prepared from active gas phase by electronbeam dispersion of polyethylene and silver nitride. The influences of laser assisted electronbeam dispersion and annealing on the formation degree of plasmon effect, the chemical composition and structure of the layer were determined. The results show that metal nanoparticles could be produced by laser assisting at the dispersion stage affecting the autocatalytic process of decomposition of the salt. Annealing leads to a more homogeneous structure with a smaller protuberance on the surface of the coatings.
Keywords: electronbeam dispersion, laser assistant, nanocomposite coating, polyethylene, silver nanoparticles, heat treatment.
Zhubo Liu – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.A. Rogachev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
M.A. Yarmolenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
X.H. Jiang – Nanjing University of Science and Technology, Nanjing, PR China
A.V. Rogachev – Rector of F. Skorina Gomel State University, Gomel, Belarus
D.L. Gorbachyov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Shilova I.V., Belskaya Î.À., Sotsky À.B. Electrodynamic model of the bending fiberoptic sensor
Bending radiation loss caused by elliptical deformation in the sensitive element of the fiberoptic pressure sensor was investigated on the basis of the fiberoptic loop antenna model.
Keywords: optical fiber, fiber optical sensor of pressure.
I.V. Shilova – BelarusianRussian University, Mogilev, Belarus
Î.À. Belskaya – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
À.B. Sotsky – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
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Shushkevich G.Ch., Kiseleva N.N. Calculation of the attenuation coefficient of the sound field of a spherical radiator by penetrable spherical shell
The analytical solution of the boundary problem which describes the process of penetration of the sound field of a spherical radiator located inside a thin unclosed spherical shell, through the permeable spherical shell is constructed. The influence of some parameters of the problem on the value of the attenuation coefficient (screening) of a sound field inside the spherical shell is numerically investigated.
Keywords: dual series equations for Legendre polynomials, infinite system of linear algebraic equations of the second kind with a completely continuous operator, attenuation coefficient of a sound field.
G.Ch. Shushkevich – Y. Kupala Grodno State University, Grodno, Belarus
N.N. Kiseleva – Y. Kupala Grodno State University, Grodno, Belarus
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MATHEMATICS
Gal'mak A.M., Vorobiev G.N. On PostGluskinHosszu theorem
PostGluskinHosszu theorem is known as GluskinHosszu or HosszuGluskin theorem.
In the formulation of this theorem there is an nary group <A, [ ] > and some binary group
<A, o >. These groups have a common carrier A.
E. Post formulated and proved this theorem considering isomorphous copy of À_{0} (associated group)
instead of group < A, o >. In our opinion the absence of the name of E. Post in the title of the theorem is an embarrassing mistake which must be corrected. Apparently, M. Hosszu didn’t know anything about the results of E. Post. It is necessary to note that L.M. Gluskin was not engaged in the study of nary groups. He investigated a large class of algebraic systems – positional operatives, and achieved a series of important results. PostGluskinHosszu theorem is among numerous consequences of these results.
Keywords: group, nary group, automorphism.
A.M. Gal’mak – Mogilev State University of Food Technologies, Mogilev, Belarus
G.N. Vorobiev – Mogilev State University of Food Technologies, Mogilev, Belarus
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Gritsuk D.V., Monakhov V.S., Shpyrko O.A. On finite solvable groups with bicyclic Sylow subgroups
The group is called a bicyclic group if it is the product of two cyclic subgroups. It is proved that the solvable group with bicyclic Sylow psubgroups for any is at most 6 and if , then the derived length of a solvable group with bicyclic Sylow psubgroups for any is at most 3.
Keywords: finite group, solvable group, bicyclic group, Sylow subgroup, derived length.
D.V. Gritsuk – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
V.S. Monakhov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
O.A. Shpyrko – Branch of the M.V. Lomonosov Moscow State University, Sevastopol, Ukraine
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Lomovtsev F.E., Lyakhov D.A. Weak solutions of hyperbolic evenorder operatordifferential equations with variable domains
We prove the existence and uniqueness of weak solutions of boundary value problem for a twoterm evenorder hyperbolic operatordifferential equation with unbounded operator coefficient A(t), having tdepending domain D(A(t)). It is shown that for a smooth righthand part the weak solutions of boundary value problem are smooth, i. e. they satisfy the equation almost everywhere on ]0,T[ in H and the boundary conditions in the usual sense. An example of the new correct boundary value problem for fourthorder partial differential equation with unsteady boundary conditions on the space variables is given.
Keywords: ñorrectness by Hadamard, operatordifferential equation, unbounded operator, variable domain, weak solution.
F.E. Lomovtsev – Belarusian State University, Minsk, Belarus
D.A. Lyakhov – Belarusian State University, Minsk, Belarus
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Murashka V.I. On partially conjugatepermutable subgroups of finite groups
Let R be a subgroup of a group G. We shall call a subgroup H of G the Rconjugatepermutable subgroup if for all In this work the properties and the influence of Rconjugatepermutable subgroups (maximal, Sylow, cyclic primary) on the structure of finite groups are studied. As R we consider the Fitting subgroup F(G) quasinilpotent radical and the generalized Fitting subgroup that was introduced by P. Shmid. In particular, it was shown that group G is nilpotent iff all its maximal subgroups are conjugatepermutable.
Keywords: finite group, nilpotent group, Rconjugatepermutable subgroup, conjugatepermutable subgroup, the Fitting subgroup.
V.I. Murashka – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Novikov S.P. About belonging of prefrattini subalgebras of multirings to class
Starovoitov A.P. HermitePade approximants of the system MittagLeffler functions
Fedartsova N.M. Correction method for solving perturbed parametric linearquadratic optimal control problems in the neighbourhood of irregular parameter value
A family of oneparametric linearquadratic optimal control problems with singular arcs is considered. A method for solving perturbed problems in the neighbourhood of irregular parameter value on condition that unperturbed problem solution is known is given.
Keywords: optimal control, parametric optimization, perturbed problems, linearquadratic problems, singular arcs.
N.M. Fedartsova – Design and Technology center of the Belarusian railway, Minsk
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INFORMATION SCIENCE
Erofeeva E.A. Technological stages of imitating modeling traffic volume processing by railway station
In the paper the definition and features of the technological line of processing of train a traffic volume are presented. The basic requirements with which the developed means of imitating modeling of work of a switchyard should satisfy are formulated. The structure of the developed program complex is given. The technology of application of a program complex for the solution of production tasks is described.
Keywords: simulation of complex engineering systems, switchyard.
E.A. Erofeeva – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Pekar D.V., Sadov V.S. Decision making algorithm in the safety system based on the fuzzy logic
At the present time the volume of handled data is rapidly growing. A large volume of voice data processing is impossible without usage of automatic speech systems with the ability to make decision based on speech signal analysis and lingual component processing. In this paper fuzzy logic based decision making algorithm is proposed. Described algorithm has a lot of advantages such as ability to be configured to meet certain requirements, easiness of creating a set of fuzzy rules, computational effectiveness and similar decision making process as in human beings.
Keywords: decision making, fuzzy logic, speech processing.
D.V. Pekar – Belarusian State University, Minsk, Belarus
V.S. Sadov – Belarusian State University, Minsk, Belarus
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