
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N4 (13) 2012
PHYSICS
Andreev V.V., Chebotareva E.S. The search of critical parameter values for semirelativistic coulomb problem
The paper presents a new calculation method of upper bounds of critical values for the semirelativistic Coulomb problem with the trial pseudoColumbian wave functions.
Keywords: critical value, Coulomb potential, trial wave functions, Salpeter equation.
V.V. Andreev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
E.S. Chebotareva – I.G. Petrovsky Bryansk State University, Russia
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Kapshai V.N., Shamyna A.A. Transmission of plane electromagnetic waves trough a multilayer biisotropic structure
The problem of normal incidence of a plane electromagnetic wave on a system of biisotropic layers is solved in general case using the multiple reflection method as well as the matrix method. The resulting formulas are applied in order to numerically calculate periodic structures of biisotropic layers. Periodically repeating peaks and troughs for the transmission coefficient modulus with the changing thickness of biisotropic layers are found.
Keywords: constitutive equations, biisotropic medium, layer, transmission and reflection coefficients, periodic structure.
V.N. Kapshai – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.A. Shamyna – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Konstantinova A.F., Golovina T.G., Evdischenko E.A., Nabatov B.V., Konstantinov K.K. Special cases of low symmetry absorbing crystals
Peculiarities of eigenwaves in absorbing low symmetry crystals were investigated. As it was shown by F.I. Fedorov and A.M. Goncharenko, there are substantial differences in monoclinic crystals. Six variants of existence of optical axes in such crystals were considered in details. Changes in ellipticity of eigenwaves were investigated. Substantial difference between these cases is shown. This difference can be clearly seen on dependencies of ellipticity and intensity of the transmitted light from the angle of incidence in the cases when the incident light has right or left circular polarization.
Keywords: low symmetry crystals, monoclinic crystals, absorption, eigenwaves.
A.F. Konstantinova – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia
T.G. Golovina – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia
E.A. Evdischenko – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia
B.V. Nabatov – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia
K.K. Konstantinov – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia
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Makarevich V.V., Katsiashou Y.O. FDTD simulation of femtosecond pulses in semiconductor laser under DC pumping current
Simulation results of semiconductor laser dynamics using finitedifferences time domain (FDTD) method of solving MaxwellBloch equations are presented. The ~ 100 fs pulse train regimes under continuous pumping were found to be possible for GaAs vertical cavity surface emitting lasers in the 628 nm wavelength region.
Keywords: finitedifference time domain method, semiconductor laser, femtosecond pulses, coherent interaction.
V.V. Makarevich – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
Y.O. Katsiashou – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
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MalyutinaBronskaya V.V., Zalesskiy V.B., Leonova T.R., Polikanin A.M., Mudryy V.A., Semchenko A.V., Sidsky V.V. Active layers doped with rareearth metals for increased efficiency solar cells
This paper presents the characteristics of photovoltaic structures AlNi/ZnO:Er/Si, obtained by magnetron sputtering, and structures AlNi/ZnO:Tb/Si, obtained by the combined method using electrochemical deposition and magnetron sputtering.
Keywords: solgel, ZnO, photoelectric characteristics, electrochemical deposition, magnetron sputtering.
V.V. MalyutinaBronskaya – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
V.B. Zalesskiy – 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
V.A. Mudryy – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
A.V. Semchenko – F. Skorina Gomel State University, Gomel, Belarus
V.V. Sidsky – F. Skorina Gomel State University, Gomel, Belarus
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Pilipovich V.A., Zalesski V.B., Konojko A.I., Malevich N.A., Polikanin A.M., Sednev R.G. Two channel vibration resistant interferometer with superposed probing channels
The method of transmission of light fluxes based on the birefringent elements and the polarization transformations is considered. The method allows to exclude the effect of destabilizing influence, since, light beams of the interferometer pass through the same optical elements. This method allows to combine two probing channels.
Keywords: interference, polarization, birefringent element, phase difference, the rotational polarization, anisotropy.
V.A. Pilipovich – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
V.B. Zalesski – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
A.I. Konojko – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
N.A. Malevich – 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
R.G. Sednev – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
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Pinchuk V.G., Korotkevich S.V., Bobovich S.O., Morozov V.N. Investigation of the kinetics of hardening and destruction of the surface layer of nickel at friction loading
The authors investigated the kinetics of hardening of the surface layer of nickel at friction by the method of ferromagnetic resonance (FMR), electron microscopy and Xray analysis. The cyclical changes in the dislocation density with time trials were determined. The characteristic stages of hardening at friction were defined. The processes that cause cycling of the material strength properties of the surface layer were studied. The basic mechanisms of hardening and destruction were determined. The interrelation of the kinetics of the strength characteristics and wear of metal at friction were investigated. The radarcyclical nature of the wear layer by layer was determined.
Keywords: effective slipping zones (areas), shear deformation, cellular structure, zone stratification, transcrystalline and intercrystalline destruction.
V.G. Pinchuk – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
S.V. Korotkevich – Republican Unitary Enterprise of Power Industy, Gomel, Belarus
S.O. Bobovich – Republican Unitary Enterprise of Power Industy, Gomel, Belarus
V.N. Morozov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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MATHEMATICS
Gal'mak A.M. The conujgate vectormatrix and spacematrix
The conujgate vectormatrix and spacematrix are defined and studied in this paper.
Keywords: matrix, vectormatrix, spacematrix.
A.M. Gal'mak – Mogilev State University of Food Technologies, Mogilev, Belarus
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Korzhik R.I., Zhogal S.P. The regimes functioning of nonautonomous van der Pol oscillator with delay and external harmonic effect
The effect of delay on the dynamical regimes of nonautonomous van der Pol oscillator with an external harmonic influence was investigated. The maps of dynamical regimes for oscillator with delay and without delay were presented.
Keywords: van der Pol oscillator, stationary states, delays, abridged equation, external periodic effect, bifurcation.
R.I. Korzhik – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
S.P. Zhogal – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Semenchuk V.N., Veliasnitski V.F. On the finite groups factorizable by generalized subnormal subgroups
This work is devoted to the study of finite groups factorizable by generalized subnormal subgroups.
Keywords: group, formation, coradical, generalized subnormal subgroup, index, Schmidt group.
V.N. Semenchuk – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
V.F. Veliasnitski – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Sinyugina J.V. On the waiting time in the system with limited gated service and adaptive vacations
We consider the queueing system with limited gated service and adaptive vacations of the server: in one cycle of service only a limited number of customers that were presenting in the system at the moment of the vacation completion may be served; the length of the vacation period depends on whether or not the queue was empty at the previous vacation completion epoch. Distribution of the waiting time is computed.
Keywords: queueing system, limited gated service, adaptive vacations, waiting time.
J.V. Sinyugina – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Starovoitov A.N. Queueing system with batch arrivals, batch service, failing server and regaining
The author considers a singleserver queueing system with batch arrivals and batch service. A server can fail. The failure completely clears the queue of the system if it is not empty. The time of the service and time of regaining are exponentially distributed. Stationary distribution of the states of the process describing the queueing system behavior is found.
Keywords: queueing system, batch arrivals, batch service.
Starovoitov A.N. – Belarusian State University of Transport, Gomel, Belarus
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Tyutyanov V.N. Product of two solvable subgroups of 3' index
The restrictions on the indices of subgroups play an important role in the study of finite groups. This theme was considered by R. Guralnik, L.S. Kazarin, V.S. Monahov and other authors. Some authors investigated restrictions on the indices in the consideration of the factorization. L.S. Kazarin proved the solubility of a finite group which is the product of two soluble subgroups of odd index. V.S. Monahov studied the structure of a finite group which is factorized by the factors of prime index. He also studied the structure of a finite group which is factorized by soluble factors of odd index with a number of additional restrictions and without using the theorem on the classification of simple nonAbelian groups.
Keywords: finite group, simple nonabelian group, Frobenius group, factorized group.
N.V. Tyutyanov – Gomel Branch of International University, Gomel, Belarus
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Yakubovich O.V., Dudovskaya Y.E. Multiregime queueing network with random staying time of different types of negative customers
This paper considers an open queueing network with different types of positive, negative customers and multiregime service strategies. Staying time of negative customers in each node is the random value having exponential distribution. Every node can operate in several regimes answering different degrees of their working capacity. The conditions of multiplicativity and an analytical view of stationary distribution of the network states probabilities are found.
Keywords: queueing network, different types of positive, negative customers, multiregime service, stationary distribution.
O.V. Yakubovich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Y.E. Dudovskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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INFORMATION SCIENCE
Bykhautsau V.E., Bondareva V.V., Prokopenko D.V., Torgonskaya S.V. Analytical algorithm of construction and research of the mathematical model of nonlinear deformations of the earth bases of the bases
In the paper soil are considered as nonlineardeformable firm bodies. Law of deformation process corresponds to an approximating curve of parabolic type. Features of approximating function in the present work are used for definition of parameters of the equation of deformation process. The algorithm of construction and research of mathematical model of system of the nonlineardeformable earth basis are developed on the basis of the principle of a minimum of full energy of a system and a power linearization method.
Keywords: deformations soil, nonlinear mathematical models, algorithm of construction and research of models.
V.E. Bykhautsau – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
V.V. Bondareva – Belarusian Trade and Economic University of Consumer Cooperatives, Gomel, Belarus
D.V. Prokopenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
S.V. Torgonskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Erofeenko V.Т., Shushkevich G.Ch., Kuts A.I. Investigation of the composite plane screen properties with impact of a lowfrequency magnetic field
Solution of the boundary problem with nonclassical conditions about lowfrequency magnetic field through planar thinwalled composite screen is given. A computing experiment was carried out and graphs of the secondary magnetic field intensity which is shielded by a composite screen were drawn.
Keywords: lowfrequency magnetic field, composite screen, secondary magnetic field intensity.
V.Т. Erofeenko – Belarusian State University, Minsk, Belarus
G.Ch. Shushkevich – Y. Kupala Grodno State University, Grodno, Belarus
A.I. Kuts – Y. Kupala Grodno State University, Grodno, Belarus
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Sukach E.I., Ratobylskaya D.V., Maslovich S.F., Kamornikova Т.Y. An approach to the assessment of reliability of networks
One of the approaches to the estimation of the probability characteristics of the reliability of networks with two inputs and two outputs is considered. The approach is based on the allocation of probability state security networks, developed as part of the apparatus of probabilityalgebraic simulation and implementing preliminary calculations when assessing the reliability of largescale networks.
Keywords: structurallydifficult system, network reliability, probabilistic reliability assessment.
E.I. Sukach – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
D.V. Ratobylskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
S.F. Maslovich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Т.Y. Kamornikova – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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