
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (12) 2012
PHYSICS
Belyi V.N., Kramoreva L.I., Petrova E.S., Khilo N.A., Savitski A.I. Features of energy flux distribution under the condition of quasi–nondiffraction light beams propagation in absorbing media
Interaction of the quasinondiffraction beam with semiinfinite medium has been investigated. It has been shown that in case when we deal with absorbing medium, new features of energy flux behavior and the spatial profile of heat generation occurre. Such behavior of energy flux isn’t typicall for plane wave or Gaussian beam. The combination of the detected features, suppressed diffraction divergence of beam, selfreconstruction phenomenon is of interest of laser technologies and diagnostics.
Keywords: quasinondiffraction beam, semiinfinite medium, energy flux, heat generation region.
V.N. Belyi – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
L.I. Kramoreva – Gomel State Medical University, Gomel, Belarus
E.S. Petrova – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus
N.A. Khilo – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
A.I. Savitski – Gomel State Medical University, Gomel, Belarus
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Valko N.G., Hurtavy V.G. The electrical properties of the alloys CoNi, electroplated under the influence of the Xray irradiation
Basic laws governing of the forming of the electroplated films CoNi under the influence of Xray irradiation are presented. The dependences of the electrical properties from electrolysis conditions are discovered. The reasons for the change of the resistivity in the films CoNi obtained under irradiation, caused by the change in the morphology of surface, element composition, by the decrease of porous in the coating and by the increase in the speed of electrodeposition under the effect of X rayirradiation are considered.
Keywords: Xray irradiation, electroplated films, Co Ni alloys, resistivity.
N.G. Valko – Y. Kupala Grodno State University, Grodno, Belarus
V.G. Hurtavy – Sctantific and Practical Materials Research Center of NAS of Belarus, Minsk, Belarus
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Girgel S.S. Polarizable and energy properties of the vector paraxial gaussian light beams
Polarization and energy flux density of an electromagnetic field for the vector paraxial Gaussian light beams with the homogeneous and nonhomogeneous polarization of various types are discovered and explored. Some new types of the vector paraxial Gaussian light beams, for example, beams with spiral elliptic polarization are featured.
Keywords: paraxial beams, vector beams, light beams, Gaussian beams, polarizable properties, energy properties, nonhomogeneous polarization.
S.S. Girgel – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Esman A.K., Kuleshov V.K., Zykov G.L., Zalesski V.B. Absorbing coating in the terahertz part of spectrum
Absorption of electromagnetic radiation in the frequency range of 35 to 55 THz by the multilayer coating, in which the top layer contains an array of pyramids arranged in a strictly geometric pattern in two mutually perpendicular directions is investigated. It is shown that the proposed structure provides a return loss better than 39.5 dB at the resonance frequency of 42.3 THz and a change of temperature of the sensitive layer of 3 mK at the input power density of radiation of 0.1 W/m^{2}.
Keywords: absorbing structure, multilayer coating, the array of pyramids, thermal sensitivity.
A.K. Esman – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
V.K. Kuleshov – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
G.L. Zykov – 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
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Zazhogin A.P., Umreiko D.S., Zazhogin A.A., Komyak A.I., Umreiko S.D. Spectralstructural and photocatalytic properties of wateracetone solutions of uranyl nitrate and perchlorate
Luminescence and absorbance spectra of uranyl nitrate and perchlorate solutions in water and some organic solvents such as acetone and acetonitrile have been studied. Distinction of the emerging structures is defined depending on the position of the shortwave band which is assigned to purely electronic transition. The possible explanation of the adherent processes is given. In addition, acetone polymerization resulted from uranyl UO_{2}^{2+} excited ions, serving as a catalyst, is found.
Keywords: luminescence and absorption spectra, structure, uranyl nitrate, uranyl perchlorate, acetone, photochemistry.
A.P. Zazhogin – Belarusian State University, Minsk, Belarus
D.S. Umreiko – A.N. Sevchenko Institute of Applied Physics Problems, Minsk, Belarus
A.A. Zazhogin – Belarusian State University, Minsk, Belarus
A.I. Komyak – Belarusian State University, Minsk, Belarus
S.D. Umreiko – Belarusian State University, Minsk, Belarus
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Piliptsov D.G., Rogachev A.V., Fedosenko N.N., Rudenkov A.S. Morphology and mechanical properties of carbon coatings obtained from plazma of combined pulse cathodearc discharge
The PVD method of formation of carbon coatings from plasma of pulse cathodearc discharge was proposed. The character of the influence of the parameters of discharge on the growth rate and morphology of carbon coatings was states.
Keywords: carbon coating, pulse cathodearc discharge, morphology, growth rate.
D.G. Piliptsov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.V. Rogachev – Rector of F. Skorina Gomel State University, Gomel, Belarus
N.N. Fedosenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.S. Rudenkov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Serdykov A.N., Shalupaev S.V., Nikitjuk Y.V., Sereda A.A. Process research of laser splitting silicon wafers cutout in the plane (110)
Results of laser thermosplitting process modelling of singlecrystalline silicon are presented. Calculation of the thermoelastic fields formed in a silicon plate as a result of consecutive laser heating and coolant influence was carried out for a section (110) in three different variants of laser beam movement, namely in directions [1–10], [001], [1–11].
Keywords: crack, laser splitting, silicon wafer.
A.N. Serdykov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
S.V. Shalupaev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Y.V. Nikitjuk – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.A. Sereda – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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MATHEMATICS
Adarchenko N.M. On maximal subgroups of finite groups
Akhmatova A.A. On spectral properties of weighted shift operators generated by linear mappings with Perron’s conditions
Vitko E.A. On the structure of the smallest element of the Lockett section of a soluble fitting functor
Dashkova O.Yu. Locally soluble AFNgroups
Let A be an RGmodule, where R is a commutative noetherian ring with the unit, G is a locally soluble group, and each proper subgroup H of a group G for which is not a noetherian Rmodule, is finitely generated. It is proved that a locally soluble group G with these conditions is hyperabelian. It is described the structure of a group G under consideration if is a finitely generated soluble group and the quotient module is not a noetherian Rmodule.
Keywords: group ring, locally soluble group, noetherian Rmodule.
O.Yu. Dashkova – O. Honchar Dnepropetrovsk National University, Dnepropetrovsk, Ukraine
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Zarenok M.A. Convergence of the Fourier series for differentiable functions of a multidimensional padic argument
This article discusses the convergence of the Fourier series for functions of the multidimensional padic argument. For this purpose we define the multidimensional Mahler function and partial sums of Fourier series for the functions of multidimensional padic argument. We calculate the norm of the m th derivatives of multidimensional Mahler functions and prove the criterion of m times continuously differentiability in terms of Mahler coefficients. We represent coefficients and partial sums of multidimensional Fourier series in terms of coefficients and partial sums of onedimensional Fourier series. The main result states that for positive integers the Fourier series for function converges uniformly. An example of with divergent Fourier series is given.
Keywords: function of multidimensional padic argument, Fourier series, Fourier coefficients, Mahler function.
Zarenok Maxim – Department of Mechanics and Mathematics, Belarussian State University, Minsk, Belarus
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Kovalyova V.A., Zhao Xiaoyu. Finite groups with given systems of quasipermutable subgroups
Let G be a finite group. A subgroup A of G is said to be quasipermutable in G if A either covers or avoids every maximal pair (K,H) of G. We study the finite groups with given systems of quasipermutable subgroups.
Keywords: finite group, maximal pair, (weakly) quasipermutable subgroup, generalized Fitting subgroup, pnilpotent group, hypercentre.
V.A. Kovalyova – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Zhao Xiaoyu – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Kosenok N.S. Finite groups with given generalized primitive subgroups
A new criterion for supersolubility of finite groups has been found.
Keywords: primitive subgroups, finite group, soluble group, supersoluble group, subnormally primitive subgroup, normally primitive subgroup.
N.S. Kosenok – Belarusian Trade and Economics University of Consumer Cooperatives, Gomel
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Kuzmenkov D.S. Parallelization of the calculations at the solution of the optimal control problem of a thermal process in the rod
The optimal control problem of a thermal process in the rod with the heat exchange on one of its ends is considered in the article. It’s reduced to the optimal control problem of the special largescale differential equations system. This problem is solved by a method of quasidecomposition. The algorithm of the operation of the optimal regulator which forms current values of the optimal feedback in real time is described. The numerical example illustrating the use of the quasidecomposition method is brought.
Keywords: thermal process, optimal control problem, method of quasidecomposition, optimal feedback, optimal regulator.
D.S. Kuzmenkov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Polevikov V.K., Volotovskaya Y.N. Numerical modeling of equilibrium capillary surfaces with irregular boundary conditions
The algorithm for numerical modeling of equilibrium capillary surfaces with irregular contact conditions is presented. It is a combination of an iterationdifference method to solve the boundaryvalue problem and a RungeKutta method to solve the initialvalue problem for modeling of equilibrium shapes of a capillary surface in contact with the fracture line of a solid wall. The algorithm is approved on the wellknown problem of capillary hydrostatics about fluid flowing out of the capillary.
Keywords: capillary surface, parametric differential equations, irregular boundary conditions, numerical modeling, computational algorithm, numerical results.
V.K. Polevikov – Belarusian State University, Minsk
Y.N. Volotovskaya – Belarusian State University, Minsk
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Tyutyanov V.N., Tyutyanova V.A. A nonsimple criterion for finite factorized groups
In the study of factorizable groups the authors consider some natural restrictions on the factors. Ito Theorem about twostep solubility of a finite group which is factorized by abelian subgroups, and KegelWielandt Theorem about solubility of a finite group which is a product of two nilpotent subgroups are the classical examples in this trend. We should also note that L.S. Kazarin have obtained validity of the hypothesis of S.A. Chunikhin about nonsimplicity of a finite group which is factorized by subgroups with nontrivial center.
Keywords: finite group, simple nonabelian group, factorized group.
N.V. Tyutyanov – International Institute of Labor and Social Relations, Gomel
V.A. Tyutyanova – International Institute of Labor and Social Relations, Gomel
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INFORMATION SCIENCE
Smorodin V.S. Analysis of the technological processes functioning with the elements of potential danger
The technique analysis of reliability of probabilistic production systems allowing to define the parameters of the technological operations providing a given level of reliability of the technological cycle. The implementation of the procedure for the assessment of probability values of the parameters of reliability of the components production system to ensure optimal variants of the structure of the technological cycle within specified criterion of the quality evaluation of the technological cycle is proved to be of exceptional practical significance.
Keywords: reliability analysis, state space, estimation of parameter values, structure of the technological cycle.
V.S. Smorodin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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TECHNICS
Vrublevsky I.A., Dick S.K., Tereh A.S., Smirnov A.V., Chernyakova K.V. Structure of the porous aluminium oxide films formed in the solutions of organic acids
The study deals with the experimental results of the peculiarities of the anodic growth of the porous aluminium oxide films formed in aqueous solutions of oxalic and malonic acids. The results obtained show that during galvanostatic aluminum anodizing in 0.3 M and 0.8 M solutions of oxalic and malonic acids, the films with regular porous structure are formed. Aluminum anodizing in the solutions of malonic and tartaric acids leads to the forming of the porous films with interporous spacing in the range of 90–270 nm.
Keywords: aluminium oxide, oxalic acid, malonic acid, porous film.
I.A. Vrublevsky – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
S.K. Dick – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
A.S. Tereh – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
A.V. Smirnov – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
K.V. Chernyakova – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
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