
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N2 (19) 2014
PHYSICS
Andreev V.V. Calculation of Feynman diagrams using the blocks technique
A technique for calculating matrix elements of elementary particles interaction reactions using the “building” blocks (basic elements of Feynman diagrams) method is presented. In this approach, the matrix element is reduced to basic matrix elements involving basis spinors. Such blocks are calculated in advance using the Method of Basis Spinors (MBS) and then used for further calculations.
Keywords: basis spinor, Feynman diagram, Dirac matrix, fermion.
V.V. Andreev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Grishechkin Yu.A., Kapshai V.N. Relativistic scattering problem for twoparticle systems with oneboson exchange potentials
Numerical solutions of quantum field theory equations describing scattering sstates of two scalar particles are found in cases of a oneboson exchange potential and the Yukawa potential. Scattering amplitudes, scattering lengths and phase shifts are calculated on the basis of the solutions obtained. It is shown that the scattering amplitudes found satisfy a unitarity condition. The comparison of the results obtained in this simple model with experimental data for neutronproton systems is carried out.
Keywords: twoparticle equations, relativistic configurational representation, oneboson exchange potential, scattering amplitude, scattering length, phase shift, composite Gaussian quadrature, deuteron.
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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Shmatok E.V., Ostrikov O.M. Calculation of stresses and displacements in Ni_{2}MnGa have lenticular twin using tetrafunctional model with a continuous distribution of twinning dislocations at the twin boundaries
Dislocation model was developed for the calculation of the stressstrain state in a double lenticular. The model is suitable for use in the case of complex shape of the twin boundaries. Displacement fields and internal stresses caused by double lenticular in Ni_{2}MnGa were calculated on the based of the model in the approximation of a continuous distribution of twinning dislocations at the twin boundaries. It was found that stress is localized at the twin boundaries, and can be observed within the twin compensation voltages.
Keywords: twinning, dislocations, stress fields.
E.V. Shmatok – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus
O.M. Ostrikov – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus
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Shushkevich G.Ch., Shushkevich S.V., Kiseleva N.N. Penetration of the sound field of à spherical radiator through the spherical elastic shell
The analytical solution of a boundary problem, describing the process of penetration of the sound field of a spherical radiator, located inside a thin unclosed spherical shell, through the elastic spherical shell is developed. Influence of some parameters of a 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
S.V. Shushkevich – Y. Kupala Grodno State University, Grodno, Belarus
N.N. Kiseleva – Y. Kupala Grodno State University, Grodno, Belarus
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MATHEMATICS
Borodich R.V., Borodich E.N., Selkin M.V. On intersection of maximal subgroups of the set indexes in groups with operators
In the paper the properties of intersection of maximal subgroups in groups with the operators are studied.
Keywords: maximal subgroup, formation, residual, group of operators.
R.V. Borodich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
E.N. Borodich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
M.V. Selkin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Vasil'eva T.I., Prokopenko À.I. On the construction of
Schunk classes of finite soluble groups
Veliasnitski V.F. On supersoluble groups
The characterization of supersolvable groups with generalized subnormal subgroups is given.
Keywords: formation, Sylow subgroup, soluble group, critical subgroup, Frattini subgroup, generelized subnormal subgroup.
V.F. Veliasnitski – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Gal'mak A.M., Shchuchkin N.A. Cyclic nary groups and their generalizations
The authors define and study msemicyclic nary groups for any divisor m–1 of natural number
n–1. The class of all msemicyclic nary groups is included in the class of all msemiabelian
nary groups identified by E. Post. Moreover, the class of all msemicyclic nary groups includes the class of all cyclic nary groups and belongs to the class of all semicyclic nary groups. New criteria of cyclicity
for nary group and for msemicyclicity of nary group formulated by one of the subgroups of the universal covering group of Post are determined.
Keywords: nary group, cyclic group, semicyclic group, msemicyclic group.
A.M. Gal'mak – Mogilev State University of Food Technologies, Mogilev, Belarus
N.A. Shchuchkin – Volgograd State SocioPedagogical University, Volgograd, Russia
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Gritsuk D.V. Derived length of a
solvable group in which the Sylow psubgroups are either bicyclic or of order
p^{3}
Kovaleva V.A., Yi Xiaolan. Finite groups with all nmaximal
(n=2,3) subgroups subnormal
A full classification of finite groups with all nmaximal (n=2,3) subgroups
subnormal is given.
Keywords: subnormal subgroup,
subnormal subgroup, supersoluble group, minimal nonsupersoluble group, SDHgroup.
V.A. Kovaleva – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Xiaolan Yi – Zhejiang SciTech University, Hangzhou, China
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Myslovets E.N. On finite groups
INFORMATION SCIENCE
Demidenko Î.Ì., Sukach E.I., Ratobylskaya D.V., Zherdetsky Y.V. The reliability analysis of electric power systems based on the probabilisticalgebraic simulation
The application of probabilisticalgebraic simulation is proposed to use in the control of the electropower systems. The technique estimates the probabilistic characteristics of the reliability of the power grid structures including many elements with probabilistic reliability parameters.
Keywords: structurallydifficult system, network reliability, power systems.
O.Ì. Demidenko – F. Skorina Gomel State University, Gomel, Belarus
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
Y.V. Zherdetsky – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Maslovich S.F., Halushko V.N., Bakhur S.V. Mathematical simulation parameters of reliability and energy consumption
The idea of creating software and statistical tools, with which you can simulate, analyze and take decisions to reduce the impact vibrations, voltage unbalance, frequency deviations in the electrical network and higher reliability of electric facilities and systems is considered.
Keywords: mathematical simulation, reliability, power consumption, electrics, electrical schema.
S.F. Maslovich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
V.N. Halushko – Belarusian State University of Transport, Gomel, Belarus
S.V. Bakhur – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus
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Melnikau I.A., Demedenkov K.A., Yeuseyenka I.A. Automation of the traffic flow data collection and analysis process to avoid traffic congestions in Mogilev
The analysis of commonly used traffic detectors and advantages and disadvantages of optical traffic detectors (IPcameras) is given. The model of the traffic flow data collection and analysis automation system and the method of modification of the MultiLayer Background Subtraction algorithm using parallel computing based on the graphic processors are suggested. The experimental investigations show that the modified method can help to decrease video frame processing speed in 1.9 times.
Keywords: traffic flow, traffic detector, traffic density, traffic flow intensity, MultiLayer Background Subtraction algorithm.
I.A. Melnikau – BelarusianRussian University, Mogilev, Belarus
K.A. Demedenkov – BelarusianRussian University, Mogilev, Belarus
I.A. Yeuseyenka – BelarusianRussian University, Mogilev, Belarus
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Shevchenko D.N., Krivenkov S.V. Technique of the testing and use of generator of pseudorandom sequences
The existing approaches to software testing of pseudorandom sequences, their advantages and disadvantages are reviewed. The methods for testing multiple generators in order to select one of them for use in a certain subject area is offered. Some results of testing famous generators for the numerical integration by Monte Carlo method are shown.
Keywords: random number generator, pseudorandom number sequences, Monte Carlo method, testing of pseudorandom sequences.
D.N. Shevchenko – Belarusian State University of Transport, Gomel, Belarus
S.V. Krivenkov – Belarusian State University of Transport, Gomel, Belarus
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TECHNICS
AlDilami Ahmed A., Vrublevsky I.A., Chernyakova K.V., Pykhir G.A. Absorption of energy of electromagnetic radiation in interference insulated structures with nanoporous alumina
Transmittance and reflectance spectra of electromagnetic radiation by doublelayer interference structures made of lithium niobate plate and naporous alumina membrane with evaporated thin nichrome film were studied. In the quarterwave range the effect of nichrome film thickness on reflective characteristics of the proposed doublelayer interference structures was also established in the frequency range of 8–12 HGz.
Keywords: electromagnetic radiation, resonant absorption, reflection coefficient, multilayer interference structure, nanoporous alumina.
Ahmed A. AlDilami – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
I.A. Vrublevsky – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
K.V. Chernyakova – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
G.A. Pykhir – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
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