
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N2 (31) 2017
PHYSICS
Akhramenko N.A. Gravitational defect of massive ball
The resulting expression defining the gravitational mass defect of massive ball is given. It is shown that the gravitational mass defect increases with increasing density and the mass of the ball. The resulting ratio is a generalization for magnitudes of the gravitational mass defect in the nonrelativistic case.
Keywords: theory of gravitation, massive ball, gravitational mass defect.
N.A. Akhramenko – Belarusian State University of Transport, Gomel
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Girgel S.S. Generalized asymmetric of Bessel – Gaussian beams of the continuous order
The new solutions of the parabolic equation featuring the generalized asymmetric of Bessel – Gaussian beams of the continuous order are offered. They are characterized by five free continuous parametres and possess a spiral wavefront. Restrictions on these parametres at which explored fractional beams transfer terminating power are discovered. Pictorial modeling of such beams which confirms the main analytical calculations is fulfilled.
Keywords: asymmetric beams, beams of Bessel – Gaussian, a square intergrability.
S.S. Girgel – Department of Physics, F. Skorina Gomel State University
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Grishechkin Yu.A., Kapshai V.N., Danilchenko M.S. Relativistic bound sstates problem for superposition of two potentials «sphere» type
The exact solutions of relativistic twoparticle quasipotential type equations for bound states in the case of the potential «sphere» in the relativistic configuration representation and in the case of the superposition of two such potentials are considered. The signs of the coefficients in the potentials that allow the existence of bound states and the maximum possible number of this states are defined on the basis of the analysis of the energy quantization conditions.
Keywords: relativistic twoparticle equation, relativistic configurational representation, deltafunction potential, bound state, energy quantization condition.
Yu.A. Grishechkin – Department of Physics, F. Skorina Gomel State University
V.N. Kapshai – Department of Physics, F. Skorina Gomel State University
M.S. Danilchenko – Department of Physics, F. Skorina Gomel State University
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Kalosha L.A., Gaida L.S., Komar V.N., Zaerko D.V. Modeling of dielectric gratings to control the redistribution of energy in the spectrum of the scattered microwave optical and electromagnetic fields
The choice of the periodic structures based on hollow dielectric rods with filling, which offer the possibility to vary the dielectric constant is considered. The simulation results obtained for scattering of microwave and optical ranges electromagnetic radiation in equidistant structures based on dielectric rods with variable electrophysical parameters are given. The effect of variations in the dielectric constant of the structural components on the energy redistribution of harmonics of the scattered electromagnetic radiation is demonstrated.
Keywords: periodic dielectric structures, dielectric constant, sparameter changes, control of the propagation characteristics of microwave and optical ranges electromagnetic radiation.
L.A. Kalosha – Grodno State College of Engineering, Technology and Design
L.S. Gaida – Y. Kupala Grodno State University
V.N. Komar – Y. Kupala Grodno State University
D.V. Zaerko – Y. Kupala Grodno State University
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Rudenkov A.S., Rogachev A.V., Piliptsov D.G., Xiaohong Jiang, Fedosenko N.N. Influence of carbideforming metals nature on the phase composition and structure of alloyed carbon coatings
Structuralphase features of carbon coatings deposited from impulse cathode plasma doped with titanium and chromium are determined. It is established that metalcontaining formations with an average size of 40..90 nm are formed in the volume of an amorphous carbon matrix during electric arc evaporation of metals. The introduction of chromium into the carbon matrix leads to an increase in the content of carbon atoms in the sp^{3} state, doping the same carbon coating with titanium helps reduce the number of atoms with sp^{3} hybridization, increase in the size and ordering of Csp^{2} clusters.
Keywords: carbon coatings, alloyed, titanium, chromium, phase composition, morphology.
A.S. Rudenkov – Department of Physics, F. Skorina Gomel State University
A.V. Rogachev – Department of Physics, F. Skorina Gomel State University
D.G. Piliptsov – Department of Physics, F. Skorina Gomel State University
Xiaohong Jiang – Nanjing University of Science and Technology
N.N. Fedosenko – Department of Physics, F. Skorina Gomel State University
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MATHEMATICS
Belokon L.M. Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup mfunctor
Bin Hu, Jianhong Huang, Skiba A.N. Finite groups whose nmaximal subgroups are generalized Squasinormal
Dergacheva I.M., Shabalina I.P., Zadorozhnyuk E.A. A criterion for a finite group to belong a saturated formation
Zhogal S.P., Zhogal S.I., Klimenko A.V. On existence and uniqueness of solutions of one complex stochastic differential system with delay
Problems of the existence and uniqueness of solutions of systems of differential equations containing a stochastic differential equation in partial derivatives of hyperbolic type and ordinary stochastic differential equations with delay connected with each other by retarded connections are investigated.
Keywords: stochastic differential equations, delay, stochastic partial differential equations, units with lumped parameters, units with distributed parameters.
S.P. Zhogal – F. Skorina Gomel State University
S.I. Zhogal – Belarusian State University of Transport, Gomel
A.V. Klimenko – F. Skorina Gomel State University
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Kovaleva V.A. Finite groups with given generalized maximal subgroups (Review). II. From the maximal chains to the maximal pairs
Let G be a finite group. Recall that a maximal chain of G of length n is a chain such that
is a maximal subgroup of
for every
In this review we continue the analysis of the most famous papers in which finite groups with given maximal chains are developed.
Keywords: finite group, maximal chain, nmaximal subgroup, maximal pair of subgroups.
V.A. Kovaleva – Department of Mathematics, F. Skorina Gomel State University
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Semenchuk V.N., Selkin M.V., Selkin V.M. On finite groups with generalized subnormal subgroups
The structure of finite groups with subnormal subgroup is studed.
Keywords: finite group, subnormal subgroup, saturated formation, hereditury formation.
V.N. Semenchuk – Department of Mathematics, F. Skorina Gomel State University
M.V. Selkin – Department of Mathematics, F. Skorina Gomel State University
V.M. Selkin – Department of Mathematics, F. Skorina Gomel State University
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Sidortsov M.V., Drapeza A.A., Starovoitov A.P. Asymptotics of Hermite – Pade degenerate hypergeometric functions
The asymptotic behavior of diagonal Hermite – Pade polynomials and diagonal Hermite – Pade approximations of type II for the system
consisting of degenerate hypergeometric functions in which while the rest
are the roots of the equation
– is a complex number belonging to the set
was stated. The theorems complement known results of H. Pade, D. Braess, A.I. Aptekarev, H. Stahl, F. Wielonsky, W. Van Assche, A. B. J. Kuijlaars, A.P. Starovoitov, obtained for the case, where the – different real numbers.
Keywords: Hermite integrals, Hermite – Pade polynomials, Hermite – Pade approximations, asymptotic equality, degenerate hypergeometric functions.
M.V. Sidortsov – Department of Mathematics, F. Sñorina Gomel State University
N.A. Starovoitova – F. Sñorina Gomel State University
A.P. Starovoitov – Department of Mathematics, F. Sñorina Gomel State University
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Yakubovich O.V., Letunovich Y.E., Evdokimovich V.E. Open queueing network with quarantine node
An open Markov queueing network with quarantine node is considered. Customers arrive in usual exponential nodes and are verified for standard. If a customer does not comply with the standard it is sent to the quarantine node, where its quality is restored. After that the customer continues to move through the network. The conditions of ergodicity and an analytical view of stationary distribution of the network states probabilities are found.
Keywords: queueing network, quarantine node, ergodicity, stationary distribution.
O.V. Yakubovich – Department of Mathematics, F. Sñorina Gomel State University
Y.E. Letunovich – Department of Mathematics, F. Sñorina Gomel State University
V.E. Evdokimovich – Belarusian State University of Transport, Gomel
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Yarovaya A.V. Forced vibrations of circular sandwich plates under local suddenly applied loads
Axisymmetric transverse vibrations of a circular elastic threelayer plate under the influence of local surface, force and torque loads are considered. The hypothesis of a broken normal is accepted for the kinematics description of asymmetrical on the thickness of package. Kirchhoff's hypotheses are valid in the carrier layers. In a comparatively thick lightweight aggregate, the normal remains straight, but rotates by some additional angle. Analytical solutions are obtained by expanding the series in terms of a system of proper orthonormal functions. Their numerical analysis is made.
Keywords: threelayer circular plate, axisymmetric vibrations, local suddenly applied loads.
A.V. Yarovaya – Belarusian State University of Transport, Gomel
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INFORMATION SCIENCE
Listopad N.I., Vorotnitsky Y.I., Bortnovsky V.V., Hayder A.A. Multicriterial routing of information flows
Traditionally, path selection within routing is formulated as the shortest path optimization problem. In this paper, multicriteria routing based on a mixed weight is considered. It is shown how this approach can be used to develop two heuristic algorithms for searching the optimal path with minimum delay, minimum delay variation, providing the given bandwidth, minimum loss probability and minimum cost of information transmission.
Keywords: multicriteria routing, mixed weight, delay, delay variation, loss probability, bandwidth, shortest path, Dijkstra’s Algorithm, cost of information transmission.
N.I. Listopad – Belarusian State University of Informatics and Radioelectronics, Minsk
Y.I. Vorotnitsky – Belarusian State University, Minsk
V.V. Bortnovsky – Belarusian State University of Informatics and Radioelectronics, Minsk
A.A. Hayder – Belarusian State University of Informatics and Radioelectronics, Minsk
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Sokolov A.V., Tsevukh I.V. On the existence of binary Ccodes of length N = 32 with a predetermined value of papr of Walsh – Hadamard spectrum
The spectral classification of sequences of length N = 32 in accordance with the structure and the value of the PAPR (PeaktoAverage Power Ratio) of Walsh – Hadamard spectrum resulting in 40 different spectral sets was performed. The maximal achievable cardinality of Ccodes with a predetermined value of PAPR was calculated. Taking into account the interconnection between PAPR value of the Walsh – Hadamard spectrum and nonlinearity distance of binary sequence of length N = 32, the cardinalities of classes of sequences with a determined value of nonlinearity distance were found.
Keywords: Walsh – Hadamard transform, PAPR, nonlinearity distance.
A.V. Sokolov – Odessa National Polytechnic University
I.V. Tsevukh – Odessa National Polytechnic University
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