
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (40) 2019
PHYSICS
Zhou B., Piliptsov D.G., Jiang X., Kulesh E.A., Rudenkov A.S. Boroncarbon coatings: methods of deposition, structure features and mechanical properties
The main methods of forming coatings based on boron and carbon are considered. The main phase States formed during the synthesis of such coatings are described. Attention is paid to the analysis of the relationship between the structure and mechanical properties. A method and device for deposition of boroncarbon coatings from combined flows of carbon plasma formed by electrospark evaporation of graphite cathode by pulsed arc and boron ions generated by evaporation of the target by pulsed laser radiation is proposed.
Keywords: carbon coatings, doped, boron, microhardness, wear, coefficient of friction.
B. Zhou – Nanjing University of Science and Technology
D.G. Piliptsov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
X. Jiang – Nanjing University of Science and Technology
E.A. Kulesh – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Kulak G.V., Krokh G.V., Nikolaenko Ò.V. Acoustooptical diognostics of ultrasonic lamb waves by the Bessel light beams in gyrotropic sillenite type crystels
It is shown that, for Bessel light beam, it is possible to separately observe isotropic and anisotropic Bragg diffraction of circularly polarized waves on Lamb modes in gyrotropic cubic crystals. In this case, the effective acoustooptical interaction in the transmitted and reflected diffraction orders is realized in a narrow range of layer thickness near the mode cutoff thickness. Of greatest for acoustooptic diagnostics of Lamb modes is the zero mode of a Bessel light beam under the condition of isotropic diffraction of circularly polarized waves with accurate transverse phase synchronism of the diffracted beams.
Keywords: planparallel slab, Lamb's waves, acoustooptical diffraction, gyrotropic cubic crystal, reflection coefficients and transmission coefficients.
G.V. Kulak – I.P. Shamyakin Mozyr State Pedagogical University
G.V. Krokh – I.P. Shamyakin Mozyr State Pedagogical University
Ò.V. Nikolaenko – I.P. Shamyakin Mozyr State Pedagogical University
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Ovsiyuk E.M., Koral'kov A.D. Relativistic particle with spin 1 in presence of Coulomb field, quantum states with minimal angular momentum j=0 in Lobachevsky an Riemann models
Previously, the nonrelativistic problems of a vector particle in the Coulomb field on the background of Lobachevsky and Riemann space models were studied, when a s modified Duffin  Kemmer equation was applied with additional spinorbital interaction, which permitted to get three independent second order differential equations in nonrelativistic Paulilike approximation and obtain three series of energies levels. However, the states with minimal value for quantum number of total angular momentum j=0 were not considered, in the present paper these states are investigated. Conventional and modified Duffin  Kemmer equations provide us with solutions in hypergeometric and transcendental general Heun functions, even without transition to the nonrelativistic limit. These equations lead to slightly different energy spectra. Because the difference between two energy spectra at j=0 turn out to be insignificant, we may expect similar property for states with larger values of j, even though solutions for conventional equation in Pauli approximation are not known.
Keywords: particle with spin 1, Duffin  Kemmer equation, Coulomb potential, minimal values of total angular momentum, Heun equation, exact solution, energy spectrum.
E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University
A.D. Koral'kov – I.P. Shamyakin Mosyr State Pedagogical University
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Semchenko I.V., Khakhomov S.A., Samofalov A.L., Faniayeu I.A., Mikhalka I.S., Song Y., Fan S., Wang J. The development of a doublesided nonreflecting microwaves absorber based on the metamaterials with rectangular omega elements
The paper aims to identify the interaction patterns of the microwaves with the metamaterials, consisting of rectangular omega elements, as well as to develop a onesided and doublesided “ideal” microwave absorber based on such structures.
Keywords: omegaelement, metamaterial, absorber, microwave range, reflection, absorption.
I.V. Semchenko – F. Skorina Gomel State University
S.A. Khakhomov – F. Skorina Gomel State University
A.L. Samofalov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
I.A. Faniayeu – Faculty of Physics and Information Technology, F. Skorina Gomel State University
I.S. Mikhalka – Faculty of Physics and Information Technology, F. Skorina Gomel State University
Y. Song – Nanjing University of Science and Technology
S. Fan – Nanjing University of Science and Technology
J. Wang – Jiangnan University, Wuxi
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Serdyukova M.A., Serdyukov A.N. A massive gravitational field in flat spacetime. II. Conservation laws and gravitational variability of the inertial mass
For a linear massive spinless field adapted as a gaugeinvariant model of gravity in the framework of the special theory of relativity, a canonical energymomentum tensor is constructed and the laws of conservation of energy and momentum are formulated. It is shown that the general requirement of a positive definiteness of the energy density of any physical reality in the case of an attractive field determines its scalar nature and farreaching gravitational variability of the inertial mass of matter particles.
Keywords: spinless massive gravity, gravitational energy, variable mass.
M.A. Serdyukova – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.N. Serdyukov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Serdyukova M.A. A massive gravitational field in flat spacetime. III. Gravitational dependence of radioactive decay
It is shown that a change in the inertial mass of unstable particles (and atomic nuclei) in a scalar gravitational field that occurs as a result of the transfer of part of the rest energy of particles to the field, or, conversely, when their rest energy increases due to accretion of field energy, is accompanied by a change in the rate of radioactive decay. The application of the scalar theory of gravity to the homogeneous universe predicts the secular acceleration of the rate of decay of unstable nuclei and particles in the current era. On a cosmological time scale, this process is confirmed by the observed (1+z)stretching of the light curves of supernovae type Ia afterglow caused by the hard gammaradiation from the decaying unstable 56Ni and 56Co nuclides created by the explosion of accreting white dwarfs.
Keywords: spinless massive gravity, variable mass, radioactive decay.
M.A. Serdyukova – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Timoschenko E.V., Yurevich Yu.V. Estimation of the bistable thinfilm reflector efficiency
The analytical evaluation of the hysteresis reflection properties of a thin layer on the basis of a dense resonant medium on the power scale and the linear frequency detuning of the external signal is carried out. The role of such a resonant reflector as a
Qfactor (compact modulator) of the resonator in the laser circuit is determined.
Keywords: resonant reflection, thin optical films, dense resonant medium, dipoledipolar interaction, quasiresonance polarization.
E.V. Timoschenko – Mogilev State A. Kuleshov University
Yu.V. Yurevich – Mogilev State University of Food Technologies
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Zhao J., Song Y., Wang L., Semchenko I.V., Samofalov A.L. Design of a multilayer structure of a bifilar helical antenna
Based on the design experience of traditional helical antenna and multilayer PCB structure, a multilayer PCB bifilar helical antenna that works in C band is proposed in this paper. The antenna is composed of several symmetrical metal arcs, which are distributed on different layers and connected by plated viaholes. Meanwhile, the design and the simulation results are given in the paper. The results show that the antenna has low profile, circularly polarized radiation and better impedance matching, providing a novel solution for the design of multilayer structure antenna.
Keywords: low profile, bifilar helical antenna, multilayer PCB, circular polarization.
J. Zhao – Nanjing University of Science and Technology
Y. Song – Nanjing University of Science and Technology
L. Wang – Nanjing University of Science and Technology
I.V. Semchenko – F. Skorina Gomel State University
A.L. Samofalov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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MATHEMATICS
Antonevich A.B., Shahava T.R. Rational mnemofunctions on circle
The method of embedding of the space of distributions on the circle into the algebra of mnemofunctions was considered in this paper. The subalgebra of mnemofunctions, generated by rational mnemofunctions, was detached. A complete description of this subalgebra was given. Its generators were singled out, the multiplication rule of distributions in this subalgebra was formulated explicitly.
Keywords: mnemofunction, analytical representation of distribution, algebra of rational mnemofunctions.
A.B. Antonevich – Belarusian State University
T.R. Shahava – Belarusian State University
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Dergacheva I.M., Zadorozhnyuk E.A., Shabalina I.P. On psupersolubility of one class finite groups
The following is proved: A finite group G is psupersoluble if and only if it has a normal subgroup N with psupersoluble quotient G/N such that either N is p'group or p divides N and G:N_{G}(L) equals to a power of p for any cyclic psubgroup L of N of order p or order 4 (if p=2 and a Sylow 2subgroup of N is nonabelian).
Keywords: finite group, pnilpotent group, psupersoluble group.
I.M. Dergacheva – Belarusian State University of Transport
E.A. Zadorozhnyuk – Belarusian State University of Transport
I.P. Shabalina – Belarusian State University of Transport
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Zhogal S.P., Zhogal S.I., Kulyba A.I. Research of the van der Pol oscillator with delayed reflection from load at various types of random effects
Singlefrequency oscillations in a van der Pol selfoscillating system with delays in the feedback circuit and from the reflected load under simultaneous additive and multiplicative random influences are investigated.
Keywords: stochastic differential equations, singlefrequency oscillations, delay, van der Pol oscillator, additive random effects, multiplicative random effects.
S.P. Zhogal – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
S.I. Zhogal – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
A.I. Kulyba – F. Skorina Gomel State University
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Lubochkin A.V. The given motions realization of dynamic systems by bounded optimal controls of linearquadratic problems
The problem of the given motions realization of dynamic systems in the bounded control class is considered. The regulator operation algorithm is constructing with optimal control methods. According to this algorithm, in realtime, the current values of limited feedbacks are calculated (generates), with the help of which the closedloop system stably carries out a given movement. To solve the problem the feedback optimal control realization of linearquadratic problem with restrictions is suggested. The results are illustrated on the problem of dynamic systems synthesis, realizing limited cycles.
Keywords: dynamic system, given motions realization problem, bounded stabilizing feedback, auxiliary optimal control problem, regulator.
A.V. Lubochkin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Mehraliev Ya.T., Alizade U.S. On the problem of identifying a linear source for the thirdorder hyperbolic equation with integral condition
The identification of a linear source for the thirdorder single equation that describes the propagation of longitudinal waves in a dispersive medium with an integral condition of the first kind is investigated. At first, the original problem reduces to an equivalent problem in a certain sense. Using the Fourier method, the equivalent problem is reduced to solving a system of integral equations. With the help of the method of compressed mappings, the existence and uniqueness of the solution of a system of integral equations, which is also the only solution to an equivalent problem, are proved. Using equivalence, it is possible to prove the existence and uniqueness of the classical solution of the original problem.
Keywords: inverse problem, thirdorder equations, Fourier method, classical solution.
Ya.T. Mehraliev – Baku State University
U.S. Alizade – Baku State University
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Monakhov V.S., Trofimuk A.A., Zubei E.V. Finite groups with restrictions on two maximal subgroups
A subgroup A of a group G is called seminormal in G, if there exists a subgroup B such that G=AB and AB_{1} is a proper subgroup of G for every proper subgroup B_{1} of B. We introduce the new concept that unites subnormality and seminormality. A subgroup A of a group G is called semisubnormal in G, if either A is subnormal in G, or is seminormal in G. In this paper we proved the supersolubility of a group G under the condition that all Sylow subgroups of two nonconjugate maximal subgroups of G are semisubnormal in G. Also we obtained the nilpotency of the second derived subgroup (G')' of a group G under the condition that all maximal subgroups of two nonconjugate maximal subgroups are semisubnormal in G.
Keywords: supersoluble groups, semisubnormal subgroup, derived subgroup, Sylow subgroup, maximal subgroup.
V.S. Monakhov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
A.A. Trofimuk – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
E.V. Zubei – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Murashka V.I. Generalized rank composition formations of finite groups
Starovoitov A.P., Ryabchenko N.V., Drapeza A.À. On the existence and uniqueness of type I Hermite – Pade polynomials
New concepts are introduced in the work.They are quite normal index and a quite perfect system of functions. Using these concepts, a uniqueness criterion was formulated and proved, explicit determinant representations of type I Hermite – Pade polynomials for an arbitrary system of power series were obtained. The results obtained complement and generalize the wellknown result in the theory of Hermite – Pade approximations.
Keywords: HermitePade polynomials, normal index, perfect system, Hadamard determinant, Hankel determinant.
A.P. Starovoitov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
N.V. Ryabchenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
A.À. Drapeza – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Tyutyanov V.N. Simple nonabelian groups with second maximal pronormal subgroups
V.I. Zenkov put in the Kourovskaya notebook the following problem 19.109: is it true that in a nonabelian finite simple group G all maximal subgroups are Hall subgroups if and only if every second maximal subgroup is pronormal in G? This paper shows that this problem is solved negatively.
Keywords: finite group, second maximal subgroup, pronormal subgroup.
V.N. Tyutyanov – International University MITSO, Gomel
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Hu B., Huang J., Skiba A.N. Finite groups with given local sections
A group is called primary if it is a finite pgroup for some prime p.
If is some partition of that is,
and for all then we say that a finite group G is:
primary if it is a
group for some i;
nilpotent if for some
primary groups
If for some primary nonidentity subgroup A of G, then we say that
is a local section of G. In this paper, we study a finite group G under hypothesis that all proper local sections of G belong to a saturated hereditary formation and we determine the normal structure of G in the case when all local sections of G are nilpotent.
Keywords: finite group, hereditary saturated formation, hypercentre, local section, nilpotent group.
B. Hu – Jiangsu Normal University, Xuzhou
J. Huang – Jiangsu Normal University, Xuzhou
A.N. Skiba – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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INFORMATION SCIENCE
Glubokov A.V., Zhadan M.I., Berezovskaya E.M. Web service of the automated design and calculation of the bases
The automated design and calculation of various types of the bases of a small depth are presented. The change under loading of physicomechanical characteristics of soil of the bases is considered. The created application allows making calculations, according to the norms and rules of Construction Norms and Regulations. For writing of web service the framework of Spring and architectural style of programming of REST are used. Interaction of the user with web service is realized through the client application on the basis of the JavaFX technology.
Keywords: base, soil, layers, levels, buildings and constructions, loadings, diagnostics, report, design.
A.V. Glubokov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
M.I. Zhadan – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
E.M. Berezovskaya – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Taranchuk V.B. Tools and examples of intelligent data processing for geological models
The problems of development, tool filling, and usages of the integrated program complex of the composer of digital geological models are considered. Possibilities of interactive graphics visualization and comparison of results are marked. The results of application of artificial neural networks in the analysis and interpretation of geospatial data are presented and discussed.
Keywords: digital geological model, Computer Algebra System Mathematica, interactive graphics visualization, artificial neural network.
V.B. Taranchuk – Belarusian State University, Minsk
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