
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N1 (42) 2020
PHYSICS
Amanova M.A., Naunyka V.N., Shepelevich V.V. Study of twowave interaction on a mixed reflective hologram in a (001) cut Bi_{12}TiO_{20} crystal
The regularities of amplification of subject wave for contra directional twowave interaction on a volume reflection mixed hologram formed in a cubic optically active photorefractive piezocrystal are studied. The dependence of the relative intensity of the object light wave on the input azimuths of the linear polarization of the reference and subject waves during their simultaneous diffraction by a mixed reflection hologram in a Bi_{12}TiO_{20} (BTO) crystal is analyzed. The polarization condition for achieving the maximum relative intensity of the subject wave for mixed reflection hologram is established. It is shown that the conditions for achieving the maximum relative intensity of the subject wave for phase and mixed reflection holograms are highly different.
Keywords: mixed hologram, twowave interaction, relative intensity of the subject wave, polarization azimuth, optical activity.
M.A. Amanova – I.P. Shamyakin Mozyr State Pedagogical University
V.N. Naunyka – I.P. Shamyakin Mozyr State Pedagogical University
V.V. Shepelevich – I.P. Shamyakin Mozyr State Pedagogical University
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Villa N., Golosov D.A., Melnikov S.N., Nguyen T.D., Golosov A.D., Litvin E.E., Lam N.N. Formation of tantalum oxide films on substrates with a diameter of 200 mm
As a result of studies of the processes of reactive magnetron sputtering of a Ta target in an Ar/O_{2} working gas mixture, it is found that the formation of dielectric films is observed at the concentration of O_{2} higher than 50% and it is determined by the enthalpy of oxide formation from the source metal. The use of highvacuum sputtering allows stabilizing the process without the use of feedback systems. It is shown that when depositing tantalum oxide films on a diameter of 200 mm rotating substrate, it is possible to obtain layers with a thickness nonuniformity of less than ±2.4%, a capacitance and dielectric loss tangent nonuniformity of less than ±18%.
Keywords: tantalum oxide, thin films, reactive magnetron sputtering, MOS structure, dielectric properties.
N. Villa – Belarusian State University of Informatics and Radioelectronics, Minsk
D.A. Golosov –Belarusian State University of Informatics and Radioelectronics, Minsk
S.N. Melnikov – Belarusian State University of Informatics and Radioelectronics, Minsk
T.D. Nguyen – Belarusian State University of Informatics and Radioelectronics, Minsk
A.D. Golosov – Belarusian State University of Informatics and Radioelectronics, Minsk
E.E. Litvin – Belarusian State University of Informatics and Radioelectronics, Minsk
N.N. Lam – Belarusian State University of Informatics and Radioelectronics, Minsk
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Voynova Ya.A., Ovsiyuk E.M. On the manifestation of the cosmological curvature of space in a model of a neutral fermion with three mass parameters
In this work a generalized fermion model with spin 1/2, which is characterized by three physical mass parameters M_{i} are studied. The additional interaction is determined by the tensor of the external electromagnetic field and the scalar spacetime curvature. It joints three bispinors into one physical system. The model also remains valid for neutral Majorana fermions. The coupling of three bispinors into a single system is ensured by the nonzero scalar curvature of the spacetime. We study a model situation where it can be assumed that locally the use of Cartesian coordinates is permissible, and the external geometric background can be effectively taken into account by a constant Ricci curvature R. For simplicity, we restrict ourselves to the onedimensional case (t,x). Using the diagonalization of the mixing matrix in a complex system of equations, we reduce the problem to three separate Diractype equations with new effective masses
M_{i} the values of which are determined numerically depending on the internal parameter of the model and the spacetime curvature. A numerical analysis of the necessary diagonalizing transformations S and S^{–1} is given. The solutions of three separate equations of the Majorana type are constructed in the momentum–helicity basis. Using the expression for the transformation matrices S and S^{–1}, these solutions are decomposed into linear combinations by solutions with physical masses and vice versa.
Keywords: fermion with three mass parameters, Majorana particle, of spacetime scalar curvature, Dirac equation
Ya.A. Voynova – B.I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
E.M. Ovsiyuk – I.P. Shamyakin Mozyr State Pedagogical University
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Deryuzhkova O.M., Parakhnevich A.S., Revenok M.A. Shape and size parameters of deformed nuclei obtained on the basis of the assessed nuclear data
The parameters of the quadrupole and axial deformations of lead isotopes with the nucleons number A=178–215 have been studied in the Nilsson model, which is a combination of the collective model and the modified model of nuclear shells. The analysis of experimental information is carried out using the database «Map of the shape and size parameters of the nuclei».
Keywords: nuclei deformation, quadrupole moment, shape and size parameters of nuclei, singleparticle and collective levels, lead isotopes.
O.M. Deryuzhkova – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.S. Parakhnevich – Faculty of Physics and Information Technology, F. Skorina Gomel State University
M.A. Revenok – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Esman A.K., Zykov G.L., Potachits V.A. Thinfilm solar cell with a thermoelectric layer
One of the economically viable solutions of the thinfilm solar cell on the basis of: the photoelectric converter, based on
CuInSe_{2}CdS, and the thermoelectric layer, based on CuInSe_{2}, is considered in this paper. This construction of the solar cell is implemented in the COMSOL Multiphysics software package. During the simulation, conditions close to operational conditions were taken into account. The temperature patterns and the temperature gradient patterns of the solar cell are obtained by using numerical methods. The use of the thermoelectric layer, the solar radiation concentration as well as maintenance of the operating temperature of the photoelectric converter due to the temperature stabilization of the substrate back side made it possible to achieve an increase in the output power of the solar cell up to 5%.
Keywords: thermoelectric layer, photoelectric converter, concentrated solar radiation, COMSOL Multiphysics, temperature gradient.
A.K. Esman – Belarusian National Technical University, Minsk
G.L. Zykov – Belarusian National Technical University, Minsk
V.A. Potachits – Belarusian National Technical University, Minsk
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Kozadaev K.V. Integration of data from inertial, barometric, magnetometric and satellite navigation systems
The use of a twostage Kalman filter scheme for integrating data from autonomous and satellite navigation systems is considered. This allows us to solve the problem of different data update rates in autonomous and satellite navigation systems, as well as to obtain an optimal estimate of the state of a dynamic system based on measurements that inevitably contain errors.
Keywords: inertialsatellite navigation systems, Kalman filter, data stream aggregation, navigation solution.
K.V. Kozadaev – Belarusian State University, Minsk
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Kulak G.V., Krokh G.V., Nikolaenko T.V., Shakin O.V. Diffraction of Bessel light beams by the surfacå Gulyaev – Blustein’s acoustical waves in cubic piezoelectrical crystals
It is shown that for acoustooptic diffraction and modulation of Bessel light beams diffracted on Gulyaev – Blustein surface acoustic waves, reflected diffraction orders should be used along with the transmission diffraction orders. Acoustooptic diffraction of Bessel light beams can be used to diagnose Gulyaev – Blustein surface waves in cubic piezoelectric crystals. Diffraction of Bessel light beams of lower orders on crystal structures: air – GaAs – AlGaAs can be used to create multicoordinate acoustooptic deflectors and modulators.
Keywords: planparallel slab, Gulyaev – Blustein’s waves, acoustooptical diffraction, cubic crystal, coefficients of reflection and transmission, light modulation.
G.V. Kulak – I.P. Shamyakin Mozyr State Pedagogical University
G.V. Krokh – I.P. Shamyakin Mozyr State Pedagogical University
T.V. Nikolaenko – I.P. Shamyakin Mozyr State Pedagogical University
O.V. Shakin – State University of Aerospace Instrumentation, SaintPetersburg
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Miheev S.S., Sotsky A.B., Nazarov M.M., Sotskaya L.I. Calculation of the waveguide probe for terahertz spectroscopy of a layered medium
Using the Kirchhoff approximation, an analytical solution of the diffraction problem on finding the spectra of the amplitudes of the modes of a waveguide probe at reflection of a terahertz pulse from the open end of a hollow core waveguide contacting with a layered medium, is obtained. On example of the electrodynamic model of the skin as two layers of an aqueous albumin solution excited by the modes of a hollow metal waveguide, the effect of epidermal humidity on the spectra of amplitudes of reflected waveguide modes, which can be measured using the time domain spectroscopy, is studied. It is established that the optimal choice of the frequency range refers to singlemode regime of the waveguide work.
Keywords: hollowcore waveguide, waveguide probe, terahertz time domain spectroscopy, layered medium, biologic sensor.
S.S. Miheev – Mogilev State A. Kuleshov University
A.B. Sotsky – Mogilev State A. Kuleshov University
M.M. Nazarov – Kurchatov Institute National Research Center, Moscow
L.I. Sotskaya – BelarusianRussian University, Mogilev
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Khoroshko V.V., Gremenok V.F., Shneiderov E.N., Tereshkova, A.S. Aksyonov O.A., Bruj N.M. Polycrystalline solar cells electrical characteristics forecasting based on their degradation models
In this paper we present the results of accelerated tests B class based solar cells. It is established that the selfsimilarity of the experiment is observed at temperatures up to 150–160° C and lighting levels up to 2000 W/m^{2}. During over 168 h of accelerated testing the relative degradation of efficiency was 5,8%. The pattern of degradation of the duty cycle (ff) and shortcircuit current (I_{sc}) of the solar cells at the initial and final time points of the tests is established.
Keywords: polycrystalline solar cells, tests, degradation models, renewable energy sources.
V.V. Khoroshko – Belarusian State University of Informatics and Radioelectronics, Minsk
V.F. Gremenok – Scientific and Practical Materials Research Centre of NAS Belarus, Minsk
E.N. Shneiderov – Belarusian State University of Informatics and Radioelectronics, Minsk
A.S. Tereshkova – Belarusian State University of Informatics and Radioelectronics, Minsk
O.A. Aksyonov – Belarusian State University of Informatics and Radioelectronics, Minsk
N.M. Bruj – Belarusian State University of Informatics and Radioelectronics, Minsk
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MATHEMATICS
Adarchenko N.M., Skiba A.N. Finite groups with generalized
subnormal and
permutable subgroups
Throughout this paper, all groups are finite and G always denotes a finite group. We say that a subgroup H of G is nearly modular in G if either A is normal in G or and every chief factor H / K of G between H_{G} and H^{G} is nearly central in G, that is,
divides pq for some primes p and q. We say that a subgroup A of G is:
(i) nearly subnormal in G if
where L is a nearly modular subgroup and T is a subnormal subgroup of G;
(ii) nearly permutable in G if where LL is a nearly modular subgroup and T is a
permutable subgroup of G.
(iii) weakly permutable in G if there are a nearly permutable subgroup S and a subgroup T of G such that G=HT and
In the given paper, we study finite groups with some systems of nearly
subnormal, nearly
permutable and weakly
permutable subgroups. Some known results are generalized.
Keywords: finite group, nmaximal subgroup, nearly
subnormal subgroup, nearly
permutable subgroup,
nearly nilpotent group.
N.M. Adarchenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
A.N. Skiba – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State Universit
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Balychev S.V., Vegera A.S. Soluble saturated formations with the
property for finite groups
The finite groups that can be represented as a product of pairwise permutable subgroups with formational restrictions on factors and their partial products are studied. In particular, the description of solvable hereditary saturated formations of groups with the property introduced by B. Amberg, A.S. Kazarin and Hefling is obtained.
Keywords: finite group, product of pairwise permutable subgroups, formation with the property, formation with the Kegel property, formation with the Shemetkov property.
S.V. Balychev – F. Skorina Gomel State University
A.S. Vegera – F. Skorina Gomel State University
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Kechko E.P. The convergence rate of Hermite – Pade approximations of the three exponent system
The convergence rate of type II Hermite – Pade approximants for the system is found. The theorems proved in the paper complement the results obtained earlier by O. Perron, D. Braess, A.I. Aptekarev, A.P. Starovoitov and other authors.
Keywords: type II Hermite – Pade approximations, system of exponential functions, asymptotic equalities, Hermite integrals.
E.P. Kechko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Nestsiarovich A.V. Deformation of a threelayer circular plate under cosine loading in its plane
The displacements in a round threelayer plate asymmetric in thickness under nonaxisymmetric loading in its plane are investigated. The distributed load, depending on the radial and tangential coordinates, is applied in the median plane of the aggregate. Equilibrium equations are obtained by the variational Lagrange method. The general decision is written out in the Fourier series. The final solution is given for a cosine load. It was numerically tested.
Keywords: threelayer round plate, displacements, axisymmetric tensioncompression, cosine load.
A.V. Nestsiarovich – Belarusian State University of Transport, Gomel
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INFORMATION SCIENCE
Demidenko O.M., E.A. Yakimov, Denisevich D.A. The research of rational cutting algorithms of sheet material
The study of rational cutting algorithms of sheet material is considered. The results of the study of three algorithms are presented: the first suitable, the first suitable with ordering and the genetic algorithm. A method for comparing algorithms for solving problems of onedimensional cutting by the criterion of “useless material” is proposed.
Keywords: rational cutting of material, cutting algorithms.
O.M. Demidenko – F. Skorina Gomel State University
E.A. Yakimov – BelarusianRussian University, Mogilev
D.A. Denisevich – BelarusianRussian University, Mogilev
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