Main - Problems of physics, mathematics and technics

Balmakov A.P., Semchenko I.V., Khakhomov S.A., Nagatsu M. Microwave circular polarizer based on bifilar helical particles

In this paper, we describe practical realization of a new type of circular polarizer based on metallic double-stranded (ds-) array particles, operating under normal to the helix axis wave propagation. The latter is the key distinction of this array from a number of analogous operating under propagation along the helix axis. Theoretical foundation of ds-helices polarization selectivity is given for a wave propagation perpendicular to the helix�s axis. A computer model is created to study electrodynamic properties of arrays of helices, which confirms the circular polarizer feasibility for a microwave wavelength region.

Keywords: helix, array, polarization, metamaterial.

A.P. Balmakov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

I.V. Semchenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

S.A. Khakhomov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

M. Nagatsu – Shizuoka University, Hamamatsu, Japan

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Veko O.V., Ovsiyuk E.M., Red�kov V.M. Jones 4-spinors for the partially polarized light

The known group-theory based description of constructing of 4-tensors based on the second rank 4-spinor permits to introduce definition for Jones 4-spinor of a partially polarized light and relates this object with Stokes 4-vector and Stokes antisymmetric 4-tensor. It provides us with extension of the known attitude to the problem when only Jones 2-spinors relevant to a completely polarized light are used.

Keywords: polarization optics, Jones 4-spinors, Stokes parameters.

O.V. Veko – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus

E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus

V.M. Red�kov – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

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Girgel S.S. Kummer-Gaussian scalar astigmatic three-dimensional light beams

The formalism for the description of paraxial 3D Gaussian-like light Kummer-Gaussian beams by a simple astigmatism is offered. Conditions of their physical realizability are formulated. New types of Kummer-Gaussian beams are found. Such beams are presented by Gaussian product on Kummer function of a complex argument and a nonnegative integer index n.

Keywords: paraxial beams, Hermite-Gaussian beams, Kummer-Gaussian beams, Gaussian-like beams.

S.S. Girgel – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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Grishechkin Yu.A., Kapshai V.N. Relativistic bound state problem for two-particle systems with energy dependent one boson exchange potential

Numerical solutions of quantum field theory equations describing bound s-states of two scalar particles with equal masses are found in the case of one-boson exchange potential dependent on the system energy. The mass of the scalar exchange boson is chosen to be equal to zero. The constants of scalar particle-antiparticle system decay into two photons are calculated based on obtained solutions.

Keywords: relativistic two-particle equations, one-boson exchange potential, wave functions, bound states, normalization condition, energy eigenvalues, decay constant.

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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Zalesski V.B., Kravchenko V.M., Leonova T.R., Polikanin A.M., Zaretskaya E.P., Petrosyan S.G., Kechiantz A.M. CIGS solar cells with efficiency 10,1% on perlite galssceramic substrates

For the first time thin film solar cells with CuInGaSe₂ absorber layer were formed on a specially designed non-conductive ceramic substrates on the basis of pearlite to produce photovoltaic devices fully integrated into building constructions. This glass ceramic satisfies the physical demands of the substrate material as well as the requirements of cost reduction of solar cells production. This paper presents preliminary results which show that these type solar cells with the efficiency higher than 10 % may be designed.

Keywords: thin films, CIGS, solar cells, glass ceramic.

V.B. Zalesski – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

V.M. Kravchenko – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

T.R. Leonova – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

A.M. Polikanin – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

E.P. Zaretskaya – Scientific and Practical Materials Research Centre of NAS Belarus, Minsk, Belarus

S.G. Petrosyan – Institute of Radiophysics and Electronics, NAS RA Ashtarak, Armenia

A.M. Kechiantz – Institute of Radiophysics and Electronics, NAS RA Ashtarak, Armenia

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Tsyrelchuk I.N., Khoroshko V.V., Gremenok V.F., Mishuto V.A. The optical properties of thin films of solid solutions CU_XIn_XZn_2-2XSe₂, obtained by a two-stage selenization

This paper discusses the results of studies in the temperature range of 80 and 300 K absorption spectra and photoluminescence spectra of thin films of Zn_2-2XCu_XIn_XSe2 with the concentration of zinc atoms 0�10 at.%. Polycrystalline films of p-type conductivity were obtained on glass substrates by a two-stage selenization base layers ZnSe / (Cu + In) under an inert atmosphere. The authors established the character of the width of the band gap and photoluminescence spectra of the concentration of zinc atoms.

Keywords: thin film, two-stage selenization, absorption coefficient, photoluminescence, band gap.

I.N. Tsyrelchuk – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

V.V. Khoroshko – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

V.F. Gremenok – Institute of Solid State and Semiconductor Physics of NAS Belarus, Minsk, Belarus

V.A. Mishuto – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

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Zhubo Liu, Rogach�v A.A., Yarmolenko M.A., Jiang X.H., Rogach�v A.V., Gorbachev D.L. Influence of assisting laser radiation at electron-beam dispersion on the molecular structure of polye-thylene-silver nanocomposite coatings

The paper deals with the study of the molecular structure and morphology of polyethylene-silver nanocomposite coatings. Polyethylene-silver nanocomposite coatings were prepared from active gas phase by electron-beam dispersion of polyethylene and silver nitride. The influences of laser assisted electron-beam dispersion and annealing on the formation degree of plasmon effect, the chemical composition and structure of the layer were determined. The results show that metal nanoparticles could be produced by laser assisting at the dispersion stage affecting the autocatalytic process of decomposition of the salt. Annealing leads to a more homogeneous structure with a smaller protuberance on the surface of the coatings.

Keywords: electron-beam dispersion, laser assistant, nanocomposite coating, polyethylene, silver nanoparticles, heat treatment.

Zhubo Liu – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A.A. Rogachev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

M.A. Yarmolenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

X.H. Jiang – Nanjing University of Science and Technology, Nanjing, PR China

A.V. Rogachev – Rector of F. Skorina Gomel State University, Gomel, Belarus

D.L. Gorbachyov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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Shilova I.V., Belskaya �.�., Sotsky �.B. Electrodynamic model of the bending fiber-optic sensor

Bending radiation loss caused by elliptical deformation in the sensitive element of the fiber-optic pressure sensor was investigated on the basis of the fiber-optic loop antenna model.

Keywords: optical fiber, fiber optical sensor of pressure.

I.V. Shilova – Belarusian-Russian University, Mogilev, Belarus

�.�. Belskaya – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

�.B. Sotsky – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

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Shushkevich G.Ch., Kiseleva N.N. Calculation of the attenuation coefficient of the sound field of a spherical radiator by penetrable spherical shell

The analytical solution of the boundary problem which describes the process of penetration of the sound field of a spherical radiator located inside a thin unclosed spherical shell, through the permeable spherical shell is constructed. The influence of some parameters of the 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

N.N. Kiseleva – Y. Kupala Grodno State University, Grodno, Belarus

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Gal'mak A.M., Vorobiev G.N. On Post-Gluskin-Hosszu theorem

Post-Gluskin-Hosszu theorem is known as Gluskin-Hosszu or Hosszu-Gluskin theorem. In the formulation of this theorem there is an n-ary group <A, [ ] > and some binary group <A, o >. These groups have a common carrier A. E. Post formulated and proved this theorem considering isomorphous copy of �₀ (associated group) instead of group < A, o >. In our opinion the absence of the name of E. Post in the title of the theorem is an embarrassing mistake which must be corrected. Apparently, M. Hosszu didn�t know anything about the results of E. Post. It is necessary to note that L.M. Gluskin was not engaged in the study of n-ary groups. He investigated a large class of algebraic systems � positional operatives, and achieved a series of important results. Post-Gluskin-Hosszu theorem is among numerous consequences of these results.

Keywords: group, n-ary group, automorphism.

A.M. Gal�mak – Mogilev State University of Food Technologies, Mogilev, Belarus

G.N. Vorobiev – Mogilev State University of Food Technologies, Mogilev, Belarus

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Gritsuk D.V., Monakhov V.S., Shpyrko O.A. On finite -solvable groups with bicyclic Sylow subgroups

The group is called a bicyclic group if it is the product of two cyclic subgroups. It is proved that the -solvable group with bicyclic Sylow p-subgroups for any is at most 6 and if , then the derived -length of a -solvable group with bicyclic Sylow p-subgroups for any is at most 3.

Keywords: finite group, -solvable group, bicyclic group, Sylow subgroup, derived -length.

D.V. Gritsuk – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

V.S. Monakhov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

O.A. Shpyrko – Branch of the M.V. Lomonosov Moscow State University, Sevastopol, Ukraine

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Lomovtsev F.E., Lyakhov D.A. Weak solutions of hyperbolic even-order operator-differential equations with variable domains

We prove the existence and uniqueness of weak solutions of boundary value problem for a two-term even-order hyperbolic operator-differential equation with unbounded operator coefficient A(t), having t-depending domain D(A(t)). It is shown that for a smooth right-hand part the weak solutions of boundary value problem are smooth, i. e. they satisfy the equation almost everywhere on ]0,T[ in H and the boundary conditions in the usual sense. An example of the new correct boundary value problem for fourth-order partial differential equation with unsteady boundary conditions on the space variables is given.

Keywords: �orrectness by Hadamard, operator-differential equation, unbounded operator, variable domain, weak solution.

F.E. Lomovtsev – Belarusian State University, Minsk, Belarus

D.A. Lyakhov – Belarusian State University, Minsk, Belarus

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Murashka V.I. On partially conjugate-permutable subgroups of finite groups

Let R be a subgroup of a group G. We shall call a subgroup H of G the R-conjugate-permutable subgroup if

for all

In this work the properties and the influence of R-conjugate-permutable subgroups (maximal, Sylow, cyclic primary) on the structure of finite groups are studied. As R we consider the Fitting subgroup F(G) quasinilpotent radical

and the generalized Fitting subgroup

that was introduced by P. Shmid. In particular, it was shown that group G is nilpotent iff all its maximal subgroups are

-conjugate-permutable.

Keywords: finite group, nilpotent group, R-conjugate-permutable subgroup, conjugate-permutable subgroup, the Fitting subgroup.

V.I. Murashka – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

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Novikov S.P. About belonging of -prefrattini subalgebras of multirings to class

Conditions at which any -prefrattini subalgebra of multiring A belong to class , are considered.

Keywords: multirings, -central factor, frattini chief factor, -prefrattini subalgebra, -normalizer.

S.P. Novikov – Belarusian State University of Transport, Gomel, Belarus

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Starovoitov A.P. Hermite-Pade approximants of the system Mittag-Leffler functions

The paper deals with asymptotic properties of Hermite integrals. In particular, the asymptotics of diagonal Hermite-Pade approximations for the system of exponents are determined when and . Similar results are proved for the system of confluent hypergeometric functions

Keywords: Hermite integrals, joint Pade approximations, Hermite-Pade approximations, asymptotic equality.

A.P. Starovoitov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

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Fedartsova N.M. Correction method for solving perturbed parametric linear-quadratic optimal control problems in the neighbourhood of irregular parameter value

A family of one-parametric linear-quadratic optimal control problems with singular arcs is considered. A method for solving perturbed problems in the neighbourhood of irregular parameter value on condition that unperturbed problem solution is known is given.

Keywords: optimal control, parametric optimization, perturbed problems, linear-quadratic problems, singular arcs.

N.M. Fedartsova – Design and Technology center of the Belarusian railway, Minsk

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Erofeeva E.A. Technological stages of imitating modeling traffic volume processing by railway station

In the paper the definition and features of the technological line of processing of train a traffic volume are presented. The basic requirements with which the developed means of imitating modeling of work of a switchyard should satisfy are formulated. The structure of the developed program complex is given. The technology of application of a program complex for the solution of production tasks is described.

Keywords: simulation of complex engineering systems, switchyard.

E.A. Erofeeva – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

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Pekar D.V., Sadov V.S. Decision making algorithm in the safety system based on the fuzzy logic

At the present time the volume of handled data is rapidly growing. A large volume of voice data processing is impossible without usage of automatic speech systems with the ability to make decision based on speech signal analysis and lingual component processing. In this paper fuzzy logic based decision making algorithm is proposed. Described algorithm has a lot of advantages such as ability to be configured to meet certain requirements, easiness of creating a set of fuzzy rules, computational effectiveness and similar decision making process as in human beings.

Keywords: decision making, fuzzy logic, speech processing.

D.V. Pekar – Belarusian State University, Minsk, Belarus

V.S. Sadov – Belarusian State University, Minsk, Belarus

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	PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N1 (14) 2013 PHYSICS Balmakov A.P., Semchenko I.V., Khakhomov S.A., Nagatsu M. Microwave circular polarizer based on bifilar helical particles In this paper, we describe practical realization of a new type of circular polarizer based on metallic double-stranded (ds-) array particles, operating under normal to the helix axis wave propagation. The latter is the key distinction of this array from a number of analogous operating under propagation along the helix axis. Theoretical foundation of ds-helices polarization selectivity is given for a wave propagation perpendicular to the helix�s axis. A computer model is created to study electrodynamic properties of arrays of helices, which confirms the circular polarizer feasibility for a microwave wavelength region. Keywords: helix, array, polarization, metamaterial. A.P. Balmakov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus I.V. Semchenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus S.A. Khakhomov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus M. Nagatsu – Shizuoka University, Hamamatsu, Japan Download PDF (580 KB) Veko O.V., Ovsiyuk E.M., Red�kov V.M. Jones 4-spinors for the partially polarized light The known group-theory based description of constructing of 4-tensors based on the second rank 4-spinor permits to introduce definition for Jones 4-spinor of a partially polarized light and relates this object with Stokes 4-vector and Stokes antisymmetric 4-tensor. It provides us with extension of the known attitude to the problem when only Jones 2-spinors relevant to a completely polarized light are used. Keywords: polarization optics, Jones 4-spinors, Stokes parameters. O.V. Veko – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus V.M. Red�kov – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus Download PDF (333 KB) Girgel S.S. Kummer-Gaussian scalar astigmatic three-dimensional light beams The formalism for the description of paraxial 3D Gaussian-like light Kummer-Gaussian beams by a simple astigmatism is offered. Conditions of their physical realizability are formulated. New types of Kummer-Gaussian beams are found. Such beams are presented by Gaussian product on Kummer function of a complex argument and a nonnegative integer index n. Keywords: paraxial beams, Hermite-Gaussian beams, Kummer-Gaussian beams, Gaussian-like beams. S.S. Girgel – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus Download PDF (335 KB) Grishechkin Yu.A., Kapshai V.N. Relativistic bound state problem for two-particle systems with energy dependent one boson exchange potential Numerical solutions of quantum field theory equations describing bound s-states of two scalar particles with equal masses are found in the case of one-boson exchange potential dependent on the system energy. The mass of the scalar exchange boson is chosen to be equal to zero. The constants of scalar particle-antiparticle system decay into two photons are calculated based on obtained solutions. Keywords: relativistic two-particle equations, one-boson exchange potential, wave functions, bound states, normalization condition, energy eigenvalues, decay constant. 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 Download PDF (300 KB) Zalesski V.B., Kravchenko V.M., Leonova T.R., Polikanin A.M., Zaretskaya E.P., Petrosyan S.G., Kechiantz A.M. CIGS solar cells with efficiency 10,1% on perlite galssceramic substrates For the first time thin film solar cells with CuInGaSe₂ absorber layer were formed on a specially designed non-conductive ceramic substrates on the basis of pearlite to produce photovoltaic devices fully integrated into building constructions. This glass ceramic satisfies the physical demands of the substrate material as well as the requirements of cost reduction of solar cells production. This paper presents preliminary results which show that these type solar cells with the efficiency higher than 10 % may be designed. Keywords: thin films, CIGS, solar cells, glass ceramic. V.B. Zalesski – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus V.M. Kravchenko – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus T.R. Leonova – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus A.M. Polikanin – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus E.P. Zaretskaya – Scientific and Practical Materials Research Centre of NAS Belarus, Minsk, Belarus S.G. Petrosyan – Institute of Radiophysics and Electronics, NAS RA Ashtarak, Armenia A.M. Kechiantz – Institute of Radiophysics and Electronics, NAS RA Ashtarak, Armenia Download PDF (924 KB) Tsyrelchuk I.N., Khoroshko V.V., Gremenok V.F., Mishuto V.A. The optical properties of thin films of solid solutions CU_XIn_XZn_2-2XSe₂, obtained by a two-stage selenization This paper discusses the results of studies in the temperature range of 80 and 300 K absorption spectra and photoluminescence spectra of thin films of Zn_2-2XCu_XIn_XSe2 with the concentration of zinc atoms 0�10 at.%. Polycrystalline films of p-type conductivity were obtained on glass substrates by a two-stage selenization base layers ZnSe / (Cu + In) under an inert atmosphere. The authors established the character of the width of the band gap and photoluminescence spectra of the concentration of zinc atoms. Keywords: thin film, two-stage selenization, absorption coefficient, photoluminescence, band gap. I.N. Tsyrelchuk – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus V.V. Khoroshko – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus V.F. Gremenok – Institute of Solid State and Semiconductor Physics of NAS Belarus, Minsk, Belarus V.A. Mishuto – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus Download PDF (362 KB) Zhubo Liu, Rogach�v A.A., Yarmolenko M.A., Jiang X.H., Rogach�v A.V., Gorbachev D.L. Influence of assisting laser radiation at electron-beam dispersion on the molecular structure of polye-thylene-silver nanocomposite coatings The paper deals with the study of the molecular structure and morphology of polyethylene-silver nanocomposite coatings. Polyethylene-silver nanocomposite coatings were prepared from active gas phase by electron-beam dispersion of polyethylene and silver nitride. The influences of laser assisted electron-beam dispersion and annealing on the formation degree of plasmon effect, the chemical composition and structure of the layer were determined. The results show that metal nanoparticles could be produced by laser assisting at the dispersion stage affecting the autocatalytic process of decomposition of the salt. Annealing leads to a more homogeneous structure with a smaller protuberance on the surface of the coatings. Keywords: electron-beam dispersion, laser assistant, nanocomposite coating, polyethylene, silver nanoparticles, heat treatment. Zhubo Liu – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus A.A. Rogachev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus M.A. Yarmolenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus X.H. Jiang – Nanjing University of Science and Technology, Nanjing, PR China A.V. Rogachev – Rector of F. Skorina Gomel State University, Gomel, Belarus D.L. Gorbachyov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus Download PDF (1,46 MB) Shilova I.V., Belskaya �.�., Sotsky �.B. Electrodynamic model of the bending fiber-optic sensor Bending radiation loss caused by elliptical deformation in the sensitive element of the fiber-optic pressure sensor was investigated on the basis of the fiber-optic loop antenna model. Keywords: optical fiber, fiber optical sensor of pressure. I.V. Shilova – Belarusian-Russian University, Mogilev, Belarus �.�. Belskaya – A.A. Kuleshov Mogilev State University, Mogilev, Belarus �.B. Sotsky – A.A. Kuleshov Mogilev State University, Mogilev, Belarus Download PDF (413 KB) Shushkevich G.Ch., Kiseleva N.N. Calculation of the attenuation coefficient of the sound field of a spherical radiator by penetrable spherical shell The analytical solution of the boundary problem which describes the process of penetration of the sound field of a spherical radiator located inside a thin unclosed spherical shell, through the permeable spherical shell is constructed. The influence of some parameters of the 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 N.N. Kiseleva – Y. Kupala Grodno State University, Grodno, Belarus Download PDF (473 KB) MATHEMATICS Gal'mak A.M., Vorobiev G.N. On Post-Gluskin-Hosszu theorem Post-Gluskin-Hosszu theorem is known as Gluskin-Hosszu or Hosszu-Gluskin theorem. In the formulation of this theorem there is an n-ary group <A, [ ] > and some binary group <A, o >. These groups have a common carrier A. E. Post formulated and proved this theorem considering isomorphous copy of �₀ (associated group) instead of group < A, o >. In our opinion the absence of the name of E. Post in the title of the theorem is an embarrassing mistake which must be corrected. Apparently, M. Hosszu didn�t know anything about the results of E. Post. It is necessary to note that L.M. Gluskin was not engaged in the study of n-ary groups. He investigated a large class of algebraic systems � positional operatives, and achieved a series of important results. Post-Gluskin-Hosszu theorem is among numerous consequences of these results. Keywords: group, n-ary group, automorphism. A.M. Gal�mak – Mogilev State University of Food Technologies, Mogilev, Belarus G.N. Vorobiev – Mogilev State University of Food Technologies, Mogilev, Belarus Download PDF (355 KB) Gritsuk D.V., Monakhov V.S., Shpyrko O.A. On finite -solvable groups with bicyclic Sylow subgroups The group is called a bicyclic group if it is the product of two cyclic subgroups. It is proved that the -solvable group with bicyclic Sylow p-subgroups for any is at most 6 and if , then the derived -length of a -solvable group with bicyclic Sylow p-subgroups for any is at most 3. Keywords: finite group, -solvable group, bicyclic group, Sylow subgroup, derived -length. D.V. Gritsuk – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus V.S. Monakhov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus O.A. Shpyrko – Branch of the M.V. Lomonosov Moscow State University, Sevastopol, Ukraine Download PDF (362 KB) Lomovtsev F.E., Lyakhov D.A. Weak solutions of hyperbolic even-order operator-differential equations with variable domains We prove the existence and uniqueness of weak solutions of boundary value problem for a two-term even-order hyperbolic operator-differential equation with unbounded operator coefficient A(t), having t-depending domain D(A(t)). It is shown that for a smooth right-hand part the weak solutions of boundary value problem are smooth, i. e. they satisfy the equation almost everywhere on ]0,T[ in H and the boundary conditions in the usual sense. An example of the new correct boundary value problem for fourth-order partial differential equation with unsteady boundary conditions on the space variables is given. Keywords: �orrectness by Hadamard, operator-differential equation, unbounded operator, variable domain, weak solution. F.E. Lomovtsev – Belarusian State University, Minsk, Belarus D.A. Lyakhov – Belarusian State University, Minsk, Belarus Download PDF (373 KB) Murashka V.I. On partially conjugate-permutable subgroups of finite groups Let R be a subgroup of a group G. We shall call a subgroup H of G the R-conjugate-permutable subgroup if for all In this work the properties and the influence of R-conjugate-permutable subgroups (maximal, Sylow, cyclic primary) on the structure of finite groups are studied. As R we consider the Fitting subgroup F(G) quasinilpotent radical and the generalized Fitting subgroup that was introduced by P. Shmid. In particular, it was shown that group G is nilpotent iff all its maximal subgroups are -conjugate-permutable. Keywords: finite group, nilpotent group, R-conjugate-permutable subgroup, conjugate-permutable subgroup, the Fitting subgroup. V.I. Murashka – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus Download PDF (325 KB) Novikov S.P. About belonging of -prefrattini subalgebras of multirings to class Conditions at which any -prefrattini subalgebra of multiring A belong to class , are considered. Keywords: multirings, -central factor, frattini chief factor, -prefrattini subalgebra, -normalizer. S.P. Novikov – Belarusian State University of Transport, Gomel, Belarus Download PDF (294 KB) Starovoitov A.P. Hermite-Pade approximants of the system Mittag-Leffler functions The paper deals with asymptotic properties of Hermite integrals. In particular, the asymptotics of diagonal Hermite-Pade approximations for the system of exponents are determined when and . Similar results are proved for the system of confluent hypergeometric functions Keywords: Hermite integrals, joint Pade approximations, Hermite-Pade approximations, asymptotic equality. A.P. Starovoitov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus Download PDF (385 KB) Fedartsova N.M. Correction method for solving perturbed parametric linear-quadratic optimal control problems in the neighbourhood of irregular parameter value A family of one-parametric linear-quadratic optimal control problems with singular arcs is considered. A method for solving perturbed problems in the neighbourhood of irregular parameter value on condition that unperturbed problem solution is known is given. Keywords: optimal control, parametric optimization, perturbed problems, linear-quadratic problems, singular arcs. N.M. Fedartsova – Design and Technology center of the Belarusian railway, Minsk Download PDF (424 KB) INFORMATION SCIENCE Erofeeva E.A. Technological stages of imitating modeling traffic volume processing by railway station In the paper the definition and features of the technological line of processing of train a traffic volume are presented. The basic requirements with which the developed means of imitating modeling of work of a switchyard should satisfy are formulated. The structure of the developed program complex is given. The technology of application of a program complex for the solution of production tasks is described. Keywords: simulation of complex engineering systems, switchyard. E.A. Erofeeva – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus Download PDF (336 KB) Pekar D.V., Sadov V.S. Decision making algorithm in the safety system based on the fuzzy logic At the present time the volume of handled data is rapidly growing. A large volume of voice data processing is impossible without usage of automatic speech systems with the ability to make decision based on speech signal analysis and lingual component processing. In this paper fuzzy logic based decision making algorithm is proposed. Described algorithm has a lot of advantages such as ability to be configured to meet certain requirements, easiness of creating a set of fuzzy rules, computational effectiveness and similar decision making process as in human beings. Keywords: decision making, fuzzy logic, speech processing. D.V. Pekar – Belarusian State University, Minsk, Belarus V.S. Sadov – Belarusian State University, Minsk, Belarus Download PDF (671 KB)

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