
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (20) 2014
PHYSICS
Andreev V.V., Deryuzhkova O.M., Maksimenko N.V. The covariant representation spin polarizability of the nucleon
The option of relativisticinvariant definition of spin polarizability on the basis of covariant creation of the induced dipolar moments and phenomenological effective Lagrangian interactions of an electromagnetic field with these moments is offered.
Keywords: polarizability, Lagrangian, Compton scattering.
V.V. Andreev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
O.M. Deryuzhkova – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
N.V. Maksimenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Akhramenko N.A., Bulauko L.M. Mass of massive spherical shell with regard to gravitational defect
The expression defining the mass of the spherical dustlike shell with regard to the gravitational defect is obtained. It is shown that the mass of a spherical dustlike shell increases with its radius. In the limiting case, the mass tends to the value of free, not connected with gravitational interaction of mass.
Keywords: theory of gravitation, dustlike spherical shell, gravitational mass defect.
N.A. Akhramenko – Belarusian State University of Transport, Gomel, Belarus
L.M. Bulauko – Belarusian State University of Transport, Gomel, Belarus
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Barsukov S.D., Balmakou A.P., Semchenko I.V., Khakhomov S.A., Dzerzhauskaya T.A., Slobozhanyuk A.P., Krasnok A.E., Belov P.A. Experimental studies of the directional antenna based on helical elements
Experimental results obtained for a single helical radiator, as well as for the system of helical elements similar to the directional antenna Yagi – Uda are presented. These results suggest that for a helical antenna with optimized parameters, it is possible to obtain an effective lateral radiation and design of the directional antenna based on such helical elements. However, it is necessary to optimize the system parameters of helical elements forming an antenna for higher directivity and polarization of the radiation required.
Keywords: antenna, polarization, doubleturn helix, ellipticity coefficient.
S.D. Barsukov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.P. Balmakou – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
I.V. Semchenko – F. Skorina Gomel State University, Gomel, Belarus
S.A. Khakhomov – F. Skorina Gomel State University, Gomel, Belarus
T.A. Dzerzhauskaya – F. Skorina Gomel State University, Gomel, Belarus
A.P. Slobozhanyuk – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia
A.E. Krasnok – St. Petersburg National Research University of Information Technologies,
Mechanics and Optics, St. Petersburg, Russia
P.A. Belov – St. Petersburg National Research University of Information Technologies,
Mechanics and Optics, St. Petersburg, Russia
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Grishechkin Y.A., Danilchenko M.S., Kapshai V.N. Complex scaling method for twoparticle equations in the momentum representation and resonance states
The complex scaling method is applied to the nonrelativistic and relativistic twoparticle equations in the momentum representation for resonance sates finding. The comparison of the resonance states spectra obtained in the momentum representation with the similar results obtained in the coordinate representation for the Schrodinger equation and in the relativistic configurational representation for the twoparticle relativistic equations is carried out. A good agreement of the results obtained in different representations is shown.
Keywords: relativistic twobody equations, complex scaling method, resonance states, momentum representation, relativistic configuration representation.
Y.A. Grishechkin – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
M.S. Danilchenko – 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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Kosenok Ya.À., Gaishun V.E., Tyulenkova O.I., Denisman V.G. Aqueous compositions based on nanosized silica particles for chemicalmechanical polishing of silicon wafers
The method of preparation of suspensions based on nanosized particles of fumed silica is described. The process and results of chemicalmechanical polishing of silicon wafers carried out in industrial environments are investigated. Recommendations on the use of polishing compositions in the chemicalmechanical polishing are making. When using the polishing suspensions SPS81M and SPS55M in the process of singlecrystal silicon wafer CMP, high structural perfection and atomic smoothness of the surface roughness are achieved at the level of tenths of a nanometer.
Keywords: chemicalmechanical polishing, fumed silica, nanosized particles, surface, roughness.
Ya.À. Kosenok – F. Skorina Gomel State University, Gomel, Belarus
V.E. Gaishun – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
O.I. Tyulenkova – F. Skorina Gomel State University, Gomel, Belarus
V.G. Denisman – «Kamerton» subsidiary of JSC «INTEGRAL», Pinsk, Belarus
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Ovsiyuk E.M., Veko O.V., Kazmerchuk K.V. Scalar particle with intrinsic structure in the electromagnetic field in curved spacetime
Relativistic theory of the Cox’s scalar not pointlike particle with intrinsic structure is developed in the presence of external electromagnetic and gravitational fields; the latter is described by pseudoRiemannian spacetime geometry. It is shown that the generalized Procalike tensor system of equations of the first order contains non minimal interaction terms through electromagnetic tensor and Ricci tensor . Generalized scalar equation of the Klein – Fock – Gordon type turns out to be much more complicated than the ordinary wave equation.
Keywords: spin zero, intrinsic structure, Cox’s particle, generalized wave equation, Riemannian space.
E.M. Ovsiyuk – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
O.V. Veko – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
K.V. Kazmerchuk – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
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Sidsky V.V., Semchenko A.V., Rybàkov A.G., Kolos V.V., Turtsevych A.S. Effect of the annealing temperature and type of impurities on the size of the nanoparticles
SrBi_{2}(Ta_{õ}Ìå_{1õ})_{2}O_{9}
The data of the influence of the impurity Nb, La and annealing temperature on the structural characteristics of the layers
SrBi_{2}(Ta_{õ}Ìå_{1õ})_{2}O_{9}
are discussed. As research methods the atomic force microscopy and Xray diffraction method were used.
Keywords: solgel method, ferroelectric sol, heat treatment, SBTfilm perovskite, Xray diffraction method, method of atomic force microscopy.
V.V. Sidsky – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.V. Semchenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.G. Rybàkov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
V.V. Kolos – JSC «INTEGRAL», Minsk, Belarus
A.S. Turtsevych – JSC «INTEGRAL», Minsk, Belarus
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Shepelevich V.V., Makarevich A.V., Shandarov S.M. Optimization of the output characteristics of mixed holograms in the cut BTO photorefractive piezocrystal
The results of theoretical research of the optimization process of readout mixed transmission holograms formed in the
cut Bi_{12}TiO_{20} photorefractive piezoelectric crystal are presented. It is shown that in comparison with the case of pure phase holograms, traditionally regarded in photorefractive crystals, additional accounting of the amplitude component of the holographic grating leads to a qualitative and quantitative changes in the orientation dependence of the polarizationoptimized values of the diffraction efficiency of holograms recorded in this crystal.
Keywords: diffraction efficiency, phase grating, amplitude grating, mixed hologram, photorefractive piezocrystal, BTO.
V.V. Shepelevich – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
A.V. Makarevich – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
S.M. Shandarov – Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia
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MATHEMATICS
Baojun Li, Aming Liu. On Pproperty of subgroups of finite groups
Let H be a subgroup of a group G. We say that H has Pproperty in G
if is a pnumber for any pdchief factor L/K of G. Using this property of subgroups, some new criterions of pnilpotency of groups are obtained.
Keywords: finite group, pnilpotent group, Pproperty of subgroup.
Baojun Li – College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China
Aming Liu – College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China
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Vegera A.S. On local properties of the formations of groups with
subnormal Sylow subgroups
The class of all finite groups with Sylow
subnormal subgroups is considered. The condition of saturation of this class is investigated, as well as the local screen in solvable case is established.
Keywords: finite group, Sylow subgroup,
subnormal subgroup, saturated formation, local formation.
A.S. Vegera – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Gritsuk D.V. Dependence of the derived plength of a psolvable group on the order of its Sylow psubgroup
Kamornikov S.F. One example of hyperradical formation
The existence of hyperradical formations which are not hereditary is established.
Keywords: formation, hyperradical formation, superradical formation, finite group.
S.F. Kamornikov – Gomel Branch of International University «MITSO», Gomel, Belarus
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Kulahina M.V. The algorithm for determination of immobile indixes in convex sip problems with polyhedral index sets
The convex SemiInfinite Programming (SIP) problems with polyhedral index sets are considered. For these problems a finite algorithm for determination of immobile indixes and their immobility orders along the feasible directions is described and justified. An example illustrating the application of the algorithm is provided.
Keywords: semiinfinite programming, convex programming, immobile index, immobility order, cone of feasible directions, extreme ray.
M.V. Kulahina – Institute of Mathematics of National Academy of Sciences of Belarus, Minsk, Belarus
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Mirotin A.R., Atvinovskii A.A. Inversion of a linear combination of values of the resolvent of a closed operator
The problem of the computation of the left inverse of a linear combination of values of the resolvent of a closed operator in a Banach space is solved. Several unsolved problems are formulated.
Keywords: closed operator, left inverse of an operator, resolvent, Banach space, functional calculus, Markov function.
A.R. Mirotin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
A.A. Atvinovskii – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Sazonova A.T. On the solutions of the simplified system of nonlinear differential equations in the motion of four particles in a plane
A system describing the motion of four bodies under the action of gravity is considered. By elementary algebraic manipulations a simple system consisting of nonlinear differential equations, each of which has a second order is selected. For each simplified system there are sets of constants of interparticle interaction, in which the general solution is meromorphic.
Keywords: movement of four bodies, constant interaction, Painleve property, meromorphic function.
A.T. Sazonava – Y. Kupala Grodno State University, Grodno, Belarus
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Tyutyanov V.N., Tihonenko T.V. On finite groups with given system of Sylow subgroups
The solvability of the finite group in which any Sylow subgroup is either
subnormal or abnormal, was proved.
Keywords: Sylow subgroup, simple nonabelian group,
subnormal subgroup, abnormal subgroup.
V.N. Tyutyanov – Gomel Branch of International University, Gomel, Belarus
T.V. Tihonenko – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus
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INFORMATION SCIENCE
Kirhintsava S.V. Computer analysis of efficiency of reinforcing of the soil bases of RITpiles
Sag of RITpiles on condition of linear and nonlinear deformation of soil taking into account and without consolidation of the soil basis in the field of explosion is investigated.
Keywords: pileRIT, camouflage broadening, soils, mathematical model, computer simulation.
S.V. Kirhintsava – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Osipenko A.N., Osipenko N.B. Concept of problemoriented technology of modelling of active systems
Problem of effective technology of modeling of the creation of the socalled active system (AS) is considered. The active system differs from other systems by its source of organization which is internally independent and has the ability to change structure and parameters of functioning of the system based on its own needs. As alternative to the traditional methodoriented approach to technological designing of ASmodels the basic circuit of problemoriented technology of modeling is offered. The peculiarity of this technology is that the interaction and development of the formed models of the desired ASoperation are provided due to the introduction of the block of conceptual modeling and special research functioning. The new approaches to simulate experiment (SE) are considered at design AS modeling. At the heart of the proposed technologies of SE is the operational and process way of formalization and technique of AS research. The practical use of the proposed technology is interpreted by the problem of modeling activities of the production unit.
Keywords: active system, problemoriented technologies of modeling, conceptual modeling, target functioning, intellectual system.
A.N. Osipenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
N.B. Osipenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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