
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (16) 2013
PHYSICS
Andreev Vasili V., Pankov A.A. Analysis of
Z'bosons effects at the LHC within ATLAS experiment
Vakulina E.V., Maksimenko N.V. Polarizability of the pion in the formalism of Duffin – Kemmer
The Lagrangian in the covariant form and the equation of motion of the pion in the electromagnetic field, taking into account its electric and magnetic polarizabilities were defined in the formalism of Duffin – Kemmer on the basis of the principle of gauge invariance. The amplitude of Compton scattering was defined on the basis of the solution of the equation of the interaction of the pion with the electromagnetic field produced by the method of Green's function, taking into account the impact and polarizabilities of the pion.
Keywords: Compton scattering amplitude, fieldtheoretical approach, Lagrangian, electric polarizability, magnetic polarizability, formalism of Duffin – Kemmer.
E.V. Vakulina – I.G. Petrovsky Bryansk State University, Novozibkov, Russia
N.V. Maksimenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (303 KB)
Gaishun V.E., Kovalenko D.L., Semchenko A.V., Vaskevich V.V. Functional nanostructured SiO_{2}–GeO_{2} films synthesised by solgel method
Creating lowdimensional systems and nanostructured composites in the form of functional, special glasses and oxide films based on the solid matrix and uniformly distributed in them highly organized semiconductors with sizes of 5–100 nm, is one of the most important areas of research in the field of synthesis and characterization of inorganic materials and dispersed systems. Nanostructures based on Ge–Si, despite the difference in lattice parameters of 4%, attracted the attention of engineers because of great strides in creating new advanced devices using quantum effects. There are lightemitting and photo detecting silicongermanium devices in silicon technology to compete successfully with traditional optoelectronic materials. An effective way of obtaining inorganic materials with controlled opticalmechanical and physicochemical characteristics is solgel process of formation of nanoscale particles and clusters dispersed in the silicate matrices of different types: monoliths, films, and quasispherical structures.
Keywords: solgel technology,
GeO_{2} solgel films,
SiO_{2} solgel films, optical properties, structure.
V.E. Gaishun – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
D.L. Kovalenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.V. Semchenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
V.V. Vaskevich – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (806 KB)
Laskovnev A.P., Cherenda N.N., Basalai A.V., Uglov V.V., Anischik V.M., Astashynski V.M., Kuzmitski A.M. Modification of the copper surface layer by the compression plasma flow
The surface morphology and microstructure of copper Ì1 treated by the compression plasma flow have been investigated by the methods of optical microscopy and Xray structural analysis. The correlation between the structure, microhardness and the amount of energy absorbed by the sample surface (5–18 J/cm^{2}) has been found. The thickness of the modified layer is about 36
(at the absorbed energy density – 18 J/cm^{2}).
Keywords: copper, compression plasma flow, surface morphology, microstructure.
A.P. Laskovnev – PhysicalTechnical Institute of the National Academy of Sciences of Belarus, Minsk, Belarus
N.N. Cherenda – Belarusian State University, Minsk, Belarus
A.V. Basalai – PhysicalTechnical Institute of the National Academy of Sciences of Belarus, Minsk, Belarus
V.V. Uglov – Belarusian State University, Minsk, Belarus
V.M. Anischik – Belarusian State University, Minsk, Belarus
V.M. Astashynski – A.V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus, Minsk, Belarus
A.M. Kuzmitski – A.V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus, Minsk, Belarus
Download PDF (1,43 MB)
Novikova O.V., Tyumenkov G.Yu. Analysis of the reduced modifications of the Peng – Robinson equation of state in the framework of the Joule – Tomson process
In the framework of thermodynamic method the modifications of the Peng – Robinson equations of state are considered in the paper. Critical parameters of the modified equations are calculated and their reduced forms are found as well. On this basis the Joule – Tomson process is analyzed and the explicit forms of effect sign inversion curves are built.
Keywords: critical parameters, the Peng – Robinson equation of state, modified equation, reduced variables, the Joule – Tomson process, inversion curve, positive effect.
O.V. Novikova – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
G.Yu. Tyumenkov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (400 KB)
Samofalov A.L., Faniayeu I.A., Semchenko I.V., Khakhomov S.A. Polarization transformers of electromagnetic waves based on composite media with a helical structure
Computer simulation was carried out in the microwave range based on the finite element method for the frequency dependence of the ellipticity coefficient of reflected wave for singleturn and doubleturn helices and twodimensional arrays consisting of the same helices. The possibility of the transformation of the incident linearly polarized electromagnetic waves in a circularly polarized wave reflected from the twodimensional array on the basis of a singleturn and doubleturn helices was shown. Reflected circularly polarized wave is observed at frequencies close to the resonance and doesn’t depend on the orientation of the plane polarization of incident wave relative to the axis of the helices.
Keywords: simulation, transformation of polarization, singleturn and doubleturn helices, ellipticity coefficient.
A.L. Samofalov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
I.A. Faniayeu – 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
Download PDF (533 KB)
Shershnev E.B., Nikitjuk Yu.V., Sokolov S.I. Features of controlled laser thermal cleavage of quartz glass
This paper presents finite element analysis based on the remeshing technique to predict laserinduced crack propagation in quartz glass. The simulation process is accomplished by the analysis of the coupled temperature and stress fields together with the criteria of fracture mechanics of the crack growth.
Keywords: crack, laser ñleaving, quartz glass.
E.B. Shershnev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Yu.V. Nikitjuk – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
S.I. Sokolov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (453 KB)
MATHEMATICS
Antonevich A.B., Pantsialeyeva E.V. Rightside resolvents of discrete weighted shift operators with matrix weights
Rightside resolvents are constructed for discrete weighted shift operator and estimates of their norms are given.
Keywords: discrete weighted shift operator, rightside resolvent, stable vectorial subset.
A.B. Antonevich – Belarusian State University, Minsk, Belarus
E.V. Pantsialeyeva – Belarusian State University, Minsk, Belarus
Download PDF (429 KB)
Atvinovskii A.A., Mirotin A.R. The inverse of some class of operators in Banach space and its several applications
The paper deals with the method proposed for the inverse of some class of operators. The result is applied to some equations with closed operators. The examples are considered.
Keywords: Markov function, Krein class, functional calculus, closed operator, operator equation.
A.A. Atvinovskii – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
A.R. Mirotin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (349 KB)
Vasil’ev V.A. On pnilpotency of one class of finite groups
A subgroup H of a group G is called modular in G if H is a modular element (in sense of Kurosh) of the lattice
L(G) of all subgroups of
G. The subgroup of H generated by all modular subgroups of G contained in
H is called the modular core of
H and denoted by H_{mG}. In the paper a new criterion of the
pnilpotency of a group was obtained on the basis of the concept of the
msupplemented subgroup which is the extension of concepts of modular and supplemented subgroups respectively.
Keywords: finite group,
pnilpotent group, modular subgroup, modular core, msupplemented subgroup, maximal subgroup, cyclic subgroup,
Sylow psubgroup.
V.A. Vasil’ev – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (343 KB)
Kovaliova I.S., Mirotin A.R. Convolution theorem for the Markov – Stieltjes transformation
A convolution theorem for the Markov – Stieltjes transformation is stated and its application to a class of singular integral equations is given.
Keywords: integral transform, Markov – Stieltjes function, convolution, integral equation.
I.S. Kovaliova – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
A.R. Mirotin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (353 KB)
Malinkovsky Yu.V., Zhao Yue. Steadystate exponential networks with bypassing of communications and with generation of arriving and servicing random size customer batches
The exponential queueing networks class with Jackson traffic of communications and with possibility of instant bypassing of nodes by communications with probabilities depending on their states is considered. The communications taking over by thenodes generate customers’ batches of random sizes and will be joined to these nodes. Customers’ batch of random size is served simultaneously, the size being determinated at the moment of completing the service due to the assembletransfer batch service discipline. When customers batch service is finished it leaves the network and sends communication to other nodes or leaves the network with according to some routing matrix. Sufficient conditions are established for the product form stationary network distribution in terms of insulating nodes in fictitious random environment. As an example we considered the case when the sizes of customers’ batches taking over by nodes have a geometric distribution and the network state stationary distribution has the product form of factors which have shift quasigeometric distribution.
Keywords: queueing networks, batches movements, communications, bypassing of nodes, quasireversibility, productform of shift quasigeometric distributions.
Yu.V. Malinkovsky – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Zhao Yue – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (398 KB)
Martynov I.P., Parmanchuk O.N., Pecevich V.M. On a cross system of two differential equations
The article deals with the crosssystem of the two differential equations of the second degree and fourthdegree derivative of the variables. The necessary and sufficient conditions for the Painleve, property for solutions of the system are found.
Keywords: system of the differential equations, property of Painleve, simplified differential equation.
I.P. Martynov – Y. Kupala Grodno State University, Grodno, Belarus
O.N. Parmanchuk – Grodno State Agrarian University, Grodno, Belarus
V.M. Pecevich – Y. Kupala Grodno State University, Grodno, Belarus
Download PDF (321 KB)
Murashka V.I. On one generalization of Baer’s theorems about hypercenter and nilpotent residual
Semenchuk V.N., Veliasnitski V.F. Finite groups with given properties of critical subgroups
This work is devoted to the study of finite groups with given properties of critical subgroups.
Keywords: group, formation, coradical, generalized subnormal subgroup, Shmidt group.
V.N. Semenchuk – – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
V.F. Veliasnitski – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (328 KB)
TECHNICS
Dick S.K., Tereh A.S., Smirnov A.V., Êonopelko V.K. Designing a system for video recording of man’s extremities tremor
The known devices for tremor recording are considered and their drawbacks are analyzed. A system and methods for video recording of man’s extremities tremor are developed. The laboratory researches of medical therapy have been carried out. The tremor at Parkinson’s disease and at essential tremor has been spectrally evaluated.
Keywords: tremor, oscillations, Parkinson’s disease, essential tremor, amplitudefrequency analysis, neurology, video recording, video camera, video analysis.
S.K. Dick – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
A.S. Tereh – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
A.V. Smirnov – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
V.K. Êonopelko – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
Download PDF (409 KB)
Kuznetsov D.I., Kupin A.I. Method of identification of electrical motor with the use of neural networks
Different kinds of malfunction or damage of the parts may occur in the operation of electrical equipment. It is therefore very important to detect defects in the early stages. The paper presents the method of identification of electrical equipment on the basis of the analysis of the products current. The results of experimental tests are given.
Keywords: identification, spectral noise, high harmonic, neural network.
D.I. Kuznetsov – Krivoy Rog National University, Krivoy Rog, Ukraine
A.I. Kupin – Krivoy Rog National University, Krivoy Rog, Ukraine
Download PDF (297 KB)
