
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N1 (6) 2010
PHYSICS
Andreev V.V., Krutov A.F. Electromagnetic form factors of mesons
Meansquare radii and electromagnetic form factors of light mesons are obtained in the framework of Poincare covariant quark model based on the point form of relativistic Hamiltonian dynamics. Calculations are performed with the use of the requirement of selfconsistent description of electroweak properties and masses of pseudoscalar and vector mesons.
Keywords: meson, quark model, electromagnetic form factor, leptonic decay constant.
Andreev V.V. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Krutov A.F. – Department of Physics, Samara State University, Samara, Russia
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Girgel S.S. Properties of vectorial paraxial light beams. I. Homogeneous polarization
The simple formalism for the description of the vector paraxial light beams of general type is offered. Simple expressions for the energy flux density of the electromagnetic field S of the vector light beams with the homogeneous polarization are discovered. It is discovered that paraxial circular polarized light beams are spread independently, and their streams of energy are parted and they are also independent.
Keywords: paraxial beams, vector beams, light beams, polarizable properties, energy properties, polarization.
Girgel S.S. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Gudelev V.G., Kulak G.V., Matveeva A.G. Laser excitation of surface acoustic waves pulses in solid state bodies
Features of laser excitation of the pulses of surface acoustic Rayleigh waves in solid state bodies through a prism by a source of radiation of the round form are investigated. It is shown, that at increase in the azimuth angle there is increase in the amplitude and reduction of duration of the ultrasound pulse; at increase in the angle of the prism inclination the amplitude of the acoustic pulse decreases, and the duration increases. It is established, that at increase in the radius of an aperture of the round form the pulse amplitude increases and the duration decreases; with the increase in the factor of absorption of a hypersound the pulse amplitude decreases, and the duration increases.
Keywords: acoustic pulse, surface acoustic wave, solid state body, hypersound absorption.
Gudelev V.G. – B.I. Stepanov Institute of Physics NASB, Minsk, Belarus
Kulak G.V. – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
Matveeva A.G. – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
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Kapshai V.N., Korsun L.D. The stationary perturbation theory in case of a potentialseries
The procedure for constructing of stationary perturbation theory for the Schrodinger equation and corrections to the energy spectrum and corresponding wave functions is implemented in case of the potential, represented in the form of a series in powers of a small parameter (potentialseries). The application of the obtained scheme for the anharmonic oscillator is examined as a physical example.
Keywords: stationary perturbation theory, Schrodinger equation, wave function, energy spectrum, potential, correction, anharmonic oscillator.
Kapshai V.N. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Korsun L.D. – Department of Automation and Information Systems, P. Sukhoi State Technical University, Gomel, Belarus
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Nikitjuk Yu.V., Sholoh V.F. Research of the process of operated thermosplitting of fragile nonmetallic materials under the influence of the stream of hot air
The paper presents the results of research of the process of cutting of fragile nonmetallic materials by the influence of the directed stream of hot air and coolant. The finite element method was used to decide the problems of thermo elasticity. The features of spatial localization of thermo elastic fields are defined and the mechanism of dividing crack formation is revealed.
Keywords: hot air jet, glass, crack.
Nikitjuk Yu.V. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Sholoh V.F. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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Sarkisov O.A., Rogachev A.A., Rogachou A.V., Egorov A.I. Molecular structure and morphology of surface layers of polyimidefluoropolymer film treated by glow discharge plasma
The change of morphology and molecular structure of surface layers of polyimidefluoropolymer film after lowfrequency glow discharge plasma treatment by the method of infrared spectroscopy and atomic force microscopy is determined. In case polyimide layer treatment occur mainly layerbylayer etching and formed layers have cyclic variations of polar and disperse fraction of surface energy. The etching of molecules aligned primary parallel to the surface of a substrate in case fluoropolymer layer treatment is shown.
Keywords: lowfrequency glow discharge plasma, polyimidefluoropolymer film, infrared spectroscopy, molecular orientation, Kelvin mode of scanning probe microscopy.
Sarkisov O.A. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Rogachev A.A. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Rogachev A.V. – Rector of F. Skorina Gomel State University, Gomel, Belarus
Egorov A.I. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
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MATHEMATICS
Vorob’ev N.N., Mekhovich A.P. În direct decompositions of nmultiply saturated formations
All groups considered are finite. Let
be a set of nonempty subclasses of a class of groups
such that
for all distinct
. We write
to denote the collection of all groups of the form , where
for some
. We proved the following theorem.
Theorem. Let
where
is a formation. Then
is
nmultiply
saturated formation if and only if
is
nmultiply
saturated for all
Keywords: formation of finite groups, complemented subformation, direct decomposition of a class of groups,
local satellite,
nmultiply
saturated formation.
Vorob’ev N.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Mekhovich A.P. – Department of Mathematics, P.M. Masherov Vitebsk State University, Vitebsk, Belarus
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Gal’mak A.M. Transposed vectormatrices
The transposed vectormatrices are defined and studied in this paper.
Keywords: matrix, vectormatrix, ring, field, semigroups, nary group.
Gal’mak A.M. – Department of Economic, Mogilev State University of Food Technologies, Mogilev, Belarus
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Kovalyova V.A., Skiba A.N. Criteria of psupersolubility and supersolubility of finite groups
Let
G be a finite group,
A a subgroup of
G. Then we say that
A is generalized quasinormal in
G if
A either covers or avoids every maximal pair
(K,H) of
G. We say that
A is
msupplemented in
G if
G has a subgroup
T and a generalized quasinormal subgroup
C such that
G=AT and
Based on these concepts new characterizations of finite
psupersoluble and supersoluble groups are obtained.
Keywords: maximal pair, generalized quasinormal subgroup,
msupplemented subgroup,
psupersoluble group, supersoluble group.
Kovalyova V.A. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Skiba A.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Kosenok N.S. On one class of finite supersoluble groups
The following theorem is proved.
Theorem. If in a nonidentity finite group
G every primitive subgroup has a prime power index, then
G=[
D]
H, where
D and
H are Hall nilpotent subgroups of
G and
D coincides with the
residual
of
G.
Keywords: primitive subgroups, finite group, soluble group, supersoluble group, nilpotent group.
Kosenok N.S. – Gomel Branch of International Institute of Labor and Social Relations, Gomel
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Kulazhenko Yu.I. Vectors and semiabelian criteria of nary groups
New criteria of semiabelian of nary groups expressed in terms of the properties of vectors G are determined.
Keywords: symmetrical points, parallelogram G, semiabelian nary group, vector G.
Kulazhenko Yu.I. – Vice Rector of F. Skorina Gomel State University, Gomel, Belarus
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Labych Yu.A., Starovoitov A.P. Approximation of continuous functions by rational Pade–Chebyshev fractions
The paper is concerned with the description of the asymptotic behaviour of parabolic sequences of the elements of PadeChebyshev table for some continuous functions represented by Chebyshev series. The asymptotic form of the best rational approximations for such functions is determined.
Keywords: best approximations in the uniform norm, Pade–Chebyshev approximant, trigonometric Pade approximant, rational approximation, the accurate constants of rational approximation.
Labych Yu.A. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Starovoitov A.P. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Sidoryk H.G. Characteristic of UMD spaces with Hilbert transformation of vectorvalued functions on the field of padic numbers
We consider Hilbert transformation of vectorvalued functions on the group of padic integers Z_{p} taking values in Banach space X, and squareintegrable in Bochner sense. If Hilbert transformation
with
is a bounded operator, then Banach space
X is an UMD space.
Keywords: Hilbert transformation, UMD space, padic numbers, Fourier transformation.
Sidoryk H.G. – MechanicsÌathematical Department, Belarusian State University, Minsk, Belarus
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Shnyparkov À.V. Supersolvability of a finite group with supplemented subgroups
INFORMATION SCIENCE
Bykhautsau V.E. Methodology, methods and technology of computer objectoriented modelling of nonlinear systems of deformable solid bodies
The paper presents one of the ways of decision of the problem of perfection of the resourcesaving technology in industrial and civil construction. Materials of the original researches are considered on the basis of concepts of the system approach, modern computer technologies and the developed methods of decision of boundary problems of the nonlinear theory of elasticity.
Keywords: nonlinear systems, deformable solid bodies, construction, methods, means and technology of optimization.
Bykhautsau V.E. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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