
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N2 (15) 2013
PHYSICS
Vardanian R.S. On the problem of radiation reflection of stochastic media
We derive a closed equation for the conditional probability of reflection of radiation from the stochastic environment in the case of rapid fluctuations in the quantum scattering albedo. Numerical calculations are given.
Keywords: radiation transfer, albedo, random field, infinitesimal operator.
R.S. Vardanian – Belarusian State Economic University, Bobruisk Branch, Bobruisk, Belarus
Download PDF (297 KB)
Kurhuzenkava I.I., Guzatov D.V., Gaida L.S. Radiation pressure on the spherical nanoparticle with a concentric shell in the field of a plane electromagnetic wave
In this paper we study theoretically the radiation pressure on a spherical nanoparticle with a concentric shell in the field of a plane electromagnetic wave. The dependencies of the radiation pressure and absorption cross sections on the wavelength of the incident radiation for different thickness of nanoshell at the fixed size of the silica nanoparticle with gold shell located in water are investigated. The authors also study the dependence of the wavelength corresponding to the maxima of the cross sections on the thickness of the shell. The dependencies of the maximal displacement of the nanoparticle on the time of the radiation acting and on the thickness of the nanoshells are considered.
Keywords: radiation pressure, spherical nanoshell, absorption cross section, nanoparticle displacement.
I.I. Kurhuzenkava – Y. Kupala Grodno State University, Grodno, Belarus
D.V. Guzatov – Y. Kupala Grodno State University, Grodno, Belarus
L.S. Gaida – Y. Kupala Grodno State University, Grodno, Belarus
Download PDF (386 KB)
Stas’kov N.I., Ivashkevich I.V., Krekoten N.A. Ellipsometry of the transitive layers semiconductor – dielectric
The polarizability bound of the layer with its optical thickness is established for thin oxide surfaces on a silicon substrate. It is revealed that the structure of the inhomogeneous surface layer can be interpreted by a fivelayer model with 11 parameters at the heat treatment of the silicon plates.
Keywords: ellipsometry, optical model, transition layer, rough and optically inhomogeneous layers, polarizability.
N.I. Stas’kov – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
I.V. Ivashkevich – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
N.A. Krekoten – Belmicrosystems Reserch & Desing Center Branch of the JSC INTEGRAL, Minsk, Belarus
Download PDF (390 KB)
Khilo P.A., Petrova E.S., Khilo N.A. Generation of Bessel light beams frequency doubling in quadratic nonlinear crystals with radial structure of the domain polarized
In the paper the scheme of the second harmonic generation of Bessel light beams in quadratic nonlinear crystals with radial periodic structure of domains is described. Nonlinear polarization at the fundamental and double frequencies is calculated and spatial structure of interacting fields is founded. The overlap integrals that characterize the efficiency of the frequency doubling of Bessel light beams of arbitrary order are numerically investigated.
Keywords: second harmonic generation, quadratic nonlinear crystals with radial periodic structure of domains, Bessel light beams.
P.A. Khilo – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus
E.S. Petrova – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus
N.A. Khilo – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus
Download PDF (311 KB)
Shalupaev S.V., Serdykov A.N., Nikitjuk Yu.V., Sereda A.A. Modelling of the process of the twobeam laser thermosplitting of silicate glasses within the limits of the linear fracture mechanics
Within the limits of the theories of thermoelasticity and linear fracture mechanics finiteelement modelling of the laserinduced crack extension in silicate glasses at twobeam laser controllable thermosplitting is executed on the basis of the developed algorithm. It is shown that crack initiation takes place on a surface of material in the zone of a coolant feeding and at its extension in the depth the flaw shape has the characteristic deflection, which is verified by the results of experimental researches.
Keywords: crack, laser splitting, fracture mechanics.
S.V. Shalupaev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.N. Serdykov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Yu.V. Nikitjuk – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
A.A. Sereda – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (608 KB)
MATHEMATICS
Vasil'ev A.F., Vasil'ev V.A., Vasil'eva T.I. Permuteral subgroups and their applications in finite groups
Let H be a subgroup of a group
G. The permutizer of H
in G is the subgroup
The subgroup
H of a group
G is called permuteral in
G, if strongly permuteral in G, if
whenever
The properties of finite groups with given systems of permuteral and strongly permuteral subgroups are obtained. New criteria of wsupersolubility and supersolubility of groups are received.
Keywords: finite group, permutizer of a subgroup, permuteral subgroup, supersoluble group, wsupersoluble group, Psubnormal subgroup.
A.F. Vasil'ev – F. Skorina Gomel State University, Gomel, Belarus
V.A. Vasil'ev – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
T.I. Vasil'eva – Belarusian State University of Transport, Gomel, Belarus
Download PDF (333 KB)
Vorob’ev S.N. On normal subclasses of Fischer class of finite groups
Gal'mak A.M. Generalizing poliadic operations
Gubkina E.V., Zabello K.V., Prokhorovich M.A., Radyna Ya.M. The Luzin approximation of functions from Sobolev classes on the space of a multidimensional padic argument
In this paper we will prove an analog of the Luzin theorem on correction for spaces of Sobolev type over padic vectors. The results were announced in «Doklady of the National Academy of Sciences of Belarus».
Keywords: space of padic vectors, Sobolev spaces, Luzin approximation.
E.V. Gubkina – GornoAltaisk State University, GornoAltaisk, Russia
K.V. Zabello – Belarusian State University, Minsk, Belarus
M.A. Prokhorovich – Belarusian State University, Minsk, Belarus
Ya.M. Radyna – Belarusian State University, Minsk, Belarus
Download PDF (421 KB)
Kamornikov S.F., Tyutyanov V.N. Critical groups of hereditary local superradical formation
In this paper all critical groups with an identity Frattini subgroup for hereditary local superradical formation are described. New examples of hereditary local superradical formations are obtained.
Keywords: formation, superradical formation, critical group, simple nonabelian group.
S.F. Kamornikov – Gomel Branch of International University «MITSO», Gomel, Belarus
V.N. Tyutyanov – Gomel Branch of International University «MITSO», Gomel, Belarus
Download PDF (428 KB)
Kulazhenko Yu.I. On semicenters of
lary groupoids
Tihonenko T.V. Finite groups containing a given system of permutable subgroups
Signs of nonsimplicity of a solvable radical and criteria of nonsimplicity of a finite group, which contains the given system of permutable subgroups were obtained in this paper.
Keywords: finite group, permutable subgroups, solvable radical, nonabelian simple group.
T.V. Tihonenko – P.O. Sukhoi Gomel State Technical University, Gomel
Download PDF (314 KB)
INFORMATION SCIENCE
Bykhoutsev V.E., Prokopenko D.V., Torgonskaya S.V. Mathematical and computer modelling of the bearing ability of the reinforced soil bases of the bases of buildings
The paper deals with the abalysis of the bearing ability of the soil basis slab the base which has the inclusion of the weak ground strengthened by screw piles of small section. For research of the bearing ability the program complex «Energy 3D» was used.
Keywords: slab foundation, computer modelling, mathematical model, screw pile, bearing ability.
V.E. Bykhautsau – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
D.V. Prokopenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
S.V. Torgonskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (437 KB)
Listopad N.I., Zdorovtsev S.V., Kruglov I.G., Petrovich A.G. Functionality of the hardware and software complex for laboratory work
The article describes the hardware and software complex to deal with educational tasks in the practical training of experts in electronics and instrumentation. The complex is built on the basis of the informationmeasuring system using LabVIEW software package for input/output of the measurement information, control of functional blocks of the complex, analysis of the measurement results and electronic reporting. The features of building of individual components and the entire complex as a whole are described.
Keywords: hardware and software complex, informationmeasuring system, USB device, control module.
N.I. Listopad – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
S.V. Zdorovtsev – Public Joint Stock Company «MNIPI», Minsk, Belarus
I.G. Kruglov – Public Joint Stock Company «MNIPI», Minsk, Belarus
A.G. Petrovich – Public Joint Stock Company «MNIPI», Minsk, Belarus
Download PDF (903 KB)
