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

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

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 five-layer 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

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 ar-bitrary 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

Within the limits of the theories of thermoelasticity and linear fracture mechanics finite-element modelling of the laser-induced crack extension in silicate glasses at two-beam 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

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 w-supersolubility and super-solubility of groups are received.

Keywords: finite group, permutizer of a subgroup, permuteral subgroup, supersoluble group, w-supersoluble group, P-subnormal 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

Let be a -solvable Fischer class. In the paper we studied -saturated Fitting classes, which are normal in . It is proved, that intersection of any set of such classes is a -saturated Fitting class, which is normal in .

Keywords: Fitting class, -injector, Fischer class, semilocal Fitting class.

S.N. Vorob’ev – P.M. Masherov Vitebsk State University, Vitebsk

For any integers of a subset T of the symmetric group and semi-group A on the Cartesian product an l-ary operation is determined. This l-ary operation is similar to the Post poliadic operations, which he defined on the set of poliadic permulations. In the paper the properties of the operation are studied.

Keywords: operation, semigroup, group, l-ary semigroup, l-ary group, skew element, idempotent.

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

In this paper we will prove an analog of the Luzin theorem on correction for spaces of Sobolev type over p-adic vectors. The results were announced in «Doklady of the National Academy of Sciences of Belarus».

Keywords: space of p-adic vectors, Sobolev spaces, Luzin approximation.

E.V. Gubkina – Gorno-Altaisk State University, Gorno-Altaisk, 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

In this paper all critical groups with an identity Frattini subgroup for hereditary local superradical formation are described. New exam-ples of hereditary local superradical formations are obtained.

Keywords: formation, superradical formation, critical group, simple non-abelian group.

S.F. Kamornikov – Gomel Branch of International University «MITSO», Gomel, Belarus

V.N. Tyutyanov – Gomel Branch of International University «MITSO», Gomel, Belarus

In the paper the author continues to describe his research dedicated to the study of the properties of the l-ary groupoid where is a set of all mappings of an arbitrary set J in an arbitrary groupoid A, and the l-ary operation is defined for any integer and for any permutation of the set J. In particular, some semiabelian criteria of this l-ary groupoid are found.

Keywords: n-ary group, l-ary groupoid, semiabelity, l-ary operation.

Yu.I. Kulazhenko – F. Skorina Gomel State University, Gomel, Belarus

Signs of non-simplicity of a solvable radical and criteria of non-simplicity 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

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

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 information-measuring system using LabVIEW software package for in-put/output of the measurement information, control of functional blocks of the complex, analysis of the measurement results and elec-tronic reporting. The features of building of individual components and the entire complex as a whole are described.

Keywords: hardware and software complex, information-measuring 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