The problem of electromagnetic wave scattering on biisotropic sphere in biisotropic medium is solved. Analytical expressions for expansion coefficients of the scattered and inner fields on the complete orthonormal system of spherical vectors are obtained. These coefficients are numerically analyzed depending on the parameters of biisotropic media. It is shown that in the particular case of gyrotropic media our results yield solutions known earlier.

Keywords: biisotropic medium, constitutive relations, Mie theory, spherical vectors, spherical waves.

V.N. Kapshai – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

V.V. Kondratjuk – Department of Automation and Information Systems, P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

New cut optimization technique with using gene Algorithms is proposed. The main advantage of this method is completely automatic search for cut points. This allows finding cut points without of human intervention. Moreover, precision of cut points obtained by automatic searching is much higher than for those obtained «by hand». Preliminary results of the veto system cut optimization in the E391 [1] experiment is presented. The developed technique is applicable to other experiments.

Keywords: rare decay, KL – meson, gene algorithms, cuts

N.V. Maksimenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A.S. Kurilin – JINR, Dzelepov Laboratory of Nuclear Problems, Leader scientific worker, PhD, Dubna, Moscow region, Russia

S.V. Podolsky – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

V.V. Andreev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A.A. Yuchko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

K.S. Babich – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Yu.Yu. Stepanenko – JINR, Dzelepov Laboratory of Nuclear Problems, Scientific worker, Dubna, Moscow region, Russia

In the present paper the copper alloying of single-component and titanium- containing diamond-like coatings obtained from cathodic pulse plasma is examined. The pecularities of the influence of the copper alloying of such coatings on their microhardness, internal mechanical stresses and morphology have been defined. It is shown, that copper-containing carbon coatings have non-uniform structure, they are characterised by lower microhardness and they keep high tribotechnical properties. Microhardness increases after annealing the coatings containing carbon, titanium and copper. Copper implantation into the coating leads to decrease of internal mechanical stresses and changes their character; at high copper concentration they become compressing.

Keywords: carbon coatings, mechanical properties, friction, alloying, copper, titanium, morphology.

D.G. Piliptsov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A.V. Rogachev – Rector of F. Skorina Gomel State University, Gomel, Belarus

N.N. Fedosenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

R.V. Bekarevich – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

It was determined, that the processing of composition coatings on the basis of carbon and titanium by ions of nitrogen essentially disperses the structure of coating (the size of formation becomes 10 times less). After annealing of coatings the morphology becomes more homogeneous.

Keywords: composition coatings, ion processing, morphology, structure formation.

D.G. Piliptsov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A.S. Rudenkov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

R.V. Bekarevich – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Modelling of the process of laser thermosplitting of glass products of the tubular form is executed. Calculations of thermoelastic fields for one-beam and two-beam variants of realisation of technology of laser thermosplitting have been performed. It is shown, that for practical use the application of a two-beam way laser cutting of fragile glass tubes is expedient.

Keywords: laser cutting, dual-laser-beam method, glass.

S.V. Shalupaev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Y.V. Nikitjuk – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A subgroup H of a finite group G is said to be s -conditionally permutably embedded (or in brevity, s-c -permutably embedded) in G if for each every Sylow p -subgroup of H is a Sylow p -subgroup of some s -conditionally permutable subgroup of G . In this paper, we use some s-c -permutably embedded subgroups to study the structure of some groups. Some known results are generalized.

Keywords: finite group, s -conditionally permutably embedded subgroup, formation, Sylow subgroup, maximal subgroup.

Jianhong Huang – Department of Mathematics, University of Science and Technology of China, Hefei, China

Fengyan Xie – Humanistic Management College, Anyang Normal University, Anyang, China

Xiaolan Yi – Zhejiang of Science and Technology University, Hangzhou, China

In this paper the equivalence of the k-th generalized modulus of smothness determined with the help of the generalized shift operator and Peetres K-functional is proved.

Keywords: Jacobi generalized shift operator, generalized modulus of smoothness, K-functional.

G.N. Kazimirov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The system of the nonlinear equations describing the condition of static balance of the flexible triangular suspension in a plane force field, coplanar to the plane of the constant triangle of kinematic relations is received.

Keywords: flexible triangular suspension, static balance, kinematic relations, not extensible flexible string.

Y.A. Kashin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

M.I. Zhadan – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

R.E. Kashina – Department of Mechanical Engineering, P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

Let be a class of groups. A subgroup H of a group G is said to be a maximal -subgroup of G if and G has no a subgroup such that . The symbol denotes the intersection of all maximal -subgroups of G We study the influence of the subgroup on the structure of G.

Keywords: saturated formation, hereditary formation, minimal subgroup, maximal -subgroup, -hypercentre, soluble group, supersoluble group, -quasinormal subgroup.

A.N. Skiba – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Let G be a finite group and a formation of finite groups. We say that a subgroup H of G is -normal in G if there exists a normal subgroup T of G such that HT is a normal Hall subgroup of G and is contained in the -hypercenter of . In this paper, we obtain some results about the -normal subgroups and use them to study the structure of finite groups.

Keywords: finite groups, -normal subgroup, Sylow subgroup, maximal subgroup, minimal subgroup.

Yufeng Liu – School of Mathematics and Informational Science, Shandong Institute of Business and Technology, Yantai, China

Xiuxian Feng – School of Mathematics, Xuzhou Normal University, Xuzhou, China

Jianhong Huang – Department of Mathematics, University of Science and Technology of China, Hefei, China

The authors propose an adaptive way of protecting computers from unauthorized use. The original scheme of the software implementation is discussed. The advantages of creating and implementing of program tools are considered.

Keywords: authorization, identification, authentication, software system, the corporate network.

V.D. Liauchuk – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

O.M. Demidenko – Prorector of F. Skorina Gomel State University, Gomel, Belarus

A.I. Kucharau – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

The problem of the credit repayment term determination is discussed. Investment project is represented as probabilistic net diagram. Analytical and simulation methods of investigation are compared.

Keywords: credit, investment project, probabilistic net diagram, simulation.

O.I. Eskova – Belarusian Trade and Economics University of Consumer Cooperatives, Gomel

I.I. Kikot – Belarusian Trade and Economics University of Consumer Cooperatives, Gomel