Changes of the acoustical pulse form of longitudinal and shear ultrasonic waves, excited by the optical-acoustical sources of circular form from polar angle are investigated. It has been stated that the form of gaussian pulse of shear ultrasonic waves is sufficiently transformed under the increase of the polar angle; the change of the form of longitudinal ultrasonic waves pulse is more significant. It has been shown that acoustical pulse amplitude is determined by the diffraction function of the longitudinal and shear ultrasonic waves on the circular form opening.

Keywords: laser excitation, ultrasonic waves, pulse, directional diagram, solid state body.

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

Method for resonance finding, based on the Fredholm integral equation, and analysis of their influence on cross section are presented. This method is applied for several model potentials. Examples of the resonance behaviour of the cross sections of various types are presented. The results of the calculations are compared with the results obtained using other methods.

Keywords: Fredholm equation, resonance energy, resonance wave function, complex scaling, S-matrix, cross section.

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

Shilyaeva K.P. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

We have studied the theoretical uncertainties in the calculation of the inclusive jet cross section for the LHC experiments using the parton-parton NLO-generator JET-RAD (2002) and the library of parton distribution functions LHApdf-5.3.1 for CTEQ65 and CTEQ6A. For beam energy TeV the results are consistent with the original analysis, performed in CDF collaboration. For LHC beam energy TeV the main theoretical uncertainties are associated with the dependence of the QCD factorization and renormalization scales (15%), with uncertainty of PDF (10%) and parton jet clustering uncertainty (3%).

Keywords: inclusive jet cross section, quantum chromo-dynamics, parton distribution functions, large hadron collider.

Shmatov S.V. – Veksler and Baldin Laboratory of High Energy Physics, JINR, Dubna, Russia

Shulga S.G. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Main theorems about differential functions are proven with the use of the definition of the derivative which does not invoke the concept of limit.

Keywords: derivative, limit, definition, calculus, algebra and introduction to calculus.

Gavriliouk A.V. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Gavriluk A.A. – Department of Building, Belarusian State University of Transport, Gomel, Belarus

Some assertions in harmonic analysis on the infinite dimensional torus are stated and their equivalence to Riemann hypothesis is proved.

Keywords: Riemann hypothesis, infinite dimensional torus, Mobius function, Eiler function, inverse formula.

Mirotin A.R. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The method of stabilization of optimal on speed systems in the class of the bounded control based on the use of an auxiliary problem of optimal control – problem of control intensity minimization – is described. Results are illustrated by the example of dynamic system of the fourth order.

Keywords: stabilization, feedback, dynamic system, speed problem, optimal control problem.

Ruzhitskaya E.A. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

We give some conditions under which a finite group belongs to a composition formation containing all finite supersoluble groups. The main results of the papers [20]–[32], [34]–[37] are generalized.

Keywords: finite group, saturated formation, composition formation, Baer-local formation, p-nilpotent group, cyclic chief factor, supersoluble subgroup, quasisuper-soluble group, S-quasinormal subgroup, S-supplemented subgroup, S-quasinormally embedded subgroup, the SE-core of subgroup, Sylow subgroup, the generalized Fitting subgroup, maximal subgroup.

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

Determinant formulas for numerators and denominators of joint approximations of Pade of perfect system of functions are established. The analogue of the Pade theorem is proved and the obvious kind of the remainders is found at the approach by the rational function . The received theorems supplement and generalise the known results of Ermite, Pade, K. Mahler, E.M. Nikishin, A.I. Aptekarev and other authors.

Keywords: sedate a number, approximations of Pade, joint approximations of Pade, perfect system of functions, determinant representation.

Starovoitov A.P. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Rjabchenko N.V. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Some properties of the chief series of congruences of universal Mal’cev algebras are studied.

Keywords: universal algebra, series of congruences, Mal’cev algebra.

Hodalevich A.D. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The paper describes the structure of soluble finite groups in which Silov subgroups are generalized subnormal subgroups.

Keywords: saturated formation, hereditary formation, soluble group, subnormal subgroup, generalized subnormal subgroup.

Schevchuk S.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Semenchuk V.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

It is proved that every -local (by Forster) formation of finite groups is an -composition formation, where .

Keywords: finite group, formation.

Shemetkov L.A. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

This paper considers an open queueing network with different types of positive, negative customers and signals. Staying time of arriving demands in each node is the random value having exponential distribution. Stationary distribution of the network states is found in product form and each multiplier represents stationary distribution of the isolated nodes.

Keywords: queueing network, different types of positive, negative customers and signals, stationary distribution.

Yakubovich O.V. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Evdokimovich V.E. – Department of Building, Belarusian State University of Transport, Gomel, Belarus

This paper is devoted to the description of the possibilities of specific realization of the model of research teams’ interaction. A joint project – an interregional research portal of ideas aimed at overcoming the Chernobyl disaster – is considered as the realization of the model. The paper describes the scientific relevance and practical significance of a scientific portal and provides a brief characteristic of the main directions of the project. We describe the features of its creating and implementing and the prospects of development in theoretical and practical plans.

Keywords: model of interaction research teams, the Chernobyl accident, information and telecommunication technologies, the Internet portal, online scientific communities.

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

Eliseeva E.V. – I.G. Petrovsky Briansk State University, Briansk, Russia

Maslov V.P. – Chernihiv State Institute of Economics and Management, Chernihiv, Ukraine

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

Bujalskyy V.M. – Chernihiv State Institute of Economics and Management, Chernihiv, Ukraine

Regularities of the wear of silica glass at friction against a smooth steel counterbody and fastened abrasive are analyzed. Data on the kinetics and mechanisms of the frac-ture of the surface layer as well as on the pattern of the propagation of microcracks beyond the contact area are reported for both modes of loading. Regularities of the effect of the normal load and the sliding velocity on the propagation depth of fatigue microcracks and the wear rate of silica glass as well as their relation to peculiarities of the frictional heating of the surface layer of the worn body are discussed. Causes of the appearance of subsurface microcracks that result in the delamination of the glass surface layer are considered.

Keywords: wear, silica glass, fatigue microcracks, wear rate, load, sliding velocity.

Bogdanovich P.N. – Belarusian State University of Transport, Gomel, Belarus

Bliznets D.À. – Belarusian State University of Transport, Gomel, Belarus

Tkachuk D.V. – V.A. Belyi Metal-Polymer Research Institute National Academy of Sciences of Belarus, Gomel, Belarus

In the paper the basic laws of the processes taking place during the realisation of consistently spent processing in the barrier electric category of cellulosecontain ma-terials and drawing polymeric coverings from an active gas phase on their surface are defined. It is shown that such a technique allows raising water repellency of paper and firmness to abrasion of the text applied on its surface.

Keywords: cellulosecontain materials, glow discharge, polymer coating, abrasion.

Gavrilchik V.T. – Belarusian State University of Transport, Gomel, Belarus