We discuss the foreseeable sensitivity to Z' of -pair production cross sections at the International Linear Collider (ILC), especially as regards the potential of distinguishing observable effects of the Z' from the analogous ones due to competitor models with anomalous trilinear gauge couplings (AGC) that can lead to the same or similar new physics experimental signatures at the ILC. The model independent analysis of the Z' effects in the process allows to differentiate the full class of vector Z' models (except sequential SM (SSM)-like models) from those with anomalous trilinear gauge couplings. Results of model dependent analysis of a specific Z' are expressed in terms of discovery and identification reaches on the Z–Z' mixing angle and the Z' mass.

Keywords: Z'-boson, anomalous gauge couplings, Z–Z' mixing.

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

Pankov Alexander – Department of Physics, P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

The acoustooptical Bragg diffraction of light by the Lamb’s waves of higher order of a plate from isotropic solid material is investigated. It is shown that acoustooptical modulation deep is reached for diffraction of transmitted waves of the first order. Lamb’s modes are stated to be separately diagnosed by means of the acoustooptical method.

Keywords: Lamb’s waves, acoustooptical diffraction, amplitude modulation, coefficients of reflection and transmission.

A.E. Anisimova – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

The relations determining the intensity of static gravitational field of the massive spherical surface in relativistic Brillouin gravitational statics have been fixed. It has been shown that the value of intensity of the field on the surface itself is half as high as its value near external surface.

Keywords: relativistic theory of gravitation, boundary problem, nonlinear gravistatics.

N.A. Akhramenko – Belarusian State University of Transport, Gomel, Belarus

L.M. Bulauko – Belarusian State University of Transport, Gomel, Belarus

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

The technique of the forward calorimeters of CMS detector at Large hadron collider based on the use of the electromagnetic and hadron components of transverse momentum balance in single-jet events with direct photons and di-jet QCD events containing photons with sufficiently high energies is investigated. The event selection rules and the condition of applicability of the technique are defined.

Keywords: large hadron collider, hadron calorimeter, electromagnetic calorimeter, calibration.

A.V. Zarubin – Veksler and Baldin Laboratory of High Energy Physics, JINR, Dubna, Russia

V.F. Konoplianikov – Veksler and Baldin Laboratory of High Energy Physics, JINR, Dubna, Russia

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

We considered a high-ordered array of a finite number of circular cylinders characterized by a defined length and oriented perpendicu-larly to a planar substrate (so called “multimers”). On the base of the volume integral equation formalism we studied both straight and inverse dielectric systems with a honeycomb structure. The scattering direction diagrams and a field distribution into/near the cylinders included into a multimer were analyzed at different cylinder and multimer sizes and for a number of materials under condition of incident light directed along a pore axis.

Keywords: space-ordered cylinders, direction diagrams, near-field distribution.

V.A. Kovtun-Kuszhel – Y. Kupala Grodno State University, Grodno, Belarus

R.A. Dynich – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk, Belarus

A.N. Ponyavina – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk, Belarus

Several simple sets of degenerated Mueller matrices of the rank 1 and 2 having the structure of semigroups are constructed explicitly with the use of a linear expansion of real 4x4-matrices in terms of Dirac matrices. The properties important in polarization optics are considered.

Keywords: Mueller matrix, polarization optics, semigroup.

E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus

O.V. Veko – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus

V.M. Red’kov – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk, Belarus

The structure of a fiber-optical dynamic memory with series-parallel channels of input-output of the digital information and optical regeneration is developed. Influence of nonlinear phenomena in optical fiber on the information characteristics of such systems in view of fluctuation sources and effect of intersymbol interference in a fiber-optical contour at spectral multiplexing of information channels is investigated.

Keywords: fiber-optical memory, timing jitter, nonlinear phenomena, information parameters.

A.V. Polyakov – Belarusian State University, Minsk, Belarus

A.V. Zhukouski – Belarusian State University, Minsk, Belarus

This paper examines the relationship between the ferroelectric and structural properties of the films of Sr_1+yBi_2+xTa₂O₉, synthesized by the sol-gel method. It is shown that the variation of the stoichiometric ratio between the source components included in the structural formula of SBT-material leads to a structural change, and therefore the ferroelectric properties of SBT-layers. As we approach the region of instability of the system as the value of the Curie point decreases.

Keywords: sol-gel, SBT-films, hysteresis loop, dielectric constant, Curie temperature.

V.V. Sidsky – F. Skorina Gomel State University, Gomel, Belarus

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

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

V.V. Kolos – Joint Stock Company «Integral», Minsk, Belarus

A.S. Turtsevich – Joint Stock Company «Integral», Minsk, Belarus

S.A. Soroka – Joint Stock Company «Integral», Minsk, Belarus

A.N. Asadchiy – Joint Stock Company «Integral», Minsk, Belarus

The sufficient conditions for coinsidering Mironenko reflecting functions of Abel equations and where are constants are established. Obtained results are illustrated by examples.

Keywords: Abel equation, reflecting function, equivalence of differential equations, polynomial perturbations.

V.A. Belsky – Gomel Engineering Institute of the Ministry for Emergency Situations of the Republic of Belarus, Gomel, Belarus

V.I. Mironenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

In the work V.S. Monahov's results that for any soluble non-nilpotent finite group G its Frattini subgroup Ô(G) (subgroup G)) coincides with intersection of all maximal (respectively all abnormal maximal) subgroups M of group G such that MF(G) = G, are extended on arbitrary finite groups.

Keywords: finite group, maximal subgroup, Frattini subgroup, Frattini -subgroup, subgroup m-functor.

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

T.I. Vasilyeva – Belarusion State University of Transport, Gomel, Belarus

A.V. Syrokvashin – I.G. Petrovsky Bryansk State University, Bryansk, Russia

It was established , that if the first component of the Mironenko reflecting function of the system is linear with respect to x, and independent of y then the second component of the reflecting function is linear with respect to y.

Keywords: differential system, reflecting function, periodic solutions.

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

The polyadic groups of spacematrix are studied in this paper.

Keywords: matrix, vector-matrix, spacematrix, group, ring , l-ary group.

A.M. Gal’mak – Department of Economic, Mogilev State University of Food Technologies, Mogilev, Belarus

The open queueing network with polytypic demands is considered in the article. The single line units can work in some strategies. The quantity of the work which are necessary for servicing of demand and for switching from one strategy to another are random variables with arbitrary distribution function. The parameters of servicing and switching processes are dependent on the general unit state. It was proved that stationary distribution is invariant in relation to functional form of distribution of work’s quantities which are necessary for servicing of demands and switching of strategies, on condition that first moments are fast.

Keywords: queueing network, stationary distribution, multimode service, insensibility.

A.R. Eryomina – Y. Kupala Grodno State University, Grodno, Belarus

An optimal control problem of a thermal process in the rod with heat exchange on both ends is considered. The method of its approximate solution by data to optimal control problem of large-scale differential equations system is offered. The algorithm of operation of the optimal regulator forming in real time current values of an optimal feedback is described.

Keywords: thermal process, optimal control problem, optimal feedback, optimal regulator.

D.S. Kuzmenkov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The solvability of a finite group whose cofactors of maximal subgroups is supersolvable and satisfy some additional restrictions is established.

Keywords: finite group, solvable group, supersoluble group, maximal subgroup, cofactor.

I.V. Lemeshev – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

V.S. Monakhov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Let G be a finite simple group, S be its Hall Schmidt -subgroup. If then G is not a -group. If and then G is a -group.

Keywords: group, subgroup, simple group, Hall Schmidt -subgroup, -group.

N.V. Tyutyanov – International Institute of Labor and Social Relations, Gomel

P.V. Bychkov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Influence of structural features of the soil basis on the base deposit is investigated.

Keywords: soil bases, deformations, deposit of the bases, computer objective – focused modeling.

V.E. Bykhautsau – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

S.V. Torgonskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

In the article the author presents the simulation results of assessment the impact of modes of information processing computational process in a multiprocessor computer system at the time of the sharing the task. The problem is presented in the form of a network schedule. The estimation of the lengths of critical paths for different versions of the organization stresses on nodes in the dynamics of changes in the priorities of interactive and distributed applications is carried out.

Keywords: program-technological complex of simulation, simulation modeling, computer system, computer process, the working load, the distributed processing of the information.

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

The method of synthesis of structure of the technological cycle for managed production systems based on a finite set of mathematical models is proposed. Dynamic simulations are used as an instrument for the implementation of the proposed approach uses. Theoretical basis and application of dynamic simulation technology as a method of system analysis of complex systems for a class of managed production systems with the probabilistic characteristics of their functioning are provided in the paper.

Keywords: classes of complex systems, managed production systems, dynamic simulations, synthesis of structure of the technological cycle.

V.S. Smorodin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus