Light action spectra for skin chromophores are simulated. Endogenic porphyrins (Pp IX, Cp III, and Up III) are selected as target chro-mophores. They can produce singlet oxygen (SO) under tissue irradiation, which acts as a natural photosensitizer. The SO is toxic for cancer cells. This process is known to be widely used in photodynamic therapy (PDT). The irradiation at wavelengths ranging from 610 to 630 nm is significantly stimulates the production of endogenous porphyrins SO over the entire thickness of the dermis (2–3 times dermis at a depth z<0.15 mm; 10–12 times dermis z>=0.15 mm) compared with exposure to absolute absorption maxima (at about 501 nm for uroporphyrin (UpIII), 495 nm for coproporphyrin (CpIII) and 505 nm for protoporphyrin (PpIX). The presented results can pro-vide new opportunities for the selection of the irradiation wavelengths under application of traditional PDT methods.

Keywords: soft biological tissue, singlet oxygen, endogenic porphyrins, radiative transfer equation, light action spectra.

N.D. Abramovich – Belarusian State University of Informatics and Radioelectronics, Minsk

S.K. Dick – Belarusian State University of Informatics and Radioelectronics, Minsk

The new solutions of the equation of Helmholtz describing diffraction free asymmetric wave fields of Bessel of a continuous order are offered. They are characterized by five continuous parameters and possess a spiral wavefront. Restrictions on these parameters at which explored fractional beams transfer terminating power are discovered. Pictorial modeling of such beams is fulfilled.

Keywords: beams, asymmetric beams, Bessel beams.

S.S. Girgel – Department of Physics, F. Skorina Gomel State University

The study of restorative and crystallization annealing on ferroelectric properties of SBTN-films with concentration of niobium 10–50 wt. % synthesized by the sol-gel method is presents. Effect of recovery annealing on the oxygen content in the SBTN ferroelectric film connected with the mass concentration of niobium is described.

Keywords: ferroelectric, non-volatile memory, sol-gel method, perovskite structure, crystallization and recovery annealing, capacitor layer, defects, residual polarization, SBTN-film.

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

A.V. Semchenko – F. Skorina Gomel State University

V.V. Kolos – JSC “INTEGRAL” Minsk

A.N. Pyatlitski – JSC “INTEGRAL” Minsk

V.A. Solodukha – JSC “INTEGRAL” Minsk

N.S. Kovalchuk – JSC “INTEGRAL” Minsk

Simulated diamond crystals processing by laser infrared, green and ultraviolet range was done. The analysis of temperature fields and thermal stress fields generated in the diamond crystals as a result of laser exposure was carried out for three different options: an analysis of the effect of laser radiation along the axis of symmetry of the second (L₂), third (L₃) and fourth-order (L₄).

Keywords: laser treatment, diamond, finite element method.

E.B. Shershnev – F. Sñorina Gomel State University

Y.V. Nikitjuk – F. Sñorina Gomel State University

S.I. Sokolov – F. Sñorina Gomel State University

A.E. Shershnev – F. Sñorina Gomel State University

Let be a set of primes, a local formation of finite groups. The conditions of factorability of a subnormal subgroup H of a finite group G by normal subgroups H₁ è H₂ such that H₂ belongs to some generalized Frattini subgroup of a group G and are investigated. Statements, equivalent to the statements on the respective factorizations, functorially generalized, with the consequences for are achieved. The structure of formation radicals of factorgroups of subnormal subgroups of finite groups in connection with generalized Frattini subgroups is investigated.

Keywords: local and radical local formations of finite groups, generalized Frattini subgroups, subgroup m-functor, -radicals.

L.M. Belokon – Mogilev State University of Food Technologies

Random fluctuations in the self-oscillatory systems were investigated by canonical representations. The equations to find the most probable values of the amplitude and phase of the steadystate oscillations in systems with additive wideband noises are obtained.

Keywords: self-oscillatory system, stochastic oscillations, method of canonical representations, amplitude of stationary stochastic oscillations.

S.P. Zhogal – F. Skorina Gomel State University

S.I. Zhogal – Belarusian State University of Transport, Gomel

A.V. Klimenko – F. Skorina Gomel State University

Statement of a boundary problem about a bend of an elastic three-layer circular plate on the basis of Pasternak is given. General analytical solution for the asymmetrical on thickness plate is obtained. It can serve as a source for the study of any case of symmetric bending a circular three-layer plate, simply supported on an elastic foundation of Pasternak’s.

Keywords: three-layer circular plate, symmetric bend, Pasternak's basis.

A.G. Kozel – Belarusian State University of Transport, Gomel

Convex semi-infinite programming problem with polyhedral index sets and faithfully convex constraint functions are considered. An explicit optimality criterion is formulated and proved for the given class of problems. A comparative analysis of this criterion with known optimality conditions is performed. An illustrative example is presented.

Keywords: semi-infinite programming, convex programming, immobile index, immobility order, faithfully convex function.

O.I. Kostyukova – Institute of Mathematics of National Academy of Sciences of Belarus, Minsk

M.V. Kulahina – F. Skorina Gomel State University

The advantage of the reflecting function theory have been demonstrated on the study of the linear non-autonomous two-dimensional systems.

Keywords: differential system, Reflecting Function, Poincare mapping.

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

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

The method of building of compact mathematical models, as use of recurrent attitudes in the kinematic and dynamic models of locomotion of the person, designed for computer modelling is analysed. Problems of the analysis and locomotion synthesis at the kinematic and dynamic level are surveyed. Existing methods of definition of geometry of masses of a human body are investigated and calculations by definition extents of static indefinability of a locomotorium of the person are executed. Problems in research of interacting of the person with an elastic support are shown during locomotion of biomechanical system. New method of research of a three-dimensional motion of the person are offered.

Keywords: recurrent ratioes, analysis, synthesis, elastic leg, three-dimensional motion, motion capture.

A.E. Pokatilov – Mogilev State University of Food Technologies

M.A. Kirkor – Mogilev State University of Food Technologies

Sufficient conditions of nonsemiassociativity of a polyadic operation which is determined on a Cartesian power A^k n-ary semigroup with substitution of a range {1,...,k} and n-ary operation are found.

Keywords: polyadic operation, groupoid, semigroup, semiassociativity, neutral sequence.

A.D. Rusakou – F. Skorina Gomel State University

The asymptotic behavior of diagonal Hermite – Pade polynomials and diagonal Hermite – Pade approximations of type II for the system of exponentials in which while the rest are the roots of the equation is determined. The theorems complement known results of H. Pade, D. Braess, A.I. Aptekarev, H. Stahl, F. Wielonsky, W. Van Assche, A. B. J. Kuijlaars, A.P. Starovoitov, obtained for the case, where the – different real numbers.

Keywords: Hermite integrals, Hermite – Pade polynomials, Hermite – Pade approximations, asymptotic equality.

The structure of the software emulator of PC-compatible controller ADAM 5510M modules with digital and analog IO ADAM 5050, ADAM 5017, ADAM 5024. The implementation of a parser for the Borland Turbo C ++ 3.0 with the ability to use language and custom library functions Advantech is considered. An example of using the emulator to create a virtual stand equipment XY stepper drive are given.

Keywords: PC-compatible controller ADAM 5510M, software emulator, parser Turbo C ++ code, simulation of IO modules ADAM 5050, ADAM 5017, ADAM 5024.

Yu.R. Beytuk – Y. Kupala Grodno State University

G.P. Sebrovskaya – Y. Kupala Grodno State University

V.M. Ramazanov – Y. Kupala Grodno State University

Ability to develop models of dynamic processes of real technical systems with reproducing the physical effects of the interaction of objects is justified. The results of states calculations are presented in the form of 3D objects. Model reconstruction of physical processes with the 3D image will allow solving many practical problems on a new level of quality. Virtual simulation can replace complex and expensive field tests.

Keywords: modeling, technical systems, interaction bodies physical processes.

A.K. Golovnich – Belarusian State University of Transport, Gomel