# Доклады Национальной академии наук Беларуси, 2004, Том 48, No.2

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2004, Том 48, No.2

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Monastyrnyi P. I., Kremen E. V.*
**On method of complete reduction with pseudo-Newtonian interations.** pp. 5--9

*Summary:* In this paper, an iteration generalization of complete reduction method to grid boundary value problems with separate boundary conditions is constructed and justified.

*Kirsanova-Yevkhuta O. N.*

**Convergence theorems of method of quickest descent and method of minimal errors.** pp. 10--15

*Tikhonov S. V.*

**On Pythagoras number of function fields of hyperelliptic curves defined over real formal power series field.** pp. 16--18

*Summary:* Hyperelliptic curves over real formal power series field such that the pythagoras number of their function fields is bigger then 2 are found.

*Suprunenko I. D.*

**On behavior of unipotent elements in representations of special linear group with large highest weights.** pp. 19--23

*Summary:* Lower estimates for the number of Jordan blocks of the maximal dimension in the images of unipotent elements of nonprime order in irreducible modular representations of the special linear group with large highest weights with respect to the ground field characteristic are obtained (in terms of the group rank and the order of a relevant element).

*Demenchuk A. K.*

**Criterion of existence of periodic solutions of nonlinear quasiperiodic perturbed differential systems with two-frequency basis.** pp. 24--26

*Summary:* We consider the system x^{.} = F(t, x) + G(t, x), where F, C are periodic in t with incommensurable periods to and O respectively. The necessary and sufficient existence conditions for W-periodic solutions are obtained. These conditions do not use the averaging operator.

*Balashevich N. V.*

**Real-time optimal control of high-order systems.** pp. 27--31

*Summary:* For a linear dynamical system with an uncertain initial state, an algorithm of real-time realization of optimal guaranteeing control is justified.

*Lepin V. V.*

**Minimizing of half-perimeters of hyperedges in layout of hypergraph into grid.** pp. 32--35

*Summary:* The problem: A hypergraph is given; place its vertices on a 2-dimensional grid to minimize the total half-perimeter of the hyperedges. By the half-perimeter of the hyperedge, we mean the half-perimeter of the convex hull of the hyperedge vertices in the layout. We obtained an *O*(log^{3} *n*) approximation algorithm for this problem.

*Gorokhovik V. V., Malashevich D. S.*

**Direct optimality conditions of the third order for solutions of optimization problem with inequality constraints.** pp. 36--40

*Summary:* For an optimization problem with inequality constraints, we prove both necessary and sufficient optimality conditions of the third order presented in a primal form without using dual variables (Lagrange multipliers).

**ФИЗИКА**

*Grinchik N. N., Nogotov E. F.*
**To problem of interaction of electromagnetic waves with polarized environments taking into account relaxation processes.** pp. 41--45

*Summary:* For modeling distribution and absorption of electromagnetic waves in polarized environment, account of dielectrics of losses, it is offered to take into account delay of electrical and magnetic polarization with introduction of electrical and magnetic relaxation. The decision of a task of distribution of a periodic boundary mode is made in view of the hereditary characteristics of environment, which qualitatively corresponds to experimental data.

*Soika A. K.*

**Hall effect in indium arsenide in unipolar pulsed magnetic fields with induction of up to 56 Т.** pp. 46--47

*Summary:* The Hall effect is experimentally studied for *InAs* at room temperature and unipolar high pulsed magnetic field with induction of up to 56 T. It is found that under these conditions, the Hall constant for *InAs*. is practically invariable.

*Gusakov V. E.*

**Quantum-chemical calculation of oxygen atom diffusivity in crystalline silicon.** pp. 48--51

*Summary:* A theoretical method of calculations of the oxygen diffusivity in crystalline silicon both at normal and high hydrostatic pressure has been devised. It has been found that the diffusion process of an interstitial oxygen atom (Oj) is controlled by optimum configuration of three nearest silicon atoms. Just their configuration corresponding to a local minimum of total energy determines the values of activation energy DE_{a} = 2.59 eV and pre-exponential factor D_{0} = 0.28 cm^{2} s^{-1}. The calculated values are in a good agreement with experimental ones and for the first time describe perfectly an experimental dependence of the O_{i} diffusion constant in the temperature range 350--1200 °C. Hydrostatic pressure (P £ 80 kbar ) results
in a linear decrease in the diffusion barrier (¶pDE_{a}(P) = - 4.38 • 10^{-3} eV kbar^{-1}). The calculated pressure dependence of O_{i} diffusivity agrees well with the pressure enhanced initial growth of oxygen-related thermal donors.

*Matyuk V. F., Osipov A. A.*

**Mathematical model of magnetic hysteresis loop.** pp. 52--55

*Summary:* The equation suggested permits, on four general characteristics of ferromagnetic material (initial magnetic susceptibility, saturation magnetization, residual magnetization, coercive force), to describe (with sufficient for practical purposes accuracy) the hysteresis cycle of alternating magnetization of a ferromagnet in the wide range of changes of the remagnetization fields and of the magnetic characteristics of the material.

*Zhestkov S. V.*

**Direct method of building of multidimensional plane solitons.** pp. 56--58

*Summary:* A direct method of constructing multidimensional plane solitons is suggested. On its basis, the dark (*l* + 1)-dimensional soliton solutions of the composite form are constructed for the system of second-order coupled nonlinear Schrodinger equations. The necessary and sufficient conditions of existence of these solutions are obtained.

*Borisevich N. A., Raichyonok T. F., Dubovski V. L.*

**Spectral-fluorescent characteristics of physiologically active 8-azasteroid solutions in hexane.** pp. 59--63

*Summary:* Intermolecular interaction of 8-azasteroids exert essential influence on their absorption spectra in polar solutions. Fluorescence spectra of the hexane solution studied substances depend on absorbing radiation wavelength, which is connected with photo- and thermochemical transformations of the structure molecules.

*Komarov F. F., Vlasukova L. A., Yuvchenko V. N., Petlitskaya T. V.*

**Ion-Induced track annealing in GaAs.** pp. 64--70

*Summary:* Track formation in GaAs crystals irradiated into fluence range from 5 • 10^{10} to 1 • 10^{12} cm^{-2} with U and Bi swift ions had been investigated by means of selective chemical etching and atomic force microscopy. Ion tracks are registered in samples irradiated with fluence of 5 • 10^{10} cm^{-2}. Tracks density correlates with fluence in accordance with atomic force microscopy data. The annealing of tracks created on former irradiation stages takes place at fluence growth to 1 • 10^{12} cm^{-2}. Modified thermal spike model taking into account temperature dependence of material thermophysical properties and containing no free parameters has been used to simulate track formation processes in GaAs crystals. The results of computer simulation have been compared with experimental data.

**ХИМИЯ**

*Naumova M. V., Korik E. O., Semak I. V.*
**Structural patterns of interaction of mono-, di-, and trihydroxy-flavones with copper.** pp. 71--74

*Summary:* Interaction of mono-, di- and trihydroxyflavones with copper ions was studied. It was shown that presence of hydroxygroup in position 3 or 5 is essential for helating activity of flavonoids. Interaction with copper is accompanied by changes in absorbance spectrarum of flavonoids. Addition of EDTA causes reduction of initial spectra of flavonoids expressed in different extent that confirms the phenomenon of formation of flavonoid-copper complexes.

**БИОЛОГИЯ**

*Alekhnovich A. V.*
**Daily ration as function of specific growth rate of water invertebrates.** pp. 75--78

*Summary:* It is established that daily rations and specific growth rate are related by the linear relationship through the species-specific regression coefficients.

*Buchmakina I. M., Skorinko E. V., Martynova M. A., Konev S. V.*

**On rifampicin stabilization in lipid vesicles.** pp. 79--81

*Summary:* Antimycobacterial drug rifampicin entrapment into liposomes and fheir stability at retaintion depending on drag concentration is reviewed. Stable liposomal rifampicin is formed by administration of 75 mkg antibiotic/ 1 mg of lipids.

*Shukanova N. A., Lobanok E. S., Yanushko A. V., Ostrovsky U. P., Shved I. A., Vladimirskaya T.E., Sugak N. K.*

**Merocyanin 540 photosensitized inhibition of hyperplasia vein graft wall.** pp. 82--84

*Summary:* Merocyanine 540-induced photooxidation is effective in the inhibition of neointimal formation of vien graft interposed in the arterial circculation for 4.5 months in vivo. There was much less increase in formation of the neointima in the implanted photooxidized vein graft compared with implanted nonphotooxidized vein grafts.

*Shapturenko M. N.*

**Genetic heterogeneity of Opal spring wheat disomic lines and estimation of relationship between methods of its determination.** pp. 85--89

*Summary:* Genetic heterogeneity of disomic lines in spring wheat Opal was studied by means of biochemical, PCR, and biometric analyses. The lines were shown to differ from each other and cultivars in both protein-enzyme systems and DNA-markers, with the differences being observed not only between individual lines but also between genomes. Disomics of A- and B-genomes turned out to be most polymorphic and D-disomics turned out to be less polymorphic. The biometric approach has also made it possible to reveal substantial differences among lines and cultivars. Ал optimum number of statistically significant differences was determined for D-lines. The relationship between approaches of genetic divergence estimation proved to be high and positive only for PCR_GD and Euclidean_GD.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Isaevich L. A., Kozhevnikova G. V.*
**Stress distribution at cross rolling.** pp. 90--93

*Summary:* The fields of slide lines with cross rolling of unlimited cylinder with flat plates are offered with degrees of cogging 5 > 1.025 with the centered deformation field, and with little degrees of cogging 6 < 1.025 when the deformations in the cylinder cut do not penetrate upon the axis and touch stresses are non-uniformly distributed.

*Azizov R. O.*

**Structure and residual stresses of gas-thermal coatings hardened by carbonitriding.** pp. 94--97

*Summary:* The results of investigation of structure and internal stress of the thermo-spraying steel coatings after carbonitriding are presented in the paper. It is shown that the saturation of steel coatings made with nitrogen and carbon provides for a forming of layers with high hardness, high tearing strength and compression stress during the thermochemical treatment.

*Sviridenok A. I., Chizhik S. A., Louis H., Ihnatouski M. I.*

**Features of water-drop erosive destruction of polymeric surface at nano level.** pp. 98--102

*Summary:* Surface topography and physical-mechanical behaviors of polymethylmethacrylate samples eroded by water-drop jet have been studied at nano level. The methods are based on digital image processing atomic force microscopes. The investigation results turned to be useful for characterizing the effect of the water jet on mechanisms and parameters of erosion.

*Ulyanova T. M., Krut'ko N. P., Vityaz P. A., Titova L. V., Medichenko S. V.*

**Peculiarities of formation of refractory compounds structure based on ZrO**_{2}, A_{2}O_{3}. pp. 103--108

*Summary:* The study performed allowed us to establish the mechanism of formation of fibrous oxide with a complex architecture, including metal oxide nanoparticles, nanopores and microcapillaries.
Based on the calculations of crystallite sizes, it is found that crystallographic transformations of fiber oxides cause substance to disperse. Structural changes in fibrous oxides are followed by varying the porosity nature and pore size. The obtained regularities permit us to predict the properties and to control the technology of producing nanostructural fibrous oxide materials.

*Pyatov V. V., Sheleg V. K., Kovchur A. S.*

**Universal device Thribometer for powder materials.** pp. 109--111

*Summary:* The device Thribometer is designed for measurement of factors of internal and external friction of powder materials, study of dependence of these factors on the intense status and temperature. Also, the device allows to measure thribotech-nical constants used in the nonlinear laws of friction. Measurement of condense of powders and factor of lateral pressure are also possible.

*Dorozhkin N. N., Klimenko S. E., Khudoley A. L.*

**Compression kinetics and volume strain of powder layer at radial distribution.** pp. 112--114

*Summary:* In view of geometrical parameters of calibrating element, volumetric deformations of powder system are determined. Expression for definition of pressure upon the condensed layer, caused by summing action of centrifugal forces and forces of radial distribution is received. The equation of condensation kinetics of covering from powder material is offered during its burning with radial distribution.

**СОЦИАЛЬНО-ГУМАНИТАРНЫЕ НАУКИ**

*Palchikov N. N., Sayanova I. G.*
**Comparative analysis of financial coefficients in building companies in the Republic of Belarus and the Russian Federation.** pp. 115--119

*Summary:* The creation of the single Union State is required to establish certain procedure of financial results forming acceptable for the Russian Federation and the Republic of Belarus. Analyzing the forms of reports of receipts and losses made in these states, one can find some similar moments, but at the same time, there are some differences that do not allow to find the common denominator. It is connected with different terms, financial results forming methods and tax system.
For example, in the Russian Federation, there are such terms as gross receipts reflected in income statement, receipts after taxes, extraordinary receipts and losses, included in receipts after taxes. There are different coefficients in income statement in the Republic of Belarus and this is not corresponding to main coefficients of the Union State. It is necessary, in spite of differences in tax system, come to a common ground in forming the uniform statements and create universal report documents to meet the needs of both states and allow the information users to see more really the work of building companies both in the Russian Federation the and in the Republic of Belarus.

*Ivanova D. V.*

**Invention as industrial property.** pp. 120--123

*Summary:* Existing points of view on the industrial property and invention are considered. It is shown thata new approach to their content is necessary, in particular the opinion on the perspectives of development of the juridical category of patentable invention is presented. The conclusions can be used for improvement of the legislation of the Republic of Belarus.

/ Издания академии / Научные журналы / К началу страницы

Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *15 ноября 2006 г.*

Создана при участии Игнатия И. Корсака

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