# Доклады Национальной академии наук Беларуси, 2000, Том 44, No.5

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2000, Том 44, No.5

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Suprunenko I. D.*
**Recognition of natural realizations of classical algebraic groups by matrixes withlarge Jordan blocks.** pp. 5--8

*Summary:* For each type of the classical algebraic groups of rank > 1 a quadratic function *f* is indicated such that if the image of a rational irreducible representation j of a group *G* of such type contains a matrix with a Jordan block of size *k* and the dimension dim j < *f*(*k*), then either j(*G*) is the standard realization of *G*, or the pair (*G*, j) belongs to a well-defined relatively small list. In particular, it is proved that j(*G*) is the standard realization of *G* if 64 < dim j < (*k*^{2} + 4*k* - 13) / 8.

*Bakhtin V.I.*

**Superregular perturbations of fiber ergodic semigroups.** pp. 9--11

*Summary:* Semigroups of conditional expectation operators generated by stochastic systems with slow and intermixing fast motions possess three remarkable properties: superregularity, fiberness, ergodicity. Here we define and investigate an abstract notion of superregular perturbation of fiber ergodic semigroup.

*Gabasova O.R.*

**Elaboration of optimal corporate strategy in running 2 processes.** pp. 12--15

*Summary:* Using optimal control methods, policy of investments, dividends and distribution of capital between two production activities is constructed for a dynamic model of the firm.

*Benediktovich V.I., Sarvanov V.I.*

**Straight topological graphs.** pp. 16--19

*Summary:* Straight topological graph (ST-graph) is a topological graph with edges formed straight line. It has been proved that the noncrossing chain (cycle), the noncrossing spanning tree, the noncrossing perfect matching problems in ST-graph are NP-complete.

*Tikhonov S.V., Yanchevsky V.I.*

**Brauer groups of split elliptic curves defined over field of rational numbers.** pp. 20--22

*Summary:* The criterion of nontriviality of generators of 2-torsion part of the Brauer group of split elliptic curve over field of rational numbers is obtained.

*Semenchuk V.N., Shemetkov L.A.*

**Superradical formations.** pp. 23--25

*Summary:* All groups considered are finite. A formation **F** is called superradical if the following two conditions hold;
1) **F** is a *S*_{n}-closed formation;
2) **F** contains every group *G* = *AB* where *A* and *B* are **F**-subnormal **F**-subgroups of *G*. It is proved that if **X** = **XX** is *S*-closed formation then every formation of the form **F** = Ç_{i,jÎI} **X**_{pi} **X**_{pj} is superradical. If is non-empty soluble S-closed formation then the following conditions are equivalent;
1) **F** is a superradical formation;
2) **F** = Ç_{i,jÎI} **s**_{pi} **s**_{pj}.
Here **s**_{p} is the class of all p-groups in **s**.

*Benyash-Krivetz V.V.*

**Decomposition of generalized triangle groups.** pp. 26--29

*Summary:* The problem of decomposing generalized triangle groups having generators of finite order into non-trivial free products with amalgamation is studied in this paper. The following theorem is proved.

*Borukhov V.T., Gaishun I.V.*

**Linear differential systems with varying structure.** pp. 30--33

*Summary:* A new notion of Cauchy correspondence is determined for varying structure differential equations and the solution is obtained. The presented results are used in the multipoint boundary problem for linear nonstationary systems.

*Tishchenko K.I.*

**Application of linear independent polynomials in Wirsing problem.** pp. 34--36

*Summary:* An improvement of the Wirsing's theorem on approximation to real numbers by algebraic numbers is obtained.

*Beresnevich V.V.*

**Regular systems and linear Diophantine approximations on manifolds.** pp. 37--39

*Summary:* The method proving divergence of Khintchine--Groshev theorem for Diophantine approximation on non-degenerate manifolds is given.

*Knyazhishche L.B.*

**Lyapunov functionals and conditions of uniform asymptotic stability for delay equations.** pp. 40--43

*Summary:* Necessary conditions of the uniform asymptotic stability are obtained for delay equations using non-monotone Lyapunov functionals.

**ФИЗИКА**

*Zaretskaya E.P., Gremenok V.F., Victorov I.V., Ivanov V.A., Zalessky V.B., Kovalesky V.I., Yermakov O.V., Leonova T.R.*
**Structural characteristics of CuInSe**_{2} films obtained by 2-stage selenization of Cu-In layers. pp. 44--48

*Summary:* CuInSe_{2} films of chalcopyrite structure have been fabricated by selenizaton of co-evaporated Cu-In films in closed system. The films showed preferential orientation in (112) plane and wide range Cu/In composition of 0.52--1.29. The surface morphology and phase composition of films is dependent on Cu/In ratio of the starting alloy. These properties were clearly reflected in low temperature photolumenescence studies, indicating broad emission for thin films containing high concentrations of indium.

*Kovalenko O.E., Voytenko A.I., Redko V.P.*

**Photoconductivity of quantum size structures CdSe/dielectric.** pp. 49--50

*Summary:* High photoconductivity of structures made from CdSe/polyethylene terephthalate by alternating vacuum electron-beam evaporation is observed.

*Zhestkov S.V., Kuvshinov V.I.*

**Generalization of Hirota's method for the systems of second order coupled non-linear Schrodinger equations.** pp. 51--55

*Summary:* For common system of second order coupled nonlinear Schrodinger equations the one-soliton solution is found. The necessary and sufficient conditions for this solution are formulated.

**ХИМИЯ**

*Grozhik V.A., Bychko G.V., Zonov Yu.G.*
**Stabilization of glass phase in fine inorganic oxide films by laser plasma.** pp. 56--59

*Summary:* Processes induced by heat treatment and action of corrosive media in thin films of leadborate glasses doped with CoO, ZrO_{2}, Sb_{2}O_{5}, V_{2}O_{5}, MoO_{3}, deposited in vacuum at evaporation of initial materials by the Nd-laser were revealed. It is shown that influence of high-energy laser plasma on the growing glass films promotes higher corrosion stability of glassy phase in comparison with similar films obtained by low-energy methods of vacuum evaporation.

*Kirillov S.A., Lesnikovich A.I.*

**Mathematical model of self-organization of highly complex dissipative structure during liquid-flame combustion.** pp. 60--64

*Summary:* The mathematical model of self-organization of dissipative structure during liquid-flame combustion is developed. It is shown that evolution of liquid phase in the course of liquid-flame combustion is determined by nonlinear Schrodinger equation for amplutude of pressure field envelope. The mechanism of self-organization of reaction zone into *L*-sphere is discussed on the basis of obtained solutions.

**БИОЛОГИЯ**

*Kharitonchik S.A., Osipovich A.B., Fomin I.K.*
**High pecombination rate in the leader region of retroviral genome.** pp. 65--68

*Summary:* Retroviruses are RNA viruses that replicate through DNA intermediate. The unique characteristic of retroviruses is that their particles contain two complete copies of RNA genomes. The diploidy of retroviruses determines the high rate of recombination during reverse transcription. However, the role of two genomic RNA molecules for replication of retroviruses is not clear yet. We have designer experimental system to study the involvement of two genomic RNA molecules in the process of reverse transcription. For this aim we have used two MoMuLV-based retroviral vectors. One of them (wild type) was able to replicate and another one was defective with deletion of PBS or inverted reaped. The particulary of our experimental system was that the efficiency of copackaging defective genomes in the same virions with genomes of wild type was close to 100%. The high frequency of complementation of defective vectors (12.5%) by the vector of a wild type was shown. In this system the complementation could be carried out by means of recombination in a leader region of retroviral genome. The high frequency of this process allows to assume, that the ledder region contains a specialized sequence ensuring the formation of provirus with involvement of two genomic molecules of RNA.

*Pinchuk S.V., Vorobey A.V.*

**Chlorophorm modification of photophysical and photochemical processes in tryptophan.** pp. 69--72

*Summary:* It is shown that UV-irradiation of tryptophan water solutions containing chlorophorm results in photoinduced formation of radicals of one-electron reduction of halogencarbohydrate. Mechanism of the radical formation consist in distant transfer of electron from tryptophan in singlet excited state to chlorophorm. The transfer efficiency exponentially decreases with increase of distance between donor and acceptor. Formed radicals of chlorophorm initiate degkadation of biomolecules.

*Kirillov V.A., Dubovsky S.V., Tolstik S.V.*

**Generation of mechanically-induced radicals in tooth enamel.** pp. 73--76

*Summary:* It was shown that formed during mechanical enamel-dentin separation long-living radicals had symmetric singlet view with *g* = 2.0029 and D*H*_{pp} = 0.094 mTl. We differentiated the addition of mechanically induced component in "dosimetric" signal, which results in overestimation of the reconstructed dose. Short-living radicals formed during tooth crushing faded during 24 hours.

*Goman N.M., Radyuk M.S., Fradkin L.I.*

**Control of photochlorophyllide synthesis from 5-aminolevulinic acid in greening barley leaves.** pp. 77--80

*Summary:* 6--7-day-old greening barley leaves were redarkened and exposed to the solution of 5-aminolevulinic acid (ALA). The rate of protochlorophyllide (Pchlide) accumulation was studied as a function of ALA concentration and the time of irradiation. The Pchlide amount in greening leaves was also determined. The saturating ALA concentration was 20 mM regardless of the greening stage. In contrast, the rate of dark Pchlide accumulation from saturation ALA concentration increased till 10 h of greening, somewhat later than the maximal rate of chlorophyll (Chl) accumulation was reached, and then decreased. The amount of Pchlide in irradiated leaves was changed in similar way. It was concluded that activity of the enzyme system transforming ALA into Pchlide changes during greening and reaches its maximum when Chl accumulates rapidly.

*Giginyak Yu.G., Moroz M.D.*

**Ecological and biotopical features of the relict amphipod Synurella ambulans from springs of Belarus.** pp. 81--83

*Summary:* In the paper ecological and biotopical features of the relict freshwater amphipod crustacean Synurella ambulans from Belarusian springs are considered. Concrete finding sites are reported. General biological parameters such as mass, size, fecundity etc are originally presented. Some problems of an evolution of the species are discussed.
Spring water in Synurella biotopes is extremely clear and characterized by low content of chemical elements such as potassium, sodium, chlorides and low general mineralization. Possibility of entering this species in the Red Book of Belarus is debated.

*Reutsky V.G., Gigolashvili T.S.*

**Deficit of water saturation in assimilative tissue of Solanum tuberosum L. in the course of microcloning in vitro.** pp. 84--86

*Summary:* The deficit of water saturation of potato plant assimilative tissue were revealed in water saturation atmosphere condition in vitro. It was proposed that this kind of deficit induce the water transport through xylem vessels.

*Gavrilov V.B., Kravchenko O.N., Vetushko D.A., Gurevich G.L., Konev S.V.*

**New method of evaluating erythrocyte damage by cationic dye binding.** pp. 87--90

*Summary:* Accumulation of a cationic dye Nile blue (NB) in intact and damaged erythrocytes treated by detergent at different initial dye concentrations and media/cell volume ratios was studied. The optimal conditions of NB incubation with cells providing for maximal sensitivity of method to erythrocyte damage were determined. The NB accumulation in erythrocytes of pulmonary TB patients increased 10 fold in comparison with norm, whereas value of methylene blue accumulation, measured by the known method, was only 20% ligher.

*Konoplya E.F., Popov E.G., Kutz F.I., Belousov O.L., Klunduk L.F.*

**Androgenreceptor interaction in reproductive tissues of test animals accumulating **^{137}Cs. pp. 91--94

*Summary:* The paper presents new data on dose-dependence in rat reproductive system, obtained by radioimmunoassay and gravimetric techniques: we studied dynamics of the testicular plus prostate androgen -- receptor disfunctions and changes in the ventral lobe mass of a prostate gland after 160 and 320 KBq per rat radioactive caesium injections and 6-month maintenance of animals in different reference points of radionuclide-polluted Mogilev- and Gomel-regions.

*Denisenko N.P., Gurin V.N.*

**Ultrastructure of rat liver parenchyma cells under experimental fever.** pp. 95--98

*Summary:* Studies on the hepatic parenchymal cells in rats suffering from experimental fever revealed ultrastructural changes involved in the formation of the liver response to lipopolysaccharide, which differed from those induced by high ambient temperature that led mainly to adapto-compensatory responses.

**НАУКИ О ЗЕМЛЕ**

*Levykh N.N., Bulkin Yu.S., Abramenko V.I.*
**Trace elements behavior in pre-Cambrian weathering crusts developed over intermediate rocks of Belarus crystalline basement Strakh L. I. Regularities of Cs**_{137} distribution in Mozyr Polesye landscapes. pp. 99--102

*Summary:* Data obtained on the trace elements migration in the Pre-Cambrian weathering crusts developed over intermediate rocks showed that it is dependent on the concentrator minerals, media conditions and attendant processes.

*Strakh L.I.*

**Regularities of Cs**^{137} distribution in Mozyr Polesye landscapes. pp. 103--106

*Summary:* Multiyear investigations revealed lateral redistribution of ^{137}Cs in geochemical conjugation of elementary landscapes of Mozyr Palesse. The systenmatic study allowed to separate the zones of accumulation and of prevalently biogenic and mechanical transport of ^{137}Cs and to establish their correlation with landscape-geochemical structure of territory.

*Veretennikov N.V., Korzun V.P., Makhnach A.S., Laptsevich A.G.*

**Upper Devonian volcanogenic formations in Gomel structural system.** pp. 107--109

*Summary:* Volcanic-magmatic formations detected in the Gomel region arc composed of effusive, volcanoclastic and other medium and basic alkaline rocks: alkaline basaltoids and their tuffs, alkaline and subalkaline trachytes, syenite-porphyries, trachybasalts.

*Matveev A.V., Nichiporenko L.A., Chizhikov Yu.A.*

**Classification of Belarus regions as potential areas of extreme geomorphological processes.** pp. 110--112

*Summary:* The areas with the highest, high, medium, low, and very low probability of extreme forms of geomorphological processes are distinguished taking into account the peculiarities of modern morphodynamics.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Roman O.V., Andilevko S.K., Dybov O.A., Karpenko S.S., Koval O.I.*
**Experimental effeciency assessment of superdeep penetration of SiC particles into steel.** pp. 113--115

*Summary:* The results of experiments assessing effeciency of super-deep penetration are being considered. The rest energy and velocity distribution of penetrating flux of the discrete particles are being established experimentally. The quantitative method to evaluate effectiveness of the process based on complex sampling with a set of foils-detectors was proposed.

*Butylin V.G., Ivanov V.G.*

**Intellectual system of braking control for mobile machines.** pp. 116--118

*Summary:* Theoretical calculations have shown that optimum road coupling conditions of a car wheel in possible traffic situations with traditional design of system of active safety (SAS), can not be ensured with universal control algorithm, hence the variant of constructing highly effective intellectual SAS operated by algorithm of preextreme control is offered.

*Sviridenok A.I., Kovalevskaya T.I., Krantson A.G., Bernatskaya U.I.*

**Polarization and depolarization of polyamide films filled with fibreglass.** pp. 119--122

*Summary:* The electretisation of polyamide films, filled with glass fibers, was investigated. The films were fabricated by thermal pressing. Formation of an electret condition was observed only in area of a polymeric matrix. The charge was localized near surface of the films. Polarization of glass fibers at temperature of pressing did not occur.

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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *6 сентября 2008 г.*

Создана при участии Игнатия И. Корсака

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