# Доклады Национальной академии наук Беларуси, 2002, Том 46, No.4

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2002, Том 46, No.4

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Gabasov R., Kirillova F.M.*
**Synthesis of nonlinear observers of dynamic systems by methods of optimal control.** pp. 5--8

*Summary:* A problem of restoring states and disturbances which influence dynamical systems under incomplete and inexact measurements is under consideration. A method of synthesis of nonlinear observers constructing estimates of unknown parameters in real time mode are suggested and justified. The method is based on fast algorithms of optimal control.

*Belousov M.V.*

**On one generalization of the Carleman problem.** pp. 9--12

*Summary:* A generalization of the Carleman boundary problem is considered. For the problem under consideration, the criterion of Fredholm property in appropriate Sobolev spaces is obtained.

*Beresnevich V.V., Bernik V.I., Kovalevskaya E.I.*

**Metric theorems on p-adic number approximation by bounded degree literal numbers.** pp. 13--15

*Summary:* A complete analogue of the metric Khinchine theorem for polynomials of arbitrary degree over the p-adic field is proved.

*Tikhonov S.V., Yanchevskii V.I.*

**Indices of central simple algebras over function fields of projective spaces.** pp. 16--20

*Summary:* Let *K* be a field of zero characteristic, Br *K* be its Brauer group. Bounds of indices of elements of Br *K* as function of their exponent are obtained for function fields of projective spaces defined over *P*_{n,r}-fields.

*Trelina L.A.*

**Dynamic units of number fields and squares as products of periodic points.** pp. 21--23

*Summary:* Integral points of a family of elliptic curves with dynamic unit discriminant are studied.

*Dymkov M.P., Kalinin A.I.*

**On necessary conditions of optimality in discrete 2-D control systems.** pp. 24--26

*Summary:* In the paper, the necessary conditions are given for a discrete 2-D optimization problem. These conditions are formulated in terms of a function that is constructed along the optimal control by the method similar to the dynamic programming approach.

*Gaishun I.V.*

**Stability of two-parameter discrete systems over topological fields.** pp. 27--29

*Summary:* Some conditions of stability for two-parameter discrete systems over topological fields are obtained.

*Jovanovich B.S., Lemeshevsky S.V., Matus P.P.*

**Global stability of second-order differential-operator equations and three-level operator-difference schemes.** pp. 30--34

*Summary:* One of the most important requirements of computational problem-solving methods for mathematical physics problems is the coordination of these methods with the original differential problem. Asymptotic behavior of solutions of first-order differential-operator equations and two-level difference schemes is one of such typical properties. Unfortunately, for second-order equations, such asymptotic behavior of solutions does not occur. However, in this case, we can say about global stability, i.e. stability of solution of the second-order differential-operator equation when *t* ® ¥. In this paper, for the second-order differential-operator equation *D u"* (*t*) + *B u'* (*t*) + *A u* (*t*) = *f* (*t*), *t* > 0; *u* (0) = *u*_{0}, *u'* (0) = *u*_{1}, *a priori* estimates of global stability are obtained for wide class of input data. Moreover, presented are the estimates of stability of three-level operator-difference schemes when *t* ® ¥, conforming with corresponding estimates for original differential problem.

*Borukhov V.T., Zelenyak D.M.*

**Exact solutions for a one class of algebraic Riccati equations.** pp. 35--37

*Summary:* Exact solutions for a one class of algebraic Riccati equations in terms of elliptic Jacobi coordinates are obtained. Some properties of the extremal solutions are investigated. Applications to the relaxation system theory and problem of recoverable work in linear viscoelasticity are considered.

*Zverovich I.E., Orlovich Yu.L.*

**On partition graphs.** pp. 38--42

*Summary:* A partition graph is an intersection graph for a collection of subsets of a universal set *S* with the property that e'ach maximal independent set of vertices corresponds to a partition of *S*. A clique in a graph *G* is called a *universal* one if it intersects all maximal independent sets of *G*. In 1993, McAvaney, Robertson, and DeTemple provided a characterization of partition graphs in terms of covers by universal cliques and formulated some related problems. We present solutions of two of them. Besides, we show that the problem NON-UNIVERSAL CLIQUE is NP-complete.

*Lomovtsev F.E.*

**Cauchy problems for hyperbolic differential operator equations of even orders with variable regions of determination of rapture coefficients.** pp. 43--47

*Summary:* Existence and uniqueness theorem of strong solutions of the Cauchy problems for hyperbolic factorized even-order differential equations with variable domains of nonsmooth and discontinuous operator coefficients is proved.

*Rasolko G.A., Sheshko M.A.*

**Decomposition of vector singular characteristic integral operator with Cauchy's kernel into Chebyshev's polynomials.** pp. 48--51

*Summary:* Decomposition of vector singular characteristic integral operator with Cauchy's kernel in the form of linear combination of orthogonal polynomials (Chebyshev's polynomials of the first and second kind) is obtained.

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

**Triple factorizations in finite groups.** pp. 52--55

*Summary:* It is proved that a finite K-group is not a simple one if it contains proper subgroups *A, B, C* with pairwise coprime indices. There exists a finite simple group *G* containing proper subgroups *A, B, C* so that *G* = *AB* = *AC* = *BC*.

**ФИЗИКА**

*Baikov V.I., Korobko E.V.*
**Kinetics of fluid drop spreading over horizontal surface.** pp. 56--58
SummeryA physical and mathematical model of the process of fluid drop spreading is suggested which quantitatively describes all stages of spreading kinetics on the basic of a unified approach. It has been established that gravity force exerts a pronounced influence on the process of fluid drop spreading over horizontal solid surface.

**ХИМИЯ**

*Ul'yanova T.M., Krut'ko N.P., Titova L.V.*
**Multicomponent fibers based on aluminum oxide.** pp. 59--62

*Summary:* Based on performed investigation, it has been found that in multicomponent Al_{2}O_{3}--MgO fibres, spinel is formed over two temperature regions. For stoichiometric oxide fibres to be produced, Al_{2}O_{3} and MgO ratio must be within 50: 50 to 55 : 45 mol.%.
In three component fibres, such as Al_{2}O_{3} -- ZrO_{2} -- MgO, the formation of nano-sized oxide particles generates a tetragonal solid ZrO_{2}--MgO solution that still persists in a system at heating up to 1200 °C. Then, it undergoes partial decay, and magnesium oxide separated interacts with aluminium oxide and generates spinel; the fibre form remains unchanged.

*Pashkovsky F.S., Khlebnicova T.S., Lakhvich F.A.*

**General approach to synthesis of carboplatin analogues containing fragments of carboxylic fatty acids in acidoligand.** pp. 63--65

*Summary:* A method for synthesis of new carboplatin analogues containing fragments of saturated or unsaturated carboxylic fatty acids in acidoligand has been developed. The synthesis of cis-(diamrnine)[3-(octadeca-9,12-dieneamido)-1,1-cyclobutanedi-carboxylato]platinum(II) has been described.

*Stepanova L.I., Mozolevskaya T.V., Bodrykh T.I., Sviridov V.V.*

**Electrochemical formation of nickel-superdispersed molybdenum or tungsten oxide composite films in aqueous solutions.** pp. 66--70

*Summary:* Investigation results to synthesis possibility and tribological behavior of new type composite films (Ni-superdispersed molybdenum or tungsten oxide particles) are presented in this paper.

**БИОЛОГИЯ**

*Bushmakina I.M., Melnikova A.M., Nekrashevich N.I., Konev S.V.*
**Prevention of lipid peroxidation in liposomal rifampicin under a-tocopherol.** pp. 71--73

*Summary:* Stability is a major indicator of quality of newly developed drugs. The effect of different a-tocopherol concentrations on lipid peroxidation (LP) processes in rifampicin-containing liposomes is studied. If is found that the addition of a-tocopherol of 0.02--0.06 mg/mg of lipids to liposome-forming composition considerably reduces intensity of LPO growth under Fe^{2+}-ascorbate and atmospheric oxygen. The high level of protection against oxidation over four months of storage is established by the analysis of LPO products when the liposomal rifampicin was lyophilic dried and at N_{2} atmosphere soldeved into the ampoules.

*Vadetskaya T.N., Laznev K.V., Vorobei A.V.*

**Importance of glutathione for erythrocyte resistance to delayed hemolysis induced by photodynamic influence.** pp. 74--76

*Summary:* The decrease of erythrocyte resistance to merocyanin-540-photosensitized delayed hemolysis following reduction of glutathione content in cells was shown. The resistance of erythrocytes to photoinduced hemolysis was restored after injection of exogenous glutathione to cell suspension and after induction of antioxidant resynthesis in cells either before or after photodynamic influence. On the basis of the results obtained it may be concluded that the delayed hemolysis photosensitized by merocyanin-540 is a result of membrane damage that can be repaired by cellular enzyme systems using glutathione as reducing equivalent.

*Urbanovich O.Yu., Dolmatovich T.V., Kartel N.A.*

**Use of RAPD-method for analysis of genome of alloplasmic wheat lines.** pp. 77--81

*Summary:* Molecular changes in genome were studied in 46 alloplasmic wheat lines grown as a result of backcrossing. Random primers 11 of which revealed polymorphism between the studied wheat lines were used. Ninety-one loci fifty-nine of which were polymorphic were analyzed in terms of amplification results. Based on the amplification results, dendrogram displaying genetic similarity between alloplasmic wheat lines, genome donor of which was one cultivars, forms an individual cluster. However, within the cluster these lines are rather heterogeneous and differ from both each other and genome donor. Thus, completeness of genetic material transfer and possible genome changes in substituted and supplemented lines should be controlled by molecular-genetic markers and considered in application of alloplasmic lines in genetic investigations.

*Yakovleva G.A., Semanyuk T.V., Monarkhovich S.V., Podobed N.I.*

**Obtaining potato late blight resistance sources by somatic hybridization with Solanum Bulbocastanum.** pp. 82--85

*Summary:* Potato late blight resistance sources were obtained by means of somatic hybridization of tetraploid S. Tuberosum (78563-76) with sexually incompatible wild species S. Bulbocastanum. They were resistant to haulm and tuber late blight in epiphytic 2000 and 2001 when growed without fungicides. Selected lines of somatic hybrids Sb3-2, Sb5-2, Sb6-7, Sb7 had proper morphological characteristics, formed commercial tubers and berries with seeds by free pollination and crosses with high fertile breeding samples. 54.4% of evaluated plants of sexual progeny from these somatic hybrids were resistant to late blight when inoculated by local isolates of Phytophthora infestans.

*Finin V.S., Soklakov V.I., Savchenko N.E. †*

**Estimatins of efficiency of extra-kidney blood purification by the electronic paramagnetic resonance method.** pp. 86--88

*Summary:* The estimation of haemodialysis adequacy by the paramagnetic resonance method with the application of three spin labels was carried out. The given method is more effective than *Kt/V* method. In peritoneal dialysis, the label parameters approximate the values in healthy persons, which testified to the fact, that peritoneal dialysis is more effective in comparison with haemodialysis.

**НАУКИ О ЗЕМЛЕ**

*Savchenko I.E., Yakubovskaya T.V., Pavlovskaya I.E.*
**On Early Poozerian paleogeography in eastern Belarus.** pp. 89--93

*Summary:* The paper represents results of geological and paleobotanical study of buried lake deposits in the Okunevka section (eastern Belarus). The geological evidence allows to suppose that vertical lithofacial succession reflects regional climatic fluctuations. Based on palaeocarpological and palinological data, two Early Poozerian (Weichsclian) cryochrons, separated presumably by Brorup thermochron, have been revealed.

*Golubtsov V. K. †, Tolstosheyev V. I., Kruchek S.A.*

**Stratigraphy of coal deposits in southwestern Belarus.** pp. 94--98

*Summary:* Coal deposits (Dregovichi Suite) in southwestern Belarus (Volyn monocline) are subdivided into three subsuites: lower, middle, and upper one which are correlated with the Tula, Aleksin, and Mikhailovka horizons of the Visean stage of the unified stratigraphic chart of the carbon of the Pripyat Trough.

*Levykh N.N., Bulkin Yu.S., Abramenko V.I.*

**Behavioral peculiarities of Y, Yb, La, and Sc in Mesozoic and Mesocainozoic weathering products of rocks of crystalline basement of Belarus.** pp. 99--101

*Summary:* It has been shown that among studied elements, yttrium and ytterbium show the highest migration capacity (removal is about 50--67%) in the weathering products developed over the various composition rocks except fare sections. Lanthanum proved to be poorly mobile and scandium was found inert. Their mineral indicators and factors being responsible for the trace elements participation in the hypergene migration cycle have been determined.

*Komarovsky M.E.*

**Glacial structure of the Dnieper ice sheet marginal formation in the Middle Pleistocene within the territory of Belarus.** pp. 102--106

*Summary:* New data were used to identify in the territory of central and southern Belarus three glacial complexes, which correspond to the Maximum, Minsk, and Oshmyany Stages of the Dnieper glaciation. The limits of geomorphological sectors and boundaries of glacial complexes, formed during the phases and oscillations of the Dnieper ice sheet have been established more exactly within some border belts. The relief and structure of the Dnieper ice sheet landformes have been described in an attempt to reflect the main peculiarities of the ice sheet geological activities.

*Sokolik G.A., Ovsyannikova S.V., Kimlenko I.M.*

**Organic components and plutonium and americium state in soil and soil solutions.** pp. 107--112

*Summary:* The fraction composition of humus substances (HS) of different type soils and soil solutions have been studied. A distribution of ^{239,240}Pu and ^{241}Am between HS fractions of different dispersity and mobility in soil-vegetation cover has been established. It was shown that humus of organic soils fixes plutonium and americium in soil medium to a greater extent than humus of mineral soils. That leads to lower migration ability of radionuclides in organic soils. The lower ability of americium to form difficultly soluble organic and organic-mineral complexes and predomination of its anion complexes in soil solutions may be a reason for higher mobility and biological availability of americium in comparison to plutonium during soil-plant transfer.

*Kudelsky A.V., Kapora M.S., Pashkevich V.I., Korkin V.D.*

**Hydrosulfuric mineral water in northwestern Belarus: localization, composition and perspectives of utilization.** pp. 113--118

*Summary:* Ground hydrosulfuric mineral water of natural origin is discovered for the first time within the territory of Belams near the village Vidzy Lovehinsky (Vitebsk Region). The chemical description, origin, and future utilization of the discovered ground hydrosulfuric mineral water in the sanatorium practice are shown and discussed.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Baranov V.V., Dostanko A.P., Solovyev Ya.A.*
**Distribution of residual mechanical stress in thin films.** pp. 119--122

*Summary:* A distribution of mechanical stresses in thin molybdenum films has been investigated. The films were formed by a magnetron sputtering method under different technological conditions. It has been shown that the conditions influence on the thin films profile shape indicated by SEM and on the total mechanical stress.

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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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