# Доклады Национальной академии наук Беларуси, 2000, Том 44, No.4

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2000, Том 44, No.4

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Gabasov R.F., Kirillova F.M.*
**Constructing method of guaranteeing optimization of nonlinear dynamic systems.** pp. 5--8

*Summary:* The principles of constructing optimal guaranteeing controls (of discrete type) are investigated for the nonlinear dynamic systems with unknown but bounded disturbances. A scheme of the realization of the controls is based on piecewise-linear approximations and the small parameter method.

*Erovenko V.A., Ivanov Yu.G.*

**Essential spectra of power of the Cesaro operators in the Banach sequence spaces.** pp. 9--13

*Summary:* The paper describes the fine spectra and the essential spectra of power of the discrete Cesaro operators *C*_{0}, *C*_{¥}, *C*_{p} in the spaces *c*_{0}, *l*_{¥}, *l*_{p}, 1 < *p* < ¥, respectively.

*Alekhno A.G.*

**The solvability conditions of the Remmann boundary value problem in the space of bounded analytic functions.** pp. 14--17

*Summary:* The solvability conditions have been provided for the Riemann boundary value problem in the space of the bounded analytic functions.

*Bouzar Sh.*

**Local estimates for pseudodifferential operators.** pp. 18--20

*Summary:* We obtain the local estimates in the Sobolev spaces for the operators defined as the sum of squares of pseudodifferential operators.

*Malafei D.A.*

**Economical monotone difference schemes for multidimensional problem of convection diffusion on nonunifom grids.** pp. 21--25

*Summary:* The economical unconditionally monotone difference schemes (the maximum principle is satisfied without constraints on the relations involving scheme coefficients and grid steps) for the multidimensional inhomogeneous boundary value problems of the convection-diffusion with variable coefficients are constructed. Schemes suggested have the second order of local approximation on a nonuniform spatial grid. A priori estimate in the maximum norm *C* is proved.

*Emelichev V.A., Nikulin Yu.V.*

**Stability of an efficient solution of vector problem of integer linear programming problem.** pp. 26--28

*Summary:* We consider a multicriterial integer linear programming problem. A formula of the stability radius of the efficient (Pareto optimal, Slater optimal, Smale optimal) solutions has been proved for the case where the Chebyshev norm is defined in the space of perturbing matrices.

*Kovalenok A.P.*

**Rotation pseudomonotone vector fields and boundary value problem for the 2-nd order ordinary differential equations.** pp. 29--33

*Summary:* The paper presents the theorems on solvability and existence of nontrivial solutions of boundary value problems for the 2-nd order ordinary differential equations of the elliptic type. These theorems are based on the rotation of pseudomonotone vector fields and corresponding calculating the index of a zero and asymptotic index.

*Lesnevsky V.E.*

**On approach of solutions of stochastic differential equations containing the random Poisson process.** pp. 34--36

*Summary:* In this paper a complete classification of methods of approximation of the stochastic integrals containing the random Poisson process have been provided. The marginal behavior of solutions of the finite difference equations with averaging is considered.

*Benyash-Krivetz V.V.*

**Representation varieties of non- Euclidean crystallographic groups.** pp. 37--41

*Summary:* It is found all irreducible components of the representation variety *R*_{n} (G_{g}) of a non-Euclidean crystallographic group G_{g} of genus g ³ 3 and it is proved their rationality.

*Beresnevich V.V.*

**Analog of the Khintchine--Groshev theorem for the nondegenerated manifolds in R**^{n}. pp. 42--45

*Summary:* The Khintchine--Groshev theorem is generalized to Diophantine approximation on the smooth non-degenerate manifolds in **R**^{n} .

*Morozova I.M.*

**On approach of zero by integer polynomial significances with small derivative in root.** pp. 46--49

*Summary:* It is proved the set of special real algebraic numbers forms the best possible regular system.

**ИНФОРМАТИКА**

*Bakhanovich S.V., Likhoded N.A.*
**Vector scheduling function for space-time mapping.** pp. 50--52

*Summary:* A new method to schedule algorithms with the uniform dependencies for n-dimensional to (n-r)-dimensional linear space mapping is presented. The method is based on the multidimensional scheduling.

**ФИЗИКА**

*Margolin A.E., Strazhev V.I.*
**Chiral anomalies in quantum noncompact sigma-models.** pp. 53--55

*Summary:* The criterion of lack of the chiral anomalies in a the noncompact G/H-sigma models, where G is the semisimple noncompact group, H is the maximal compact subgroup G is formulated. It is obtained that criterion in a case of the sigma-models of pseudoorthogonal and pseudounitary types is sufficient.

*Ryzhkovsky V.M., Dymont V.P., Nekrashevich E.M.*

**Structure and magnetic propeties of MnNiAs alloy.** pp. 56--58

*Summary:* MnNiAs alloy with the hexagonal crystal structure of Fe_{2}P has been synthesized from the starting components. The unit cell parameters are: *a* = 0.6186 nm, *c* = 0.3722 nm. This alloy exists only at high temperatures (more then 1000 K). The crystal structure is not affected by high pressure at 7 GPa and temperature up to 1400 K. Below 230 K the alloy exhibits the antiferromagnetic type ordering. At T = 25 K the magnetic transition to the spin cluster glass state is observed.

**ХИМИЯ**

*Kaputskii F.N., Starobinets G.L., Yurkshtovich T.L., Bychkovskii P.M., Zimatkina T.I.*
**The influence of hydrophobic interactions on the sorption of biological active electrolytes by monocarboxylcellulose.** pp. 59--63

*Summary:* The sorption of three organical electrolytes of anticancer action (AE): spyrobromine chloride (SP), prospidine chloride (PR) and hydrobromid oxythiamin bromid (OT) on a macromolecular bearer monocarboxylcellulose (MCC) in H^{+} -- form from water solutions at 293 K has been studied. The constants and Gibbs energy of the sorption process has been calculated. Estimation of hydrophobic interaction of the cation radikals with the (MCC) matrix is carried out. The interaction strength is decreased by transition from (SP) and (PR) to (OT). The release of the (AE) with a physiological solution passes across two stages. The medicobiological trials on defeat animals indicates that at treatment by a drug MCC-OT duration of life of animals increases in 2.7--3.3 times in comparison with the control and at treatment by a drug MCC-SP a positive effect is not observed. This is conditioned by differense of hydrophobic interactions. Thus the received results are a basis for creation a macromolecular therapeutic system MCC-OT.

*Matusevich Yu.I., Krul L.P.*

**Interchain interaction in crosslinked thermoplastics.** pp. 64--67

*Summary:* The activation energy values of mechanical destruction obtained at temperature lower than the melting point of the crosslinked polyethylene, as well as the activation energy values calculated from curves of dynamic thermogravimetric analyses at the initial stages of thermal oxidative destruction corresponding to the mass loss of the polymer up to 2--3 % have been shown to used in calculation of the intermolecular interaction energy in the crosslinked polyethylene.

**БИОЛОГИЯ**

*Abramchik L.M., Serdyuchenko E.V., Chaika M.T. †*
**Thermal effect on formation of reaction centre of photosystem 1 in greening barley seedlings.** pp. 68--70

*Summary:* The influence of the heat periodical shock on etiolated barley seedlings and on greening process was investigated. It was revealed that the high temperature led to slowing of the chlorophyll biosynthesis. RC PSI apoprotein content was reduced in the greening seedlings. The influence of temperature factor on the structural organization of the photosynthesis system is discussed.

*Shkodich A.P., Zavodnik L.B., Laman N.A., Buko V.U.*

**Antioxidant effects of genistein-8-C glycoside in vitro.** pp. 71--73

*Summary:* The aim of this work is to study an antioxidant effect of genistein-8-C-glycoside isolated from the lupine flower buds. The compound develops the clear antioxidant effect in the liver homogenates and microsomes. Genistein-8-C-glycoside prevents the destruction of cytochrome P-450 and its conversion to an inactive form cytochrome P-420.

*Volynets A.P., Zankevich N.P.*

**Decretion of flavonoid glycosides by healthy and infected plants of rye.** pp. 74--77

*Summary:* The composition and content of the flavonoid glycosides secreted by healthy and infected plants of rye on the surface of photosynthetic organs is studied. In water washing from the plant surfaces the flavonoid glycosides have been revealed similar to one of internal tissues. Content of the eksogenic flavonoid glycosides fewer than the endogenic flavonoids on one order. It is assumed that the flavonoid glycosides take part in relationships of rye and rust fungi.

*Shimko V.E., Kalitukho L.N., Kabashnikova L.F., Gordei I.A.*

**Peculiarities of microsporogenesis and accumulation of photosynthetic pigments in rye, triticale and secalotriticum.** pp. 78--82

*Summary:* At the stages of a stalk-shooting and earing of secalotriticum line Novosibirskaya x L-246 a homeological heterosis has been revealed on the photosynthetic pigments quantity and chlorophylls (CHL) contents in the light-harvesting complex. A high determination of a fatherly type of inheritance has been shown for the dynamics of meiosis infringements at the stages MI-tetrades and change of photosynthetic parameters during transition from the phase of stalk-shooting to earing. Authentic positive correlation has been proved between the value of CHL *a*/CHL *b* ratio, contents of CHL *a*, CHL (*a* + *b*) and carotenoids and the normal process of meiosis at researched cultures: rye, triticale and secalotriticum.

*Grinko I.V.*

**Laminin expression by fat-storing cells in experimental liver pathology.** pp. 83--86

*Summary:* In present study we investigated an expression of the structural glycoprotein of the basement membrane laminin by fat-storing cells, isolated from 1-week cholestatic rat liver by the methods of molecular biology. It is found that in cholestatic liver fat-storing cells synthetize laminin at 3-fold higher levels than in normal rats due to the transcriptional upregulation and play an important role in deposition of this component of the liver connective tissue matrix in the secondary biliary cirrhosis.

**НАУКИ О ЗЕМЛЕ**

*Kuznetzov V.A., Veremchuk S.N., Glaz A.S.*
**New data about the structure and progress of r.Sozh valley in Holocene.** pp. 87--90

*Summary:* Some indications of the display of morfostructures and neotectonic stages, including geochemical ones, are investigated. The neotectonic movement of some earth's crust blocks are reconstructed.

*Naidenkov I.V., Derevyankin Yu.A.*

**Perspectives of founding of metals of platinum group in crystalline basement of Belarus.** pp. 91--94

*Summary:* The formations of the crystalline basement of Belarus show a good promise for the metals of the platinum group. Meta-ultrabasites and metabasites of the Rusinovo complex, ilmenite-magnetite ores of the Korelichi type and graphite- and sulfide-rich gneisses of the Okolovo series may be suggested as the first candidates for studying and exploration.

*Bulkin Yu.S.*

**Peculiarities of chemical composition of feldspars heterogenic granitoids of the Belarus Anteclise.** pp. 95--99

*Summary:* The revealed chemical peculiarities of feldspars with respect of petrographical investigation results may be used for genetic typical division of granitoids of the region.

*Kovkhuto A.M., Mamchik S.O., Zakharenko A.A.*

**Peculiarities of the Famennian gypsum deposits deformation in the western part of the Pripyat Trough.** pp. 100--104

*Summary:* The tectonic cracks weren on the Brinev gypsum deposit. They are fill in gypsum, disturbing marl sublayers within gypsum bed and penetrating in the Carboniferous deposits. The fracturing zones are revealed which are a prolongation of sublatitudinal faults on an extension. The facts gypsum tectonics are established which actively has been exhibits in limits of the IV gypsum layer in the western part of the deposit and in limits of III gypsum layer in the eastern part of the Brinev gypsum deposit. This is the confirmation of damping of tectonic activity in the Pripyat Paleorift in east direction.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Kashevsky B.E.*
**Dissipative self-organization of paniculate subsystem in a fluid-disperse magnetic system.** pp. 105--108

*Summary:* An approach is developed for the fluid-disperse magnetic systems (FDMS) which puts forward the careful examination of the mesoscopic transport phenomena in the systems of interacting ferroparticles acted on by external magnetic and hydrodynamic fields. The results of both computer and experimental simulations are presented for the behaviour of the particulate systems acted on by a rotating magnetic field. It is shown that the disperse phase of FDMS being far from orientational equilibrium manifests the possibility of self-organisation that leads to forming coherent colloidal structures.

*Bannyi V.A., Makarevich A.V.Pinchuk L.S.*

**The influence of dimensional and composition parameters of polymer composites on their radiophysical characteristics.** pp. 109--111

*Summary:* The reflection factors *R* of the plane normally falling electromagnetic waves (8, 10 and 12 GHz frequency) from PE samples filled with dispersed carbonyl iron and magneto-soft manganese-zinc ferrite or nickel have been investigated. *R* dependencies on the sample thickness and filling degree have been determined. On the base of an analysis of obtained dependencies the recommendations are proposed on the dimensional and composition optimization of the protecting elements (which are made from polymer composites) aimed at attaining best characteristics of the radio absorption. It is proved that optimization principles are a high level of the electromagnetic and interference losses in the conditions of conformity between the composite wave resistance and the "free space".

*Lynkov L.M., Petrov N.P., Belyatko D.P.*

**Heat treatment of thin film decrepitates of Zr-Ti alloy on Si.** pp. 112--115

*Summary:* The heat treatment of Zr-Ti alloy (50 %) on Si in temperature range 200--950°C is investigated. The temporary intervals of the heat treatment of alloy leading to its destruction are established. With the help of the methods of a raster submicroscopy and Auger-submicroscopy it is shown, that the oxidation of alloy takes place at the expense of a difference of the generation rate of Ti and Zr oxides.

*Makushok E.M., Reut O.P.*

**Complicated contact model of powder compacting process.** pp. 116--119

*Summary:* A complicated model of powder compacting process is presented considering a principle of self-organizing of inhomogeneous deformation processes representing both the basic kinematics and deformation principles. The advantages of the model are in providing of the analyses of influence of structural parameters on properties of a workpiece, except of the analyses of a tension.

*Chichko A.N., Drozdov E.A.*

**Cell - automation model for the description of claster formations in Al-Si alloy.** pp. 120--122

*Summary:* The model of Al-Si claster formations based on the three-dimension cell automation synthesis and configuration model of material is suggested.

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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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