# Доклады Национальной академии наук Беларуси, 2001, Том 45, No.5

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2001, Том 45, No.5

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Zabreiko P. P., Kovalenok A. P.*
**On solvability and existence of nontrivial solutions for the two-dimensional Dirichlet problem.** pp. 5--8.

*Summary:* New conditions on solvability and existence of nontrivial solutions for the two-dimensional divergent Dirichlet problem are obtained. The Browder -- Skrypnik theory of rotation of quasi-monotone vector fields enable one to consider equations with a nonlinear leading part, while the theorems for calculating the index of quasimonotone vector fields at zero and infinity allow one to investigate both nondegenerate and degenerate cases. On the other hand, it is possible to study equations with a nonleading part having the exponential growth, due to the embedding *W*^{1}_{2} Ì *L*_{M} (*M* (*t*) = e^{t2} -1) which holds exclusively for *n* = 2.

*Sel'kin V. M.*

**Concerning the problem of the theory of w-local formations.** pp. 9--11

*Summary:* A description of minimal w-local t-closed non-*N*-formations is given, when *N* is a formation of classic type.

*Metel'skii Yu. M., Tyshkevich R. I.*

**Graphs as r-minoes.** pp. 12--15

*Summary:* A graph is called an *r-mino* if its every vertex belongs to at most *r* maximal cliques. The class of *r*-minoes is denoted by *M*_{r}. It is shown that *M*_{r} is the class of line graphs of Helly hypergraphs with the rank not higher than *r*. For an arbitrary *r*, the existence of a finite list of forbidden induced subgraphs characterizing *M*_{r} is proved. Such finite characterization is given for *M*_{3}. An *r*-mino is called *linear* if its every edge belongs to exactly one maximal clique. We prove that the GRAPH 3-COLORABILITY problem remains NP-complete when restricted to *K*_{4}-free linear dominoes with vertex degrees 4 at the most.

*Alekhno A. G.*

**Construction of the analytic, in the angular domain, function by the given indicator.** pp. 16--19

*Summary:* An analytic, in the angular domain, function is constructed by the given indicator.

*Gabasov R., Kirillova F. M.*

**Synthesis of optimal feedback for dynamic systems under disturbances.** pp. 20--24

*Summary:* An approach to constructing discrete closable and closed-loop feedbacks providing guaranteed results for dynamic systems under bounded disturbances is justified based on a procedure of the correction of optimal open-loop controls at closure moments.

*Sheinin S. A., Tuzikov A. V.*

**Formulae for volume and surface moments of polyhedral objects.** pp. 25--27

*Summary:* The new formulae for calculation of volume and surface moments of arbitrary dimensional polytopes are presented. The formulae are especially convenient for polygonal representations of 3D objects.

*Iovanovich B. S., Shcheglik V. S.*

**Concerning the convergence of a certain difference scheme for a two-dimensional quasilinear heat conduction equation with generalized solutions.** pp. 28--31.

*Summary:* In this paper we study noniterative difference scheme for nonlinear heat conduction equation. It is supposed that the solution of the differential problem belongs to Sobolev space *W*_{2}^{3+e,(3+e)/2} (*Q*_{T}) , e > 0 and heat coefficient is Lipschitz-continuous function. Convergence of approximate solution to exact solution with the rate O(|h|^{2} + t) is proved.

*Uss A. T.*

**Concerning the boundary-value problems for three-dimensional analogs of the Cauchy--Riemann system with complex coefficients.** pp. 32--35

*Summary:* In the present paper the homotopical unity of Cauchy-Riemann's type systems in **R**^{3} with complex coefficients is proved. The simple condition of boundary -- value problems regularizability for this systems is given. (A boundary-value problem is said to be regularizable if the well-known Lopatinskii condition is fulfilled.) It is shown that the index of any regularizable boundary -- value problem for indicated elliptic system is equal to minus 1.

*Vasil'ev D. V.*

**Zero approximations by linear forms of the values of the Riemann zeta-function.** pp. 36--40

*Summary:* We construct a sequence of small linear forms with integer coefficients yielding certain information on the arithmetic nature of the Riemann zeta function at integers.

*Sheshko M. A., Rasol'ko G. A.*

**Expansion of the singular characteristic integral operator with the Cauchy kernel in Chebyshev polynomials.** pp. 41--44

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

*Tsegel'nik V. V.*

**Gamiltonians related to the fivst Painleve equation.** pp. 45--47

*Summary:* There have been obtained the formula which defines the general form of the polynomial hamiltonian associated with first Painleve equation. It's uniqueness has been proved. There have been shown the existence of hamiltonians that differ from the polynomial one's, associated with the first Painleve equation.

*Melnikov O. V.*

**Pro-***p*-groups nearly freely acting on two-dimentional aspherical complexes. pp. 48--50

*Summary:* A pro-*p*-group is named aspherical if one of its relation modules is permutional. The paper contains results on common properties of such groups. Moreover, the structure of aspherical pro-*p*-groups having nontrivial solvable normal subgroups is investigated in detail.

**ФИЗИКА**

*Martynenko O. G., Khramtsov P. P.*
**Special features of high-intensity transient processes in liquid evaporation.** pp. 51--54

*Summary:* On the basis of the phenomenological theory of the thermodynamics of irreversible processes an analysis of nonstationary evaporation of liquid is carried out. It is shown that in the case of a sharp change in the magnitude of a heat flux in a system ascillating relaxation of vapor generation is observed.

*Bazylev N. B., Vlasenko S. M., Lavinskaya E. I., Fomin N. A.*

**Quasi-real time digital speckle-photography of dynamic processes.** pp. 55--59

*Summary:* The basic principles of single- and double-exposure digital speckle-photography are considered. It is shown that the cross-correlation technique applied to double-exposure digital speckle-photography allows one to study the low frequency processes (up to 10 Hz) and can be used in biomedicine for investigations of subskin blood flows in quasi-real time. Higher frequency processes (up to 100 kHz and more) can be investigated using the autocorrelation technique applied to single-exposure digital speckle-photography. The theoretical conclusions were experimentally verified using the setup for digital speckle-photography and original software.

*Kudryashov V. V., Vanne Yu. V.*

**Quasi-uniform approximation for the Schrodinger equation with a double-well potential.** pp. 60--63

*Summary:* The analytical solutions of the Schrodinger equation with an arbitrary double-well potential are obtained within the framework of the new quasi-uniform approximation. The problem with four real turning points is solved for energies lying below the barrier's top. The numerical verification in the special cases of symmetric and asymmetric double wells shows that the new method gives fairly accurate results.

*Bushinskii M. V., Pushkarev N. V., Shapovalova E. F., Troyanchuk I. O.*

**The magnetic phase diagram of the La**_{1-x}Sr_{x}(Mn_{1-x/2}Nb_{x/2})O_{3} system. pp. 64--66

*Summary:* It is shown that in solid solutions La_{1-x}Sr_{x}(Mn_{1-x/2}Nb_{x/2})O_{3} with the perovskite structure there is a ferromagnetic state realized in the concentration interval 0.1 £ x £ 0.2. Large magnetoresistance effect is found in ferromagnetic phases despite the absence of different valence manganese ions. The data obtained are interpreted in the frame of the superexchange interactions theory.

**ХИМИЯ**

*Shevchenko E. V., Kurnevich G. I., Kulak A. I., Sviridov V. V.*
**Electrochemical behavior of thermally splitted graphite.** pp. 67--69

*Summary:* The electrochemical behavior of native graphite and thermal splitted graphite (TSG) electrodes in aqueous sodium sulfate solutions (initial, and in the presence of ferro-ferricyanide redox couple and ascorbic acid) has been studied. TSG was characterized by electrocatalytic activity approximately two order more than of native graphite. Owing to combination of electrochemical, mechanical and other useful properties TSG may be used as an advanced material for the preparation of novel carbon electrodes.

*Komarov V. S., Repina N. S., Rat'ko A. I.*

**Synthesis of bipore adsorbents and catalysts.** pp. 70--74.

*Summary:* The method of the synthesis of biporous adsorbents consisting in mixing of two hydroxides obtained from salts of various concentrations has been worked out for the first time. It is found that certain conformity in the natural laws of displacement of the second maximum with increase in the concentration of salt solution, from which the hydroxide is obtained, is observed on the curve of the distribution of pore volume on effective radii.
It is shown that when correlation in a mixture of hydroxides (one of them was obtained from 1% salt solution and the other -- from 10, 20 and 30% salt solution) is changed, a height of the maximum on the curve of distribution of pore volume on effective radii can be changed in some limits.

*Soldatov V. S., Zelenkovskii V. M., Bez'yazychnaya T. V.*

**The relative positions of ions in hydrate structures of p-ethyl benzene sulfonates.** pp. 75--80

*Summary:* The relative positions of anion p-ethyl benzene sulfonate and cations H^{+}, Li^{+}, Na^{+}, K^{+}, Rb^{+} and Cs^{+} in systems containing N molecules of water (N = 0, 1, 2„10) were computed using the nonempiric quantum chemical calculation in approximation of molecular fragments. The systems closely imitate repeated units of the polymeric structure of sulfostyrene ion exchangers. The results obtained were summarized as follows. In the absence of water the metal cations are bound to two oxygen atoms of the sulfonic groups. The situations in the systems with successively increasing hydration were considered. At the high degrees of hydration, corresponding to the real ion exchangers, two types of hydrates were found. In the firet one (the structure making ions: H^{+}, Li^{+}, Na^{+}) the cations are separated from the sulfonic groups by water molecules. In the second one (the structure breaking ions: K^{+}, Rb^{+}, Cs^{+}) the cation is always bound to one of the oxygen atoms of the sulfonic group. Dissociation of -SO_{3}H group starts when the third water molecule joins the relative dihydrate.

**БИОЛОГИЯ**

*Alekhnovich A. V.*
**Formation of the size structure in populations of narrow-clawed crayfish.** pp. 81--83

*Summary:* Size structure of narrow-clawed crayfish *Astacus leptodactylus* populations has been analyzed in water-bodies of Belarus. Internal structure of its populations is characterized by an aggregation on such a criterion as similarity of sizes. Crayfish in homogeneous habitats distribute themselves among individuals of similar size. This regularity is broken under a high density of population. In trap catches from the depth of 1.5--2.5 m the coefficients of variation of males and females decrease when the density is increased.

*Samoilenko S. G., Rakovich A. A., Levko A. V., Konev S. V.*

**Effect of hypoosmotic swelling with synaptosome on the structural state of the plasmic membrane.** pp. 84--86

*Summary:* Hypoosmotic swelling of rat brain synaptosomes has been found to induce structural modification of plasma membrane proteins as revealed by both the increased amount of membrane SH-groups and the decreased efficiency of protein fluorescence quenching with cetylpiridinium chloride. As the fluorescent probe diphenylhexatriene show, the microviscosity of the lipid phase is lowered. Thus, the hypoosmotic swelling induces the generalized structural rearrangement of synaptic plasma membranes.

*Pyatin V. F., Miroshnichenko I. V., Kul'chitskii V. A.*

**The role of nitric oxide in the central mechanisms of respiratory rhythmogenesis.** pp. 87--89

*Summary:* Electrophysiological experiments on bulbospinal preparations from the neonatal rats showed that both stimulation of the endogenous NO production by its precursor L-arginine and exogenous NO (application of nitroprusside) led to an increase in the duration of respiratory activity. Involvement of NO in the interaction of respiratory neurons is mediated by ventral medullary structures, the chemosensitive drive from which is necessary for coordinated operation of different nerve cell populations of the respiratory center.

*Yakimovich A. V.*

**Genetic control of the sign of self-incompatibility in white cabbage.** pp. 90--92

*Summary:* The modified algorithm of hierarchical cluster analysis was applied for identification of homo- and heterozygotes on alleles of a gene of self-incompatibility. The method presented makes it possible to avoid errors of genetical analysis, as the strength of a seed parent's self-incompatibility depends on activity of a *S*-alleles and also is affected by conditions in the field.
The researches performed make it possible to develop a program as a module of the integrated system of a statistical analysis Statistica 5.0 on the programming language Statistica Basic, which implements the suggested algorithm.

**НАУКИ О ЗЕМЛЕ**

*Bulkin Yu. S., Levykh N. N., Il'kevich G. I., Varaksa V. V., Kuz'menkova O. F.*
**Petrogeochemical evaluation of the ore-bearing potential of the Bershty massive granitoids (Belarus).** pp. 93--95

*Summary:* Metallogenic specialization of potentially ore-bearing aplitic granitoids of the Bershty massive was revealed. Recommendations for further prospecting are given.

*Kudel'skii A. V., Krishtopa N. A., Tsemkalo M. M., Gracheva O. N., Levashkevich V. G., Kapora M. S., Rudenok A. A., Pashkevich V. I.*

**Technogenic manifestation of hydrosulfuric mineral waters in Belarus.** pp. 96--100

*Summary:* The ground hydrosulfuric mineral waters of natural origin are unknown in Belarus. But technogenic analogues of the like waters is discovered now (2000 year) in the geological section of the Osipovichy underground gas storage. The chemical description, origin and the future utilization of the discovered ground hydrosulfuric mineral waters in the sanatorium practice is shown and discussed.

*Loginov V. F., Zhuchkevich V. V., Krasinskaya N. G., Krasovskii A. N., Lyudchik A. M., Stankevich Yu. A.*

**Special features of the dynamics of the ozonosphere above the European continent.** pp. 101--105

*Summary:* Anomalously heightened content of ozone in the atmosphere of middle latitudes of Northern hemisphere in 199S and "ozone mini-holes" regularly transiting above Europe early in winter, are considered as climatic fluctuations.

*Taran L. N., Distler V. V., Varaksa V. V.*

**Prospects for platinum metals in high-carbonaceous rocks of the Southeastern part of the Belarussian crystalline massif.** pp. 106--109

*Summary:* Horizons of graphite-riched rocks included in the 2.0-Ga Okolovo metavolcanic-sedimentary unit are crosscut by drillcores in the south-western part of the Belarussian crystalline massif (the Puchovschina deposit). Geological and tectonic position, geochemical-mineialogical data, and results of MPG analysis suggest good MGP prospecting for these rocks.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Yashcheritsyn P. I., Rakomsin A. P., Kozhuro L. M., Mrochek Zh. A.*
**Mathematical simulation of thermal processes in electromagnetic facing.** pp. 110--113

*Summary:* The mathematical model for definition of time of a crystallization of a drip of a melt is obtained at an electromagnetic surfacing.

*Burskii V. A., Karpushin V. A., Pozdnyakov M. G.*

**Graphoanalytical calculation of the mechanism of a discrete attenuator.** pp. 114--118

*Summary:* Description of the mechanism is given, as well as graph-analytic calculation of the module with regard to the friction forces and inertia forces of the concrete design model.

*Kheifets M. L.*

**Analysis of the algorithms of the production of machine parts by models of von Neumann's self-reproduction.** pp. 119--122

*Summary:* Accoding to von Neumann's model of self-reproduction, the algorithms are suggested that describ the methods of the praduction of machine parts without formbuilding equipment. Using the self-organization of surface effects by solid form fabrication of details allows one to form the layers of certain thickness along all the surface of difficult profile and to control the materials characteristics by currents of energy during laminate synthesis.

/ Издания академии / Научные журналы / К началу страницы

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

Создана при участии Игнатия И. Корсака

Копирайт © 2001-2008 Национальная академия наук Беларуси

Копирайт © 2001 Издательство "Беларуская навука"