Doklady of the National Academy of Sciences of Belarus, 2001, Vol.45, No.5
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Doklady of the National Academy of Sciences of Belarus, 2001, Vol.45, No.5

DOKLADY OF THE NATIONAL ACADEMY OF SCIENCES OF BELARUS
(Doklady Natsionalnoi Akademii Nauk Belarusi)Published by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Zabreiko P. P., Kovalenok A. P.
On solvability and existence of nontrivial solutions for the twodimensional Dirichlet problem. pp. 58.
Summary: New conditions on solvability and existence of nontrivial solutions for the twodimensional divergent Dirichlet problem are obtained. The Browder  Skrypnik theory of rotation of quasimonotone 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 wlocal formations. pp. 911
Summary: A description of minimal wlocal tclosed nonNformations is given, when N is a formation of classic type.
Metel'skii Yu. M., Tyshkevich R. I.
Graphs as rminoes. pp. 1215
Summary: A graph is called an rmino if its every vertex belongs to at most r maximal cliques. The class of rminoes 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 rmino is called linear if its every edge belongs to exactly one maximal clique. We prove that the GRAPH 3COLORABILITY problem remains NPcomplete 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. 1619
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. 2024
Summary: An approach to constructing discrete closable and closedloop feedbacks providing guaranteed results for dynamic systems under bounded disturbances is justified based on a procedure of the correction of optimal openloop controls at closure moments.
Sheinin S. A., Tuzikov A. V.
Formulae for volume and surface moments of polyhedral objects. pp. 2527
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 twodimensional quasilinear heat conduction equation with generalized solutions. pp. 2831.
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 Lipschitzcontinuous function. Convergence of approximate solution to exact solution with the rate O(h^{2} + t) is proved.
Uss A. T.
Concerning the boundaryvalue problems for threedimensional analogs of the CauchyRiemann system with complex coefficients. pp. 3235
Summary: In the present paper the homotopical unity of CauchyRiemann'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 boundaryvalue problem is said to be regularizable if the wellknown 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 zetafunction. pp. 3640
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. 4144
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. 4547
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.
Propgroups nearly freely acting on twodimentional aspherical complexes. pp. 4850
Summary: A propgroup 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 propgroups having nontrivial solvable normal subgroups is investigated in detail.
PHYSICS
Martynenko O. G., Khramtsov P. P.
Special features of highintensity transient processes in liquid evaporation. pp. 5154
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.
Quasireal time digital specklephotography of dynamic processes. pp. 5559
Summary: The basic principles of single and doubleexposure digital specklephotography are considered. It is shown that the crosscorrelation technique applied to doubleexposure digital specklephotography 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 quasireal time. Higher frequency processes (up to 100 kHz and more) can be investigated using the autocorrelation technique applied to singleexposure digital specklephotography. The theoretical conclusions were experimentally verified using the setup for digital specklephotography and original software.
Kudryashov V. V., Vanne Yu. V.
Quasiuniform approximation for the Schrodinger equation with a doublewell potential. pp. 6063
Summary: The analytical solutions of the Schrodinger equation with an arbitrary doublewell potential are obtained within the framework of the new quasiuniform 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_{1x}Sr_{x}(Mn_{1x/2}Nb_{x/2})O_{3} system. pp. 6466
Summary: It is shown that in solid solutions La_{1x}Sr_{x}(Mn_{1x/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.
CHEMISTRY
Shevchenko E. V., Kurnevich G. I., Kulak A. I., Sviridov V. V.
Electrochemical behavior of thermally splitted graphite. pp. 6769
Summary: The electrochemical behavior of native graphite and thermal splitted graphite (TSG) electrodes in aqueous sodium sulfate solutions (initial, and in the presence of ferroferricyanide 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. 7074.
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 pethyl benzene sulfonates. pp. 7580
Summary: The relative positions of anion pethyl 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.
BIOLOGY
Alekhnovich A. V.
Formation of the size structure in populations of narrowclawed crayfish. pp. 8183
Summary: Size structure of narrowclawed crayfish Astacus leptodactylus populations has been analyzed in waterbodies 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 1.52.5 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. 8486
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 SHgroups 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. 8789
Summary: Electrophysiological experiments on bulbospinal preparations from the neonatal rats showed that both stimulation of the endogenous NO production by its precursor Larginine 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 selfincompatibility in white cabbage. pp. 9092
Summary: The modified algorithm of hierarchical cluster analysis was applied for identification of homo and heterozygotes on alleles of a gene of selfincompatibility. The method presented makes it possible to avoid errors of genetical analysis, as the strength of a seed parent's selfincompatibility depends on activity of a Salleles 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.
EARTH SCIENCES
Bulkin Yu. S., Levykh N. N., Il'kevich G. I., Varaksa V. V., Kuz'menkova O. F.
Petrogeochemical evaluation of the orebearing potential of the Bershty massive granitoids (Belarus). pp. 9395
Summary: Metallogenic specialization of potentially orebearing 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. 96100
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. 101105
Summary: Anomalously heightened content of ozone in the atmosphere of middle latitudes of Northern hemisphere in 199S and "ozone miniholes" 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 highcarbonaceous rocks of the Southeastern part of the Belarussian crystalline massif. pp. 106109
Summary: Horizons of graphiteriched rocks included in the 2.0Ga Okolovo metavolcanicsedimentary unit are crosscut by drillcores in the southwestern part of the Belarussian crystalline massif (the Puchovschina deposit). Geological and tectonic position, geochemicalmineialogical data, and results of MPG analysis suggest good MGP prospecting for these rocks.
TECHNICAL SCIENCES
Yashcheritsyn P. I., Rakomsin A. P., Kozhuro L. M., Mrochek Zh. A.
Mathematical simulation of thermal processes in electromagnetic facing. pp. 110113
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. 114118
Summary: Description of the mechanism is given, as well as graphanalytic 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 selfreproduction. pp. 119122
Summary: Accoding to von Neumann's model of selfreproduction, the algorithms are suggested that describ the methods of the praduction of machine parts without formbuilding equipment. Using the selforganization 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.
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