Doklady of the National Academy of Sciences of Belarus, 2002, Vol.46, No.6
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Doklady of the National Academy of Sciences of Belarus, 2002, Vol.46, No.6

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
Lomovtsev F.E.
An interior approximation method of the approximate solution of the Cauchy problem for parabolic firstorder differentialoperator equations with variable domains. pp. 510
Summary: An abstract interior approximation method (MIA) of the approximate integration of the Cauchy problem for parabolic firstorder differential equations with variable domains and unbounded operator coefficient is suggested. This method is stable with respect to the operator coefficients, the righthand sides of equations and the initial data in nonweakened energetic inequalities. A priori error estimates of the approximate solutions have been established. The approximate solutions obtained with the use of MIA converge to the exact strong solutions of the Cauchy problem with the rate O(Öh_{R}) with respect to the operator coefficients and the righthand sides of equations.
Lebedev A.V., Odzievich A.
C*algebras generated by components of polar decomposition. pp. 1113
Summary: The paper presents a description of structure of C* algebra generated by the components of the polar decompositin of an operator acting in a Hilbert space.
Belousov M.V.
Symbolic calculus of boundaryvalue problems with shifts and complex conjugation. pp. 1417
Summary: Symbolic calculus and Fredholm properties for nonlocal boundaryvalue problems generated by Bouted de Monvel operators, complex conjugation operators and normally acting shifts on the boundary are obtained.
Beresnevich V.V., Bernik V.I., Dodson M.M.
On the Hausdorff dimensionality of set of well approximable points on nondegenerative curves. pp. 1820
Summary: In this paper, we consider a set of Imearly wapproximable points (w > n) lying on a nondegenerate curve. For approximation exponents in the range of n < w < n + c/n, where с > 0 is an effectively computable constant close to 0.25, it is proved that the Hausdorff dimension of this set is (n + 1)/(w + 1).
Bazylev D.F., van Geel J., Yanchevskii V.I.
Walgebras over rational function field with special fields of constants. pp. 2122
Summary: The proof of the local Pfister conjecture for Walgebras defined over R((t))(x) is obtained in case when points of Branching are of special type.
Lazakovich N.V., Stashulenok S.P., Yablonskii O.L.
Integrodifferential equations for functionals of stochastic Levy processes. Symmetric case. pp. 2327
Summary: The definition of symmetric stochastic integral on stochastic Levy processes is offered. The relationship between the solutions of lto stochastic differential equations and the solutions of respective symmetric stochastic differential equations is investigated. The Kolmogorov equations for functionals of the solutions of symmetric stochastic differential equations containing stochastic Levy processes are obtained.
Sheinin S.A., Tuzikov A.V., Vasiliev P.V.
Computation of 3D object volume through nonparallel section. pp. 2830
Summary: We describe an algorithm for volume evaluation of a 3D object based on area measurements done in nonparallel crosssections. The algorithm is based on Watanabe formula for volume computation and uses an interpolation by cubic splines. The same splines are also applied for computation of object area and centroid in every crosssection. This allowed to derive an explicit formula for volume computation and to extend an algorithm developed earlier.
Semenchuk N.P., Datsyk V.T.
On a class of nonlinear differential equations with higher derivative of fraction order. pp. 3135
Summary: Cauchy problem for ordinary differential equation of fraction order is studied. Conditions existence of a unique solution of this problem are given in a special space of differentiable functions. The estimation of approximation of the solution by solutions of AbelGummerstein operator equations, constructed using methods of summation of Fourier integrals, is established.
Bukhtoyarov S.E., Yemelichev V.A.
End alliance games: parametrization of principle of optimality ("from Pareto to Nash") and stability of generally efficient situations. pp. 3638
Summary: Vector discrete optimization problem is considered. The problem can be interpreted as an end alliance game. For any fixed partition of players between coalitions, a concept of generally efficient situation is introduced. Extreme levels of independent perturbations of payoff function parameters are investigated, for which a given generally efficient situation remains efficient.
Rabtsevich V.A.
Asymptotic estimates of nonoscillatory singular Kneser solutions of EmdenFowler systems. pp. 3940
Summary: For EmdenFowler type systems of differential equations, twosided asymptotic estimates of nonoscillatory singular Kneser solutions about a singular point are obtained.
Sabut A.V.
Classification of positively defined integer quadratic forms. pp. 4145
Summary: In this paper, we described the method of classification of integral positive quadratic forms with invariant factors 1, 1, ..., 1, d. The method bases on concept of dclsses, which are defined in the paper.
INFORMATICS
Nesenchuk A.A.
Dynamic system root locus fields and their application in robust quality tasks. pp. 4649
Summary: The problem of ensuring quality of uncertain dynamic systems is considered. It is solved by introduction of root locus fields. For attaining required quality, the fields are located in the plane of system fundamental frequencies in a special way.
PHYSICS
Margolin A.E., Strazhev V.I.
Unitarity in semiclassical approximation in quantum cosmology. pp. 5052
Summary: It is shown that the Wave Function in semiclassical approximation in quantum cosmology submits to unitary evolution. Here, space of states with indefinite metrics generated by the WheelerDeWitt. equation is used.
CHEMISTRY
Smolyak L.Yu., Prokopchuk N.R., Losev Yu.P., Kochetkova Yu.V.
Polyethylene thermostabilizeis of polydisulfide class with intramolecular synergism. pp. 5356
Summary: Some polydisulfide class substances have been investigated as thermostabilizers of polyethylene. Concentration influence on efficiency has been investigated, and optimal concentration has been found. The influence of molecular structure of polydisulphides on their efficiency has been shown and discussed. Synergetic action of SS and NH groups in one molecule has been observed, and mechanism that explaind high efficience of aliphatic polydisulphide of biuret has been proposed.
Polkhovsky E.M., Sosinovich Z.I., Soldatov V.S.
Mathematical model of overequivalent sorption of electrolytes by ionexchangers. pp. 5759
Summary: Overequivalent uptake of HCl and NaCl by ionexchanger Dowex 1x8 has been investigated. The model of electrolyte uptake process has been offered. The total sorption of electrolytes and contribution of particular factors have been calculated. Also, the main factors which have an influence on the sorption process have been determined. For the salt, it is Donnan equilibrium, and for acid, it is formation of R^{+} An^{}(HAn)_{n} associates.
BIOLOGY
Potapovich A.I., Vladykovskaya E.N., Kostyuk V.A.
Influence of metal ions on biological activity of natural flavonoids. pp. 6063
Summary: Influence of metal ions (Fe^{2+}, Fe^{3+}, Cu^{2+}) on antiradical properties of rutin, dihydroquercetin, ECG, EGCG, and cytoprotective action of flavonoid metal complexes against asbestosinduced oxidative cell injury was studied. It was found that the metals increase the capacity of rutin and dihydroquercetin to protect peritoneal macrophages and neutrophiles against injury caused by chrysotile asbestos fibers. This effect is due to the formation of the flavonoid metal complexes with high antiradical activity against superoxide. The results also demonstrate that the flavonoid metal complexes were absorbed by chrysotile fibers much better than uncomplexed compounds, and therefore, flavonoid metal complexes are better protectors against asbestosinduced hemolysis. The flavonoid metal complexes may result in better clinical therapies for diseases mediated by ROS.
Giginyak Yu.G., Moroz M.D., Vlasov B.P.
Ecological dependence of species diversity in water reservoirs with different salinity. pp. 6466
Summary: Salinity is an important factor in determination of hydrobiont species diversity. Relationship between species diversity and mineralization is shown as a succession: freshwater lakes  springs  estuaries  seas  hyperhaline water reservoirs. Salinity of lakes in Belarus ranges between 20 and 440 mg/l, while species diversity does between tens and hundreds species. In 200 studied springs, this index is 100700 mg/l, a number of species is 24 to 2025, altogether about 250. In a graphic interpretation, the relationship obtained is represented as a twopeak curve with a maximum species number at the salinity index of 150250 mg/l and 34‰. The minimum of species is registered in springs, estuaries, and hyperhaline water reservoirs.
Pshibytko N.L., Kalitukho L.N., Kabashnikova L.F., Volotovsky I.D.
Effect of thermal shock on photosynthesis in barley seedlings of different age. pp. 6770
Summary: Effect of heat shock (40°C, 3 h) on photosynthesis in 4, 7, and 11dayold barley seedlings was studied. Under heat shock, the rate of CO, gas exchange in 4 and 7dayold leaves did not change, while the high temperature affected both average quantum yield and shape of light response curves of photosynthesis in 11dayold seedlings. The suppression of photosynthesis by heat shock in old leaves was caused by the damage of Calvin cycle enzymes. This led to increase in transthylakoid proton gradient and reduction in electron transport.
Shapturenko M.N., Khotyleva L.V.
Ways of formation of genetic variance in disomic lines of soft spring wheat Opal. pp. 7173
Summary: Intramolecular heterogeneity of a complete series of Opal common wheat disomic lines was investigated by PCR (polymerasic chain reaction) method and isoenzyme analysis. The lines were shown to differ among themselves in both the spectra of amplification products and spectra of some enzyme systems. The data presented show that the changes which are caused to some or other degree by plant passing over the aneuploid state have taken place in genetic apparatus.
EARTH SCIENCES
Kakareka S.V., Kukharchik T.I., Kurman P.V., Khomich V.S., Chuduk V.N.
Study of polycyclic aromatic hydrocarbon emissions resulting from wood combustion. pp. 7479
Summary: The results of pilot study on polycyclic aromatic hydrocarbons (PAH) content in emissions resulting from wood combustion, are discussed. PAH content in fly ash and soot as well as in flue gases from wood (pine, birch, polluted wood) combustion in a Russian stove, heating furnace, and kitchen range was analysed. 16 indicator PAHs were tested. It was found that among furnaces, highest level of PAHs is typical for the Russian stoves. The ratio of aerosol and that of gaseous phases of PAHs emitted are described also.
Bordon V.E., Matveev A.V., Ol'khovik E.T., Bordon S.V., Anoshko Ya.I., Nechiporenko L.A.
Clarkes of trace elements in the Quaternary deposits in Belarus. pp. 8081
Summary: Clarkes of 31 trace elements in the Quaternary deposits in Belarus are defined. Correlation between these values and clarkes of the lithosphere and sedimentary cover is obtained. Also, importance of these values for geological prospecting and environmental assessment is emphasized.
Abramenko V.I., Levykh N.N., Makhnach A.S.
Garnets in the Middle Devonian deposits in northern Belarus as indicators of ablation regions. pp. 8284
Summary: The similarity of the chemical composition of garnets in the Middle Devonian sandstones in nonhern Belarus and those from the crystalline basement and its overlying weathering crusts was used to reveal sourcelands of terrigenous material which was supplied into a paleobasin.
Garetsky R.G., Karataev G.I., Astapenko V.N., Dankevich I.V.
PolotskKurzern fault belt. pp. 8589
Summary: On the basis of integrated analysis of the geological and geophysical data, in the structure of the East European platform, a new major tectonic element  PolotskKurzern fanit belt  is established.
Tolstosheev V.I.
Dawsonite deposit in the North Zolotukha Syncline within the Pripyat Trough. pp. 9095
Summary: Stratigraphy and tectonics of the GostovBogutichi deposits of the Visean in the NorthZolotukha Syncline have been studied, and the Dawsonite deposit was determined to be confined to the upper subsuite of the Gostov suite.
Konishchev V.S.
Tectonic criteria and perspectives regarding diamond formation in Belarus. pp. 96100
Summary: Perspectives of Belarus for prospecting diamond diatrems are analysed, and it is shown that some structures of Bragin and Vitebsk granulite blocks are most perspective.
TECHNICAL SCIENCES
Chichko O.I., Sobolev V.F., Makhnach V.I., Chichko A.N.
Computer simulation of movement of melt being cooled down and system analysis of gating. pp. 101106
Summary: Computer calculations of flow process of aluminum melt in gating with different construction elements are performed. It is shown that the distribution of melt elements number by velocities and flow directions depends on construction elements of the gate channels. Functional dependences for the estimation of melt flow process in the gating and pattern are discussed.
Sviridyonok A.I., Kovalevskaya T.I., Abramenko V.V.
Study of phase and structural features of electrically conducting lubricant. pp. 107110
Summary: Rheological and electrical properties of electrically conducting lubricant of high filling (1040 vol%) are investigated. Filler is ultradispersed (~ 10^{8} m) grafit with copper coating. Heterogeneous phase nature, interface interaction, and its influence on the electrical conduction are discussed.
Kozhevnikova G.V.
Rolling force calculation for crosswedge rolling of infinite cylinder by three rolls. pp. 111114
Summary: A new speed field scheme of infinite cylinder cross section for a crosswedge rolling by three rolls is suggested for determination of rolling force using the method of upper evaluation.
Burskii V.A., Karpushin V.A., Pozdnyakov M.G.
Kinematical analysis of the mechanism of the drive of discontinuous attenuator. pp. 115118
Summary: Kinematic analysis of the mechanism of the drive of discontinuous attenuator is given with regard to the acting forces, forces of inertia, and counter forces of the opposing spring.
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Created with assistance of Dr. Ignatii I. Korsak
Copyright © 2003 The National Academy of Sciences of Belarus
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