# Доклады Национальной академии наук Беларуси, 2002, Том 46, No.6

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2002, Том 46, No.6

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Lomovtsev F.E.*
**An interior approximation method of the approximate solution of the Cauchy problem for parabolic first-order differential-operator equations with variable domains.** pp. 5--10

*Summary:* An abstract interior approximation method (MIA) of the approximate integration of the Cauchy problem for parabolic first-order differential equations with variable domains and unbounded operator coefficient is suggested. This method is stable with respect to the operator coefficients, the right-hand sides of equations and the initial data in non-weakened 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 right-hand sides of equations.

*Lebedev A.V., Odzievich A.*

**C*-algebras generated by components of polar decomposition.** pp. 11--13

*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 boundary-value problems with shifts and complex conjugation.** pp. 14--17

*Summary:* Symbolic calculus and Fredholm properties for non-local boundary-value 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. 18--20

*Summary:* In this paper, we consider a set of Imearly *w*-approximable points (*w* > *n*) lying on a non-degenerate 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.*

**W-algebras over rational function field with special fields of constants.** pp. 21--22

*Summary:* The proof of the local Pfister conjecture for W-algebras 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.*

**Integro-differential equations for functionals of stochastic Levy processes. Symmetric case.** pp. 23--27

*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 non-parallel section.** pp. 28--30

*Summary:* We describe an algorithm for volume evaluation of a 3D object based on area measurements done in non-parallel 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 cross-section. 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. 31--35

*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 Abel-Gummerstein 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. 36--38

*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 Emden--Fowler systems.** pp. 39--40

*Summary:* For Emden--Fowler type systems of differential equations, two-sided asymptotic estimates of nonoscillatory singular Kneser solutions about a singular point are obtained.

*Sabut A.V.*

**Classification of positively defined integer quadratic forms.** pp. 41--45

*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 d-clsses, which are defined in the paper.

**ИНФОРМАТИКА**

*Nesenchuk A.A.*
**Dynamic system root locus fields and their application in robust quality tasks.** pp. 46--49

*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.

**ФИЗИКА**

*Margolin A.E., Strazhev V.I.*
**Unitarity in semiclassical approximation in quantum cosmology.** pp. 50--52

*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 Wheeler--DeWitt. equation is used.

**ХИМИЯ**

*Smolyak L.Yu., Prokopchuk N.R., Losev Yu.P., Kochetkova Yu.V.*
**Polyethylene thermostabilizeis of polydisulfide class with intramolecular synergism.** pp. 53--56

*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 -S-S- 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 over-equivalent sorption of electrolytes by ion-exchangers.** pp. 57--59

*Summary:* Over-equivalent uptake of HCl and NaCl by ion-exchanger 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.

**БИОЛОГИЯ**

*Potapovich A.I., Vladykovskaya E.N., Kostyuk V.A.*
**Influence of metal ions on biological activity of natural flavonoids.** pp. 60--63

*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 asbestos-induced 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 asbestos-induced 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. 64--66

*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 100--700 mg/l, a number of species is 2--4 to 20--25, altogether about 250. In a graphic interpretation, the relationship obtained is represented as a two-peak curve with a maximum species number at the salinity index of 150--250 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. 67--70

*Summary:* Effect of heat shock (40°C, 3 h) on photosynthesis in 4-, 7-, and 11-day-old barley seedlings was studied. Under heat shock, the rate of CO, gas exchange in 4- and 7-day-old leaves did not change, while the high temperature affected both average quantum yield and shape of light response curves of photosynthesis in 11-day-old 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. 71--73

*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.

**НАУКИ О ЗЕМЛЕ**

*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. 74--79

*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. 80--81

*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. 82--84

*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.*

**Polotsk-Kurzern fault belt.** pp. 85--89

*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 -- Polotsk-Kurzern fanit belt -- is established.

*Tolstosheev V.I.*

**Dawsonite deposit in the North Zolotukha Syncline within the Pripyat Trough.** pp. 90--95

*Summary:* Stratigraphy and tectonics of the Gostov--Bogutichi deposits of the Visean in the North-Zolotukha 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. 96--100

*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.

**ТЕХНИЧЕСКИЕ НАУКИ**

*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. 101--106

*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. 107--110

*Summary:* Rheological and electrical properties of electrically conducting lubricant of high filling (10--40 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 cross-wedge rolling of infinite cylinder by three rolls.** pp. 111--114

*Summary:* A new speed field scheme of infinite cylinder cross section for a cross-wedge 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. 115--118

*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.

/ 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 © 2003-2008 Национальная академия наук Беларуси

Копирайт © 2002 Издательство "Беларуская навука"