# Доклады Академии наук Беларуси, 1996, Том 40, No.4

/ Издания академии / Научные журналы

Доклады Академии наук Беларуси, 1996, Том 40, No.4

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Mukhin V.V.*
**Quasi-invariant measure on topological semigroups.** pp. 5--8

*Summary:* Characterization of quasi-invariant measures was obtained on topological semigroups.

*Kilbas A.A., Saigo M.*

**Generalized fractional integrals with Fox ***H*-function on spaces *F*_{p,µ} and *F'*_{p,µ}. pp. 9--14

*Summary:* The generalized fractional integration operators involving Fox *H*-function as kernels and generalizing classical integration operators of fractional calculus are introduced. The conditions for the existence of such generalized fractional integrals on the special spaces of tested and generalized functions *F*_{p,µ} and *F'*_{p,µ} are given, their Mellin transform is evaluated and the relation of integration by parts is proved.

*Melnikov O.I., Yutskevich V.Yu.*

**Tree-like realization of hypergraphs.** pp. 15--18

*Summary:* The paper presents an algorithm of checking the possibility of realizing a hypergraph *H* by tree. The complexity of the algorithm is: O{min(|*VH*|, |*EH*|) summa |*e*_{i}|}, *e*_{i} Î *EH*.

*Dubatovskaya M.V., Rogozin S.V.*

**Homogeneous characteristic equation with infinite index in the exceptional case.** pp. 19--23

*Summary:* The equivalence of the homogeneous singular integral equation with infinite index in the exceptional case and the corresponding Riemann boundary value problem has been proved. The general solution of the equation has been constructed.

*Ryzhkov A, A., Chernousov V.I.*

**Maximality criterion for arithmetic subgroups.** pp. 24--28

*Summary:* A maximality criterion for an arithmetic subgroup Ã of a simple simply connected algebraic group *G* c GL_{n}(*C*) defined over a number field *K* is obtained. Using the criterion we give a classification of maximal arithmetic subgroups of the groups of types *B*_{l} (l > 2) and *E*_{7}.

*Yemelichev V.A., Kravtsov M.K., Yanushkevich O.A.*

**Solvability of vector path bottleneck problem by linear convolution criteria algorithm.** pp. 29--33

*Summary:* The algorithm proposed by the authors makes it possible to reduce any vector path bottleneck problem to an equivalent vector problem solvable by linear convolution criteria algorithm.

*Kruger A.Ya.*

**On calculus of strict e-semidifferentials.** pp. 34--39

*Summary:* Strict e-semidifferentials are introduced for nonsmooth functions on Banach space. They are compared with classical notions of strict derivative and subdifferential as well as with the generalized gradient of Clarke. The main calculus results are presented: the relations for strict tower epsilon-semidifferentials of a sum, a maximum and a superposition of nonsmooth functions.

**ФИЗИКА**

*Sirota N.N., Kholodovsky V.E., Sidorov A.A.*
**Anharmonicity in expression for the atomic mean-square displacements.** pp. 40--44

*Summary:* The anharmonic contributions to the Debye--Waller expression for the atomic mean-square displacements as well as to those for internal energy were introduced taking into account the effect of temperature and pressure on the cut-off frequency of Debye phonon spectrum.

*Rubinov A.N., Efendiev T.Sh.*

**DFB dye laser with stable wavelength.** pp. 45--48

*Summary:* Compact DFB dye laser with stable wavelength is developed. The laser includes an active element and a glass prism, two sides of which are covered with reflecting coatings. Interfering pumping beams are formed inside the laser in such a manner that any dependence of the laser wavelength on the angle of pumping beam incidence on an entering side of prism is practically excluded. At the same time temperature sensitivity of the laser frequency in the proposed DFB laser is reduced by the order.

*Bogush A.A., Fedorovykh A.M.*

**On one generalization of algebra of complex numbers on multidimensional case with nonlinear operation of multiplication.** pp. 49--53

*Summary:* An operation of multiplication of vectors in a real *n*-dimensional space (*n* is arbitrary) based on using plane transformations of the rotation group SO(n.R) is suggested. It generalizes the ordinary operation of multiplication of complex numbers. The introduced operation is nonlinear and nondistributive with respect to the first factor. A description of the real *n*-component Higgs field as a generalized complex field is given in terms of the developed formalism, including the elimination of *n*-1 Goldstone fields.

*Korostik K.N., Malevich I.A., Polyakov A.V.*

**Temperature influence on parameters of optoelectronic dynamic memory device.** pp. 54--58

*Summary:* Temperature influence on the signal to noise ratio and probability of error at the dynamic storage of information succession in reserved contour on the basis of injection laser, optical fiber and germanium avalanche photodiode is analysed. Conditions of optimization of the contour at instable environment temperature have been found.

*Makarenko L.F.*

**Energy levels of oxygen -- vacancy complex in silicon.** pp. 59--63

*Summary:* It has been shown that single-level model is not applicable to describe Hall-effect data in Czohralski-grown *n*-Si crystals irradiated by Co-60 gamma-rays. To explain experimental data, *A*-center in silicon is suggested to be an amphoteric center with close energy levels *E*(0/+) = *E*_{c} - 0.20 eV and *E*(-/0) = *E*_{c} - 0.16 eV.

*Knyasev M.A.*

**Direct method of constructing soliton-like solutions for nonlinear equations.** pp. 64--67

*Summary:* The paper presents a new direct method of integration nonlinear problems of mathematical physics in general form. This method makes it possible to construct the explicit soliton-like solution that corresponds to the coupled state of *N* solitons.

**ХИМИЯ**

*Krutko N.P., Kondratyuk A.V., Dubkova V.I., Kulak A.I.*
**Electrochemical behaviour of carbon fibre electrodes under the action of ultrasound.** pp. 68--72

*Summary:* The effect of ultrasound cavitation on the electrochemical behaviour of the carbon fibres electrode has been investigated. A drastic increase in the efficiency of ultrasonically-induced electrochemical processes at the carbon fibres uniformly distributed in the volume of the electrochemical cell in contrast to the compact carbon electrode was electrochemically revealed and substantiated theoretically.

*Mironov V.S., Pleskachevsky Yu.M.*

**On evaluation of the effective range of the surface forces of dispersed and fibrous materials.** pp. 73--77

*Summary:* The feasibility of applying the method of measuring the boundary layer thickness of testing liquid crystalline media to evaluate the effective range of the surface forces of dispersed and fibrous materials is shown. Significant increase of the surface forces effective range of the particles as the result of triboactivation is established.

*Potkin V.I., Lyakhov A.S., Zapolsky V.A., Govorova A.A., Kaberdin R.V.*

**Crystalline and molecular structure of 1,3-dinitro-1,4,4-trichloro-1,3-butadiene.** pp. 78--81

*Summary:* It has been established by the *X*-ray structural analysis method that the diene chain in the 1,3-dinitro-1,4,4-trichloro-1,3-butadiene molecule has approximately plane *s-trans*-conformation.

**БИОЛОГИЯ**

*Mikhailov N.D., Kovalyukh N.N., Klimovich Yu.A., Kolkovsky V.M., Petrovich A.A.*
**Radiocarbon distribution in vegetation of some regions in Belarus.** pp. 82--85

*Summary:* Radiocarbon concentrations were determined in vegetation of some regions in Belarus. The maximum ^{14}C concentrations were due to the Chernobyl NPP accident.

*Barai V.N., Kukharskaya T.A., Zinchenko A.I.*

**RNA production from yeast using Ca**^{2+} ions and its chemicoenzymatic hydrolysis to nucleosides. pp. 86--90

*Summary:* The article presents a new approach to production of natural ribonucleosides. It is based on isolation of high-purified RNA from backer's yeast using Ca^{2+} ions, RNA hydrolysis under the action of Ca^{2+} ions followed by dephosphorylation of produced mononucleotide calcium salts to ribonucleosides using intact mycelium of *Spicaria violacea*.

*Pavlova I.V., Deeva V.P.*

**Epibrassinolide effect on ATPase activity of plasma-lemma and other cell components from buckwheat seedlings of a different ploidy level.** pp. 91--94

*Summary:* As was revealed by biochemical method under in vitro conditions epibrassinolide (10^{-7} M) increased ATPase activity of plasma membranes isolated in sucrose isopicnic density gradient from tetraploid buckwheat (*Fagopyrum esculentum Moench.*) seedlings and did not change it in diploid ones within 30 min of exposure. Under in vivo conditions epibrassinolide (10^{-7} M, 30 min) inhibited ATPase activity of plasma membranes irrespective of buckwheat seedling ploidy. The total ATPase activity increased by 35% in tetraploid seedlings and decreased twice in diploid ones. It was due to similar changes in the activity of ATPases that were not inhibited by uabain and orthovanadate.

*Amvrosiev A.P., Nikolaevich L.N., Shimanovich E.A.*

**Statistical analysis of chromosome aberration frequency in human peripheral blood lymphocytes.** pp. 95--99

*Summary:* As a result of statistical analysis of cytogenetic examination results of the adult population in Gomel region, a significant increase in the chromosome aberration level and aberrant cell number was revealed. No direct dependence between the taken irradiation dose and the value of chromosome anomalies was observed. The results of the analysis of distribution parameters presenting the empiric histogrammes indicate the existence of a special mechanism of chromosome aberration formation in the form of dicentrics and rings.

*Rozhdestvenskaya A.S.*

**Phenotypic structure of bank vole (***Clethrionomys glareolus*) population in Belarus. pp. 100--103

*Summary:* Phenotypic structure of bank vole, Clethrionomys glareolus, was studied on the basis of variations in *M*^{3}, *M*_{1} structure and cranial foramens. The mean phene number increases from the centre to the north and the south of the Belarus region. The portion of rare phenes increases from the north to the south, but the number of asymmetrical individuals decreases in the same direction.

**НАУКИ О ЗЕМЛЕ**

*Levykh N.N., Makhnach A.S.*
**Recognition criteria of weathering crusts on terrigenous rocks.** pp. 104--107

*Summary:* Recognition criteria of weathering crusts on terrigenous rocks are considered. The criteria include the kaolinite content and its crystallinity degree, secondary transformations of minerals and, first of all, biotite, muscovite and feldspar, alcaline and alcaline -- earth element dominant removal, breaking and jointing of terrigenous material, diversity of rock colours and an elevated iron content, and occurrence on surfaces of unconformity.

*Kuznetsov V.A., Generalova V.A., Yelovicheva Va.K.*

**New evidence for sedimentation of early holocoen in the Dnieper River valley.** pp. 108--112

*Summary:* Paleogeographical and paleogeochemical conditions of the sedimentation in the lake-reservoir in the Dnieper River valley (section Staraya Trosno) during Preboreal-Boreal epoch are defined.

*Makhnach A.A., Streltsova G.D., Kolosov I.L.*

**On isotopic composition of sulphide sulphur in coal-bearing deposits in Belarus.** pp. 113--117

*Summary:* The diagenetic sulphide formation in the Carboniferous coal-bearing sequence of Belarus and the epigenetic nature of sulphides from the Jurassic one are revealed on the basis of the sulphur isotope investigation.

**ТЕХНИЧЕСКИЕ НАУКИ**

*German M.L., Nekrasov V.P., Nogotov E.F.*
**Numerical method for radiative transfer calculation in two-phase medium with complex geometry.** pp. 118--122

*Summary:* A numerical methods for calculating the problem of radiation transfer in two-phase media is proposed. The presented method is based on the well-known integro-differential equation of radiative transfer. Resolution algorithm of above mentioned equation is a combination of the finite element method, discrete-ordinate method and method of iterations. Accuracy of the proposed method is discussed.

/ 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 © 1997-2008 Национальная академия наук Беларуси

Копирайт © 1996 Издательство "Беларуская навука"