# Доклады Национальной академии наук Беларуси, 1998, Том 42, No.1

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 1998, Том 42, No.1

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Chernyavski A.F., Kolyada A.A., Kravtsov V.K., Revinski V.V., Selyaninov M.Yu.*
**The theoretical bases of minimal redundant quadratic modular number systems.** pp. 5--12

__Summary:__ The structure of a complete system of residues (CSR) on the complex modulus is investigated. For its construction an effective constructive rule realizing isomorphism of CSR and an adequate ring of the real integer residues is offered. Within the framework of the given isomorphism a quadratic minimum redundant modular number system is determined. The base theorem of the apparatus of the interval modular forms making a basis of minimal redundant quadratic modular arithmetic is proved.

*Samarskii A.A., Vabishchevich P.N., Zyl A.N., Matus P.P.*

**Difference scheme of higher order of approximation for Dirichlet's problem in random domain.** pp. 13--17

__Summary:__ Difference scheme of the second order of approximation for multidimensional Poisson equation is constructed. Calculated area W is covered by rectangular grid with fixed steps on each direction. Difference scheme on the near boundary nodes is constructed on the basis of approximation in specially chosen point. High efficiency of the method for numerical solution ini irregular areas is shown in fulfilled calculations.

*Gabasov R.F., Kirillova F.M.*

**Stabilization of dynamic systems by optimal control methods.** pp. 18--22

__Summary:__ On the basis optimal control problems new principles of constructing bounded stabilizing feedbacks for dynamical systems are proposed. It is shown that the methods under question may be applied to stabilize control systems which are uncontrollable according to Kalman.

*Kruger A.Ya.*

**On extremality of sets systems.** pp. 24--28

__Summary:__ New extremality notion is introduced for sets systems. It defines sets joint disposition in space. Extrernal systems arise when investigating various optimization problems. The proposed definition of extremality is satisfied by sets corresponding to a broad class of "almost optimal" points. Extremality conditions are stated in the form of the generalized Euler equation and appear to be necessary and sufficient.

*Antonevich A.B., Lebedev A.V.*

**Symbols of functional pseudodifferential operators in the scale of the Sobolev spaces.** pp. 29--33

__Summary:__ The paper describes the principal symbol calculus for nonlocal functional pseudodifferential operators acting in the Sobolev spaces.

*Babaitsev A.Yu.*

**The strong perfect graph conjecture of Berge for line graphs of linear 3-colored hypergraphs.** pp. 34--37

__Summary:__ The well-known Strong Perfect Graph Conjecture of C.Berge states that a graph **G** is perfect if and only if neither **G** nor its complement **G**^{--} contain odd holes (*i.e.* induced simple cycles of odd length greater than 3). The Strong Perfect Graph Conjecture is proved for line graphs of linear 3-colored hypergraphs (it means the strong coloring).

*Kovalev M.M., Zaporozhets A.A., Girlikh E.*

**Characterization of some subclasses of Monge matrices.** pp. 38-44

__Summary:__ We consider matrices *C = (c*_{ij})_{m ´ n} as functions *f(i, j) = c*_{ij} defined on integer lattice {1, 2, ..., *m*} ´ {1, 2, ..., *n*} and characterize some classes of matrices having properties closely related to the convexity and concavity of functions. On this basis we present a classification of matrices by using submodularity and convexity of the corresponding functions. Introduced subclasses of matrices (modular, linear, convex, isotone submodular) form cones. We have characterized these cones via sets of extremal rays. Thus for some special cases the fundamental problem of extremal ray description of cones of various submodular function families is solved.

*Milovanov M.V.*

**On Mishchenko--Fomenko hypothesis and integrability of solvable algebras.** pp. 45--49

__Summary:__ Mishchenko -- Fomenko hypothesis on integrability of finitedimensional Lie algebra is proved for any solvable Lie algebra.

*Tikhonov S.V., Yanchevskii V.I.*

**Three-primary torsion part of the Brauer group of local elliptic curves with additive reduction.** pp. 50--54

__Summary:__ Let char *k*^{--} be the characteristic of the residue field *k*^{--} of the local field *k*. The presentation of three-primary torsion part of the Brauer group of local elliptic curves with additive reduction by means of unramified division algebras is determined in the case where char *k*^{--} ¹ 3.

**ФИЗИКА**

*Grushevskaya G.V., Gursky L.I., Dorozhkin N.N.*
**The Green function method for crystal in complex energy--momentum space: the case of nonspherical inter atomic potential.** pp. 55--62

__Summary:__ The Green function method based on the proposed modified numerical methods of tetrahedrons in the case of nonlocal distribution of electron density in solids and nonspherical interatomic potential in complex energy--momentum space has been developed.

*Knyazev M.A., Goncharenko E.A.*

**Coupled states of two kinks for the system of two scalar fields.** pp. 63--66

__Summary:__ The system of two coupled real scalar fields in the case of the fourth order potential is considered. Solutions of the appropriate system of nonlinear motion equations which correspond to coupled states of two kinks or antikinks are analytically constructed.

*German M.L., Nekrasov V.P., Nogotov E.F.*

**Analytical and numerical method for Solution of integrodifferential equation of radiative transfer in enclosure of arbitrary geometry.** pp. 67--73

__Summary:__ Hybrid analytical/numerical method is proposed for solution of integrodifferential equation of radiative transfer in multidimensional media with arbitrary optical and geometric boundary conditions. Resolution algorithm is a combination of discrete-ordinates method and ray-tracing method -- radiation intensity is calculated along the ray trajectory with allowance for the optical properties of media and boundary surfase using the piece-analytical solution of mentioned equation. The proposed method extends the range of resolution problems with increasing the accuracy and speed of radiative transfer calculations and decreasing the computer resources.

**ХИМИЯ**

*Kuvaeva Z.I.*
**The influence of cation nature on association of alkylnaphthaline sulfonates.** pp. 74--78

__Summary:__ Correlation between water uptake and the association degree of some dinonylnaphthaline and didodecylnaphthaline sulfonic acid salts was established. Deviation from this correlation was shown to be an attribute of specific interaction of such ions as hydrogen, silver and some others.

**БИОЛОГИЯ**

*Vasilenko V.Yu., Petruchuk T.A., Golubovich V.P., Galyuk E.N., Yegorova S.V., Akhrem A.A., Gourine V.N.*
**Activity and thermosensitivity of neurons in rat anterior hypothalamus are modulated with bombesin fragments.** pp. 79--82

__Summary:__ Some fragments of bombesin were used in our slice experiments to determine their action on temperature dependence of neuronal firing rate in the preoptic area and anterior hypothalamus. The results show the existence of bombesin molecule fragment (Glp-Gln-Arg-OMe) which may be responsible for the bombesin-induced increase in warm sensitivity of warm-activated neurons.

*Yakushev B.I., Parfenov V.I.*

**Absorbed radiation dose in plants of natural complexes in Belarus over the past 10 years following the Chernobyl accident.** pp. 83--87

__Summary:__ An absorbed radiation dose in plants of the natural complexes in Belarus for 10 years following the Chernobyl accident was calculated. The data on dynamics of exposure dose rate in the area for 10 years were used for calculating the absorbed dose due lo external irradiation and the data on the specific activity of the plants due to incorporation of caesium-137 and strontium-90 were taken into consideration when calculating the absorbed dose due to internal irradiation The highest contribution to formation of absorbed doses of ionizing radiation in plants in the radiocontaminated zones belongs to internal irradiation of plant organisms due to incorporated radionuclides, in particular caesium-137.

*Melnikova A.M., Matus V.K., Kaler G.V., Martynova M.A., Konev S.V.*

**Ozone-induced modification of structural and functional state of plasma membrane of yeast C. utilis.** pp. 88--92

__Summary:__ Lipophylic fluorescent probes, pyrene, 1,6-diphenylhexatriene (DPH) and anthrylvinyllabeled sphingomielin (ASM) have shown that ozone treatment increases the hydrophilic nature of the plasma membrane of yeast cells. At the same O_{3} dosages, biphase changes of the microviscosities of annular and bilayer lipids were observed: all the probes displayed a decrease in the viscosity of microenvironment at low ozone doses and its increase at doses of ³ 4.5 µmole O_{3}/mg cell protein The observed biphase variations in the microviscosity of membrane lipids were correlated with changes in the proton-translocating activity of the yeast plasma membrane H^{+}-ATPase which was stimulated by low O_{3} doses.

*Titok V.V., Lemesh V.A., Rusinova O.V., Khotylyova L.V.*

**Morphophysiological traits in tomato of ***in vitro* culture in heterosis. pp. 93--97

__Summary:__ Accumulation of plant dry matter, leaf area, integral indices for work efficiency of assimilating surface and the chlorophyll content were studied in tomato varieties, lines and F_{1}-hybrids under conditions of *in vitro* tissue culture of the meristematic type. In contrast to the leaf area heterosis for biomass and the chlorophyll content was observed in all crossing combinations irrespective of genotypic feature of the original forms.

*Savchenko G.E., Klyuchareva E.A., Serdyuchenko E.V., Chaika M.T.*

**The influence of cyclic heat shock on formation of membrane system in barley etioplasts.** pp. 98--103

__Summary:__ Shortening of leaves and coleoptiles, increase in the etioplast volume and the total length of prothylakoid membranes was observed in etiolated barley plants after cyclic heat shock (HS). HS stimulated protochlorophyllide and carotenoid accumulation, increase in intensity of tryptophane fluorescence and the eximerisation degree of lipophilic fluorescent probe pyrene in prolamellar body fraction (per total protein). The latter is most likely to be caused by a decrease in microviscosity of the membrane lipid bilayer and not by pigment-mediated quenching of pyrene eximer fluorescence.

*Goncharenko G.G.*

**Gene flow in natural pine populations of Eastern Europe and Siberia.** pp. 104--109

__Summary:__ Gene flow was investigated in populations of six pine species of Eastern Europe and Siberia using allozyme genes. On the basis of Wright's F_{ST} coefficient values and frequencies for private alleles it was demonstrated that the most intensive gene flow exceeding 8 migrants per generation was found to *Pinus sylvestris* and *P. nigra* while a weak flow that in some instances was limited by 1 to 2 migrants per generation was characteristic of *P. brutia, P. mugo, P. sibirica* and *P. pumila*. A relation between the number of private alleles and the level of genetic variation was established. The use of F_{ST} values provided more accurate gene flow estimates as compared with those obtained on the basis of using frequencies for private alleles. At the same time the numerical values of gene flow calculated by the two methods appeared to be similar to each other in all pines studied.

**НАУКИ О ЗЕМЛЕ**

*Kudelsky A.V., Smit D.T., Pashkevich V.I., Ovsyannikova S.V., Petrovich A.A.*
**Potassium effect on Cs-137 behaviour in natural waters of radiocontaminated regions (Belarus).** pp. 110--113

__Summary:__ Very close relationships between ^{137}Cs activity of water objects (soil solutions, bog and lake water) and their stable potassium contents have been revealed in the radiocontaminated area in south-eastern Belarus. A universal character of these relationships are of interest when elaborating countermeasures for reducing population dose loads due to ^{137}Cs water migration.

*Konishchev V.S.*

**Developmental stages of the Pripyat Trough.** pp. 114--118

__Summary:__ The study of the Pripyat Trough faults evolution history has provided evidences to prove the position of the boundary between the rift and syneclise stages in the middle of the Visean age.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Anisimovich V.G., Dostanko A.P., Khmyl A.A.*
**The influence of pulse conditions of electrolyte plasma generation on properties of treated brass surfaces.** pp. 119--122

__Summary:__ Roughness parameters and luminance factor of the Cu-Zn alloy surfaces were investigated after their various polish techniques by the contact profilemeter, photometer and ASM. The most smooth surfaces can be achieved by plasmaelectrolytic treatment formed by pulse current. Preliminary mechanism for improving quality characteristics of brass surfaces was proposed on the basis of the experimental data.

/ 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

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Копирайт © 1998 Издательство "Беларуская навука"