# Доклады Академии наук Беларуси, 1997, Том 41, No.1

/ Издания академии / Научные журналы

Доклады Академии наук Беларуси, 1997, Том 41, No.1

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Zabreiko P.P., Laptinsky V.N.*
**Fixed point principle and non-local theorems on solvability for essentially nonlinear differential equations.** pp. 5--9

__Summary:__ This article deals with some new solvability results for operator Riccati equations. Some global existence theorems are obtained. The main idea of authors' approach is based on some modifications of the Kantorovich fixed point principle for smooth operators in Banach spaces and on elementary estimates for solutions to scalar Riccati equations which follow from theorems on differential and integral inequalities.

*Monastyrny P.I., Shanko D.V.*

**Invariant submersion for nonlinear net boundary value problems.** pp. 10--15

__Summary:__ In this paper the development of the theory of invariant submersion method is carried out. Some questions dealing with numerical algorithm construction are studied on the bases of i.s.m. for nonlinear net problems.

*Yanchevsky V.I.*

**Index reduction formulae for local hyperelliptic curves with poor reduction.** pp. 16--21

__Summary:__ The index reduction formula is obtained for special hyperelliptic curves defined over local non-dyadic field of zero characteristic.

*Leonov N.N.*

*n*-widths in non-Archimedean normed spaces. pp. 22--25

__Summary:__ A method to estimate *n*-widths in non-Archimedean normed spaces is proposed. This method is applied to evaluating *n*-widths of the class of *p*-adic functions.

*Knyazhishche L.B.*

**The limit set localization and asymptotic stability for delay equations.** pp. 26--29

__Summary:__ The limit sets localization with respect to "zeros" of an auxiliary functional is investigated for delay equation in the framework of the Lyapunov--Razumichin method. Asymptotic stability conditions are presented as a generation of the Barbachin--Krasovski theorem for delay equation.

*Lebedev A.V.*

*C*^{*}-algebras associated with automorphisms acting on the singled out ideals. pp. 30--33

__Summary:__ For a given action of a group by automorphisms of a singled out ideal of a *C*^{*}-algebra there is introduced and studied the structure which is a natural generalization of the classical cross-product.

*Benediktovich V.I., Sarvanov V.I.*

**Hamiltonian cycle problem for planar cubic graphs.** pp. 34--37

__Summary:__ It has been shown that the Hamiltonian cycle problem for planar, cubic and 3-connected graphs is reduced to the same problem for planar, cubic and cyclically 4-connected graphs.

*Krushevsky A.E., Naumovich S.A.*

**Mathematical stimulation of tooth periodontial equilibrium.** pp. 38--43

__Summary:__ The article deals with a calculated model of periodontium as a membrane bounded with two composite elliptic hyperboloids. The strained state in the region of joining periodontium and a root of the tooth was examined, the total reduction in the stress level and an increase in rigidity at tooth translations being observed, the equation of tooth turn spiral axis being written and no-displacement conditions along the axis of rotation being found out. The investigations pursued have found an application in practice of tooth prosthetics and elimination of various defects in tooth location.

**ФИЗИКА**

*Parashchuk V.V., Gribkovsky V.P.*
**On light self-channeling at streamer discharge in semiconductors.** pp. 44--49

__Summary:__ The spatial characteristics are calculated and the conditions for light self-channelling in a strong electric field are determined. It is shown that such effects were possible at streamer discharge in semiconductors.

*Markevich M.I., Piskunov F.A., Chaplanov A.M., Matusevich L.V., Chen Chao*

**Redistribution of implanted impurity during impulse laser excitation.** pp. 50--54

__Summary:__ A general numerical solution of the one-dimensional heat diffusion and diffusion equation respectively used to calculate the temperature of a surface and the redistribution of B in Si exposed to pulsed heating. The numerical solution (based on a finite difference model) is in a good agreement with experimental measurements.

**ХИМИЯ**

*Kim Te Il, Sosinovich Z.I., Soldatov V.S.*
**Computation of potentiometric titration curves of ion exchangers with weak bases.** pp. 55--58

__Summary:__ A method for computation of potentiometric titration curves of ion exchangers with weak bases has been developed. It is based on the suggested earlier equation *f*(pH, *C*, *x*) = 0 as a function of parameters of acidity of an ion exchanger and the dissociation constant of the base. It illustrated with the example of titration of a fibrous carboxylic ion exchanger by aqueous solutions of NH_{3}. The method provides an accuracy comparable with the experimental one.

*Dikhtievskaya L.V., Makarevich N.A., Mozheiko F.F.*

**Kinetics of salt adsorption in high aliphatic amines at the water solution/air interface.** pp. 59--63

__Summary:__ On the basis of the kinetic dependencies of the surface tension of cationic surfactants (the salts of high aliphatic amine C_{12}--C_{18}) at the water solution/air interface the energy of lateral interactions and activation energy of the mass-transference against the degree of packing of the adsorption layer and the length of the hydrophobic amine radical have been evaluated and compared.

*Gaponenko N.V., Borisenko V.E., Bachilo E.Ye., Grozhik V.A., Molchan I.S.*

**Thermodynamic evaluation of chemical component interaction between semiconductor substratum and thin film silica coating doped by rare-earths or II group metal oxides.** pp. 64--68

__Summary:__ The thermodynamic analysis of chemical interaction between semiconductor substratum and thin film silica coating doped by II and III group metal oxides shows that there is, in some cases, a possibility of metal reduction from its oxide. The results obtained are useful for solid-state electronics technology.

*Streltsov E.A., Osipovich N.P., Lyakhov A.S., Ivashkevich L.S.*

**Underpotential deposition of metals during cathodic electrochemical synthesis of metal selenides.** pp. 69--73

__Summary:__ The regularities of cathodic reduction of metal cations (Pb^{2+}, Cd^{2+}) on Se-electrodes in acidic water solutions are investigated. Underpotential deposition of metal atoms on Se-surface is found. Cathodic reduction of Se(IV) and metal cations at *E* > *E*_{Men+/Me0} results in the formation of appropriate selenides. This formation is due to the interaction between selenium atoms, electrodeposited overpotential, and underpotential deposited metal atoms.

**БИОЛОГИЯ**

*Khotyljova L.V., Kaminskaya L.N., Matveenko S.N.*
**Population structure and transgressive variability of quantitative traits in triticale hybrids obtained ***in vitro*. pp. 74--78

__Summary:__ Comparison of quantitative trait expression in triticale forms and *F*_{2} hybrids obtained in field and *in vitro* was carried out. The analysis of variability, count of segregated positive transgressions and characteristic of plant distribution in populations show the possibility of productivity improvement in particular triticale samples.

*Vereshchako G.G., Khodosovskaya A.M., Konoplya E.F.*

**The influence of chronic gamma-irradiation on the functional state of some radiosensitive and radioresistant tissues of rat organism.** pp. 79--83

__Summary:__ The article presents the data concerning the influence of chronic irradiation on nucleic acids and the crude protein content in rat testis, spleen and liver tissues, as well as on testis and spleen weight and blood leukocytes amount at the total 6.0 Gy dose. Chronic gamma-irradiation-induced effects resulted in significant reductions in the biochemical indices more pronounced in spermatogenic epithelium, drop in testis weight and leucopenia.

*Mongin A.A., Fedorovich S.V., Konev S.V.*

**Effect of nitric oxide generators, sodium nitroprusside and nitrosocysteine, on membrane potential of brain nerve endings.** pp. 84--87

__Summary:__ The effects of two nitrogen monoxide (NO) generators, sodium nitroprusside (SNP) and S-nitroso-L-cysteine (NC), on transmembrane electric potential of rat brain synaptosomes evaluated from steadystate accumulation of ^{3}H-tetraphenylphosphonium bromide (^{3}H-TPP^{+}) and K^{+} analogue, ^{86}Rb^{+} were studied. SNP (10 µM -- 10 mM) decreased ^{3}H-TPP^{+} as well as ^{86}Rb^{+} accumulation in dose-dependent manner with half-maximum effect at 10 -- 20 µM. The increase in drug concentration above 1 mM was not followed by further membrane depolarization. NC also depolarized synaptosomes but in contrast with SNP in the concentration range from 10 µM to 10 mM no saturation of the effect was found. SNP as well as NC did not affect mitochondrial potential evaluated from ^{3}H-TPP^{+} accumulation under high external K^{+} conditions. Thus NO causes depolarization of synaptosomal plasma membrane. A possible role of this phenomenon in NO-dependent neurotransmitter release is discussed.

*Lemesh V.A., Titok V.V., Kalitukho L.N.*

**Morphophysiological characteristic of different cultivars and varieties of flax at the seedling stage.** pp. 88--92

__Summary:__ Fiber flax seedlings of different varieties and cultivars were used for the study of a comparative analysis of morphophysiological features at early developmental stages. It was shown that seedlings of high productive cultivars were characterized by high dry matter increase. Differences in the chlorophyll content in different flax varieties and cultivars appeared to be insignificant.

*Lupei A.Yu., Voluevich E.A.*

**Effects of alien plasmon on seedling resistance to ***Septoria nodorum* of Belarusian cultivars of spring wheat. pp. 93--95

__Summary:__ Investigation of the seedling resistance to *Septoria nodorum* of wheat alloplasmic lines cv. Byelorusskaya 12 and Byelorusskaya 80 showed that manifestation of cytoplasmic effects to a great extent depends on the nuclear genetic background and on the pathogen genotype. Cytoplasms of *Triticum polonicum* and *T. turanicum *increased the level of resistance to high aggressive pathogen isolate in combination with genomes of both cultivars.

**НАУКИ О ЗЕМЛЕ**

*Naidenkov I.V.*
**Lead isotopy in rocks of Okolovo ore deposits.** pp. 96--99

__Summary:__ The analysis of relations between lead isotopes in rocks of Okolovo ore deposits and contents of uranium and thorium in their ores suggests a significant role of hydrothermalmetasomatic processes in formation of the ferriferrous rocks.

*Konishchev V.S.*

**Peculiarities of formation of salt massif internal structure.** pp. 100--103

__Summary:__ Lower parts of some salt massifs are shown to be normally stratified because they were in tectonic shadow during halokinesis.

*Velichkevich F.Yu., Sanko A.F.*

**Stratigraphy of Pleistocene in Orsha Upland.** pp. 104--109

__Summary:__ The Byelovezhian and Muravian interglacial deposits are distinguished by palaeocarpological and malacological methods in Orsha Upland during the new boring.The Belovezhian deposits lie on the Yaseldian till. The Nizhninskian, Berezinskian and Dnieperian glacial complexes are found in the Byelovezhian-Muravian space.

*Svidersky Ye.I., Altshuler P.G.*

**Prospects of oil and gas potentialities of the abovesalt Devonian complex in the Pripyat depression from isotope-hydrochemical data.** pp. 110--113

__Summary:__ The study hydrochemical conditions of the abovesalt Devonian complex in the Pripyat depression is indicative of the existence of favourable conditions for formation, accumulation and preservation of natural hydrocarbons.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Makarevich A.V., Pinchuk L.S., Dunaitsev I.A.*
**New polymer microorganism carriers in biofilters for waste water purification.** pp. 114--118

__Summary:__ Polymer fibrous elements having a stable configuration are produced by "melt-blowing" method. They serve as an excellent microorganism carriers in biofilters intended for waste water purification. These materials comply with the constructive-technological requirements imposed on biomass carriers, ensure the rapid starting period and an effective work of biofilter. Modified polymer materials possessing the controlled bioactivity should be considered as a new generation of microbe culture carriers, which determines prospects of an engineering ecology development.

*Sorokin V.V.*

**Application of Brinkman equation to description of filtration through pebble beds.** pp. 119--121

__Summary:__ The equality of effective viscosity in Brinkman equation to ordinary fluid viscosity is shown for the fluid flow through pebble beds.

/ 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 © 1997 Издательство "Беларуская навука"