# Доклады Национальной академии наук Беларуси, 2000, Том 44, No.3

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2000, Том 44, No.3

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Gaishun I.V.*
**Proper multidimensional discrete systems and its canonical forms.** pp. 5--7

*Summary:* It is proved that every proper multidimensional discrete system has a canonical form.

*Dmitruk N.M., Kirillova F.M.*

**Direct method of program optimization of multidimensional control systems.** pp. 8--11

*Summary:* An algorithm for solving a linear nonstationary optimum control problem is described.

*Tsegelnik V.V.*

**Analytical properties of solutions of one non-linear system of two differential equations.** pp. 12--13

*Summary:* Presentation of the fourth equation is given as an equivalent system of two first order differential equations determining the Becklund's reversible transformation which is the result of consecutive application of the Backlund's transformation obtained earlier by N. A. Lukashevich. The above transformations are associated with a linear matrix system containing a spectral parameter, the jointness condition being the fourth equation of Painleve'.

*De Pascale E., Zabreiko P.P., Shirokanova N.I.*

**New solvability conditions of Lyapunov--Shmidt integral equations.** pp. 14--17

*Summary:* A new result about solvability of the classical integral Ljapunov--Schmidt equation is obtained on the base of the wellknown Banach theorem about eigenvalues of multilinear operators in Hilbert spaces and the Minty principle of solvability.

*Mirotin A.R.*

**Laplace transform and Pally--Wiener- theorem for Lie semigroups.** pp. 18--20

*Summary:* Under certain conditions on the Lie semigroup *S* the image of space *L*^{2}(*S*) with respect to Laplace transform is described.

*Vorobyov N.N.*

**On inductive formations and Fitting classes lattices.** pp. 21--24

*Summary:* It is proved that in a complete lattice of t-closed totally local formations *l*^{t}_{¥} the supremum of an arbitrary set of its
elements {**F** = *LF*(f_{i}) | *i* Î *I*} where *f*_{i} is integrated *l*^{t}_{¥}-valued satellite can be defined with the help of satellite *f* the values *f*(*p*) of which are the supremums of corresponding values of the set {*f*_{i}(*p*) | *i* Î *I*}.

*Tishchenko K.I.*

**On approximation of complex numbers by algebraic numbers of limited degree.** pp. 25--28

*Summary:* In this paper we prove the following Theorem. For any complex number q which is not an algebraic number of degree £ *n*, there exist infinitely many algebraic numbers a of degree £ *n* such that |q - Å|_{c} << *H*(a)^{-A}, where << is the symbol of Vinogradov, *A* = *n*/4 + g_{n}, lim g_{n} = 3/2, *n* > 3. More precisely: *A* = *A*(*n*) is the largest root of the equation 4*X*^{2} - (*n* + 6)*X* + 3 = 0. The implicit constant in << depends on q and *n* only.

*Beresnevich V.V.*

**Analogue of the Khintchine--Groshev theorem for curves in Rn.** pp. 29--32

*Summary:* The Khintchine--Groshev theorem is generalized to Diophantine approximation on smooth non-degenerate curves in **R**^{n}.

*Kurenok W.P.*

**On "zero-one" law for integral functionals of quasi-stable processes.** pp. 33--36

*Summary:* We prove the "zero-one" law about the finiteness of integral functionals of quasistable processes which can be obtained from the stable processes of the index 1 < *p* < 2 via time change driven by speed measure of the general form. This generalizes known results for the case of the speed measure coinciding with Lebesgue measure. Some sufficient conditions for divergence of considered functionals are also given.

*Bazylev D.F., Yanchevskij V.I.*

**Gaussian torsion of cubic curves in Weierstrass form.** pp. 37--39

*Summary:* For the field of Gauss numbers a generalazation of Nagell--Lutz theorem is obtained.

**ИНФОРМАТИКА**

*Zakrevskij A.D.*
**Solving large systems of logic equations by syllogisms.** pp. 40--42

*Summary:* The problem of solving large systems of logical equations where each equation depends on restricted number of variables is considered. A new method is suggested for its solution, based on revealing some prohibited combinations of values on pairs of arguments and using the technique of syllogisms.

**ФИЗИКА**

*Goncharenko A.M.*
**Approximated theory of spatial-temporal optical solitons.** pp. 43--45

*Summary:* It is shown that, using Gaussian functions, it is possible to find a solution of the Schrodinger equation and investigate the properties of the spatial-temporal solitons.

*Komarov F.F., Leontjev A.V.*

**Ion-implanted polymer films--promising materials for optic microwaveguides.** pp. 46--49

*Summary:* Investigation results of influence of light ion irradiation on optical constants of PMMA and polystyrene films are presented. It was shown that ion implantation provides possibility to change locally the refraction index of thin organic films and approach based on molecular refraction allows to forecast *n* values.

*Khatkevich A.G., Khatkevich L.A.*

**Linear presentation of crystal optics.** pp. 50--52

*Summary:* The asymmetric tensor of refraction indices has been introduced and on this basis the extraordinarily simple linear expressions of the wave parameter correlation with direction of the wave normal in the crystal have been obtained.

**ХИМИЯ**

*Kaputskij F.N., Starobinets G.L., Yurkshtovich T.L., Bychkovskij P.M.*
**Sorption of certain anticancer substances by carboxylic cationates from water--organic nonelectrolyte binary solutions.** pp. 53--56

*Summary:* Molecular sorption of three electrolytes of anticancer action by two carboxylic ionexchangers from their solutions in six binary systems water -- organic nonelectrolytes has been studied. It has been settled that the
dependence of lg(*K*_{d}_{0}/*K*_{d}) from (s_{0} - s) (*K*_{d} is the partition constant of the electrolyte, s is the solutions surface tension,
and the index 0 refers to water phase) is very sensitive to structural changes of binary solutions, particularly to their microscopical demixture.

*Ratko A.I., Romanenkov V.Ye., Stankevich M.V., Smirnov V.G.*

**Aggregation mechanism of powder aluminium under hydrothermal conditions.** pp. 57--59

*Summary:* Theoretical analysis of powder aluminium unity process has been carried. The kinetic equation of the forming of reaction solid product in the hydrothermal conditions has been received. The kinetics of the forming of contacts between aluminium particles bases are shown to be due to the processes of the solution -- interaction with water -- solidification to the porous polycrystalline unit.

**БИОЛОГИЯ**

*Goncharenko G.G., Antonenko V.V., Vorobyov V.N.*
**Construction of genetic maps for Picea abies and Picea obovata as main structural components of spruce forests in Europe and Siberia.** pp. 60--63

*Summary:* In the analysis of 26 allozyme genes in two spruce species of Europe and Siberia 21 loci in 8 linkage groups were mapped, II genes being localized in 4 linkage groups of Picea abies and 10 genes in 4 groups of Picea obovata. The orders and locations of genes in the linkage groups in two species were similar. The data show that the genetic arrangement is highly conservative among species of genus Picea.

*Gorbunova N.V., Kalyunov V.N.*

**Effect of chemical desympathization on nerve growth factor content in mice blood during zoosocial stress.** pp. 64--66

*Summary:* The integrity of the sympathetic nerve supply is one of crucial moments that provide the release of nerve growth factor from the submandibular salivary glands into the blood stream during zoosocial stress. Elimination of the aggressive behaviour of animals after guanethidine treatment is probably causedby destructive effect of the drug on the central catecholaminergic structures dueto blood-brain barrier permeability in the neonatal period.

*Kulchitskij V.A., Azev O.A., Nikandrov V.N.*

**Ability of plasminogen and catalase to modulate electrical activity of bulbar neurons.** pp. 67--69

*Summary:* Electrophysiological investigations of anesthetized rats after microinjections of catalase or plasminogen to the solitary tract nucleus or caudal ventrolateral medulla revealed an increase in electrical activity of neurons in the dorsal motor nucleus of the vagus. It is concluded that plasminogen-plasmin, besides the specific role, can perform in the CNS functions of intercellular messengers and modulators of synaptic processes.

*Bokuts T.B., Petrusenko G.P., Danilova T.Ya.*

**Effects of weak electromagnetic fields and various intensity noises on glucose-6-phosphate dehydrogenase and nuclease activity in rat brain.** pp. 70--72

*Summary:* Experiments showed that 10-fold exposure (4 h daily) to weak electromagnetic fields (EMF) of industrial frequency (*E* = 360--480 V/m, *H* = 120--150 nT), genevated by a high-voltage line, combined with the noise of different intensity (65--68 or 83--89 dB) did not induce significant changes in the glucose-6-phosphate dehydrogenase activity in the female rat brain. The alkaline and acid ribo- and deoxyribonuclease activity depended on the noise level. A combined exposure to a weak EMF and noise of lower intensity (65--68 dB) did not change brain nuclease activity, as compared with the control values, whereas an increased noise level, 83--89 dB, combined with EMF, initiated an increase in activity of these enzymes.

*Vismont F.I., Shust O.G.*

**Role of liver and a**_{1}-antitrypsin detoxication function in progress of pyrogenalic fever. pp. 73--74

*Summary:* Acute toxic injury of the liver induced by CCl_{4} in rats and rabbits was accompanied by inhibition of detoxication function of the liver, decrease in blood level of a_{1}-antitrypsin, and by a fall of rectal temperature. Injection of S. typhi lipopolysaccharide (LPS), 5.0 µg/kg per rat and 0.5 µg/kg per rabbit stimulated detoxication function of the liver, increased the blood content of a_{1}-antitrypsin, decreased heat loss, and caused elevated body temperature. Intravenous injection of a_{1}-antitrypsin induced lasting hyperthermia in animals. In conditions of toxic lesion of the liver by CCl_{4} the hyperthermic response to LPS was absent at all. It is suggested that the state of the functional activity of the liver, and its detoxication function in particular, as well as blood level of a_{1}-antitrypsin synthesized by hepatocytes, are significant for the mechanisms of the thermoregulatory response to endotoxin.

*Radyuk M.S.*

**Fluorescence of monomer chlorophyll ***b* and longwave protochlorophyllide in etiolated barley leaves. pp. 75--77

*Summary:* It is shown that transient appearance of the 77 K fluorescence of chlorophyll *b* observed during the first hours of the etiolated barley leaves greening is accompanied by the appearance of the long-wave protochlorophyllide fluorescence. It is supposed that appearance of the chlorophyll *b* fluorescence is connected with disintegration of specific pool of chlorophyll *a/b*-binding proteins. It creates conditions for accumulation of long-wave protochlorophyllide and formation of new photo-synthetic units.

*Shcherbakov R.A., Domanskij V.P., Rudoj A.B.† *

**Effect of variable pulserate irradiation on chlorophyll synthesis in etiolated barley leaves.** pp. 78--80

*Summary:* Chlorophyll accumulation in postetiolated barley leaves, previously irradiated for 6 h with continuous light, under the pulsed light of 2 ms pulse duration was studied. The pulsed illumination was shown to be noneffective in chlorophyll accumulation, if the pulse frequency was less than 1 Hz (dark intervals about 1.5--0.74 s). The chlorophyll accumulation was observed under more frequent pulsed light and increased with frequency. These findings suggest the possibility that photosynthesis affects the chlorophyll formation.

**НАУКИ О ЗЕМЛЕ**

*Ipatyev V.A., Bulko N.I., Mitin N.V.*
**Effect of ground water level on radionuclide content in surface layer of forest hydrogenic soil.** pp. 81--83

*Summary:* It was that the water regime plays a decisive role in the rate of the root radionuclide uptake by developing woody plants and thus in radionuclide contents in the leaf- and needle litter that has a great impact on the process of removing ^{137}Cs from the forest floor and upper root layer of the bog.

*Astapenko V.N., Matveyev A.V., Nechiporenko L.A., Shishonok N.A.*

**Peculiarities of lineament zone structure revealed from topography maps of Central Belarus.** pp. 84--86

*Summary:* Increase of electric resistance of lineament zone in the upper part of sedimentary bed been revealed. This feature of geological section is explained by the density of cracks, by orientation of the structure to direction of movement of glacial covers, and by specificity of sedimentation processes,

*Shtefan L.V., Nikitin Ye.A.*

**Garnets and chrome spinelides of diatrem rocks of Zhlobin field.** pp. 87--90

*Summary:* The pipe rocks of Zhlobin field form two series: alkali-undersaturated and alkali-basaltic. It have different quality and quantity sets of mantle materials (garnets and spineles). It is shown that petrologic properties of alkali rocks are correlated with the depth of their generation in the mantle.

*Tolkachikova A.A.*

**Thermodynamic formation regime of peraluminous rocks of Ivye block of Belarusian-Baltic Granulite belt.** pp. 91--94

*Summary:* The range of conditions for 2 and 3 stages of metamorphism of peraluminous rocks in the Ivie block of the Belarusian-Baltic granulite belt -- 663-720 °C, 5.9-7.3 kB and 575-608 °C, 4.5-5.8 kB is determined. Minerological-petrographical investigations and geothermometry data indicate polimetamorphical transformation of peraluminous rocks. Comparison of chemical and microsprobe studies of rock-forming minerals has confirmed validity silicate analyses for thermobarometrical research of crystal Precambrian rocks.

*Fedenya S.A.*

**Paleo-ecological reconstruction of muravian basins in Western Belarus (by diatom analysis).** pp. 95--99

*Summary:* Diatom successions revealed in the profiles of borehole N 8 at Zelva (Zelva District) and of the borehole N 4 at Vladyki (Logojsk District) reflect the conditions of ancient lacustrine deposits formed during the Muravian Interglacial in paleobasins of different type.

*Sachok G.I., Salivonchik S.V.*

**Statistical solution of ecological ordination direct and inverse tasks exemplified by (meadow vegetation of Belarus).** pp. 100--104

*Summary:* The direct and inverse tasks of ecological ordination of meadow phytocenoses have been formulated by the ground of gauss conception of edafotop and botanical species and the statistical methods of its solution have been proposed.

*Levyh N.N., Bulkin Yu.S., Abramenko V.T.*

**Trace elements behaviour in Pro--Cambrian weathering crusts lying over intermediate rocks of crystallune basement of Belarus.** pp. 105--108

*Summary:* The data on the trace elements migration in the Pre-Cambrian weathering crusts is obtained, developed over intermediate rocks. It is shown that they are depend on the concentrator minerals, surrounding medium and the influence of attendant processes.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Klubovich V.V., Kirillov S.A., Kotin I.M.*
**Superelasticity statistical model.** pp. 109--111

*Summary:* The model allowing to describe the superelastic behavior of shape memory alloys presented. The mutidomain shape memory alloy structure evolution is described with the aid of a ferromagnet model. The model partition function is estimated by means of random walks without self-intersecting on Flory--Huggins lattice.

*Kozlov G.V., Burya A.I., Sviridyonok A.I., Shogenov V.N.*

**Crack self-inhibition effect in stretching hard chain polymers.** pp. 112--114

*Summary:* The effect of self-inhibition of cracks in films, formed from hard chain polyarilatesulphone. It is shown, that the main role in deformation of this polymer is played by orientation mechanism, which results in additional dissipation external forces.

*Makushok Ye.M., Kharchenko V.V.*

**Calibration processes in side shaping of intricate profile.** pp. 115--117

*Summary:* The paper discusses the process of shaping external side surfaces. The process conditions are given for schemes realized by impressing and radial reduction of blanks. The deformation procedure based on elastic reduction of a die with a blank is shown to ensure a maximum life of a shaping tool and it can be recommended for practical use.

*Alfer S.A., Bulgak I.A., Kvacheva I.S., Makovetskaya L.A., Shempel N.A., Shipilo V.B.*

**Property changes in synthetic diamonds under thermochemical treatment.** pp. 118--121

*Summary:* The physical and mechanical properties of synthetic diamond powders of the AC20-AC32 type subjected to thermochemical exposure are investigated. It is shown, that the process of thermochemical treatment results in hardening of diamond powders. Catalytic oxidation of synthetic diamond powders by air at 700-800 °C changes crystal morphology. The crystal strength increases at slow rates of heating and cooling and decreases at high rates of heating and cooling.

/ 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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