# Доклады Академии наук Беларуси, 1997, Том 41, No.6

/ Издания академии / Научные журналы

Доклады Академии наук Беларуси, 1997, Том 41, No.6

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Benyash-Krivets V.V.*
**On decomposition of some ***F*-groups into proper tree products with amalgamation. pp. 5--7

__Summary:__ For *h*>2 the decomposition of the *F*-groups *H = (a, b | a*^{2} = [a, b]^{h} = 1) and *G = (c, d | [c, d]*^{h} = 1) into proper free products with amalgamation is proved.

*Guletskii V.I., Margolin G.L., Yanchevskii V.I.*

**Representation of 2-torsion of Brauer groups of curves by quaternion algebras.** pp. 8--12

__Summary:__ The description of 2-torsion of Brauer groups of curves over arbitrary field *k*, char (*k*) = 0, with *k*-rational 2-torsion of their Jacobians was obtained in terms of quaternion algebras.

*Vasyuk G.B.*

**On 2-torsion of Brauer groups of 2-adic elliptic curves in nondecomposable case of poor reduction.** pp. 13--16

__Summary:__ Let *E* be an elliptic curve defined over the field of 2-adic numbers **Q**_{2} and *E* (**Q**_{2}) be its subgroup of **Q**_{2}-rational points. The presentation of the group _{2}Br*E* by unramified central simple algebras over the function field **Q**_{2} (*E*) of curve *E* having a bad reduction in irreducible case is obtained.

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

**On operator index in algebras associated with automorphisms.** pp. 17--20

__Summary:__ The index formulae for the elements of *C**-algebras associated with representations of the group *Z* by automorphisms are obtained. These formulae express the index of the element considered in terms of the Lefshets numbers of the equivariant operator built by the initial one.

*Rovba E.A., Rusak V.N.*

**On approximation rate by interpolating rational operators with ordered poles.** pp. 21--24

__Summary:__ The paper deals with approximation of analytic in unit circle | *z* | < 1 functions which have continuous derivatives of *r* order in | *z* | £ 1 with bounded variation for | *z* | = 1. The upper and lower estimates for the deviation of special interpolating rational operators are found for these classes of functions.

*Makarov E.K., Rachkovskii N.N.*

**On a unified approach to the definition of proper maximality.** pp. 25--29

__Summary:__ We present a unified approach to the definition of proper maximality in terms of dilations for the ordering cone and provide comprehensive comparison theorems for some kinds of proper efficiency.

*Mazanik S.A.*

**On non-reduction of linear differential systems to Lappo-Danilevski systems.** pp. 30--33

__Summary:__ An asymptotic equivalence of linear differential systems and Lappo-Danilevski systems is investigated. It is proved that there exist linear systems which are not asymptotically equivalent, to Lappo -- Danilevski systems.

*Knyazhishche L.B., Shcheglov V.A.*

**Use of nonmonotone Liapunov functionals for investigating solution boundedness of delay differential equations.** pp. 34--38

__Summary:__ Boundedness and uniform boundedness conditions for solutions of delay differential equations are given in terms of nonmonotone along solutions Liapunov functionals. The functionals are not supposed to be positively definite. Coefficient conditions of the boundedness are offered for linear scalar equations with concentrated and distributed delay.

*Tunitsky D.V.*

**On contact equivalence of Monge -- Ampere's equations.** pp. 39--42

__Summary:__ The problem of contact equivalence of Monge -- Ampere's equations with two independent variables is considered. In case where the Monge -- Ampere's equation in question is in a general position, it can be naturally compared with affine connection. The mentioned comparison makes it possible to formulate and prove some criteria for contact equivalence of real analytic. Mange -- Ampere's equations of a general position using appropriate properties of affine connections.

*Sheshko M.A., Rasolko G.A., Shulyaev D.S.*

**On exact and approximate solutions of singular integral equation with Cauchy kernel on the real semi-axis.** pp. 43--48

__Summary:__ The singular integral equation with Cauchy kernel taken over the arc (0, +¥) is investigated. In particular case, the solution of equation
1/p ò_{0}^{+¥} (j(t)/(t -x))*dt* = *f*(x), x > 0,
is obtained. Futhermore, the approximate solution of the equation called in the paper title with respect to all values of the index is given. An estimate for the rate of convergence is also given.

**ФИЗИКА**

*Sirota N.N.*
**Time and entropy of the isolated monoatomic system.** pp. 49-53

__Summary:__ In terms of the approximation of the Maxwell -- Boltzmann statistics and the macroscopic Gibbs distribution it is shown that the determination of the entropy of the isolated system requires the account of the excitation probability of the degree of freedom as well as the variation rate of thermodynamic state in time.

*Korshunov F.P., Kurilovich N.F., Prokhorenko T.A.*

**Investigation of charge carrier mobility at low temperatures in neutron transmutation doped GaAs irradiated with electrons.** pp. 54--58

__Summary:__ Nonmonotone decrease in charge carrier mobility measured at low temperature (*T* = 77 -- 200 K) with dose rise in neutron transmutation doped GaAs irradiated at *T* = 300 K with fast electrons (*E* = 4 MeV) was shown to be caused by charge state alteration of some dominant defect in changing Fermi level location in the forbidden gap under electron irradiation of the crystal. The value of the given defect level made up *E*_{D} = *E*_{C} - 0.11 eV.

**ХИМИЯ**

*Streltsov E.A., Osipovich N.P., Sviridov V.V.*
**The effect of Cu-adatoms on platinum electrocrystallization process.** pp. 59--63

__Summary:__ The regularities of Pt--Cu solid solution electrodeposition by reduction of cation forms of Cu(II) and Pt(IV) at E_{Cu2+}/_{Cu0} < E < E_{PtCl62-/Pt0} have been investigated. It was found that solid solution contains about 30 at.% of Cu. Cyclic voltammetry method was used for study of Cu-adatoms adsorption-description on Pt-electrode with nonstationary surface.

*Kenigsberg T.P., Agabekov V.E., Monakhova O.B., Chaplanova Zh.D.*

**Binary mixed monolayers and the Langmuir -- Blodgett films of polycyclohexadiene and stearic acid.** pp. 64--68

__Summary:__ Binary mixed monolayers of polycyclohexadiene with stearic acid at air/water interface were studied when varying the mixing molar ratio of components. The isotherms indicate a relatively high miscibility of components. The stable mixed monolayers could be transferred onto quartz supports successively by the Langmuir--Blodgett method, and the transfer ratio was equal to one.

**БИОЛОГИЯ**

*Nikolskaya V.P., Rudenok A.N., Belyanovich L.M., Konev S.V.*
** Anomalous effect of anisoosmotic conditions on thermoresistance of mitochondrial respiratory chain.** pp. 69--73

__Summary:__ Thermoresistance of proteins in the mitochondrial respiratory chain has been shown to increase essentially under hypoosmotic and especially hyperosmotic conditions.

*Lyakhnovich G.V., Dorokhin A.V., Sukhodola A.A., Lapina V.A., Volotovsky I. D.*

**The effect of polyacrylamide matrix on P**_{r}® P_{fr} phototransformation of native phytochrome. pp. 74--78

__Summary:__ The red -- far-red phototransformation of phytochrome in water solution and polyacrylamide gel matrix has been investigated by the laser flesh-photolysis method. It was shown that insertion of the native phytochrome into this matrix leads to decrease in decay of **I**_{lt} intermediate and the second component of **I**_{700} intermediate.

*Korzun V.N., Popendikite V., Berner A., Kartel N.A.*

**Application of polymerase chain reaction for the analysis of cereals genomes.** pp. 79--84

__Summary:__ The size of nontranscribed site in 5S-rDNA was determined by the polymerase chain reaction (PCR) method using specific and random (RAPD) primers, a-Amy genes were localized on 7A and 7B wheat chromosomes. Interspecific polymorphism was shown in wheat, rye and barley.

*Soltanov V.V., Levkovets V.S.*

**The role of the sympathoadrenal system in mechanisms of the met-enkephalin protective effect.** pp. 85--88

__Summary:__ The protective effect of met-enkephalin on the gastric mucosa in rats under conditions of the injured duodenum is associated with activation of the sympathoadrenal system.

*Sidorovich E.A., Sergeichik S.A., Sergeichik A.A.*

**Structural and functional organization of assimilative apparatus of arboretal plants in view of gas resistance.** pp. 89--91

__Summary:__ The physiological and anatomical aspects of arboreal plant resistances under industrial air pollution by gaseous nitrogen and sulphur compounds were studied. Unlike sensitive plants, resistant ones are characterized by a high activity of reducing the disturbed structure and function. by a high resistance of regulatory cellular systems. Activation of the synthesis of proteins, amino acids, pigments, acid-soluble phosphoric compounds, change saturated-unsaturated fatty acids ratio, plasticity of optic and photosynthetic leaf structures raise the gas resistance.

*Kulminskaya I.V., Shilko T.S., Guzyuk L.I.*

**Genotypic specificity of crossability of self-fertile rye lines with common wheat.** pp. 92--95

__Summary:__ The paper presents hybridization results of self-fertile rye lines with common wheat variety of high crossability. The efficiency of crossings is shown to be determined by the line genotype and dependent on environmental conditions, with the progamic stage being more resistant to their change in comparison with postgamic one. Great increase in the yield of viable hybrid kernels observed one year after storage.

**НАУКИ О ЗЕМЛЕ**

*Kakareka S.V., Kukharchik T.I., Lysenko A.N., Khomich V.S.*
**Mercury in soil cover of urban landscape.** pp. 96--101

__Summary:__ Spatial structure of Gomel soil contamination with mercury has been studied. It was revealed that prevalence of mercury contents close to background values with point and local anomalies is characteristic for surface horizon of urban soils. The most pronounced anomaly was noted in the region of urban purification works where increased mercury concentrations were observed not only in soils but in bottom deposits and ground waters.

*Kalinovsky P.F.*

**Vertebrates of Miculian (Miarkian) interglacier of Belarus and Lithuania.** pp. 102--106

__Summary:__ A characteristic of the environment of Miculian (Miarkian) Interglacier is given based on the study of remains of vertebrates (mammals and amphibians) from the sites of Belarus and Lithuania.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Soika A.K., Boiko B.B., Vashkevich I.M.*
**Production of high magnetic field square pulses.** pp. 107--111

__Summary:__ The paper describes a new technique for capacitor banks discharge through the magnetic field coil with additional capacitor banks connected to it at the first current maximum and subsequent short of coil terminals (power crowbar).

*Borodachev N.M., Tarikov G.P.*

**Weight function for internal circular crack in elastic body.** pp. 112--114

__Summary:__ The most general expression for weight function for plane internal circular crack occurred in elastic body of arbitrary shape is obtained.

**A list of articles published in the journal "Doklady of the Academy of Sciences of Belarus" in 1997.** pp. 115--121

/ 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 © 1998-2008 Национальная академия наук Беларуси

Копирайт © 1997 Издательство "Беларуская навука"