# Доклады Национальной академии наук Беларуси, 2000, Том 44, No.1

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2000, Том 44, No.1

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Benesh-Krivets V.V.*
**Variety of two-dimensional group characters and amalgamated products.** pp. 5--7

*Summary:* Let G be a finitely generated group. It is proved that if the variety of characters of irreducible representations of G into SL_{2}(*K*) has the dimension ³ 2 then G is a non-trivial free product with amalgamation. As a corollary we conclude that one relator two generator groups with torsion are non-trivial free products with amalgamation.

*Baranov A.A.*

**Classification of simple finitary Lie algebras over zero characteristic field.** pp. 8--10

*Summary:* An algebra is called finitary if it consists of finite-rank transformations of a vector space. Finitary simple Lie algebras over the field of zero characteristic are classified.

*Zabreiko P.P., Kovalenok A.P.*

**Calculation of asymptotic index of pseudomonotonous vector fields.** pp. 11--13

*Summary:* The article presents theorems on calculation of the infinity index for asymptotically linear pseudomonotone vector fields both when asymptotic derivative is nondegenerate linear operator and when it has finite-dimensional kernel under assumption of nonlinearity having leading homogenuous part nondegenerate on the kernel of the asymptotic derivative.

*Shilin A.P.*

**Integral equations of Volterra-type with the kernels depending on sum and difference of arguments.** pp. 14--16

*Summary:* We solve the integral equations with variable limits of integration. The kernels of equations depend on difference and sum of arguments.

*Goncharova M.N.*

**Sufficient optimas for problem of optimal control with state constraints.** pp. 17--21

*Summary:* The sufficient optimizing for conditions the problem of optimal control with state constraints are formulated. The sequence of time optimal control problems for state constraints in the form of counted number of linear inequalities is deduced.

*Lepin V.V.*

**Tree profile problem and optimal edge labeling.** pp. 22--26

*Summary:* We show that the profile problem for trees is equivalent to the problem of finding a minimal caterpillar labeling of edges of trees. This problem is to assign to each edge a positive integer such that: 1) the subset of edges with labels I spans a caterpillar with a diametral path which connects two leaves; 2) if we delete all edges with labels at most *i* then in each subtree the subset of edges with labels *i*+1 spans a caterpillar with a diametral path which connects two leaves of this subtree; 3) the sum of labels of all edges is minimal.

*Zverovich I.E.*

**Finite characterization of hereditary classes with vertex partitions.** pp. 27--29

*Summary:* A hereditary class *P* is called *finitely generated* if the set of all minimal forbidden induced subgraphs for *P* is finite. For a pair of hereditary classes *P* and *Q*, we define a hereditary class *P* * *Q* of all graphs *G* which have a partition *A* È *B = VG* such that *G(A) Î P* and *G(B) Î Q*. (The subgraph of *G* induced by *X Í VG* is denoted by *G(X)*.) We investigate the problem of recognizing finitely generated classes of the form *P * Q*.

*Kurenok V.P.*

**Existence of global solutions of stochastic differential equations with timedependent coefficients.** pp. 30--34

*Summary:* We consider one-dimensional stochastic differential equation of the form *dX*_{t} = B(t, X_{t})dW_{t}, *t* ³ 0, with the Borel measurable function *B* : (0, ¥) x *R* ® *R* and one-dimensional Wiener process *W*. Existence of (weak) solutions is proven by the assumptions of local integrability of sup_{t³0}*B*^{-2}(*t, x*) and continuity of *B*^{-2}(*t, x*) in the time variable. This generalizes the well-known results of Engeibert and Schmidt for the homogene case and guarantees unlike the cited papers, existense of global solutions.

*Monastyrny P.I.*

**Hybrid methods of solving grid equations.** pp. 35--38

*Summary:* New approach to solving grid equation problem is based on hybrid principle of integrating heterogeneous computational algorithms locally adapted on constituent subspans to equation characteristics and on bounding calculations in border zones.

*Gordon V.S., Werner F., Yanushkevich O.A.*

**The problem of minimizing weighted number of late jobs to meet strict deadlines and due processing times.** pp. 39--42

*Summary:* Single machine scheduling for *n* jobs with nested release and due date intervals is considered. Necessary and sufficient conditions for the existence of a due date feasible schedule are obtained which may be verified in *O*(*n*) time. An *O* (*n* log *n*) algorithm for minimizing the weighted number of late jobs with given deadlines for the subset of jobs and oppositely ordered weights and processing times is proposed.

**ФИЗИКА**

*Boyko B.B. †, Valiavko V.V., Moroz L.G.*
**Magnetic properties of excited atoms.** pp. 43--45

*Summary:* The process of interaction of excited atoms or ions, located in varying external magnetic field was analysed on the basis of a hydrogen atom model. In medium-range magnetic fields in which paramagnetic interaction is commensurable with diamagnetic, the behavior of an atom was modelled by three-dimensional harmonic oscillator. An investigation of the dependence of the value and the magnetic susceptibility sign of an atom on the principal coordinate quantum numbers of the oscillator has shown that when the value and combination of these quantum numbers are changed, magnetic properties of the oscillator can be changed from diamagnetic to paramagnetic and vice versa. Such dependence of magnetic properties of the atom on the degree of its excitation may be applied in particular, for magnetic recording of information in optical excitation of a medium.

*Bogush A.A.*

**Quantum vector parameters and generators of ***q*-deformed group *SL*_{g}(2.C). pp. 46--49

*Summary:* The transition *SL*(2.*C*) ® *SL*_{q}(2.*C*) is considered in the framework of the Fedorov's vector parametrization. The quantum analogue of the linearity relations is introduced and used. As a result, two sets of *q*-deformed Pauli matrices are obtained, to be used for describing the quantum matrices *L*_{q} and *L*_{q}^{-1} , respectively.

*Kuharchick P.D., Maly S.V.*

**Numerical investigation of clustering effect on radioabsorbing characteristics of composite materials.** pp. 50--53

*Summary:* The influence of particles clustering on radioabsorbing properties of composite materials was studied. As a composite model the homogeneous dielectric matrix with distributed particles was surveyed. Two types of materials were considered: with periodic and random distribution of particles. The method of minimal automous blocks was used for calculation of effective electromagnetic characteristics of composites. It was found that clustering of particles influences radioabsorbing properties of composite materials.

*Migas D.B., Shaposhnikov V.L., Filonov A.B., Dorozhkin N.N., Borisenko V.E.*

**Band structure of semiconducting rhenium silicide.** pp. 54--56

*Summary:* Theoretical findings supporting semiconducting properties of the ReSi_{1.75} phase were originally obtained by ab initio linear muffin-tin orbital method. The material was shown to be a narrow-gap semiconductor with indirect transition value of 0.16 eV. The first direct transition with appreciable oscillator strength at 0.30 eV is predicted.

**ХИМИЯ**

*Vorobyova S.A., Sobal N.S., Lesnikovich A.I., Tyavlovskaya E.A.*
**Colloidal gold prepared by interphase reduction and its characterization.** pp. 57--60

*Summary:* Stable colloidal solution of gold in hexane was obtained by interphase reduction of gold complex with quaternary ammonium salt with sodium borohydride dissolved in hexane and water, respectively, without any addition of a stabiliser. The disperse phase of the colloidal solution consists of crystal spherical particles of gold of average diameter ca. 2.6 nm (s = 0.47). Simultaneously with formation of hexane colloidal dispersion, the gold film was deposited at the walls of the reaction vessel in aqueous phase. This film is composed of spherical gold particles of average diameter 8.2 nm (s = 0.57).

*Shmanay V.V.*

**Protein immobilization on formylated polystyrene macrosupports for immunoassay.** pp. 61--64

*Summary:* Immobilization of nine different proteins on formylated polystyrene beads of 1/4 inch (0.63 cm) in diameter (FPSB), intended for use as solid-phase support in immunoassay, was studied. The density of immobilized protein (DIP) was examined as a function of initial protein concentration, content of reactive groups on the matrix, reaction time and temperature. pH of solution and low molecular weight ions were found to have a pronounced effect on DIP. The highest values of DIP (up to 104 µg/cm^{2}) were obtained in 0.1 M phosphate buffer, pH = pI, and in 0.1 M phosphate buffer containing 1 M NaCl, pH 3--4. The value of DIP was shown to decrease with increase of protein molecular weight.

**БИОЛОГИЯ**

*Melnikova A.M., Matus V.K., Konev S.V.*
**Age-dependent modification of respiratory chain in yeast mitochondria and respiratory response to ozone.** pp. 65--68

*Summary:* Ozone was found to exert monophasic or biphasic or action on respiration of yeast Candida utilis at exponential or stationary growth phase, respectively. Correlation between the type of O_{3}-induced response and age-related modification of yeast mitochondria was discussed. Ozone-generated respiratory stimulation was shown to be due to reactivation of whole respiratory chain involving site I.

*Lobanok A.G., Sapunova L.I., Kazakevich I.O., Parakhnya E.V.*

**Substrate-independent synthesis of xylose/glucose isomerase by bacteria Arthrobacter species.** pp. 69--71

*Summary:* Effect of aldo-, keto-, deoxy- and disugars, polysaccharides and acids of Crebs cycle on xylose/glucose isomerase production by Arthrobacter species B-5 was investigated. The bacteria were found to show high growth rate and rare for microorganisms inherent capacity to synthesize enzyme in absence of specific substrate. The obtained results enable to regard Arthrobacter sp. B-5 as a potential xylose/glucose isomerase source and model organism for investigation of constitutive enzyme synthesis in procariotes.

*Tarutina L.A., Kavtsevich V.N., Poskannaya S.I., Khotyleva L.V., Kapusta I.B.*

**Effect of marker genes on polygenic variability of greenhouse tomato hybrids.** pp. 72--75

*Summary:* Regulariting of inheriting major components of productivity and early ripeness were studied in intraspecific hybrids *F*_{1} of greenhouse tomatoes produced involving the lines carrying recessive markers, and their influence on induction of heterosis effect was estimated. The results of conducted genetic analysis show good prospects of applying multimarker lines Mo 500 and Mo 628 containing recessive mutant genes in a homozygous state for heterosis breeding of greenhouse tomatoes.

*Silkova T.A., Davydenko O.G., Fomchenko N.S., Mavrishcheva E.B., Tolstova V.A.*

**Recovery of fertility and manifestation of heterosis in ***F*_{1} hybrids of winter rye Aegilops kotschyi. pp. 76--78

*Summary:* The paper presents data on the pollen fertility recovery rate and heterosis manifestation as indicated by productivity elements in the *F*_{1} hybrids produced by crossing a sterile line with Ae. kotschyi cytoplasm and winter wheat varieties. No complete recovery of pollen fertility in the *F*_{1} hybrids was revealed in spite of availability of two Rfv genes in the tested varieties. In singular cases heterosis was manifested in 1000-grain weight, spike length and the number of spikelets per ear.

*Samal A.B., Adzerikho I.E., Mrochek A.G., Markova L.V., Miksha Ya.S.*

**Morpho-functional changes of human platelets induced by low-frequency ultrasound.** pp. 79--82

*Summary:* Aggregation and morphological-structural modifications in human platelets exposed to low-frequency ultrasound (US) were investigated. The US frequency was 22 kHz and intensity was 0.4--16 W/cm^{2}. It was shown that US induced platelet aggregation. The maximal rate of aggregation was reached at US-intensity of 1.9 W/cm^{2}. If the US-intensity was higher than 5 W/cm^{2}, not only platelet aggregation but their destruction, decreased concentration, volume and size resulted. According lo electronic microscopy data US (16 W/cm^{2}, 15 s) caused the formation of spherical vesicles of under-platelet size.

*Tropnikova G.K., Kulchitsky S.V., Kulchitsky V.A.*

**Nociceptive reflexes and serotonin turnover in rat brain after injection of kainic acid into the nucleus of tractus solitarii.** pp. 83--86

*Summary:* In experiments on conscious rats, it was found that at 7 days after injection of toxic doses of kainic acid lo the comissural nucleus of tractus solitarii (NTS) there was a sustained hyperalgesia, accompanied by a sharp decrease of serotonin content in the rostrodorsomedial medulla. The increased utilization of serotonin was indicated by a two-fold rise in the level of its major metabolite 5-hydroxyindolacetic acid in the NTS area.

**НАУКИ О ЗЕМЛЕ**

*Kudelsky A.V., Matveyev A.V., Lebedeva L.D., Volkova N.P.*
**Geological-hydrogeological conditions for possible waste burial in the Republic of Belarus.** pp. 87--90

*Summary:* Zoning of the Belarusian territory to point out potential burial sites for solid domestic, industrial, low- and conventionally radioactive wastes is offered. Geological structures and sedimentary rock complexes showing promise as depositories of medium- and highly radioactive wastes have been distinguished.

*Naidenkov I.V., Aksamentova N.V., Bayanova T.B., Apanasevich E.A.*

**New findings on charnockite dating in Belarusian-Baltic Granulite Belt, Belarus.** pp. 91--94

*Summary:* The paper presents results of geochronometric dating of charnockites from the Belarussian-Baltic Granulite Belt (Belarus). The isochronous age of 1850 ± 10 Ma is regarded as the period of the last granulite metamorphism. The oldest material in Belarus crust (mafic granulites) is of the Archaean age.

*Pavlovskaya E.I., Marx L.*

**Middle Pleistocene glaciolacustrine basins of Western Belarus, Eastern Poland and their palaeogeographic significance.** pp. 95--98

*Summary:* Detailed complex palaeogeographic analysis indicated that there is a thick ice-dam lacustrine series of the Middle Pleistocene in Mid-Eastern Poland and Western Belarus. Stratigraphic location of ice-dam lake sediments as well as their relation to the underlying and overlying series indicate that this sequence forms a continuous bed separating tills of two successive glaciations. Based on petrography of pebbles in tills, correspondence to key sites with organic and fluvial deposits of the Holstein Interglacial, and detailed palaeogeographic analysis, presence of this glaciolimnic complex proves wide spread of ice-dam lakes in the Polish-Belarus border area at the termination of the Elsterian (Berezina, South-Polish) Glaciation. Similar series occurs also in the Lower Vistula region in Poland and in the Lower Elbe region in Germany. In the latter, it undoubtedly passes into marine series of the Holstein Interglacial. Such facts argue for correlative significance of this glaciolimnic series in a considerable part of the Central European Lowland.

*Zakharenko A.A., Mamchick S.O.*

**Tectonics and coal presence in Jurassic deposits of Bukcha-Borovoye coalfield located in Pripyat Trough.** pp. 99--102

*Summary:* The Buckcha-Borovoye coalfield is a syncline as demonstrated by analysis of the surface and bottom structure maps of Jurassic sediments and their thickness distribution pattern. The greatest total thickness (more than 5 m) of coal deposits is confined to the axial syncline zone. The general pattern of coal bed distribution has been defined talking into account structural peculiarities.

*Davydick K.I., Yakubovskaya T.V.*

**Natural historic boundaries of Oligocene and Miocene in Belarus as related to geological developments.** pp. 103--107

*Summary:* The transition of Ecosystems within the Belarus territory on the boundaries of epochs from Eocene to Pliocene as well as related global and regional geological and biotic events are considered in the light of new stratigraphic concepts.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Anisimovich V.G., Dostanko A.P., Khmyl A.A.*
**Effect of surface preconditioning method on nickel plating quality.** pp. 108--110

*Summary:* The study on influence of different surface preconditioning methods prior to thin film deposition on contact resistance, microhardness, roughness and volumetric wear of nickel plating was conducted. It was found that plasma-electrolytic treatment of the surface allows to obtain Ni plating with high physical and mechanical characteristics. The reasons for improved plating properties are explained.

*Klubovich V.V., Abramov O.V., Abramov V.O., Kirillov S.A., Kotin I.M.*

**Effect of ultrasonic loading on superplastic metal deformation.** pp. 111--114

*Summary:* The model which allowed to consider the ultrasonic oscillations (USO) influence on the process of metal superplastic (SP) deformation was elaborated. The increasing diffusion of vacancies under USO impact was taken into account. It was shown that ultrasonic oscillations decrease both SP deformation stress and grain boundary dislocations density.

*Shevtchuk V.S.*

**Investigntion of deformation of anisotropic construction materials.** pp. 115--117

*Summary:* The character of destruction of glued glass-plastic prestressed constructions has been determined in the course of the investigation. Interface durability criteria have been obtained based on experimental data.

*Zaharik Al.M., Zaharik An.M.*

**Analytic conclusion of a assemble for gears of driving axle board reducer of a city bus with low level floor.** pp. 118--121

*Summary:* It is described in the paper a board reducer design, which allows to receive a number of advantages in comparison with the classical schemes for bus driving axles. The original scheme of a driving gear arrangement allows to cancel bulky bearing unit, that simplifies considerably and makes cheaper the design in manufacturing and in of bus operating. However there is an additional restriction on assembling for this reducer, which in aggregate with restrictions on overall dimensions and dynamic loading of a gear give an interconnected set of its parameters, which is satisfying to the requirements of durability and noise.

/ 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 © 2000-2008 Национальная академия наук Беларуси

Копирайт © 2000 Издательство "Беларуская навука"