# Доклады Национальной академии наук Беларуси, 2000, Том 44, No.6

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2000, Том 44, No.6

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Matakayev A.I.*
**Oscillation of discrete second-order differential equation.** pp. 5--6

*Summary:* Sufficient conditions of oscillation for solutions of second order discrete equations are obtained.

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

**Variational principle for calculation of spectral radius of weighted shift operetors and mathematical expectation operators.** pp. 7--10

*Summary:* The general variational principle for calculation of the spectral radius of weighted shift operators with arbitrary shifts and the corresponding mathematical expectation operators is established. The principle contains as a component a new dynamical invariant -- causality. The properties of the causality are investigated. It is proved that the logarithm of the spectral radius and the causality are linked by the Legendre transform.

*Boruhov V.T., Matus O.P.*

**Invertibility of linear time-variable dynamic systems.** pp. 11--14

*Summary:* The test of the invertibility for piecewise smooth time-variable linear input-state-output dynamic systems is obtained.

*Tikhonov S.V., Yanchevsky V.I.*

**First cohomology groups of Jacobians of projective curves with good reduction defined over the field of real formal power series.** pp. 15--17

*Summary:* The description of the first cohomology groups of Jacobians of projective curves with good reduction defined over real formal power series is obtained.

*Kilbas A.A., Bonilla B., Trujillo J.*

**Fractional integrals and derived differential equations of fractional order in weighted spaces ofcontinuous functions.** pp. 18--22

*Summary:* The properties of the Riemann--Liouville integrals and derivatives of any complex order are investigated in weighted spaces of continuous functions. The results obtained are applied to prove the equivalence of the Cauchy-type problem for the nonlinear differential equation of complex order and of the nonlinear Volterra integral equation. The existence and uniqueness of the solution of the above Cauchy-type problem is proved by using the method of successive approximations. The corresponding assertions for the Cauchy problem for ordinary differential equations are presented.

*Mazhukin V.I., Matus P.P., Mozolevsky I.E.*

**Stability of three-level schemes on nonuniform time grids.** pp. 23--25

*Summary:* The stability of three level operator finite difference schemes on non uniform in time grids is studied in Hilbert spaces of finite dimension. A priori estimates for uniform stability relative to initial conditions are obtained under natural conditions for operators and for non uniform time grid steps. The results obtained here are applied to investigate stability of three level weghted schemes and schemes of second order of approximation O (h^{2} + t^{2}_{n} ) for some parabolic equations.

*Semenchuck V.N., Shemetkov L.A.*

**A class of local formations.** pp. 26--27

*Demenchuck A.K.*

**Almost periodic solutions for a class of ordinary differential systems.** pp. 28--30

*Summary:* Necessary and sufficient conditions of almost periodic partially irregular solutions for a class of ordinary differential systems have been provided.

*Gladkov A.L.*

**The initial-boundary problem for parabolic equations of higher order.** pp. 31--32

*Summary:* We prove existence and uniqueness of the solution of the Cauchy--Dirichlet problem for semilinear parabolic equations of higher order in unbounded domain without any growth conditions at an infinity on initial data.

**ФИЗИКА**

*Korshunov F.P., Lastovsky S.B., Zhdanovich N.E., Gurinovich V.A., Shesholko V.K.*
**Measurement of direct voltage drop at 4.2--80 K in silicon ***p--n*-junctions irradiated with electrons. pp. 33--36

*Summary:* Influence of rediation defects induced by irradiation with 4 MeV electrons on temperature correlations of a direct voltage drop in silicon *p--n*-junctions are analyzed. It is established that the introduction of radiation defects results in 5--6 times sharper direct voltage drop at 4.2--40 K, than at 40--80 K, which is correlated with influence of compensation degree on low temperature conductivity of silicon.

*Knyazev M.A., Gavris D.I., Gavris I.B.*

**Coupled states of magnetic moment density in anisotropic ferromagnetic domain.** pp. 37--40

*Summary:* Inhomogeneous static distributions of magnetic moment density in anisotropic ferromagnet with a stripe domain structure corresponding to the coupled state of two soliton-like objects are considered.

**ХИМИЯ**

*Kuzmitsky B.B., Konoplya N.A., Lyubin G.S., Bondar N.F., Lahvich F.A.*
**Modeling the structure of potential immune stimulator from 7-oxo-9,11-ethano-13-thiaprostanoid series.** pp. 41--43

*Summary:* To find out the main relationships between certain fragments of prostaglandin molecules and their specific impact on the immune response, we studied immunotropic activity of a number of newly synthesized 7-oxo-9,11-ethano-13-thiaprostanoids. It was found that 6 of the 10 tested compounds enhanced the amount of antibody-forming cells in the spleen of CBA mice immunized with sheep red blood cells.
It became obvious that to display sufficient immunostimulating activity, the prostanoids of this type must have 7- or 6-carboxyalkylic (a-chain. The presence of thiophenylic residue, methyl ester of thioglycolic acid, fragment of thiolactic, acid in (w-chain resulted in decrease or complete disappearance of immunoenhancing effect.

*Shchukin D.G., Kulak A.I., Sviridov D.V.*

**Magnetically controlled dispersed photocatalysts for SO**_{2} oxidation operating in quantum yield doubling regime. pp. 44--47

*Summary:* Using a magnetic photocatalyst fabricated via deposition of photoactive a-Fe_{2}O_{3} and heteropolytungstate-doped polyaniline shells the possibility of realizing the quantum yield doubling effect arising from combination of heterogeneous and homogeneous (involving photoproduced H_{2}O_{2}) catalytic effects was demonstrated.

*Chaplanova Zh.D., Agabekov V.E., Sharendo E.V.*

**Structure of films formed by thermal deposition of bromine-modified polycyclohexadiene.** pp. 48--52

*Summary:* It was shown that amorphous-crystalline films are formed on monocrystal sodium chloride substrates during thermal vacuum deposition of polycyclohexadiene modified by bromine. The supramolecular structure and the degree of crystallinity of the films depend on temperature of the substrate. It was found that UV irradiation stimulates crystallization of the films yielding isolated single crystals.

**БИОЛОГИЯ**

*Denisov A.A., Martinovich G.G., Molchanov P.G., Drapeza A.I., Cherenkevich S.N., Gurin V.N.*
**Measurement of electric characteristics in nerve cells and tissues by sensors based on field-effect transistors.** pp. 53--55

*Summary:* The method for extracellular electric activity recording with MOSFET sensor is described. The chip insulation approach, which employs the features of microelectronic metal-glass package, is used for the protection of MOSFET micro-transducers from attack of cultural media components. An amplification system with optional differential switching of sensors is used for electrical signals recording. The method was successfully applied for long-term monitoring of electrical activity in neurons of snail Lymnaea stagnalis.

*Reshetnikov V.N., Nenadovich R.A., Gorbatsevich V.I.*

**Changes in lipid composition of rye interphase cell nuclei as a function of genome expression.** pp. 56--59

*Summary:* The relative analysis of intranuclear lipids location between separate compartments of cell nuclei, isolated from germs of resting seeds and 24- and 72-hour seedlings of winter rye was carried out. Its correlation with genome activity was established. Involvement in gene expression regulation, and in DNA attachment to nuclear matrix alongside with phospholipids and neutral lipids was demonstrated.

**НАУКИ О ЗЕМЛЕ**

*Kozhemyakina N.A.*
**Petrochemical and microelementary make-up of granitoids from Mosty complex.** pp. 60--62

*Summary:* The correlation of grenitoids of the Mosty complex with Cu--Mo granites from the Kabeliai region which, in turn, are related to the Marcinkony complex widespread in the south of Lithuania suggests their similar genetic nature and presence of inferred ores in granitoids of the Mosty complex.

*Taran L.N., Veretennikov N.V.*

**Deep-lying xenoliths of explosion pipes in Belarus.** pp. 63--65

*Summary:* Highly altered volcanoclastic rocks of Devonian age are from sub-surface diatrems in south-eastern Belarus and contain deep-lying xenoliths. Petrographically, five xenolith types are distinguished. These are ultrabasic rocks, amphibolites, mafic garnet-bearing grenulites, gabbro-anorthosites and granitoids. Mafic granulites appear to be derived from basic igneous rocks and represent the lower crust at depth of ca. 35 km while ultrabasic xenoliths could be formed at deeper levels. Gabbroanorthosites and granites presumably belong to anorthosite-rapakivi-granite suite wide-spread in north-western part of the Ukrainian Shield.

*Arkhipova A.A., Naidenkov M.V.*

**Kossovo complex of intrusive Early Proterozoic charnockitoids in Belarus.** pp. 66--69

*Summary:* The mineralogical and chemical composition of intrusive hypersthene charnockitoids exposed in hole drilled in the Belarusian-Baltic granulite belt has been described. These differed from granitoids of the Osmolovo complex and migmatitic charnockitoids of the enderbite-charnockite complex, to serve as a ground to recognize charnockites as the independent Kossovo complex, which origination was refered to the Early Proterozoic stage of tectonic-magmatic activation in this region.

*Bulkin Yu.S., Levykh N.N., Kuzmenkova O.F., Ilkevich G.I., Varaxa V.V.*

**Petrogeochemical characteristics of granitoids from Bershtyny massif, Belarus.** pp. 70--73

*Summary:* A petrographic description of granitoids is given. Behaviour of main rock-forming minerals and microelements is con-sidered during transformation of diorite and granodiorite gueisses into granites.

*Mamchyk S.O.*

**Jurassic deposits of South-Eastern Belarus.** pp. 74--78

*Summary:* Jurassic deposits in southeastern Belarus have been subdivided and comprehensively correlated with logging data and paleontological evidence. Stratigraphic logging characteristics will permit further to compare sections across southeastern Belarus.

*Kudelsky A.V., Pashkevich V.I., Karabanov A.K., Pavlovskaya I.E., Korkin V.D.*

**Belarus hydrosphere in neoteetonic period.** pp. 79--83

*Summary:* Favorable conditions for an appearance of additional hydrostatic heads up to 3.5--4 MPa in central Belarus were due to formation of relatively high end morains during Pleistocene. A consequence of that hydrostatic head was subsequent desalinization of the prepleistocene geological substrate within elevated part of Belarussian anteclise.
The paper presents stereometric model of freshwater underground stratum and reveals the main regional zones of underground water discharge.

*Starchik T.A.*

**Late Devonian geodynamics of western closure of Pripyat paleorift.** pp. 84--87

*Summary:* The Pripyat paleorift structural features (western part) were taken as an example to describe a mechanism of the negative structure flattening out. Regionally, it was a result of branching the zone of maximum tension and fragmenting its absolute value. Locally, tectonic processes were dying out within every centrocline along two sets of faults showing different genesis and kinematics.

*Matveev A.V., Astapenko V.N., Bordon V.E., Levashkevich V.G., Nikitin E.A., Khomich P.Z.*

**Diatreme prospecting in the north of Belarus.** pp. 88--91

*Summary:* Perspectives of Belarus north for prospecting diatremes are analysed using a number of geological and geophysical criteria. Data on geophysical fields over magnetic anomalies in Braslav region and bored diatremes in Zhlobin region have been compared.

*Makhnach A.A., Kolodny I., Starinsky A., Spiro B.*

**Stable strontium isotopes in sulphate minerals of Belarus.** pp. 92--95

*Summary:* It is established that evaporite brines of the Middle Devonian, Late Devonian and Early Permian basins of Belarus were differently enriched with rediogenic strontium in comparison with seawater from the respective geological periods. The degree of ^{87}Sr accumulation in postsedimentary sulphate minerals of the Vendian, Ordovician, Frasnian and Famennian non-evaporite deposits depends on the distance of migration of mineral-forming brines and on the lithology of pathway rocks.

*Makhnach A.S., Veretennikov N.V.*

**Vendian volume and boundaries.** pp. 96--99

*Summary:* It is established that the lower boundary of Vendian coincides with the base of the Vilcha Series. The upper boundary coincides with the base of the Rovno Horizon of the Cambrian. The Vendian is subdivided into the Laplandia Horizon (the Vilcha and Volyn Series), the Redkino and Kotlin Horizons.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Vlasova G.N., Makarevich A.V., Orekhov D.A., Pinchuk L.S.*
**Biodegradable thermoplastic films.** pp. 100--103

*Summary:* A group of polymer composite films based on thermoplasts with biodegradable components has been developed. Kinetics of their decomposition by soil microorganisms has been studied. It was shown that tensile strength of composite films kept for three months in soil was reduced 2--3 fold. Degradation of tested materials occurs by dissociation of bonds between intermolecular PE structures in sites of fungal conidia and mycelia aggregation, prevalently by Aspergillus niger species. Used packages and other plastic products may be rapidly utilized by microorganisms from top soil layers.

*Kovalev M.M., Listopad N.I.*

**Models of optimal hardware choice.** pp. 104--107

*Summary:* The idea and concept of compatibility analysis for sophisticated equipment is considered. New models and algorithms of rating, classification and optimal choice of hardware are proposed.
The models and algorithms applied in expert evaluation of software named "Filin" are presented. The possibilities of "Filin" system are described.

*Bursky V.A.*

**Development of the software application package for solving the problems concerned with the machining of stretched non-rigid parts.** pp. 108--111

*Summary:* Using mathematical methods, theoretical substantiation and methods of elasticity theory, the problem of modeling processes of thermoelasticity, taking place in the cylindrical non-rigid parts under effect of external thermal fields and under impact of cutting force, has been solved. The applied software package to study effects of thermoelasticity in conductive cylindrical non-rigid parts has been developed.

*Budnik A.V., Korzun A.I.*

**Physical-topological model of mosfet based on charge approximation.** pp. 112--114

*Summary:* A charging model of MOSFET adequately describing its voltampere characteristics is presented. The model is expressed in formulas valid for all domains of volt-ampere characteristics. Expressions for drain current, mobility of charge carriers, surface potential allow to obtain satisfactory modelling results.

*Reizina G.N.*

**Mathematical models of revolting factors in motortransport.** pp. 115--116

*Summary:* The method of stochastical models to describe vibration formation in automobiles, which allows toenlarge a number of factors influencing vibroloading has been presented.

**A list of articles published in the journal "Doklady of the National Academy of Sciences of Belarus" in 2000.** pp. 117--122

/ 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 © 2001-2008 Национальная академия наук Беларуси

Копирайт © 2000 Издательство "Беларуская навука"