Doklady of the National Academy of Sciences of Belarus, 2002, Vol.46, No.5
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Doklady of the National Academy of Sciences of Belarus, 2002, Vol.46, No.5

DOKLADY OF THE NATIONAL ACADEMY OF SCIENCES OF BELARUS
(Doklady Natsionalnoi Akademii Nauk Belarusi)Published by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Alekhno A. G.
Homogeneous boundaryvalue Riemann problem with nonremovable discontinuity coefficient. pp. 58
Summary: The general solution is given for the Riemann problem with nonremovable discontinuity coefficient.
Rusak V.N., Rybachenko I.V.
On one method of approximation by rational functions. pp. 911
Summary: The special summator operators of Jackson type with rational kernels in C(R) are constructed and order estimations of deviations for these operators with appropriate poles are found.
Alekhno E.A.
On interations of kernels of primitive nonnegative linear integral operator. pp. 1215
Summary: Example of primitive integral operator no power of which can be operator with positive kernel is given. Theorem on powers of primitive matrix is generalized in case of primitive kernels.
AlSharo Kh.A., Shemetkov L.A.
On influence of prime order elements on finite group structure. pp. 1618
Summary:
Milovanov M.V.
On existence of complete involutive collections of functions on cotangent bundles of nilmanifolds. pp. 1922
Summary: Existence of a complete involutive collection formed by analytical functions on cotangent fiber bundles of an arbitrary nilmanyfold is proved.
Sobolevsky S.L.
Singlevalued solutions of differential systems. pp. 2326
Summary: Singlevalued solutions of algebraic, in the dependant variable, and analytic, in the independent variable, differential systems in complex domain are considered. It is proved that at least one of the components of such a solution in a neighbourhood of a nonpolar singularity takes values in every neighbourhood of arbitrary complex number. Further properties of secondorder differential equations solutions are also considered.
Doroshko V.V.
On interrelation between interpolation by rational functions and problem of operator interpolation. pp. 2729
Summary: Interpolation formulae for operators defined on the spaces of differentiable functions are constructed on the basis of interpolation polynomials with respect to special type rational functions. These formulae are exact for appropriate classes of operator polynomials.
Uss A.T.
Homotopy classification of threedimensional analogs of CauchyRiemann system. pp. 3034
Summary: A homogeneous system of the four differential equations of order I with real constant coefficients in R^{3} is called CauchyRiemann's analog if each solution's component is a harmonic function in any bounded domain W Ì R^{3}. It is proved that the number of gomotopic components for set of all CauchyRiemann's analogs is 2.
Yadchenko A.A.
Irreducible linear prime power groups. pp. 3536
Summary: In this paper we establish some properties of irreducible complex linear groups of prime degree.
INFORMATICS
Zakrevskii A.D.
Minimization of search tree used for solving combined logical equations. pp. 3739
Summary: Two methods using tree searching technique are applied for solving systems of logical equations: the equation scanning method and argument scanning method. The time spent for solving is proportional to the number of vertices in the search tree. Two methods are suggested to minimize that number by a rational ordering of equations or arguments, which are put in correspondence with the levels of the tree.
Batura M.P., Ptichkin V.A.
Analysis of phase lock systems by means of momental equation. pp. 4043
Summary: Procedure for determination of error variance of phaselocked loop frequency control system on the basis of momental equations is considered. Possibility of approximation of discriminatory characteristic by orthogonal polynomials and neglecting highorder moments is analyzed. The solutions obtained are compared with known results. It is explained that application of Hermite polynomials allows to improve accuracy of solution in comparison with conventional procedures.
PHYSICS
Karelin N.V.
Minimal phase volume for multidimensional wave fields with given entropy. pp. 4446
Summary: It is found out that in a minimum of generalized uncertainty (reciprocity) relation for multidimensional system with given informational entropy, the specific phase volume per one effective state in statistical mixture is equal to phase volume for pure state (i. e. there is no packing of states). At the same time, as in onedimensional case, the state with minimal uncertainty is thermal.
Vlasukova L.A., Komarov F.F., Didyk A.Yu., Komarov A.A.
Track formation in germanium crystals irradiated with 710 MeV Bismuth ions. pp. 4749
Summary: Effect of track formation in germanium crystals irradiated with heavy swift ions has been registered. The threshold value of specific electronic energy losses for track formation in germanium has been estimated as 37 keV/nm. The morphology of track regions is defined by the value of energy losses in electronic subsystem of the crystal.
Rogovtsov N.N.
Inequalities and asymptotic formulas for characteristics of radiation fields in nonconcave dispersion media. pp. 5053
Summary: Some inequalities and asymptotic formulae are found for characteristics of radiation fields in nonconcave scattering media.
Pavlovich V.S.
Modulated broadening of B800 absorption bands of lightharvesting 2 antennas of purple bacteria. pp. 5457
Summary: It is shown in terms of the hystons, new quasiparticles, that the collective dipole librations in the LH2 antenna systems cause a high thermal broadening of the B800 absorption spectra. Obtained equation for the full halfwidth provides an excellent fit to the Rb. sphaeroides and Rps. acidophila B800 known data at 4.2270 K with an average hyston frequency of 63 and 50 cm^{1}, respectively.
CHEMISTRY
Matulis V.E., Ivashkevich O.A.
Quantumchemical ab initio analysis of electron and spatial structure of silver clusters by MCQDPT 2 method. pp. 5862
Summary: Electron structure and geometries of neutral and anionic silver dimers, trimers, and tetramers have been investigated by ab initio MCQDPT2 (MCSCF based on MP2) method with CRENBS effective core potential and appropriate (3s,3p,4d)®[3s,3p,3d] valence basis set. For the identification of cluster geometries, the calculated vertical detachment and excitation energies have been compared with the observed photodetachment spectroscopic pattern. The binding energies per atom and vertical ionization potentials of neutral species have been calculated. The theoretical excitation energies and binding energies per atom are found to agree with the experimental data. The obtained values of vertical detachment energies and ionization potentials need to be scaled to bring them in correspondence with the experimental data.
BIOLOGY
Sapegin L.M., Mironenko V.I., Daineko N.M., Zhogal S.P.
Mathematical modeling of functioning of meadow ecosystem. pp. 6365
Summary: A method to construct a mathematical model of a watermeadow ecosystem is proposed. This model is combined difference equations. One of the solutions of the model is socalled main trend. We can use the data of different investigations to build up this maintrend. Therefore maintrend reflects properties which are general for all ecosystems of one type. Coefficients of the model reflect peculiarities of this particular ecosystem, which we model. We can use this model to predict productivity of the ecosystem. The method gives us a possibility to compare two ecosystems and say if they close to each other.
Sidorenko A.V., Tsaryuk V.V., Gourine V.N.
Changes in bioelectric brain activity in rats under microwaves. pp. 6668
Summary: Relief of activation of brain hemispheres influenced by low intensity microwaves is shown. The occurance of desynchronization reaction in electrocorticogram as a response to light irritation. Electrodes were previously implanted into the motor region of the brain hemispheres.
Zabrodsky V.N., Bondar Yu.I., Yakushev B.I.
Study of water cycle in plants using water containing tritium marker. pp. 6973
Summary: The dynamics of processes of uptake and removal due to the transpiration of tritiated water from seedlings of rye was investigated experimentally. Analysis of tritium in fitomasse was performed by putting the sample of fitomasse into the scintillation cocktail and its following analysis by liquid scintillation counter TriCarb 2500 TR/AB. Experimental data received were treated by method of least squares to obtain the halftime of water exchange in the plants. Depending on the conditions of experiments the halftimes of water exchange vary from 5 to 20 hours.
Konoplya E.F., Vereshchako G.G., Khodosovskaya A.M., Popov E.G., Artemenko O.V.
Reproductive system state in irradiated rates and their offspring (in vitro). pp. 7477
Summary: The data on the morphofunctional state of reproductive system organs of male rats exposed to fractional irradiation at 1.0 Gy dose in early ontogenesis (I month age) and in their offspring of the first generation from the irradiated males and females are adduced.
The significant changes in relative reproductive organ weight, spermatogenic cells composition, number of metabolic indexes, molecular characteristics of androgen reception in testes, and testosterone content in blood were revealed in irradiated males (parents) at the age of 2 and 6 months.
It was determined that the relative moderate radiational effects in postnatal ontogenetic period in testes and in additional organs of reproductive system in the male rats of the fust generation were caused by their parents' irradiation in early ontogenesis.
Mikulich A.I., Tsybovsky I.S., Slominsky P.A., Limborskaya S.A., Kartel N.A.
DNA polymorphism and entogenomics of Belarusian populations. pp. 7883
Summary: In this paper, we report results of our investigation on genetic polymorphism of Belarusian populations using highly polymorphic tandem DNA markers. We have studied population diversity of 5 populations (336 samples) using microsatellite triplet loci DM, SCAI, and DRPLA (19, 6, and 12 chromosome, respectively). For all populations examined, no deviations from HardyWeinberg law are found. Values of expected and observed heterozygosity and fixation index Fst are calculated. The dendrogram of genetic relations agrees with ethnographical and anthropological data. 9 populations (713 samples) have been studied using IGHJ minisatellite locus (chromosome 14). We also present preliminary results of our studies of Ychromosome polymorphism in 5 microsatellite loci. Haplotype frequencies of populations in Belarus are compared with corresponding data on Russians and Ukrainians. Relation between haplotypes of the three Slavonic nations are analyzed by means of median nets. We discuss the possibility of application of polymorphic DNA markers in study of correlations between genetic properties of populations and environmental, ecological, geographical and other factors. Stressed is the progress on the way of development of ethnical genomics, a discipline that incorporates methods of molecular genetics and ethnography, in Belarus.
Vasim T.V., Rakovich A.A., Levko A.V., Konev S.V.
Modification of [^{14}C] glutamate and [^{14}C] GABA transport by brain synaptosomes under osmotic swelling. pp. 8486
Summary: Hypoosmotic(230mOsm) swelling of isolated nerveendings of a brain is coupled with uptake inhibition of [^{14}C] glutamate and [^{14}C] GABA from external medium. Reduce of uptake velocity of these amino acids does not depend on membranous potential and Na^{+} ions in incubation medium. Swelling of nerveendings induces release of [^{+}C] glutamate(23.09 ± 0.47%)) and ^{14}C] GABA(28.02 ± 1.49%)) into the external medium. This effect does not depend on Ca^{2+} ions and synaptosoms depolarization.
Abramchik L.M., Serdyuchenko E.V., Kabashnikova L.F.
Effect of heat shock on biogenesis of photosystem 2 during growing of etiolated barley seedlings. pp. 8790
Summary: The influence of the periodical heat shock (HS) on quantitative modification of protein components D_{1} and D_{2} of the Reaction Center of Photosystem 2 (RC PS 2) during growing of etiolated barley seedlings was studied. It was shown that HS caused the supression of the synthesis of both proteins, binding Chl680 RC PS 2. A possible mechanisms of process degradation of the proteins under HS is discussed.
Palilova A.N., Domash V.I., Zabreiko S.A., Pavlyuchuk N.V., Akhramenko A.D.
Changes in component composition of inhibitory proteins of trypsin in potato tubers initiated by selection on the basis of virus resistance. pp. 9194
Summary: Changes in component composition and electrophoretic mobility of proteinase inhibiting proteins was studied in potato tubers under the influence of selection on the basis of resistance to X and Lviruses. The direct relationship was revealed between these traits: the resistant clones contained a higher number of trypsin inhibitors than the susceptible ones with a similar genome. The conclusion was drawn about correlation between the studied traits and about involvement of inhibiting proteins in protective mechanisms against viral infection.
EARTH SCIENCES
Kudelsky A.V., Smith J.T., Zhukova O.M., Rudaya S.M., Sasina N.V.
Role of river flow for ^{90}Sr decontamination of polluted territories of Belarus. pp. 9599
Summary: ^{90}Sr pollution of the water flow of Dnieper, Pripyat, Sozh, Besed, Iput is considered. The dynamics of reducing the average years activities of ^{90}Sr and the variations of the levels of ^{90}Sr activities in river water during springautumn high water are shown. The results of investigation of ^{90}Sr activity of the bottom sediments of lowing river Pripyat and Braginka that are connected with the second effects of the pollution of the river flowing off ^{90}Sr during high water period. ^{90}Sr transfer in composition of the flowing offriver during 19901995 years (Belarus ® Ukraine) is being estimated.
TECHNICAL SCIENCES
Bosakov S.V.
On determination of displacements of rectangular die on linearly elastic foundation. pp. 100101
Summary: In this paper, determination of displacements of rigid rectangular die on elastic foundation is presented.
Yakhnitsky A.V.
Mathematical modeling of symmetric unbalanced rotor in elastic damper supports. pp. 102105
Summary: Two simple models of hard symmetric rotor were presented in this article. Models have a good graphic examples and clear proof, allow to calculate amplitudefrequency characteristic on bearing with linear or nonlinear characteristics.
Klubovich V.V., Bulavin V.A., Sakevich V.N., Stepanenko D.A., Tovpenets I.A.
Research and development of ultrasonic method of production of microsurgical needles. pp. 106109
Summary: On the basis of teoretical and practical investigations, the experimentical unit for ultrasonic machining of microsurgical needles was developed. This unit allows manufacturing highquality and higherperformance needles in comparison with traditional methods.
Sviridyonok A.I., Kovalevskaya T.I., Sechko A.E., Voina V.V.
Phase and structural peculiarities of fibrillated polypropylene films before and after isothermal heating. pp. 110113
Summary: Phase and structure features of polypropylene fibrillated films before and after constant heating were investigated. It was established that the films were greatly crystallized and consisted of the crystallites shaped like folded and straight chains. They form fibrillate structure. The particularities of process technology for production of goods with low thermal shrinkage and high toughness from olefin polymers were discussed.
Mironovich L.L., Lin D.G., Gartman E.V.
Study of cold crystallization of cryogendispersed polyethylene terephthalate. pp. 114115
Summary: Using differentialthermal analysis and optical polarization microscopy, structural transformations were established in cryogendispersed polyethylene terephthalate and its films at their cold crystallization.
A correlation has been found between processes detected by the differentialthermal analysis and the dependence of light flux passage through a hardened PETP film under similar temperature effects.
Klimenko S.E.
Parameterization of geometry of calibrating element for radial distribution of powder coverings. pp. 116119
Summary: Universal calibrating device allowing to condense layers of overcoated coverings on cylindrical products of various sizes is developed. The dependence giving opportunity to determine optimum geometrical parameters of punch calibrating element of the universal device is shown.
Yashcheritsyn P.I., Rakomsin A.P., Sergeev L.E., Sidorenko M.I.
Optimization of magnetic field parameters at final polishing of internal conical surfaces. pp. 120122
Summary: It is stated that the providing the required quality indices of surface holes of conical parts by the method of magneticabrasive treatment is reached with the difference of magnetic induction between bigger and smaller diameters of such parts not exceeding 15%.
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