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# Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, No.6

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Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, No.6
 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

Tykoun A. S.
Algorithm of evaluating the Conley index for 3D dynamical systems. pp. 5--9
E-mail: tycoon(at)im.bas-net.by

Summary: The procedure evaluating the Conley index of 3D dynamical system is considered. Different structures of isolating blocks and their exit sets are discussed. The main result of the article is constructed algorithm evaluating the Conley index of 3D dynamical system in the final number of steps.

Kilbas A. A., Kniaziuk N. V.
Fractional integrals and derivatives on the half-axis and differential equations of fractional order in the weighted spaces of continuous functions. pp. 10--16
E-mail: anatolykilbas(at)gmail.com, kniaziuknataly(at)tut.by

Summary: The properties of the fractional integrals and derivatives of any positive order on the half-axis 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 fractional order and of the nonlinear Volterra integral equations. The existence and uniqueness of the solution of the above Cauchy-type problem is proved using the Banach fixed point theorem. The corresponding assertions for the Cauchy problem for the ordinary differential equation are presented.

Lazakovich N. V., Shlykov E. V.
Systems of differential equations with generalized coefficients in the direct product of algebras of mnemonic functions. pp. 17--20
E-mail: lazakovich(at)bsu.by

Summary: Systems of differential equations with generalized coefficients are investigated. Associated solutions of differential equations in the direct product of algebras of mnemonic functions are considered. A full classification of associated solutions is given.

Osinovskaya A. A., Suprunenko I. D.
Block structure of unipotent elements of the naturally embedded subgroups of type A3 in the special modular representations of the groups of type An. pp. 21--25
E-mail: anna(at)im.bas-net.by

Summary: For p ³ 11 the Jordan block structure of images of regular unipotent elements of the naturally embedded subgroup of type A3 in p-restricted irreducible representations of the group of type An over a field of characteristic p whose highest weights have three consequent zero coefficients, is described. The article contains (references 2--5 in the reference list) on the behaviour of unipotent elements of naturally embedded subgroups of small ranks in representations of the classical algebraic groups in positive characteristic. A detailed knowledge of rare and typical properties of images of individual elements in such representations can be useful for solving recognition problems for representations and linear groups on the basis of the presence of matrices with a special block structure.

Borukhov V. T., Gaishun I. V., Timoshpolskiy V. I.
Invariant form of the functional identification of thermal conductivity. pp. 26--29
E-mail: borukhov(at)im.bas-net.by

Summary: The method of functional identification of thermal conductivity for the transient heat conduction problem in the invariant form is developed. Some properties of the solution of the inverse problem is discussed.

Zabreiko P. P., Krivko-Krasko A. V.
Conditions of a local minimum of the functions in two variables and the Newton diagram. pp. 30--34
E-mail: zabreiko(at)mail.ru

Summary: The relation between a local minimum condition of the real analytic function in two variables and the method of the Newton diagram are described.

### PHYSICS

Shwed O. L.
Influence of the medium viscosity on the fluidity surface. pp. 35--39
E-mail: swed(at)newman.bas-net.by

Summary: An experimental-theoretical method of determination of the instantaneous surface in the elastic stress space has been proposed. It has been revealed that the principle of conservation potential nature of resiliency in the active loading process with the developed method of Baushinger effect calculation allow one to describe an evolution the surface fluidity using the viscous stress as the kinematics center

Siutsou I. A.
Possibility of metric determination by Doppler tracking. pp. 40--42
E-mail: i.siutsou(at)dragon.bas-net.by

Summary: We obtain a general result of a red shift value for a signal that is reflected or retransmitted by a radially geodetically moving body in an arbitrary spherically-symmetric static metric. The task of metric determination by Doppler tracking data is unsolvable, so the obtaining of a metric with free geodetic motion reproducing "Pioneer" anomaly cannot be done without considering the data on the circular motion of astronomical objects. On these grounds we suggest a solution for the problem on the absence of anomaly acceleration in orbits of outer planets and extra-Pluto objects of Solar system.

Povedailo V. A., Yakovlev D. L.
Spectroscopy of jet-cooled complexes of carbazole and alcohols. pp. 43--47
E-mail: poved(at)imaph.bas-net.by

Summary: The analysis of fluorescence excitation spectra of jet-cooled hydrogen-bonded complexes of carbazole with alcohols (methanol, ethanol, propanol-1 and propanol-2) has been done. The frequencies of pure electronic transitions of complexes, stretching and deformation vibrations of their hydrogen bonds have been obtained. Carbazole forms two different rotational conformers with both ethanol and propanol-1.

### CHEMISTRY

Ivashkevich O. A., Kabo G. J., Blokhin A. V., Domasevich V. V., Simirskiy V. V., Shevelyova M. P.
Resources of solid biofuel produced from the grain-crops straw in the Republic of Belarus. pp. 48--50
E-mail: kabo(at)bsu.by

Summary: Heats of combustion for different sorts of the grain-crops straw were determined. The average energy equivalent of the straw is equal to 2.4 tons of a conventional fuel per hectare. The yearly harvest of the grain-crops straw in the Republic of Belarus is equal to ~ 5.0 • 106 tons of a conventional fuel. The quality of pellets of a solid fuel with packed density of ~ 0.5 kg•dm-3 was shown to be comparable with that of wood pellets widely used in Europe.

Agabekov V. E., Ivanova N. A., Dlugunovich V. A., Tsaruk A. V., Karpinchik E. V., Kosmacheva T. G.
Film structures modified with SiO2, nanoparticles for liquid crystal display units. pp. 51--54

Summary: By means of the goniophotometric Stokes polarimeter angular distribution of polarization characteristics of He-Ne laser radiation reflected by polyvinyl alcohol (PVA) films modified with SiO2 nanosol was investigated. Increasing the nanosol content in PVA films from 1.6 mas.% to 5.0 mas.% caused an increase in the intensity of a diffuse component and a decrease in the polarization degree of radiation reflected at the angles from 20° to 60-70°.

Khlebnicova T. S., Isakova V. G., Lakhvich F. A.
Reaction of 2-trifluoroacetylcyclohexane-1,3-diones and their enol methyl ethers with phenylhydrazine. pp. 55--58
E-mail: khlebnicova(at)iboch.bas-net.by, prostan(at)iboch.bas-net.by

Summary: 2-Trifluoroacetylcyclohexane-1,3-diones and their enol methyl ethers react regioselectively with phenyl hydrazine to give structural isomeric trifluoromethylated 6,7-dihydro-1H-indazol-4(5H)-ones and 6,7-dihydro-2H-indazol-4(5H)-ones, respectively. Their structures were verified by the spectroscopic data (IR, 1H, 13C, 19F, MS spectra).

Sysa A. G., Kisselev P. A., Zhabinskii V. N., Khripach V. A.
Brassinosteroids as new effectors of monooxygenases of mammals liver microsomes. pp. 59--62
E-mail: kiselev(at)iboch.bas-net.by

Summary: Synthesis of natural brassinosteroid -- 28-homobrassinolide and its stereoisomer -- (22S, 23S)-28-homobrassinolide was carried out. The essential difference in the rate of the influence of 28-homobrassinolide and (22S,23S)-28-homobrassinolide on the catalytic properties of the monooxygenase system of the mammals' liver cells participating in the metabolic activation of the procancerogenic chemicals like benz(a)pyren was shown. The physiological importance of the process for functioning an organism of mammals was discussed.

Zelenkovskii V. M., Orlovskaya L. A., Soldatov V. S., Vasag H.
Correlation of the sorption selectivity of heavy metal ions with iminodicetic groups of resins and the structure of ion-polymer complexes. pp. 63--67
E-mail: vmzel(at)ifoch.bas-net.by, lianaorlovskaya(at)msn.com, soldatov(at)ifoch.bas-net.by

Summary: The sorption selectivity of Cu(II), Ni(II), Pb(II), Cd(II) and Mn(II) cations from acetate buffer with pH6 on fibrous ion exchanger with iminodiacetic (IDA) groups have been studied in dependence on the cations concentration. The data obtained were fitted to Langmur's equation whose constants were used to calculate the dependence of the distribution coefficient on concentration and compare it to the experimental data. The calculated distribution coefficients were used for evaluation of the efficiency of the cation sorption in the range of concentration inaccessible for direct experimental determination by atomic absorption spectroscopy because the ion exchanger used in this study was intent for pre-concentration of the ions in their analytical determination. The distribution coefficients decrease with increasing the concentration of the ions but they level out at their concentrations below 10-6 mole/l. The selectivity series at the low concentrations is Cu2+>Ni2+>Pb2+>Cd2+>Mn2+. Quantum chemical calculations of the structures of the sorption complexes showed that it is substantially different for different cations. The sorption selectivity correlates well with the number of coordination bonds between the cation and the ligand of the IDA group and the degree of their covalence.

### BIOLOGY

Gorodecka E. A., Spiridovich E. V., Gorbatcevich V. I., Korevko I. A., Azharonok V. V., Filatova I. I., Nekrashenich Ya. A.
Influence of plasma-radiowave processing on the sown quality of seeds. pp. 68--72
E-mail: helgorod2003(at)mail.ru

Summary: In the article a response of seed germination characteristics of some important agricultural plants to the radio frequency electromagnetic field has been studied. The goal of these investigations was to determine if an alternate seed treatment approach based on microwave methods would offer a more effective and environmentally sound alternative compared to traditional seed processing technologies.

Sivitskaya L. N., Kushniarevich A. I., Danilenko N. G., Novogrodski T. A., Davydenko O. G.
Apolipoprotein E gene polymorphism and the risk of multifactorial diseases in the population of Belarus. pp. 73--77
E-mail: cytoplasmic(at)mail.ru

Summary: Genetic polymorphism of apoE gene was studied in the population of Belarus (771 individuals). The average rate of risk allele e4 was determined in six different Belarusian regions. The lowest allele frequency was shown in the north population (3%), the highest -- in the south (12%). In general, frequencies of e2, e3, e4 alleles in Belarussians were 5.6, 86.2, 8.2%, respectively.

Lemesh V. A.
Molecular analysis of the heterogeneity of the Belarusian flax cultivars and landraces. pp. 78--81
E-mail: v.lemesh(at)igc.bas-net.by

Summary: No evidence of genetic erosion was found over the 80-year period of executing breeding programs in the area of Belarus. Some cultivars of the Belarusian breeding with a relatively high share of fixed recessive RAPD-loci (45--52%) were revealed. Belarusian ancient cultivars and primitive accessions (landraces) differed from modern cultivars in a small share of fixed recessive RAPD-loci. This indicates that Belarusian landraces show a greater genetic heterogeneity, exhibit a higher genetic potential than modern cultivars and may be a source of useful alleles in developing new fiber flax cultivars.

### TECHNICAL SCIENCES

Huskou A. V., Huskou V. V., Radchenko P. V.
Procedure of plotting the potential and traction performances with power delivery through PTO. pp. 82--86
E-mail: huskou(at)yandex.ru

Summary: Potential and traction performances of a wheel tractor are given with power delivery through PTO.

Dyakonov O. M.
Modeling of the metal chip heating process in a continuous muffle furnace. pp. 87--99
E-mail: deaconco(at)sbeglobal.net

Summary: The physical-mathematical model of the metal chip heating process in a continuous muffle furnace has been developed. The model describes the conjugate heat- and mass transfer in these furnaces (conductive, convective, radiant), chip and furnace parts heating, lubricant-coolant evaporation, oil combustion, flue gas movement. The obtained set of the equations is completed that allow one to solve the issue of furnace height optimization under the given furnace productivity and minimum natural gas consumption.

Sosnovskiy L. A.
One type of entropy as the measure of absorption of energy spent for making damages in the mechanical-thermodynamical system. pp. 100--104
E-mail: komissarov(at)belsut.gom

Summary: The notion of tribo-fatigue entropy as the measure of irreversible energy absorption in moving and deformable systems is introduced.

Baravikou S. M., Shalak A. V., Berasnevich A. I., Emelyanov A. V.
Statistical model of degradation of the functional parameters of electronic technology devices. pp. 105--109
E-mail: borsm(at)tut.by, mpogost(at)tut.by

Summary: The method to obtain physical-statistical models of functional parameters degradation of electronic technology devices as their conditional frequency distribution is suggested. The model helps to forecast the parametric reliability of the devices.

Yashcheritsin P. I., Kusakin N. A., Kheifets M. L., Prement G. B.
Technological and operational inheritance of quality parameters at restoration of the weared surfaces of the machine details. pp. 110--115
E-mail: mlk-z(at)mail.ru

Summary: The methodology of the statistical analysis of technological and operational inheritance of quality parameters of the details of machines is offered basic difference of inheritance in the technological process of restoration of the weared surfaces from the inheritance in the rational process of machining surfaces of details is shown.

### SOCIAL SCIENCES AND HUMANITIES

Zaitseva N. V.
House building as the element of preserving the system of social assurance of the rural population of Belarus. pp. 116--119
E-mail: lockaut(at)tut.by

Summary: The article is devoted to the problems of improvement of living conditions collective farmers in 1966--1975. The main achievments in economic development, including its agricultural sector in that period, are made the necessary possibilities for modernization of the living conditions of collective farmers. For studying the social and living conditions of Belarusian collective farmers, the questions of development living conditions are general.

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Created with assistance of Dr. Ignatii I. Korsak
Copyright © 2007-2008 The National Academy of Sciences of Belarus
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