Doklady of the National Academy of Sciences of Belarus, 2006, Vol.50, No.3
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Doklady of the National Academy of Sciences of Belarus, 2006, Vol.50, No.3

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
Tykun A. S.
Relative rotation of a normal vertical field. pp. 58
Summary: For the vector fields of outer and inner normals to the relative boundary of the domain the formulas relating the relative rotation to the Euler characteristics of the domain and its boundary are obtained.
Zabreiko P. P., Kushel O. Y.
GantmakherKrein theorem for binonoperative operators in the spaces of functions. pp. 914
Summary: The existence of the second (according to the module) eigenvalue l_{2} of a completely continuous nonnegative operator A is proved under conditions that A acts at the space L_{p}(W) or C(W) and its exterior square A Ù A is also nonnegative.
For the case, when the operators A and A Ù A are indecomposable, the simplicity of the first and second eigenvalues is proved, and the connection between indices of imprimitivity of A and A Ù A is examined. For the case, when A and A Ù A are primitive, the difference (according to the module) of l_{1} and l_{2} from each other and from other eigenvalues is proved.
Gorbuzov V. N.
Inverse problem on the group analysis of the systems of total differential equations. pp. 1519
Summary: The inverse problem of the group analysis for autonomous entirely solvable systems of total differentials equations is solved, when all set of systems is built by means of infinitesimal operators and the universal invariant of the admitted multiparameter Lie group (Abelian and nonAbelian).
Monakhov V. S., Hodanovich D. A.
Finite groups with the restricted indices of maximal subgroups. pp. 2024
Summary: The structure of a finite soluble group G, in which the indices of nonsupersoluble maximal subgroups are a primenumber, a square of the prime mumber or a cube of the prime mumber, is studied. It is proved that the nilpotent length of G does not exceed 5, and the plength  2.
Yadchenko A. A.
Coprime automorphisms and normal subgroups of linear groups. pp. 2526
Summary: In this work some properties of orders of coprime automorphisms of irreducible linear groups are established. Also, some sufficient conditions for the existence of the normal Holl P subgroup in a P solvable irreducible complex linear group are obtained.
Legchekova H. V., Skiba A. N.
Finite groups with permutable 2maximal and 3maximal subgroups. pp. 2729
Summary: This article gives a description of finite groups, in which every 2maximal subgroup permutes with ail 3maximal subgroups.
Shamukova N. V., Bernik V. I.
Approximation of real numbers by integer algebraic numbers and the Khintchine theorem. pp. 3032
Summary: The authors proved the convergence case of the Khintchine theorem for the problem of zero approximation by the values of polynomials, all roots of which are integer algebraic numbers
PHYSICS
Kukharchik P. D., Serdyuk V. M., Titovitsky J. A., Purovsky M. O.
Effect of continuous modification of dielectric order in multicomponent disperse systems. pp. 3336
Summary: We introduce the concept of dielectric order of a multicomponent disperse system and connet it with the index of the power law of mixing for dielectric permittivities of various components in a lowfrequency electromagnetic radiation field. By the example of wheat grain we phenomenologically describe the effect of continuous dielectric order modification in a disperse system as a result of its moisture content change. This effect correlates with the known phenomenon of spatially arranged water structure formation and expansion inside grain kernels when their water absorption increases. A new mixing law is established, being in a good agreement with this effect.
Komarov F. F., Urbanovich A. I., Yuvchenko V. N.
Thermoelastic generation of longitudinal acoustic vibrations near the ion tracks. pp. 3742
Summary: Thermal excitation of longitudinal acoustic vibrations during highenergy ion stopping in solids is considered in the framework of the thermal spike model. It is shown that the amplitude of acoustic vibrations and thermal stresses that arise in this case have the oscillating nature in time. In the dynamic regime, the values of thermal stresses far exceed their quasistatic values. The estimations of the angular thermoelastic stresses of SiO_{2} and InP irradiated with highenergy ions have been made.
Privalchuk A. N., Tolkachev E. A.
Twopotential approach and twotype sources in (2+l)dimensional electrodynamics. pp. 4346
Summary: The twopotential formulation of (2 + l)classical electrodynamics equations is given and new types of the solutions of the socalled "zero field equations" are found. The duality of the potentials of static electric charges and vortical electric fields is shown and the corresponding sources are interpreted from the viewpoint of their embedding into the physical spacetime R^{3.1}.
Tomilchik L. M.
Possible cosmological origin of the Pioneer Anomaly. pp. 4854
Summary: Using the EinsteinPoincare clock synchronization procedure, a generalization of the special relativity spacetime interval which includes the Hubble constant is proposed. The existence of the universal blueshift drift of the emitted frequency is shown to be the direct purely kinematical property of the proposed interval. In the linear approximation in Hubble constant, this shift reproduces the observable Pioneer Anomaly effect with an accuracy of factor two.
CHEMISTRY
Vasilenko I. V., Kostjuk S. V., Gaponik L. V., Kaputskii F. N.
Polymerization of lhexene with MgC_{12}supported TiC_{14} ZieglerNatta catalysts. pp. 5559
Summary: The polymerization of 1hexene with the MgCl_{2} supported ZieglerNatta catalysts generated by the in situ reduction of TiCl_{4} using a Grignard reagent or prepared by the recrystallization of MgCl_{2} from alcohols has been investigated. It is shown that the catalysts prepared by the recrystallization method with dibutyl phthalate as an internal electron donor are characterized by high stereospecificity (up to 65% of [mmmm] isotactic pentad) and lead to the high molecular weight poly(lhexene)s (M_{h} > 10^{6}). The catalysts obtained by the in situ reduction of TiCl_{4} show high activity (98 g poly(lhexene)/g Ti h), but low stereospecificity (about 55% of [mmmm] isotactic pentad) in the 1hexene polymerization, as well as give rise to the low molecular weight polymers (M_{h} ~ 7 • 10^{4}). It is found that the maximum activity of the investigated catalysts is observed at the low [Al]/[Ti] ratios ([Al]/[Ti] = 5 ¸ 35).
Cherviakovsky E. M., Gilep A. A., Vlasova T. M., Kurchenko V. P., Usanov S. A.
Quercetin modification by myoglobin. pp. 6063
Summary: Redox interactions between methmyoglobin and quercetin have been studied. Some characteristics of the above process have been obtained. The ability of myoglobin to transform quercetin into several stable products has been shown.
Solomyansky A. E., Gracheva E. A., Hilevskaya K.S., Zhavnerko G. K., Agabekov V. E.
Mono and multimolecular organic filmsprotective coatings of silicon surface. pp. 6468
Summary: The wear stability in friction processes and the tribological behaviour of mono and multimolecular LB films of dimethyl ester octadecylmalonic acid (DiEster) were studied. For a tribotechnical test to be performed, a tribological situation steel (sphere)  silicon (plane) was used. The stability of a DiEster monomolecular film in the friction process was compared with the wear stability of a behenic acid (BehA) LB film and an octadecyltrichlorosilane (OTS) chemisorbed film. It was found that the wear stability of the OTS film is sufficiently lower than that of BehA and DiEster. The investigated LB films considerably reduce the steel  silicon friction coefficient and much increase the wear resistance of contacting surfaces. The increased wear stability of the DiEster multilayers seems to be due to a partial reversible transition of the LB films molecules between contacting surfaces.
Pashkovsky F. S., Gribovsky M. G., Lakhvich F. A.
Synthesis of 3,7interphenylene heteroprostanoid precursors on the basis of tetronic acids. pp. 6972
Summary: A simple and general approach towards the synthesis of biologically active and metabolically stable 3,7interphenylene heteroprostanoid precursors on the basis of tetronic acid and substituted aromatic aldehydes has been proposed.
BIOLOGY
Shlakhotko E. A., Sapunova L. I., Lobanok A. G., Evtushenkov A. N.
Molecular cloning and expression of the Arthrobacter sp. Xyla gene in Escherichia coli cells. pp. 7376
Summary: As a result of the completed investigations, the Arthrobacter sp. xylose isomerase gene (xylA) was isolated, its full nucleotide and corresponding amino acid sequences were determined. Hasmid pET24bxylA was engineered for the regulated expression of xylA in Escherichia coli BL21(DE3) under control of phage promoter T7. The high expression efficiency of the xylose isomerase gene from bacteria Arthrobacter sp. in heterogeneous recombinant microorganism opens broad prospects for manufacturing new commercially attractive strains superproducers of xylose isomerase.
Orlovskaya O. A., Kaminskaya L. N., Khotyleva L. V.
Creation and analysis of triticale F_{1} hybrids containing alien material Aegilops. pp. 7781
Summary: A new method for increasing and improving a gene pool of hexaploid triticales was verified experimentally by introgression of the genetic material Aegilops L. into the triticale genome. For the first time the genomesubstitution forms of Triticum aestivum L., in which the genome D of cv. Avrora was substituted by genomes of Aegilops L. diploid species, were used as a genetic bridge in transferring alien material Aegilops. This promoted the creation of optimum conditions for genetic material exchange between crossed forms as well as for the rise in the hybrid viability. The detected features in the chromosome behavior at various meiosis stages in the produced F_{1} hybrids point to the possibility of introgressing the alien material into the triticale genome. Morphological and biochemical analyses allowed the detection of the genetic material Aegilops L.of the 1^{st}, 2^{nd}, 3^{rd}, 6^{th} and 7^{th} groups of homeologous chromosomes.
MEDICINE
Churakov A. V.
Treatment of severe craniocerebral injury patients using the combined extracorporal autohemomagnetotherapy. pp. 8287
Summary: The develeped methods for treatment of neurotraumatic patients with the use of the combined extracorporal autohemomagnetotherapy (EAHMT) decrease and/or, in the majority of cases, prevent the development of secondary brain damage factors. Just these factors determine the clinical forecast and the results of treatment in the acute and remote periods after severe cranial trauma (SCT).
Belugin S. N., Mifflin S. W.
cAMP effect on GABAA receptor dependent response in NTS neurons of normotensive rats. pp. 8891
Summary: We studied the effects of cAMP on GABAA receptor dependent response in neurons dissociated from NTS of normotensive rats. GABAinduced currents obtained using the wholecell patch clamp of NTS neurons dialysed with cAMP displayed the increased extent of the desensitization and after GABA removal  the increased rate of current deactivation. These data demonstrate that modulated GABAA receptor currents in NTS neurons by increasing desensitization and deactivation suggest a role of cAMP dependent phosphorylation in regulating GABAergic inhibitory postsynaptic currents duration.
EARTH SCIENCES
Mamchyk S. O., Karymava L. A.
Division and correlation of the Callovian and Oxfordian deposits in the SouthWest of Belarus. pp. 9296
Summary: It is not usually easy to trace the boundary between the Callovian and Oxfordian deposits in the SouthWest of Belarus despite the fact that lower Oxfordian rocks are the lithologic, geophysical and biostratigraphic reference. The authors have made the approaches that permit the correlation of deposits at the contact of Callovian and Oxfordian rocks depending on their territory distinctions.
Rylova T. B.
Age and the stratigraphic position of interglacial deposits of the Korchevo section. pp. 97101
Summary: The comparison of pollen zones and the composition of sporepollen spectra of interglacial deposits of the Korchevo section and deposits from the upper (Mogilev) interval of the Belovezhian horizon suggest their similar age of origin. This is in favour of the stratigraphic position of these interglacial deposits in an interval between the oldest Pleistocene Narev and Berezina glacial horizons.
TECHNICAL SCIENCES
Artioukhina N. K.
Calculation of asphere deformation constants in mirror anastigmats. pp. 102105
Summary: This article presents the solution of the problem on calculation of asphere deformation constants in mirror anastigmats. Seidel coefficients (spherical aberration, coma, astigmatism, field curvature) are described and the formulas of aberration coefficients are given. Different variants of asphere lens designs consisting of four mirrors examination are found. The plane  field anastigmats are discussed. Results of calculation can be used for designing new optical devices using mirror optics.
Vitiaz P. A., Lyakhov N. Z., Talako T. L., Grigorieva T. F., Letsko A. I., Ilyuschenko A. F., Beliaev A. I., Barinova A. P.
Selfpropagating hightemperature synthesis of intermetallic/oxide nanocomposite powders. pp. 106110
Summary: Results of investigation of selfpropagating hightemperature synthesis of nanocomposite powders FeAl/Al_{2}O_{3} and FeAl(Cr)/Al_{2}O_{3} are presented. The use of mechanochemically produced nanocomposites as SHS precursors allows synthesizing nanostructural composites with preset structural morphology and improved interfacial strength.
Timoshpolsky V. I., Samoylovich Yu. A., Gorjainov V. A.
Analysis of the phenomena of thermal fatigue of steel continuous casting machines. pp. 111115
Summary: On the basis of mathematical modeling, stresses and deformations in support rollers of steel continuous casting machines under the influence of a ferrostatic pressure of molten metal are calculated and conditions for crack rise and development of cracks are considered.
Kozlov G. V., Burya A. I., Sviridenok A. I., Yanovskii Yu. A.
Dependence of the dynamic elasticity modulus of natural rubberbased composites on aparticle size of a carbon nanofiller. pp. 116118
Summary: Nanoscale carbon fillers with a diameter of 7520 nm increase with the natural rubber dynamic elasticity modulus from 0.05 to 40 MPa. This result depends on the dimensions of interfacial phases and nanofillers fractal structure.
ARGICULTURE
Amelchanka S. L., Tanana L. A.
Study of the dependence of the milk productivity of the cows of the Belarusian blackmotlev on selection variants. pp. 119123
Summary: The efficiency of cows of the Belarusian blackmotley breed achieved various variants of breeding selection in ABC "OctoberGrodno" of the Grodno area is investigated. The data on the efficiency are taken on the first lactation of animals born in 2000, 2001 and 2002. The relative analysis was carried out between the groups of the Cousines of different line and cross, and also between the groups of first heifers inside one line or cross, but with different year of birth. The lines of BellMayak, StarbukKlyaitus, ValerianBlekstar, RevengeNagan, in Gangway as well as the crosses of the given lines have been involved in researches.
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