Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.1
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Doklady of the National Academy of Sciences of Belarus, 2011, Vol.55, No.1

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
Khachatryan Kh. A.
Some classes of Urysohn's nonlinear integral equations on the semiaxis. pp. 59.
Email: khach82@rambler.ru
Summary: Sufficient conditions of solvability for one class of Urysohntype nonlinear integral equations on the semiaxis are obtained . The distinctive feature of the considered equations is the noncompactness of Urysohn's corresponding nonlinear operator. A oneparameter family of solutions for some subclasses of initial nonlinear integral equations is constructed.
Tsyfra I. M., Czyzycki T.
Equivalence and integrability of secondorder linear ODEs. pp. 1015.
Email: TSYFRA@math.uwb.edu.pl
Summary: The Lie algebra of the Lie group of equivalence transformations of a class of secondorder linear ODEs with variable coefficients is constructed. Further the invariants and differential invariants of this group are found. On the base of these invariants criteria of equivalence of the equations under consideration are formulated. These criteria enable one to characterize some classes that are integrable in quadratures.
Likhoded N. A.
Generalized tiling. pp. 1621.
Email: likhoded@im.basnet.by
Summary: Sufficient conditions for legality of loop partition on generalized tiles are stated and proved. Conditions for enhancement of legality when using a given coordinate of the iteration space for tile generation are obtained.
Izobov N. A., Korovin S. K.
Perron's effect of change in the sign of characteristic exponents for the solutions of two differential systems. pp. 2226.
Email: izobov@im.basnet.by, korovin@cs.msu.su
Summary: Perron's effect of change in the sing of negative characteristic exponents of a negative twodimensional linear differential system with infinetely bounded differentiable coefficients on positive values of the exponents of all solutions of a nonlinear differential system with continuosly differentiable pertutbation of any order of smallness is realized Earlier only Perron's partial (on a part of solutions) effect of change in the sign of the characteristic exponents was realied.
Zhiznevsky P. A.
Existence of critical formations. pp. 2730.
Summary:
вставка рисунком с.2730 eng
pzhiznevsky@yahoo.com
Avtushko T. S., Lazakovich N. V., Pikman Yu. A., Yablonsky O. L.
Secondorder linear differential equations with generalized coefficients in mnemofunction algebra. pp. 3135.
Email: Y_PIKMAN@live.com
Summary: Within the direct product of mnemofunction algebra considered the Cauchy and boundary problems for the secondorder differential equation with a generalized derivative in the coefficients are considered. For the Cauchy problem the associated I and S solutions, which are, in turn, the only solutions of different integral equations in the class of continuous functions, are obtained. The associated Isolution coincides with the known solution to the original Cauchy problem: the associated Ssolution is a new one. Also, two various sets of eigenvalues are obtained for the homogeneous boundary problem. The eigenvalues for the associated Isolution coincide with the already known ones, the eigenvalues for the associated Ssolution  new.
Bekryaeva E. B.
Linear differetial systems close to exponentially dichotomic systems. pp. 3640.
Email: evgenia.bekriaeva@gmail.com
Summary: We consider the class of weakly exponential dichotomic systems, i . e., those that satisfy the same conditions as the exponential dichotomic systems, but with the only difference that solution estimations are not uniform under constantsmultipliers. For every real c > 0 we describe the sets of those solutions data such as the constantsmultipliers of solution estimations do not exceed c.
PHYSICS
Gusak N. A.
Nonreciprocity of buildingup and decay processes of space charge gratings in photorefractive crystals. pp. 4145.
Email: rectorat@ipk.by
Summary: The nonreciprocity of buildingup and decay processes of space charge gratings in the photorefractive crystals, where the recombination time is substantially shorter than Maxwell relaxation and diffusion times, is determined. It is shown that the buildingup process accomplishes more quickly than the decay one when homogeneous and inhomogeneous parts of the light field appear and disappear simultaneously.
Komarov F. F., Milchanin O. V., Karpovich V. B., Vlasukova L. A.
Formation of carbon nanotubes alignied arrays during synthesis by CVD with the use of different substrates. pp. 4649.
Email: KomarovF@bsu.by
Summary: The results of carbon nanotubes (CNT) aligned arrays growing on the substrates of porous alumina and quartz glass are presented. CNTs were formed by CVD via acetylene thermal decomposition. In alumina pores nickel was deposited as catalyst, quartz was used without applying a catalyst Carbon nanotubes aligned arrays were synthesized on the both of the substrates. The SEM images of the samples surface with carbon nanotubes were obtained, morphology and structural characteristics of the carbon nanotubes were determined.
Kisel V. V., Ovsiyuk E. M., Red'kov V. M.
Wave functions and energy spectrum for a spin 1 particle in the external Coulomb field. pp. 5055.
Email: redkov@dragon.basnet.by, e.ovsiyuk@mail.ru
Summary: The relativistic wave equation for a particle with spin 1 in the DuffinKemmerPetiau form is solved exactly in the presence of the external Coulomb field. Two types of solutions are constructed, one  in terms of hypergeometric functions and the other  in terms of the confluent Heun functions. The corresponding energy spectra have been found.
Tomilchik L. M.
Determination of the luminosity distance in the expanding Universe by the cosmological red shift measurement. pp. 5662.
Email: lmt@dragon.basnet.by
Summary: The explicit expression for the dependence of the expanding Universe luminosity distance on the cosmological red shift is found. The formula contains no free parameters except the speed of light and the Hubble constant. It reproduces quite well the observational data in the investigated red shift interval up to two units and allows to give direct experimentally verifiable predictions beyond this interval.
CHEMISTRY
Hloba N. I., Prokopchuk N. R., Shiroki V. L., Krutko E. T.
New complexing metalcontaining modifier of poly(4,4'diphenyloxide)pyromellitimide. pp. 6366.
Email: Orion2308@yandex.ru
Summary: The experimental results on the modification of polypyromellitimide by hexafluorophosphatferrocene are described. The effect of modifiers on the rheological properties of a prepolymer is shown. Stressstrain and thermal properties of the modified compositions are studied. It is established that the thermal stability of these compositions reaches 18 ^{0}С, strength property  40 %, elasticity modulus  25 %.
Polyachenok O. G., Dudkina E. N., Ashmyanskaya E. I., Polyachenok L. D.
Calcium chloride hydrate thermal stability specific features. pp. 6770.
Email: polyachenok@mogilev.by
Summary: Three tensimetric methods were used to determine the temperature dependence of the water vapor pressure over two crystal modifications of calcium chloride monohydrate (a and b). Thermodynamic characteristics of the corresponding reactions and standard enthalpy of formation and entropy of these crystal modifications were obtained. The theoretical limit of the desiccating ability of CaCl_{2} was calculated, and the reasons for the observed deviations were discussed. Attention was drawn to a special case of the thermal analysis when the existing two crystal modifications of a hydrate: one of which is stable and the other is metastable, may give an erroneous evidence of an additional lower hydrate formation.
Yukhnevskii P. I., Zelenkovskii V. M., Soldatov V. S.
Quantumchemical calculations of structural and energy
characteristics of polymethelennaphthalenesulphate superplasticizer C3. pp. 7174.
Email: vmzel@ifoch.basnet.by
Summary: Quantumchemical calculations of the properties of molecules of plasticizing additives C3 are made using the semiempirical method MNDO(d). Sizes of molecules, heat of formation, and dipole moment depending on the degree of polycondensation are determined. It was found that increasing the degree of polycondensation (n > 11) of polymethelennaphthalenesulphate superplasticizer C3 leads to developing the globular structure of twisted molecules, to reducing the dipole moment and, consequently, to diminishing the ability of plasticizing additives, to slowing down the hardening of concrete at the early age.
Lesnikovich A. I., Fedotova J. A., Bayev V. G., Milevich I. A., Vorobyova S. A.
Influence of the synthesis temperature on the magnetic properties of cobalt ferritebased nanocomposites. pp. 7580.
Email: Bayev@hep.by
Summary: The magnetic properties and the phase structure of powders extracted from the CoFe_{2}O_{4} suspension and nanocomposites CoFe_{2}O_{4}/polyvinnyl alcohol (CoFe_{2}O_{4}/PVA) with a different cobalt ferrite content (1030 wt. %) were studied by Fe^{57} Mossbauer spectroscopy and vibrating sample magnetometry. Differences in the structure and the magnetic properties of samples synthesized at temperatures below 100 ^{0}C were revealed. Peculiarities of agglomeration of CoFe_{2}O_{4} nanoparticles incorporated into the polyvinyl alcohol (PVA) matrix were studied.
BIOLOGY
Rupasova Zh. A., Reshetnikov V. N., Volotovich A. A., Vasilevskaya T. I., Yakovlev A. P., Pinchukova Yu. M.
Comparative evaluation of the influence of biotic and abiotic factors on the biochemical composition of fruits of the strange kind family Ericaceae introduced to Belarus. pp. 8185.
Email: alyakovlev@tut.by
Summary: The results of relative research of the influence of biotic and abiotic factors on the variability of 32 quantitative characteristics of the biochemical composition of fruits of 30 taxon strange introduced to Belarus in 3 kinds family Ericaceae: Y. corymbosum L., Y. vitisidaea L. and Oxycoccus macrocarpus (Ait.) Pers.) in the perennial cycle of observation are presented.
EARTH SCIENCES
Aizberg R. Ye., Beskopylny V. N., Gribik Ja. G.
Division of subsalt complexes of the Pripyat oil and gas basin into structural regions. pp. 8690.
Email: chistaya@nature.basnet.by
Summary: The division of subsalt complexes of the Pripyat oil and gas basin into the structural regions is suggested The basin includes the Pripyat Trough, BraginLoyev, and the slopes of the MikashevichiZhitkovichi Uplift. The location of oil and gas promising zones of local uplifts was shown to be spatially related to the tectonic structures of the first and second orders.
TECHNICAL SCIENCES
Kovtun V. A., Pasovets V. N., Pleskachevsky Yu. M., Mihovski M., Iordanov M.
Physicomechanical characteristics of composite materials based on powder disperse coppercarbon nanotubes systems. pp. 9195.
Email: vadimkov@yandex.ru
Summary: In the present article the physicomechanical properties of composite materials based on powder coppercarbon nanotubes systems are investigated. The mechanisms for interaction of the nanofiller with the powder metal matrix, which provide the enhancement of the mechanical properties of the generated composite material, are offered.
Karabko A. O., Dostanko A. P.
Calculation of the thermal stability of modified nickel silicides. pp. 96101.
Email: kanc@bsuir.unibel.by
Summary: In the article we present the calculation way of evaluating the possibility of enhancing the thermal stability of nickel silicide by alloying with metals, which consists in determining formation heat of nickel silicide using Miedema's model. The change of the thermal stability of nickel silicides alloyed with metals Mo, Pt, Pd, W, Zr is analyzed It is found that the most negative value of the thermal stability of alloyed nickel silicide is (96.68 kJ/mol) and the most stable monosilicide phase is therefore reached on addition of 10 at. % of Pd.
Zhukova Yu. V., Terekh A. M., Semenyako A. V.
Numerical simulation of unsteady crossflow past an oval cylinder at various Reynolds numbers. pp. 102107.
Email: svaturb@htmi.ac.by
Summary: The article presents the results of experimental investigation and numerical simulation of crossflow past a single oval cylinder with the axis ratio 1:1.425 over the Reynolds number range 400017000 in comparison with a single circular cylinder. Comparative analysis of aerodynamic characteristics of oval and circular cylinders  total drag, skin friction coefficient, pressure coefficient distribution, and surface friction coefficient was made. The numerical simulation results obtained were compared with the experimental data.
Troyanchuk I. O., Chobot A. N., Teresko N. V., Mantytskaya O. S., Chobot G. M., Efimova E. A.
Intermediate magnetic phase of the Pr_{0.5}SrCo_{1x}Mn_{x}O_{3} system. pp. 108113.
Email: troyan@physics.by
Summary: The crystal structure and the magnetic properties of Pr_{0.5}SrCo_{1x}Mn_{x}O_{3} solid solutions have been studied using neutron diffraction and magnetization measurements. The intermediate magnetic phase (0.3 < x £ 0.65) with a high Curie point and in the absence of the magnetic neutron scattering was revealed It is suggested that the ferromagnetic state is realized near ferroelastic domain walls.
Pinchuk L. S., Cherniakova Yu. M., Lobanovskyi L. S., Drozd E. S., Chizhik S. A.
Magnetic susceptibility of lubricating ability of synovial fluid. pp. 114117.
Email: ychernyakova72@mail.ru
Summary: It is found that the lubricating ability of blood serum of a patient suffering from osteoarthritis is being improved after a dose of "Doxycycline"  antibiotic of the tetracycline group. The magnetic susceptibility of preparations based on blood serum and synovial liquids was measured by the induction method. All they demonstrated the properties of diamagnetic substances Changes in the blood serum structure arising from "Doxycycline" taken by a patient were registered by the atomic force microscopy method. Physicochemical mechanisms of the influence of biochemically connected with serum albumen "Doxycycline" on the structure, the real and imaginary parts of serum magnetic susceptibility are discussed An increase in the imaginary parts, which characterizes the magnetic energy absorption, is caused by the extension of the magnetic moment directed against the electromagnetic field of a joint. This intensifies the rebuilding of the lubricating layer, diminishes friction, and serves as the biophysical base of transfusal chondroprotection that causes the improvement of the state of the joints.
SOCIAL AND HUMANITIES SCIENCES
Trifonov N. Yu.
Property appraisal: from market value to user one. pp. 118121.
Email: guild@unibel.by
Summary: The article develops the concept of value which is in the centre of the valuation process and presents a new kind of value in use  "user value", which is more suitable for changing nonstable and nontransparent market of a valuation subject such as a real estate or a business.
AGRARIAN SCIENCES
Khachenkov A. A.
Hygienic evaluation of mycotoxin contaminated grain forage. pp. 122124.
Email: belniig@tut.by
Summary: The new methodological approach to hygienic estimation of mycotoxinspolluted forage grain is developed. New notions are implemented in hygienic estimation of forages: dominant for control mycotoxin, background mycotoxic pollution of grain forage.
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