Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.2
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Doklady of the National Academy of Sciences of Belarus, 2010, Vol.54, No.2

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
Vuvunikjan Yu. M.
Nonlinear evolutionary operators with compositionally symmetric generalized characteristics. pp. 511
Email: vuv(at)grsu.by
Summary:The concept of a compositionally symmetric generalized function is introduced. For evolutionary operators with the compositionally symmetric generalized pulse characteristics the general theorem about spectral characteristics of a composition of evolutionary operators is formulated and proved.
Alehno A. G.
Constructing by a given indicator of the analytical function in the plane with a section along the ray. pp. 1215
Email: alehno2004(at)pochta.ru
Summary:An analytical in the plane with a section along the ray function having a given indicator under arbitrary specified order was built.
Monakhov V. S., Trofimuk A. A.
Finite groups with bicyclic factors of normal series. pp. 1622
Email: monakhov(at)gsu.by; trofim08(at)yandex.ru
Summary:The structure of finite groups having a normal series with bicyclic factors is considered. In particular, groups of odd order and A_{4}free groups with this property are investigated. Exact estimations of the derived length of such groups are made.
Netbay O. V., Skiba A. N.
Finite groups with given systems of Х_{n}semipermeable subgroups. pp. 2325
Email: netbay_ov(at)mail.ru; skiba(at)gsu.unibel.by
Summary: Let G be a finite group andA  a subgroup of G and Æ¹XÍG. Then we can say that A is X_{4} semipermutable in G if A has a supplement T in G such that A is Xpermutable with every nilpotent subgroup of T. The article is devoted to studying the influence of the properties of X_{n}semipermutable subgroups on the structure of finite groups. In particular, new criteria of supersolubility and dispersibility of finite groups are obtained.
Beresnevich V. V., Bernik V. L, Goetze F.
Consistent approximations of zero by an integral polynomial, its derivative and small values of discriminants. pp. 2628
Email: vb8(at)york.ac.uk; bernik(at)im.basnet.by; goetze(at)math.unibielefeld.de
Summary:In the article the authors establish the lower estimate for a number of integral polynomials of given degree, height and bounded discriminant.
Kostyukova O. I.
Necessary optimality conditions for optimal control problems with the piecewise linear righthand side. pp. 2934
Email: kostyukova(at)im.basnet.by
Summary:In the article, the optimal control problem with the piecewise smooth righthand side is considered. Junction between smooth subarcs is realized along a given hyperplane in the state space. Necessary optimality conditions are obtained for a feasible trajectory that contains subarcs belonging to this hyperplane.
Erovenko V. A., Marton M. B.
Invariance of the Apostel essential spectrum under strictly singular perturbations. pp. 3539
Email: erovenko(at)bsu.by
Summary:The class of perturbations is considered, namely, strictly singular operators. The present article deals with proving the theorem of stability and invariance of the Apostle essential spectrum at commuting strictly perturbations of the operator.
INFORMATICS
Chernyavsky A. E., Kolyada A. A.
Multiplication on big simple modules on the basis of Barretts's minimally superfluous modular scheme. pp. 4053
Email: razan(at)tut.by
Summary:A new algorithm of multiplication on big simple modules p is offered. It is based on Barrett's minimally superfluous modular scheme. Optimization of base not modular procedures  procedures of scaling and code expansion is carried out. In comparison with the known analogue, a double reduction in the number of demanded tables is achieved at the expense of unification of settlement parities for performance of operational sequences (scaling; code expansion) at the first and second stages of the multiplication algorithm offered. In doing so, time expenses in the case of p to 512 bits are reduced approximately by a factor of 1.765.
PHYSICS
Kuzey A. M.
Collective and scale effects of spontaneous crystallization during superrapid cooling of Al10 mass% B0.17 mass% С. pp. 5460
Email: phti(at)belhost.by
Summary:The methods of electron scanning microscopy and Xray analyses were used for examining the microstructure of a rapidly quenched Al10 mass% B0.17 mass% С alloy and aluminum borides. It is established that superrapid cooling of melt results in forming a crystal that consists of two phases such as a and bA1B_{12}. The sizes of the crystal are commensurable with a diameter of a microcasting. It is shown that the formation of a twophase crystal is caused both by the interaction between cluster melt structure elements and the intercluster medium and by changes in the mechanism of spontaneous crystallization.
Tomilchik L. M.
Selfreciprocal M. Born's model and the dynamic picture in the conformalflat Gaussiantype metric. pp. 6164
Email: tea(at)dragon.basnet.by
Summary:It is shown that Born's selfreciprocal equation coincides in form with the D'Alembert general covariant equation in the conformalflat Gaussiantype metric and the geodesic equations reproduce the hyperbolic motion of the probe particle. The relation between the energymomentum tensor generating such a metric and the corresponding Minkowski force
Onischuk A. G., Tolkachev E. A.
Dual algebraic structures in the theory of cascade circuits of quadripoles. pp. 6569
Email: tea(at)dragon.basnet.by
Summary:
CHEMISTRY
Eryomin A. N., Zhavnerko G. K., Yashin K. D., Osipovich V. S., Agabekov V. E.
Thiol and bovine serum albumin surface functioning of CdSe/ZnS nanoparticles in reverse micelles. pp. 7076
Email: yan47(at)mail.ru
Summary: It is shown that CdSe/ZnS nanoparticles (NP) are incorporated into reverse micelles from bis(2ethylhexyl)sulfosuccinate sodium salt (AOT) with the easily, losing stabilizing hydrophobic trioctulphospin oxide shell. NP interacts effectively with thiols and bovine serum albumin (BSA) in the micelle medium forming strong complexes with them that can be easily isolated from micelles and dissolved in water. The interaction efficiency of NP with thiols and BSA depends on a means of preparing a micelle solution. It is shown that it is necessary to add NP to the solution as the last one when water, thiols, and protein have already been solubilized in reverse micelles. Thus, in the system studied, NP stabilized with thioglycerin (TG) fluoresced most strongly in comparison with NP covered with dithiothreitol (DTT) and Lcystein. In the water environment, NP covered with TG and DTT showed practically identical fluorescent properties. On the contrary to thiols, BSA present in the micelle medium quenched luminescence, but strengthened their fluorescent properties in water. NP fluorescence is enhanced in combination of thiols with BSA in the process of NP functioning, or dissolution of a complex of NP... BSA in the solution with TG or DTT.
Shestak I. V., Vorobieva E. V., Basalyha I. I., Krutko N. P., Kulbitskaya L. V.
Polyacrylic acid and polyethylene glycol influence on the crystallization of calcium carbonates and magnesium. pp. 7781
Email: Shestak_Irina(at)tut. by
Summary:The influence of differentkind polymeric additions  polyacrylic acid, polyethylene glycol and their composition on the crystallization of calcium carbonates and magnesium with an elevated temperature in dependence on the medium pH is studied. The interrelation between the phase structure of calcium carbonates and magnesium and the efficiency of inhibitory action polymers is established.
Shutova I. V., Golubovich V. P.
Development of the mathematical model and software for building of the protein's molecular surface. pp. 8286
Email: shutova(at)iboch.basnet.by
Summary:The mathematical model of the protein's molecular surface is made in terms of the surface presentation by points and the program in VC++ language is realized. Using the designed program and the tools of Jmol and RasMol programs the Oncostatin M surfaces are built. The matching of these surfaces has shown that the designed program allows building surfaces that are well compared with the surfaces built using the existing programs.
Navakouski M. J., Vashkevich I. L., Sviridov O. V.
Synthesis and bifunctional activity of a chloramphenicolbiotin conjugate. pp. 8792
Email: maxushob(at)gmail.com
Summary:A new bifunctional compound, the conjugate of antibiotic chloramphenicol and vitamin H (biotin), was obtained. The synthesized conjugate was shown to biospecifically interact with biotinbinding protein streptavidin and antibodies against chloramphenicol. This property of the conjugate allows its use in a chloramphenicol immunoassay based on the streptavidinbiotin technology.
BIOLOGY
Razlutskij V. L., Feniova I. Yu., Sushchenia L. M., Palash A. L.
Mechanisms of coexistence of species in (Cladocera) microcosms. pp. 9397
Email: vladimirrazl(at)gmail.com
Summary:The laboratory and simulation experiments show that species faster capable of consuming limited food resources win in food competition. To estimate a rate of consumption, it is proposed to use the ratio of a filtration rate to a daily food ration (F/R). Cladoceran species with close F/R could coexist for a long time (more than month) in simulation and experimental communities. Nevertheless, stronger competitors gradually supersede other species. A rate of competitive elimination is the higher, the larger the differences in F/R values.
Lemesh V. A., Orlovskaya O. A., Sakovich V. L, Khotyleva L. V.
Heterogenety of flax interspecies hybrids for anatomic stem parameters. pp. 98102
Email: V.Lemesh(at)igc.basnet.by
Summary:Interspecies hybrids F_{1} from crossing fiber flax (L. usitatissimum L.) cultivars with wild species (blue flax L. angustifolium Huds. and pale flax L. bienne Mill.) were developed for expanding and enriching fiber flax gene pool. The traits defining the content and quality of flax fiber were studied in the produced hybrids as against the parental forms. The investigations performed have shown that flax hybrids F_{1} combine resistance to lodging with good parameters of fiber productivity. There were selected accessions which are not inferior and sometimes are superior to the parental fiber flax cultivar in plant height, industrial stem length and some anatomic stem parameters. The data obtained point to a preferable use of L. angustifolium in interspecies crosses.
Pitlik T. N., Bulay P. M., Denisov A. A., Cherenkevich S. N., Kulchitsky V. A.
Hydrogen peroxide regulation of synaptic transmission in hippocampus during change of temperature and oxygenation degree. pp. 103107
Email: tpitlik(at)mail.ru
Summary:The action of hydrogen peroxide in the concentration range 0.55 mmol/1 on the amplitude of field excitatory postsynaptic potentials in the CA1 region of rat hippocampus during change of temperature and oxygenation degree was investigated. The investigation was carried out on transverse slices of rat hippocampus by using the microelectrode technique. Under normal oxygen conditions and incubation temperature of 29 ^{0}C hydrogen peroxide caused inhibition of synaptic transmission in hippocampus and depression of field excitatory postsynaptic potentials. During hypoxia or temperature increase up to 37 ^{0}C hydrogen peroxide caused the augmentation of field excitatory postsynaptic potentials.
MEDICINE
Kirillov V. A., Emeliyanova O. A., Fridman M. V., Demidchik E. P.
Karyometry in the assessment of the malignant potential of a thyroid follicular tumor. pp. 108–113
Email: kirillov(at)bsmu.by
Summary:The comparative karyometric study of the thyrocytes with follicular cancer and follicular adenoma was performed. With the help of mean values estimation, construction of histograms and regression analysis the initial database has been transformed into informative quantitative parameters. An expert system for follicular thyroid tumor nature diagnostics was developed based on a set of boundary values of quantitative parameters reflecting the regularities of pathologic changes in thyrocyte nuclei with follicular cancer and follicular adenoma and weighting coefficients.
Kashevsky B. E., Ulaschik V. S., Istomin Yu. P., Kashevsky S. В., Prokhorov I. V., Pastushenko A. G.
Lowfrequency ferromagnetic hyperthermia of experimental malignant tumors. pp. 114–117
Email: bekas(at)itmo.by
Summary:The new approach is presented for the cancer local magnetic hyperthermia based on using nanoparticles with magnetic hysteresis. The particles are injected directly into the tumor and are heated up by a strong lowfrequency magnetic field. The effect of thermal destruction of tumors is studied in experiments with rats' carcinoma RS1 subject to hyperthermia parameters.
EARTH SCIENCES
Solodilova V. V., Gaidashov A. A., Martinov A. A.
Petrography and geochemical features of rocks from the East coast of the Enderby land (Antarctica). pp. 118–124
Email: solod(at)igig.org.by
Summary:The petrographic and geochemical composition of the first sample party of various rocks (122), delivered by the Belarusian polar explorers from the east coast of the Enderby Land in the year of 2007, was investigated.
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