Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, No.2
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Doklady of the National Academy of Sciences of Belarus, 2007, Vol.51, 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
Davyalova E. V., Zverovich E. I.
Closed solution of the special case of Markuchevich's fourelement problem. pp. 510
Orlovich Yu., Gordon V. S., Zverovich I. E., Finke G.
Hardness of approximating minimum (or maximum) maximal induced matching graph problems. pp. 1116
Summary: The minimum (respectively, maximum) maximal induced matching problem asks for a minimum (respectively, maximum) maximal induced matching in a given graph. We show that for any e > 0 the minimum maximal induced matching problem for graphs of order n cannot be approximated within a factor of n^{1e} in polynomial time, unless P = NP. The result holds even if the graph in question is restricted to be bipartite. For the maximum induced matching problem, it is shown that for any e > 0 the problem cannot be approximated within a factor of (n/2)^{1e} in polynomial time, unless NP = ZPP. Here, ZPP denotes the class of languages decidable by a random expected polynomialtime algorithm that makes no errors (zeroerror, probabilistic, polynomial). Moreover, we show that the maximum induced matching problem is NPcomplete for line graphs of bipartite graphs.
Vasiliev I. L., Rulinskii Yu. G.
One condition of representation of entire functions of finite degree of the Fourier integrals of the compact functions of L_{p}. pp. 1720
Summary: It is shown that if an entire function of finite degree F(z) and its first derivative satisfy Hoelder's some local conditions on the real axis, then F(z) is the Fourier transform of a compact function that belongs to the class L_{p}(1 < p < 2).
Radyna A. Ya., Sender A. N.
pAdic splines as an apparatus for approximation of Q_{p}valued functions. pp. 2125
Gaishun I. V., Goryachkin V. V.
Matrix binomial and its application to twodimensional discrete systems. pp. 2628
Summary: Some conditions for solvability of twodimensional discrete systems are obtained.
Velichko M. V., Suprunenko I. D.
Small unipotent elements in representations of the special linear group with large highest weights. pp. 2933
Summary: For almost all prestricted irreducible representations of the group A_{n} (K) with highest weights large with respect to p, the Jordan block structure of images of small quadratic unipotent elements in these representations is determined. It is proved that if j is an irreducible prestricted representation of A_{n} (K) with highest weight m_{1}w_{1} +. + m_{n}w_{n}, S^{n}_{i  1} m_{i} ³ p  1, not too few of
the coeficients m_{i}, are less than p1 and n is large enough with respect to the codimension of the fixed subspace of an element z under consideration, then j(z) has blocks of all sizes from 1 to p.
PHYSICS
Tomilchik L. M., Molchan M. A.
Dirac oscillator as a phenomenological model of quark confinement. pp. 3439
Summary: Within the framework of the consecutive geometrical approach based on the application of the D'Alembert generally covariant equation in conformally flat spherically symmetric metrics of a special form, the D'Alembertlike equation is obtained. The precise solutions of this equation repeat qualitatively and quantitatively the basic results of the hadronisation model, the number of free parameters being reduced to one. It is also shown that the factorization procedure of the obtained equation operator leads directly to the Dirac oscillator model.
Milchanin O. V., Komarov F. F., Plebanovich V. I., Gaiduk P. I., Komarov A. F.
Improvement of the parameters of shallow p^{+}njunctions in silicon by additional carbon implantation and stepbystep thermal treatments. pp. 4045
Summary: In this article carbon coimplantation and stepbystep thermal treatments of shallow p^{+}njunctions formation were used with the purpose of extended defect suppression and reduction of boron transient enhanced diffusion. A substantial improvement of the structural and electrical parameters of shallow p^{+}njunctions has been achieved by using the additional carbon implantation and stepbystep thermal treatments.
CHEMISTRY
Potkin V. I., Petkevich S. K., Azarko V. A., Kaberdin R. V.
Convenient method of construction of 1,3thiazine and l,3thiazole heterocycles on the base of l,l,4,4tetrachlorolbuten3one. pp. 4648
Summary: The 2amino4dichloromethyl1,3thiazin6thion was synthesized by interacting 1,1,4,4tetrachlorolbuten3one with thiourea in water at 20°C. The 2amino5chloro4(2,2dichlorovinyl)1,3thiazole hydrochloride was the product of the reaction in methanol at 40°C. The compounds obtained are capable to form thin photosensitive films and are of interest for studies as materials for microelectronics.
Skorb E. V., Ustinovich E. A., Sviridov D. V.
Photocatalytically active composite coatings based on titanium dioxide. pp. 4952
Summary: The kinetic study of photodegradation of probing dyes of different polarity on the surface of TiO_{2} : In_{2}O_{3} films of different composition has enabled a conclusion that photodegradations of polar and nonpolar organic compounds in the air conditions occur through different mechanisms, i. e., via photooxidation with photogenerated hydroxyl radicals and due to direct attack with photoholes, respectively.
Soldatov V. S., Zelenkovskii V. M., Bezyazychinaya T. V., Mosunova N. V., Sosinovich Z. I.
Sorption of copper ions by polymer sorbent with amidopolyamine groups. pp. 5356
Summary: Copper sorption by ion exchange on the base of polyacrylonitrile with amidopolyamine groups has been studied as a function of the equilibrium solution pH value. High sorption selectivity indicates the formation of a strong complex of Cu^{2+} with the functional groups. Using the quantum chemical calculations it has been shown that the strong binding of the Cu^{2+} complex is due to the formation of coordination bonds with amidoamine groups of the sorbent.
BIOLOGY
Romanovskaya A. A., Nikandrov V. N.
Plasminogen and streptokinase regulation of glioma C6 and neuroblastoma IMR32 cells proliferation. pp. 5760
Summary: It is demonstrated in vitro that plasminogen and its activator streptokinase are able to sustain the vital functions even in a serumfree medium and have mitogenic effects on the cells of rat glioma C6 and human neuroblastoma IMR32 shown by the quantity of cells, cellular DNA, RNA and the protein increase.
New original facts were obtained to testify the possibility of initiation of neoplastic transformation and potentiation of a tumor growth.
Ignatovets O. S., Akhramovich T. I., Feskova E. V., Leontiev V. N.
Mechanism of simazine degradation of bacteria genus Pseudomonas. pp. 6164
Summary: In the article the results of research on degradation of striazines herbicide  simazine by ferment systems of bacteria genus Pseudomonas are shown. On the basis of kinetic researches the specific dehalogenase activity of the chosen strains was determined. Intermediates of simazine degradation are investigated by the method HPLCMS.
Kozlova N. M., Garmaza Yu. M., Krutko A. G., Zubritskaya G. P., Slobozhanina E. I.
Influence of detergents on transport of GSHconjugates from human erythrocytes. pp. 6567
Summary: It is shown that detergents exert an inhibitory influence on the efflux of GSHconjugates with xenobiotics from erythrocytes in submicellar low concentration. It is established that decreasing the output rate of conjugates from cells treated with different detergents is connected with changes of the physical condition of membrane lipids  a decrease of fluorescence polarization of a lipophilic fluorescent probe TMADPH incorporated into isolated human erythrocyte membranes under the action same detergent concentrations is revealed. It is suggested that the functional activity of membrane proteins responsible for transport of exogenous substances from cells depends on the microviscosity of a lipid bilayer.
MEDICINE
Belugin S. N.
Membrane potential shift and excitability of DiA strained neurons from NTS at renal hypertension. pp. 6871
Summary: Examination of the subset of NTS neurons exhibiting somatic DiA fluorescence revealed that DiA labeled neurons from 4week hypertensive (HT) rats had a significantly shorter duration of delayed excitation (252 ± 115 ms, n = 8, P = 0.022) than in DiA labeled neurons from normotensive (NT) rats (748 ± 152 ms, n = 7). DiA labeled neurons of HT rats had showed a more depolarized membrane potential during first 50 ms in response to the stimulation than neurons from NT rats. The data suggest that 4week hypertension reduces potassium hyperpolarizing outward currents in NTS neurons, and this contributes to the depolarizing shift of the membrane potential and reduces delayed excitation.
Beloenko E. D. †, Chernyakova Yu. M., Pinchuk L. S.
Tribiological substantiation of a chondroprotective method by means of blood serum and hyaluronates. pp. 7275
Summary: A method of chondroprotection is proposed, which involves injection of the arthritic joint with a mixture of the patient's blood serum being completely compatible with the synovial medium of his joint, and hyaluronates. Lubricity of the mixtures of blood serum (AB, Rh^{+}) and hyaluronic preparations like "Sinvisc", "Hyalgan", "Hyaject" were estimated on a pendulum tribometer equipped with a permanent magnetic field source simulating the biophysical field of the joint. The friction coefficient in the support of the tribometer lubricated by the compositions studied was found to exponentially drop with time at application of the field (H ~ 1 kA/m). The dependences of the least friction coefficient values versus hyaluronate amount in the mixture pass through a minimum. In this connection, a hypothesis is proposed that complex compounds arise in the lubricating film under the action of friction and magnetic field, said compounds comprising protein and hyalortonate macromolecules plus molecules of liquidcrystalline cholesterol derivatives are analogous to the complexes found in a healthy synovia. The results obtained constitute a tribological embodiment of anew method of chondroprotection.
EARTH SCIENCES
Konischev V. S.
Gases dissolved in the underground waters and the oil and possibilities of the sedimentary basins of Belarus. pp. 7680
Summary: It is shown that gases dissolved in the underground waters of the Orsha and PodlesseBrest depression s differ from gases of underground waters of the Pripyat depression and they are not tynical for gases of oil and gas bearing basins.
TECHNICAL SCIENCES
Rudnitsky V. A., Kren A. P., Mozgalev V. V.
Relation between the static and dynamic elasticity modulus of elastomeric materials. pp. 8184
Summary: The necessary conditions to obtain a relation between the static and dynamic elasticity modulus of elastomeric materials are established. Using the results of tests of the filled rubbers it is shown that the main reason for a difference between the readings of dynamic and static devices is the different temperature, different test time and different relaxation processes in elastomers. It is established that the heating of the elastomers and the account of the value of viscosity allows finding a unique dependence between the dynamic and static elastic ity modulus.
Pryakhin S. S., Semashko V. I.
Kinetics of heating and cooling of the surface of soldered joints at laser diagnostics. pp. 8590
Summary: Temperature kinetics parameters for soldered joints have been calculated using the experimentally measured values of their thermal radiation signals induced by laser heating. According to the developed kinetic model the determined parameters of the soldered joints were the values of the time scales of thermal processes relating to the internal and external temperature relaxation, and also the values of the corresponding saturation temperatures. The soldering defects among the groups of onetype soldered joints were revealed due to the anomalies of the values of their kinetic parameters and the relations between them.
Vysotski M. S., DouboIik D. A.
Efficiency of running systems of wheel vehicles. pp. 9194
Summary: The method for quantitative estimation of the efficiency of running systems of vehicles for curvilinear motion, taking into account the deviation of vectors of driving wheels tractive forces from the direction determined by a driver by turning a steering wheel, is offered. Results of the application of the developed method for estimation of the efficiency of running systems AWD vehicle with mass and geometrical parameters, close to an offroad vehicle MZKT 79091 with the wheel formula 8 x 8, are presented.
Vityaz P. A., Kheifets M. L.
Analysis of metastable and nonequilibrium processes using the state diagrams involving the synthesis of supersolid materials. pp. 9599
Summary: The analysis of carbon and bore nitrite diagrams has been carried out on the basis of proposed topological models according to the principles of the continuity in physical and chemical system properties and compliance of the topological model with that system.
Burya A. I., Kozlov G. V., Sviridenok A. I.
Structural aspects of the fluidity processes in the composites on the basis of phenilone with short fibers. pp. 100102
Summary: It is shown, that the structural components of the polymeric matrix supervising process of fluidity in composites filled with fibres are clasters and interphase areas, i. e. all tightlypacking areas.
Konstantinov V. M.
Enhanced diffusion of alloying elements in iron during thermochemical treatment of powders in a rotating vessel. pp. 103107
Summary: The phenomenon of enhanced solidstate diffusion during hightemperature thermochemical treatment (carburization, boronizing, siliconizing) of iron and steel powders in a rotating vessel is examined experimentally and analyzed theoretically. It is demonstrated that the enhancement of diffusion mass transfer during powder processing is connected with a local increase in a diffusion coefficient due to the generation of nonequilibrium vacancies during contact periodic plastic deformation.
The reasons for a more substantial enhancement of diffusion of substitutional atoms in comparison with interstitial atoms are discussed.
SOCIAL SCIENCES AND HUMANITIES
Khoryak A. P.
Brick eastChristian temple construction in western Belarus of the first third of XVI century. pp. 108112
Summary: Brick architecture monuments of the first third of XVI century in Synkovichy, Murovanka, Suprasl, Vilno, Novogrudok, Koden are analyzed as a continuation of the tradition of eastChristian temple constructing in the western region of Belarus. The relations with Western and Central Europe, Byzantine, eastern Slavs are considered. The transformation of Christian West and East architectural traditions is formulated as one of the features of authentic Belarusian constructing.
AGRICULTURE
Tanana L. A., Amelchenko S. L., Peshko V. V.
Genetic structure of the Belarusian blackmotley breed on the locus of the kappacasein gene. pp. 113117
Summary: Researches are devoted to studying the breeding value of bulls of various lines of the Belarusian blackmontley breed and to analyzing the genetic structure of bullproducers on the locus of the kappacasein gene. As a result of researches, it is established that the bulls of the ValerianBlackster line (I = 9929 kg) have the highest value of milk yield and those of the StarbukKlaitus line (I = 4.36%)  the highest value of milk fat content. Calculation of the genetic structure of the bulls of the Belarusian blackmotley breed on the locus of the kappacasein gene testifies that 71.4% of bulls have kappacasein genotype AA and 28.6%) of animals  kappacasein genotype AB. Kappacasein genotype BB was identified in none of the bulls. The study of the milk quality of the daughters of various bullproducers testifies that the highest maintenance of milk proteins is seen in the daughters of the bulls Grim 400011 and Pisar 400036. It is equal to 3.26 and 3.27%, respectively. It says that the bulls having allele B in the genotype give the posterity with a higher maintenance of milk proteins.
Dolmatov D. A., Pristchepa I. A.
Ways of rootknot nematode invasion load and a harmfullness decrease in the glasscovered ground. pp. 118123
Summary: The results of research on determining rootknot nematodes (Meloidogyne spp.) belonging, spread and number on tomatoes and cucumbers under greenhouse conditions are presented. The influence of thermal soil disinfection on the quantity of nematodes and harmfulness change against a background of tomato and cucumber varieties (hybrids) growing with different degree of susceptibility to rootknot nematodes is studied. It is determined that growing the resistant tomato varieties after ground steaming prevents from active reproduction and soil accumulation of rootknot nematodes and raises the economic efficiency of thermal treatment. The biological and economic efficiency of nematicides (acarine, P and phytoverm, P. izapine, w. s. c.) applied against rootknot nematodes in glasscovered ground is shown.
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