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# Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.5

/ Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.5

## CONTENTS

### MATHEMATICS

Matysik O. V., Savchuk V. F.
2-step iteration method for solution of the operator equations in the Hilbert space. pp. 5--10
E-mail: matysik(at)brsu.brest.by

Summary: An implicit 2-step iteration method for solution of the operator equations in the Hilbert space is proposed. The convergence of the method is proved in the case of an apriori choice of a number of iterations in usual and energy norm of the Hilbert space, the estimaties of an error are obtained. For the iteration method the opportunity of the application of a rule residual stop is studied.

Rovba Y. A., Smatrytski K. A.
Rational interpolation in the zeros of Chebyshev--Markov sine-fractures. pp. 11--15
E-mail: k.smotritski(at)grsu.by

Summary: The rational interpolating process with nodes in the zeros of Chebyshev--Markov sine-fractures is considered. The interpolating Lagrange function is obtained in this case. The norm of the Lagrange function Ln(x;f) in the space L2(r) of the square integrated functions with r(х) = (1 - x2)-1/2 weight on the segment [-1;1] is calculated for the fixed poles. The norm of Ln as an operator from C[-1;1] to L2(r is estimated. On the basis of this estimate the theorem on the convergence of the rational interpolating process with nodes in the zeros of Chebyshev--Markov sine-fractures in the L2(r space with fixed poles is proved. Using the Lagrange function a new quadrature formula, which generalizes the known quadrature formula in the polynomial case, is obtained. It is shown that this quadrature formula is a quadrature formula of Gaussian type and its convergence is estimated.

Yanchevskii V. L.
Another proof of one computation formula for groups of special projective conorms. pp. 16--18
E-mail: yanch(at)im.bas-net.by

Summary: A direct proof (in terms of central simple algebras) of one computation formula for groups of special projective conorms playing an important role in computation of reduced Whitehead groups of central simple algebras is given.

Samoilovich Yu. A., Timoshpolski V. I., Trusova I. A.
Correlation between the impurity segregation and the nonmetallic inclusion origin in a hardening steel ingot. pp. 19--23
E-mail: bspametall(at)mail.ru

Summary: A correlation between the process of sulphur dendritic segregation in the two-phase zone of hardening ingots and the nonmetallic inclusion origin (sulphides) is studied. The findings of investigations might be used for assessment of the detrimental impurities saturated content, providing a required quality of ingots.

### INFORMATICS

Gordon V. S., Strusevich V. A.
Schedules with due-date assignment and position-dependent processing times. pp. 24--30
E-mail: gordon(at)newman.bas-net.by

Summary: Single machine scheduling problems are considered, in which the processing times of jobs depend on positions of the jobs in a schedule and the due-dates are assigned either according to the CON rule (a due-date common to all jobs is chosen) or according to the SLK rule (the due-dates are computed by increasing the actual processing times of each job by a slack, common to all jobs). Polynomial-time dynamic programming algorithms are proposed for the problems with the objective functions that include the cost of assigning the due-dates, the total cost of discarded jobs (which are not scheduled) and, possibly, the total earliness of the scheduled jobs.

Nesenchuk A. A.
Locating the roots of the dynamic system within the arbitrarily shaped domains. pp. 31--35
E-mail: anes(at)newman.bas-net.by

Summary: The method for locating the roots of the dynamic system with a parametric uncertainty within a given domain bounded by the arbitrary algebraic curve, when the coefficients of the characteristic equation are linearly dependent upon the uncertain parameter, is considered. The peculiarity of the method consists in the fact that the given domain boundary is not set by the curve of fixed geometric shape, and the domain can be bounded by the arbitrarily shaped algebraic curve. For solving the task, the root locus fields of the circular image are applied.

### PHYSICS

Bushinsky M. V., Chobot A. N., Mantytskaya O. S.
Crystal structure, magnetic and dielectric properties of the Bi1-xCaxFe1-xTixO3 system. pp. 36--39
E-mail: bushinsky(at)ifttp.bas-net.by

Summary: The Bi1-xCaxFe1-xTixO3 solid solution exhibits a transition from the rhombohedral (R3c) to orthorhombic (Pbnm) symmetry at x ~ 0.2 which causes the spontaneous magnetization to appear and the dielectric susceptibility to increase. The crystal and magnetic structures of orthorhombic phase are determined.

Korshunov F. P., Bogatyrev Yu. V., Lastovskii S. B., Murin L. I., Markevich V. P., Govor G. A.
Radiation-induced defects in silicon n+-p-structures irradiated with fast electrons at elevated temperatures. pp. 40--43
E-mail: lastov(at)ifttp.bas-net.by

Summary: Parameters of deep levels associated with defects, which were introduced into the base region of n+-p-structures by irradiation with 6 MeV electrons in the temperature range 340¸770 K have been determined with the use of deep level transient spectroscopy (DLTS) method. It is shown that the introduction rate of interstitial related defects increases about twice upon raising the irradiation temperature from 340 to 670 K. The effect observed is associated with the suppression of the annihilation rate of Frenkel pairs at higher temperatures. It is found that the total introduction rate of electrically active radiation-induced defects decreases sharply when the samples are irradiated at temperatures higher than 670 K. Electron irradiation at Tin > 670 K also results in the introduction of thermally stable defects with deep levels at EV+0.16, EV+0.21, EV+0.27 and EV+0.31 eV into the samples.

Komarov F. F., Leontyev A. V.
Optical properties of SOG films irradiated with light ions. pp. 44--48
E-mail: komarovF(at)bsu.by, Leontyev(at)bsu.by

Summary: The results of investigation of optical constant changes for SOG-films irradiated with light ions are presented. It was shown that ion implantation is an effective method for modification of optical properties of SOG-films.

Leonov A. V., Feranchuk I. D.
Analytical investigation of the "collapse-revival" effect in the Jaynes--Cummings model. pp. 49--54
E-mail: fer(at)open.by

Summary: Specific features of the "collapse-revival" effect for the population inversion of the two-level system in the quantum field are described for the first time by means of the analytical expressions with a high accuracy. The results are obtained both in the resonant case and with detuning. The dependence of the characteristics of this effect on the physical parameters of the system is defined.

### CHEMISTRY

Boitsova T. A., Afanasiev N. I., Moshkova T. B., Makarevich N. A.
Bioconversion of technical lignosulfonates. pp. 55--59
E-mail: lignin(at)arh.ru, nikma(at)tut.by

Summary: The investigations determined an opportunity of lignosulphonate (LS) decomposition by basidiomycete Corijlus hircutu-tus. It was shown that LS degraded mostly at the fist stage of the process (during 5--10 days) under optimum conditions. The increase of a mycelium surface on a porous substratum raises a degree of full decomposition to 25--30%. The increase of LS concentration in a solution up to 10--20% suppresses the development of full micromycete. Significant oxidation of LS components occurred during bioconversion. The maintenance of oxygen-containing functional groups increased. The process of LS bioconversion was accompanied by an increase of the molecular weight.

Potkin V. I., Dikusar E. A., Petkevich S. K.
Synthesis of 5-functionally substituted 3-arylisoxazoles on the base of aryltrichloroallyl ketones. pp. 60--63
E-mail: potkin(at)ifoch.bas-net.by

Summary: By the oxime group transformation of 3-aryl-5-hydroxyiminomethylisoxazoles previously obtained by the aryltrichloroallyl ketones condensation with hydroxylamine the esters, aldehydes and azometines of isoxazole series were synthesized.

Shcherbina L. A., Geller B. E., Kharytanovich A. G., Khaleiko V. S.
Initiating the free-radical processes of homophase synthesis of fiber-forming thermo-polymers of acrylonitrile by the coordinated radical mechanism. pp. 64--67
E-mail: leoShch(at)tut.by

Summary: The kineties of the homophase synthesis in dimethylformamide of fiber-forming thercopolymers based on acrylonitrile has been studied under the conditions simulating a continuous operation of a commercial ideal mixing reactor. For the first time a possibility of speeding up a free-radical homophase synthesis of fiber-forming thercopolymers in aprotic solvents by doping small additives of "dead" polar polymers, similar to synthesized ones, into the original reaction medium was demonstrated. The hypothesis of forming the "macromolecule-prime free radical" complexes stipulating the increase of the initiator efficiency and the observable increasing effect of a gross rate of the homophase synthesis of fiber-forming thercopolymers has been made using the results of spectrophotometric investigations.

Lakhvich F. A., Ogeiko N. H., Petrusevich I. I.
Synthesis of bis(2-acylcyclohexane-1,3-diones) -- new group of b-polycarbonyl compounds. pp. 68--71
E-mail: ogeiko(at)rambler.ru

Summary: The synthesis of bis(4,4-dimethyl-2,6-dioxocyclohexyl)alkanediones has been realized. The scheme includes the preparation of monoenoles of esters from corresponding diketone and carboxylic acid chlorides, followed by their O-C isomerization. Structures of the compounds obtained were verified by the spectroscopic data (IR, 1H spectra) and the elemental analysis.

### BIOLOGY

Urbanovich O. Yu., Kozlovskaia Z. A., Kartel N. A.
Certification of apple-tree genotypes by means of SSR-markers. pp. 72--78
E-mail: o.urbanovich(at)igc.bas-net.by

Summary: The method of the SSR-analysis was used for certification of apple-tree genotypes at the molecular level. Three pairs of markers covering various genome regions CH01c06 and CH02c02b, CH02b12 and CH04h02, CH03d12 and SdSSR were selected and used in multiplex PCR, by means of which 109 apple-tree cultivars and species were identified and their phylogenetic similarity was established.

Valentovich L. N., Gubich O. I., Nikolauichik Y. A.
Role of the DspF protein of Erwina carotovora subsp. atroseptica in the functioning of the type III secretion system. pp. 79--84
E-mail: leony(at)bio.bsu.by

Summary: The DspF protein of phytopathogenic bacterium Erwinia carotovora subsp. atroseptica (Eca) is thought to be a specific secretory chaperone for the DspE effector protein. We have found that introduction of additional copies of the dspF gene coding for this chaperone into Eca cells blocks their ability to induce a hypersensitive response of nonhost plants. This phenotype has appeared to be due to a severe defect in translocation of effector proteins into plant cells. Translocation into plant cells of the DspE-Cya fusion protein has appeared to be completely blocked, while translocation of AvrPto-Cya protein -- severely reduced from Eca cells carrying dspF cloned in a relatively low copy number plasmid. These data allow us to suggest that additional molecules of DspF either block the effector translocation by specifically binding them (as in the case of DspE-Cya) or by interfering with the work of the type III secretion system (as in the case of AvrPto-Cya).

Shakhbazau A. V., Goncharova N. V., Sevyaryn I. N., Kosmacheva S. M., Kartel N. A., Potapnev M. P.
Transfection of human bone marrow mesenchymal stem cells: cationic polymers vs. lipofection. pp. 85--88
E-mail: a.shakhbazau(at)igc.bas-net.by

Summary: We report a comparative study of hMSC transfection methods based on various chemical formulations which include cationic polymers and cationic lipids. The transfection efficiency, the toxicity to cells, a proliferation rate, and other parameters are described. Optimization of the hMSC transfection methods is an important stage in the development of the hMSC-based gene and cell therapies.

### MEDICINE

Zharko V. I., Serdiuchenko N. S., Bevzeluk A. A.
Medical econometry and innovational development of the health care system. pp. 89--95
E-mail: lpulgkb(at)mail.belpak.by

Summary: Modern medical technologies make it possible to improve treatment results in the saving of the same level of hospital beds, patients ambulatory visits and medical staff number. In this connection it is necessary to underline that the problems of the health care system and health of citizens of the Republic of Belarus are linked to a certain degree with the deficit of medico-economical investigations.

### EARTH SCIENCES

Garetsky R. G., Konischev V. S., Tolstosheev V. I.
Structural position of dawsonite occurrences in carboniferous deposits of the Pripyat trough. pp. 96--101
E-mail: vkon(at)igig.org.by

Summary: The dawsonite occurrences in carboniferous deposits of the Pripyat depression were formed in the secondary compensation synclines during radaev and bobricov times as a result of reactions of soda solutions and alumosilicates. Soda solutions were formed as a result of caprock dissolution in the crests of salt domes.

Astapenko V. N.
Orsha-Ilmen magnitovariation anomaly. pp. 102--106
E-mail: astapenko(at)igig.org.by

Summary: New data obtained from magnitotelluric investigations were used to justify the position of the magnitovariation anomaly in the north-east part of Belarus. The Orsha anomaly is joined with the Ilmen magnitovariation anomaly and is an important link of transeuropean anomalies.

### TECHNICAL SCIENCES

Shapovalov V. M., Shumilin V. A., Pleskachevsky Yu. M.
Phase state of a lignohydrocarbon matrix and its change during alkane thermal treatment of wood. pp. 107--110
E-mail: v.shapovalov(at)tut.by, shumilin(at)gsu.unibel.by, pleskym(at)mail.ru

Summary: A submicrostructure of birch has been studied using a spin probe of paramagnetic resonance spectroscopy. It is supposed that a lignohydrocarbon matrix of the natural wood is found in a thermodynamic non-equilibrium state due to the incomplete phase separation of its components. The wood treated by an aqueous-alkane solution and exposed to a heat field is found to realize an additional phase separation process of the components of the lingohydrocarbon matrix. This process evidently follows the mechanism of spinodal decomposition.

### SOCIAL SCIENCES AND HUMANITIES

Rahimau A N.
Ethnic groups of the Caucasus peoples in the Republic of Belarus: estimation, factors of migration and adaptation according to the ethnological study. pp. 111--117
E-mail: aidaragimova(at)rambler.ru

Summary: The migration process during the last two decades of the 20th century is shown on the basis of official statistics, documents of the Archive of the Committee on Religions and Nations at the Cabinet of Ministers of the Republic of Belarus, mass media information. During the last decade the quantity of people from the Caucasus coming to our Republic is reducing. The state, in turn, must regulate by the law the entry and living of refugees and people without citizenship in the territory of Belarus.

### AGRARIAN SCIENCES

Golushko V. M., Furs N. L.
Use of carnitine with a high level supplement of fat for rearing and fatting pigs. pp. 118--123
E-mail: belniig(at)tut.by

Summary: The influence of carnitine and 3% fat in diets of growing pigs on their growth and production was investigated. Supplement of carnitine in a dose of 50 g/t mixed meal in diets of growing pigs provides an increase in an average daily growth by 5.1% (P < 0.001), a decrease in feed expenses per unit production by 2.5% compared to the animals of control group, which raises their slaughter outcome by 2.1%), meat content in carcass by 2.3%, decreases the fat content in carcass by 2.4%, increases the loin eye area by 8.8%.