# Доклады Национальной академии наук Беларуси, 2005, Том 49, No.5

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2005, Том 49, No.5

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Kilbas A. A., Koroleva A. A.*
**Extended generalized Mittag--Leffer type function.** pp. 5--10

*Summary:* The special function represented by the Mellin--Barnes integral and generalizing the four-parameter Mittag--Leffler type function is introduced. For this function the existence conditions are proved, the series expansions are established, and asymptotic estimates near zero and at infinity are obtained.

*Suprunenko I. D.*

**On the behavior of unipotent elements in representations of the classical groups with largem highest weights.** pp. 11--15

*Summary:* The behaviour of unipotent elements of nonprime order in modular irreducible representations of the classical algebraic groups with large highest weights with respect to the ground field characteristic is investigated. Under some small restrictions on the characteristic, lower estimates for the number of Jordan blocks of the maximal dimension in the images of these elements in such representations (in terms of the group rank and the element order) are obtained. For these groups, a class of their irreducible representations where the image of each unipotent element has at least two Jordan blocks of dimension equal to the order of that element is distinguished.

*Safonov V. G.*

**Two problems of the theory of totally saturated formations.** pp. 16--20

*Summary:* All the groups considered are finite. Each formation is 0-multiply saturated. A formation *F* is called *n*-multiply saturated (*n* ³ 1) if *F* = *LF(f)* and all the nonempty values of *f* are the (*n* - l)-saturated formations. A formation *F* is called totally saturated if it is *n*-multiply saturated for any natural number *n*.
It is proved that the lattice of totally saturated formations of finite groups is modular. Totally saturated formations with Boolean's lattice of totally saturated subformations are described.

*Orlovich Yu. L., Gordon V. S., Werner F.*

**Hamiltonian cycles in graphs of triangular grid.** pp. 21--25

*Summary:* A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. It is shown that all connected, locally connected triangular grid graphs on, at least, three vertices are fully cyclic extendable (with the only one exception). This result generalizes J. Reay and T. Zamfirescu's theorem on the hamiltonicity of 2-connected, linearly convex triangular grid graphs. Recognition of the hamiltonicity for triangular grid graphs in the general case is established to be NP-complett, but the hamiltonian cycle in the connected, locally connected triangular grid graph can be found in polynomial time.

*Minyuk S. A., Metelskii A. V.*

**Criteria for complete controllability and complete constructive identifiability of linear stationary systems of neutral type.** pp. 26--30

*Summary:* The parametric criteria for complete controllability and complete constructive identifiability of linear stationary systems of neutral type are proved on the basis of the duality relation and the constructive solving of the complete identification problem. The results obtained are examplified.

*Timoshpolsky V. I., Samoylovich Yu. A.*

**Use of the conformal mappting theory for solution of Stefan's problem. Solidification of ingots of composite form.** pp. 31--35

*Summary:* A solution of the problem on solidification of ingots of composite configuration obtained using the conformal mapping is described in this work. A comparison of the obtained solution with the experimental data is made and shows the reliability of the technique developed. This technique can be used for designing accessories of foundry processes in producing ingots in different-configuration molds.

*Gorainowa I. A., Radyno Ya. V.*

**Multiplication of the generalized functions in Q**_{p}. pp. 36--41

*Summary:* New algebra of the mnemofunctions of Egorov type is constructed. Egorov construction is shown to be natural in the case of the p-adic domain. The linear space of p-adic distributions is embedded into the algebra of the mnemofunctions with operations of multiplication and convolution. Thus, all distributions (to be exact, the corresponding mnemofunctions) can be multiplied. The embedding is in a perfect agreement with the operations of multiplication and convolution on Shwartz-Bruhat's subalgebra of locally constant functions.
The distributions of embedding and multiplication are examplified.

**ФИЗИКА**

*Vereshchagin M. N., Ostrikov O. M.*
**Quadrupole disclination model of amorphous material.** pp. 42--44

*Summary:* A quadrupole discline model of amorphous material is developed. Stress field and admixture distributions in metal a glass are calculated.

*Goncharenko A. M.*

**Propagation of the space-time solitons in nonlinear meda.** pp. 45--47

*Summary:* It is shown that taking into account the fourth-order field dependence optical index one has stable space-time solitons in Kerr's materials as in a saturating nonlinear medium.

*Barun V. V., Ivanov A. P.*

**Comparison of the radial spreading of light and thermal fields in a laser-irradiated biological tissue.** pp. 48--52

*Summary:* Effective radial sizes of a light beam and a zone with elevated temperature at varying depths in biological tissues are calculated from the analytical solutions to the radiative and heat transfer equations. Applicability limits of the separation of space variables of the source function of the thermal problem for tissue heating by a laser beam at different wavelengths are estimated.

**ХИМИЯ**

*Zhavnerko G. K., Agabekov V. E., Hulup G. Y.,Bandurko V. I., Hilevskaya K. S.*
**Layer-by-layer self-assembly of "polyelectrolyte-magnetite" thin films.** pp. 53--56

*Summary:* The construction of thin magnetic films by the layer-by-layer method via consecutive adsorption of polyelectrolyte and magnetite both on plane and spherical surfaces has been demonstrated. The possibility of magnetic beads fabrication for the medical applications has been shown.

*Makarevich N. A.*

**Adsorption activity in some modeling approximations of adsorption on nonporous and porous surfaces.** pp. 57--61

*Tsyganova O. V., Kiseleva E. P., Vashkevich I. I., Sviridov O. V.*

**Synergy effect under the binding of a pair of monoclonal antibodies with two conformational epitopes on human tyroid peroxidase.** pp. 62--67

*Summary:* A synergistic effect has been revealed upon the simultaneous binding of two monoclonal antibodies having different epitope specificities with human thyroid peroxidase. The mechanism of the synergistic effect is shown to include the allosteric conformational changes of the antigen molecule which are induced at a peripheral epitope and functionally display in the immunodominant region.

*Khlebnicova T. S., Zinovich V. G., Lakhvich F. A.*

**Synthesis of 2-trifluoroacetylcyclohexane-l,3-diones.** pp. 68--69

*Summary:* An approach to 2-trifluoroacetylcycIohexane-l,3-diones has been developed. The synthesis consists in C-acylation of cyclohexane-l,3-diones, with using 2-trifluoroacetylimidazol as an acylating agent. The synthesis of 2-trifluoroacetyl-5,5-dimethylcyclohexane-l,3-dione is described.

**БИОЛОГИЯ**

*Voluevich E. A., Buloichik A. A., Borzyak V. S.*
**Expression of the introgressive genes of resistance to biotrophic fungal pathogenes in common wheat genome.** pp. 70--72

*Summary:* Effective, perhaps, new seedling genes of resistance to brown rust and powdery mildew expressed in common wheat genome are revealed on the chromosomes of different cereals species.

*Denisov A. A., Cherenkevich S. N., Kulchitsky V. A.*

**Associative induction of long-term synaptic potentiation in the CA1 field of the rat hippocampal slice in vitro.** pp. 73--76

*Summary:* A technique for associative induction of long-term synaptic potentiation in the CA1 field of rat hippocampus in vitro involving several extracellular microelectrodes is proposed. The induction of the potentiation is based on single stimulation of the test input simultaneously with the activation of the depolarizing input by means of four stimulating pulses. The methods of stimulation and registration can be applied for several groups of synapses, allowing one to reveal homo- and heterosynaptic effects.

*Mozgova G. V., Orlov P. A., Shalygo N. V., Trukhanovets N. L.*

**Possible albinism mechanisms in wheat anther culture.** pp. 77--80

*Summary:* The processes accompanying the formation of albino regenerant plants in wheat anther culture are analyzed. Possible albinism mechanisms are considered.

*Nikolaichik Y. A., Ovchinnikova T. V., Valentovich L. N., Gubich O. I., Sholukh M. V., Evtushenkov A. N.*

**DespE protein is translocated by phytopathogenic bacteria Erwinia carotovora subsp. Atroseptica into the cells of Nicotiana tabacum and is required for the induction of the hypersensitive reaction.** pp. 81--85

*Summary:* We have investigated the role of DspE, one of the proteins secreted from *Erwinia carotovora* subsp. *atroseptica* cells via the type III secretion system, in the induction of the hypersensitive reaction in *Nicotiana tabacum* and *Vicia faba* plants. Inac-tivation of the *dspE* gene makes *Erwinia carotovora* subsp. *atroseptica* unable to induce the hypersensitive reaction in tobacco, but not in broad beans. We demonstrate by the adenylate cyclase reporter technology that the N-terminal part of DspE contains the translocation signal and enables the delivery of the chimeric DspE-Cya protein into tobacco cells. These data allow us to conclude that DspE is the first typical avirulence protein described for *Erwinia carotovora* that is translocated into plant cells and is responsible for the induction of the hypersensitive reaction during specific recognition of pathogen by a resistant plant.

*Shakhbazau A. V.*

**Expression and inheritance of bacterial endochitinase transgene in tobacco plants.** pp. 86--88

*Summary:* Antifungal genes of microbial origin, in particular chitinases, are considered as a promising tool to increase the pathogen resistance in transgenic plants. Within this work, the plant expression vector carrying endochitinase from *Serratia plymuthica* is created and used to produce an agrobacterial transformation system and, consequently, transgenic tobacco plants. Transgene presence and expression are confirmed using PCR and RT-PR, respectively. Expression of bacterial endochitinase in tobacco markedly inhibits the growth of fungal pathogen *Fusarium oxysporum*. The vector system carrying chitinase from *Serratia plymuthica*, antifungal effect of which is shown within this research, will be further used for transformation of agricultural crops in order to improve their pathogen resistance.

*Kvitko O. V., Sheiko Y. I., Koneva I. I.*

**Analysis of the infinite proliferation of the immortalized cell line with the aid of vital videomicroscopy.** pp. 89--93

*Summary:* The interrelation between the clonal proliferation and the abnormalities of mitotic divisions in the immortalized cell line established from the mouse embryo has been studied with the aid of the computerised microscopy of living cells. 3 mitoses with three daughter cells (instead of two cells in normal divisions) and 7 asymmetric mitoses which generated two daughter cells of conspicuously different sizes were registered among 71 mitotic divisions in the individual cell genealogy. Abnormal mitotic divisions either did not slow the proliferation in cell clones compared with progenies of cells that divided by means of normal mitoses or were followed by the acceleration of divisions in consecutive cell generations. These data suggest that abnormal mitotic divisions may contribute to the maintenance of the immortalized state by means of the generating chromosomal instability.

**НАУКИ О ЗЕМЛЕ**

*Garetsky R. G., Karatayev G. I., Dankevich I. V.*
**Isostatic adjustment of the lithosphere of Belarus.** pp. 94--98

*Summary:* In the article it is shown that the formation of the intricate structure of Earth's crust of Belarus is conditioned by two tectonophysics processes: isostasy in the upper part of the lithosphere and plutonic processes in astenosphere.

*Arkhipova A. A., Naidenkov I. V.*

**Metamorphism of rocks from the lower precambrian amphibolite-gneissic and blastomylonite complexes of Belarus.** pp. 99--103

*Summary:* New estimates of the rock metamorphism parameters were obtained from the blastomylonites, diaphthorites and amphi-bolite-gneissic complex (Ozery, Peretoka and Yurovichi strata) of the crystalline basement of Belarus. All these rocks were metamorphosed under the conditions proper to the high-temperature part of the epidote-amphibolite facies -- the lower-temperature part of the amphibolite facies of moderate pressure. Metamorphism temperatures varied from 530 to 650 °C and pressures -- from 2.8 to 7.8 kbar.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Zhdanov V. L., Zhukova Yu. V., Isaev S. A.*
**Influence of the outer shell geometry on the aerodynamic characteristics of a circular cylinder in the laminar flow at Pr~1.** pp. 104--108

*Summary:* Numerical results on gas flow past a circular cylinder-to-shell system at the Prandtl number Pr~l are presented. The used numerical method and computational grids are described. In the present article it is shown how the cylinder drag and the coefficient of a lifting force amplitude depend on the angular coordinates of the shell. Also, the influence of the shell geometry on the cylinder contour distributions of the pressure and surface friction coefficients and their root-mean-square deviations is found. The obtained results are compared with the identical ones for the shell-free cylinder.

*Kazakov P. P., Prokopchuk N. R.*

**Rapid method of estimation of the thermal stability of polymers.** pp. 109--113

*Summary:* The method allowing quickly and efficiently to estimate the thermal stability of polymers is developed. The method has been applied for research of granulated poly(ethylene terephthalate) and polyester fibers. The dependence of the thermal stability of a polymer on the conditions of its synthesis and on the production parameters of technical yarns is revealed.

*Khudoley A. L., Goman A. M.*

**Mechanics of contact shaft-coated bearing interaction.** pp. 114--118

*Summary:* Contact interaction of the shaft with the slide bearing is examined from the position of the strained state mechanics. The model for describing elastic contact interaction is proposed. The antifriction layer of a bearing is simulated as an elastic base operating in uniaxial compression according to the model. The problem on the impression of the shaft into the antifriction layer of limited thickness is solved. The special feature of the examined case is an insignificant difference in the radii of the contacting bodies and the commensurability of the contact area with their sizes. The dependence for determining the angle characterizing the half-width of the contact area is proposed. The value of the elastic impression of the shaft into the antifriction layer is determined. The law of the contact pressure variation, making it possible to determine the value of pressure for any contact point, is obtained. The relationship between the contact pressure and the value of wear, eccentricity and adhesion strength of a coating is established. The dependence for determining the permissible loading of the antifriction layer of the slide bearing is proposed. It is graphically shown that the decrease of the thickness of coating and the increase in the eccentricity leads to a reduction in the value of the permissible loading of an antifriction layer.

*Bazylev N. B., Bratchenia A. M., Lavinskaya E. I., Martemianov S. A., Fomin N. A.*

**Digital laser anemometry in micro channels of advances fuel cells.** pp. 119--124

*Summary:* It is shown that the digital laser dynamic speckle photography is an effective tool for quantitative flow diagnostics in micro channels of advanced fuel cells. A simple theory of dynamic statistics of speckle fields has been developed and necessary mathematical relations are presented. The software developed allows reconstructing as much as 250 000 velocity vectors in the 2d area of 20 x 30 square millimeters using optical magnification *M* = 1. The obtained results confirm the high temporal and spatial resolution of the techniques and prove the possibility of the real-time operation. Using the presented scheme, a spatial resolution of about 100 urn has been achieved. It is demonstrated that the noise reduction is an essential part of the speckle-image analysis. The software developed allows noise filtration both under direct evaluation of the correlation functions and in the Fourier space with the use of the FFT.

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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *12 ноября 2006 г.*

Создана при участии Игнатия И. Корсака

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