# Доклады Национальной академии наук Беларуси, 2003, Том 47, No.1

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2003, Том 47, No.1

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Lomovtsev F. E.*
**The Cauchy problems for factorized operator-differential equations with variable domains of non-smoothable coefficients.** pp. 5--9

*Summary:* The existence and uniqueness of strong solutions of the Cauchy problems for factorized operator-differential equations with variable domains of non-smoothable coefficients are proved.

*Akulich E. V., Lebedev A. V.*

**The symbolic logic for singular integral operators with different oscillating coefficients.** pp. 10--14

*Summary:* The symbolic calculus for elements of the algebra generated by singular integral operators with oscillating coefficients is built. In terms of this calculus the conditions for an element of the algebra to possess the Fredholm property are obtained.

*Matus P. P., Melnik R. V. N., Rybak I. V.*

**Fully conservative difference schemes for the nonlinear models for the dynamics of materials with shape memory.** pp. 15--17

*Bazylev D. F., van Geel Ya., Yanchevskii V. I.*

**The local Pfister conjecture for W-algebras with a special ramification locus.** pp. 18--20

*Summary:* The local Pfister conjecture for W-algebras is proved in the case of algebras with a special ramification locus. More precisely, a criterion for a special class of splitting fields of quaternion algebra (*t, x*) over R((*t*))(*x*) is obtained, with the help of which the local Pfister conjecture is proved.

*Tikhonov S. V., Yanchevskii V. I.*

**The Hasse principle for Witt groups of function fields of special elliptic curves and 2-torsion of their Shafarevich--Tate groups.** pp. 21--24

*Summary:* The validity of the Hasse principle for Witt groups of function fields of special elliptic curves and Shafarevich--Tate groups of function fields of conics defined over number fields is proved.

*Gabasov R., Kirillova F. M., Pavlenok N. S.*

**Maximal excitation of dynamic systems due to Lipschitzian control.** pp. 25--28

*Summary:* The problem of maximal excitation of linear nonstationary systems in the class of continuous bounded controls with bounded derivatives is under consideration. The optimality and suboptimality criteria for an open-loop solution to this problem are suggested.

*Kilbas A. A., Marzan S. A.*

**Nonlinear differential equations of fractional order in weighted spaces of continuous functions.** pp. 29--35

*Summary:* The Cauchy -- type problem for nonlinear differential equation of complex order with Riemann-Liouville derivatives in weighted spaces of continuous functions is studied. The equivalence of this problem and of the Volterra nonlinear integral equation is established. The existence and uniqueness of the solution to the above Cauchy -- type problem are proved using the method of successive approximations. The corresponding statemens for the Cauchy problem for ordinary differential equation are presented.

*Demidenko V. M., Gordon V. S., Proth J.- M.*

**Conditions of polynomial solvability and upper bounds for the optimum of the traveling salesman problem.** pp. 36--40

*Summary:* A system of linear inequalities is described that defines the set of real-valued matrices, for which a solution to the assignment problem with one fixed assignment gives an upper bound for the optimum value of the traveling salesman problem (TSP). This allows one to extend the result obtained for the TSP on strictly-upper-triangular matrices, for which E. Lawler has proved the polynomial solvability of the TSP.

*Beresnevich V. V.*

**The distribution of rational points close to the planar curves and simultaneous Diophantine approximations.** pp. 41--43

*Summary:* The best possible lower bound for a number of rational points with bounded denominators close to planar nondegenerate curves is proved. Such curves are proved to be of Khintchine type for divergence. The exact value for the Hausdorff dimension of simultaneously n-approximable points is also computed.

*Dymkov M. P.*

**Controllability of linear repetitive systems.** pp. 44--47

*Summary:* Based on the controlled map approach the controllability criteria for linear nonstationary repetitive control systems are obtained.

*Suprunenko I. D.*

**The second Jordan block and recognition of representations.** pp. 48--52

*Summary:* It is proved that if the image of an irreducible rational representation of a classical algebraic group of rank > 1 in characteristic *p* > 0 contains an element of order *p* with a difference between the size of the maximal Jordan block and that of the second maximal block larger than 6, then this image coincides with the standard realization of the group.

**ИНФОРМАТИКА**

*Batura M. P., Ptichkin V. A.*
**Analysis of the accuracy of a phase-controlled system by the method of momental equations.** pp. 53--56

*Summary:* When the method of momental equations is used for studying nonlinear systems, all nonlinear characteristics must be approximated by polynomials. To do this, it is suggested to use Hermite's polynomials with indefinite parameters that can be identified with the first moments of the coordinates being investigated. This enables one to improve the investigation accuracy using a small number of momental equations.

**ФИЗИКА**

*Red'ko V. P., Khomchenko A. V., Yurevich V. A.*
**Self-modulation of laser radiation reflected from a two-layered resonance medium.** pp. 57--61

*Summary:* The effect of self-modulation of CW laser radiation at reflection (transmission) from a thin-film structure has been found and simulated. The modulation depth is ~ 10% at a wavelength of 633 nm.

*Kozlov G. V., Burya A. I., Sviridenko A. I., Zaikov G. E.*

**An analogy between the electric conductivity-deformation dependences for dispersions of isolator-metal and cold flow stress-deformation ones for polymers.** pp. 62--64

*Summary:* The possibility is shown how to describe the cold flow of polymers in the framework of the fractal model for electrical conductivity . Such a description is possible only using the cluster model of amorphous polymers.

*Aleinikov D. V., Tolkachev E. A.*

**Vector parametrization of the Kustaanheimo--Stiefel transformation and static zero modes of the Dirac operator.** pp. 65--68

*Summary:* A general expression for zero modes of the static massless Dirac operator is obtained using the quaternion form of the expressions for planar three-dimensional rotations in vector parameterization and sections of the Kustaanheimo--Stiefel (Hopf) bundle.

*Kukhto A. V., Kolesnik E. E., Ritchik D. V.*

**Calculatiuon of a total electron scattering cross-section on complex organic molecules.** pp. 69--72

*Summary:* For 1,4[bi-(2,5-phenyloxazolyl)-benzene cross-sections of total, elastic and inelastic electron molecular interactions are calculated using the additivity method with regard for the geometry factor in the range from 10 to 100 eV. The value of the total cross-section is essentially lower than in the case of the Bethe-Born approximation but behaviour is the same. The contribution of exchange and polarization interactions at rather high electron energies is not essential and grows at low energies. The shielding effect at rather low energies results in decreasing the cross-section. The predicted elastic scattering crosssection is in a good agreement with the available experimental data.

**ХИМИЯ**

*Matulis V. E., Ivashkevich O. A.*
**Quantum-chemical ab initio study of the electronic structure and geometry of copper clusters using MCQDPT2 method.** pp. 73--77

*Summary:* The electronic structure and geometry of neutral and anionic copper dimers, trimers and tetramers are investigated using the *ab initio* MCQDPT2 (MCSCF based on MP2) method with the core potential and the corresponding valence basis set. For the assignment of cluster geometry to be assigned, the calculated vertical detachment energies (VDE) and energies of excited states the neutral clusters in the geometry of anions with respect to the ground state (T_{e}) are compared with the observed photodetachment spectroscopic pattern. Binding energies per atom and vertical ionization potentials (IP_{v}) of neutral species are calculated. The theoretical T_{e} are found to agree with the experimental data. The obtained values of VDE and IP_{v} need to be scaled to bring them into agreement with the experimental data. The data on the electronic structure and geometry of copper clusters are compared with the corresponding data for silver species. The accuracy of the calculations is found to be nearly equal for both metals, suggesting that the MCQDPT2 method can be used for bimetallic copper-silver clusters.

**БИОЛОГИЯ**

*Plaks A. V.*
**The specific features of hydraulic conductivity of vacuolar membranes.** pp. 78--81

*Summary:* Experiments on separate determination of hydraulic conductivity (*Lp*) of a tonoplast and a plasma membrane of *Nitella* cells by using tonoplast-free fragments are conducted. The tonoplast hydraulic conductivity Lp exceeded that of the plasma membrane 4.3 times and exceeded the *Lp* of a lipid bilayer by two orders to amount to 2.68 • 10^{-6} m • s^{-1} • MPa^{-1}. The results obtained favors both the facilitated transfer of water through the vacuolar membrane and the localization of specific proteins (aquaporins) in it. The conclusion is made that the tonoplast obviously performs two important functions in plants, one of which is the osmoregulation on a cell level and the other is the transcellular transfer of water on the level of tissue and entire plant.

*Shakhabazov A. V., Panyush A. S., Zabenkova K. I., Kartel N. A.*

**Introduction of AC/DC system elements into S. Chacoense plants: stage I of transposon tagging in wild potato.** pp. 82--85

*Summary:* Wild analogues of agricultural crops are a promising source of resistance genes against a variety of pests. Search for Colorado Potato Beetle resistance genes is of high importance in potato biotechnology, since the spread of virulent races of this pest is very possible. We involved the transposon tagging strategy with the use of the maize Ac/Ds transposon system to isolate leptines biosynthesis responsible genes which confer wild potato S. chacoense resistance to CРВ. Within this work the populations of Ds- and Ac/Ds-transformants were created which are a perspective material for analysis and selection of samples carrying insertion mutations of gene of interest, with the purpose of its isolation and further introduction into cultivated potato accessions.

*Grushetskaya Z. E., Poliksenova V. D., Lemesh V. A.*

**RAPD evaluation of the genetic variability of tomato through resistance to tomato leaf mould.** pp. 86--89

*Summary:* The extent of a genetic diversity among wild and cultivated tomato accessions, previously identified as highly resistant to tomato leaf mould, was evaluated by RAPD. Genetic dissimilarity values between genotypes calculated by the RAPD data were used to produce a dendrogram of relationships between accessions using the neighbour-joining method (NJ). These results will be useful in the identification of suitable parents for the development of mapping populations for tagging tomato leaf mould resistance genes.

*Veresov V. G.*

**A stochastic analysis of through passage of Ca**^{2+} and Na^{+} ions through a calcium channel using the 2+1 model. pp. 90--95

*Summary:* Based on the physical grounds and experimental data a model of a calcium channel was proposed. This model involved a pore lined with two binding sites, where negatively charged carboxylates of P-region glutamates in repeats I (El) and III (EIII) were implicated to form the outermost binding sites, while carboxylate of the side chain of glutamate in repeat IV (EIV) was involved in formation of the innermost binding site ("2+1 model"). The behavior of the model channel has computed by the Brownian dynamics technique taking into account multiion occupancy of a pore. The simulations show that the model allows one to provide a reasonably good fit to experimental data.

*Kostin D. G., Kozlova N. M., Slobozhanina E. I.*

**The influence of calcium ions on transport of glutathione-S-conjugates in human erythrocytes.** pp. 96--98

*Summary:* The influence of calcium ions on transport of glutathione-S-conjugates in human erythrocytes is studied. It is shown that incubation of erythrocyte with 1 mM/L CDNB (15 min, 37 ° C) results in forming DNP-SG-conjugates in both intact control cells and erythrocytes pretreated with Ca^{2+}-ionophore A23187 (30 min, 37 ° C). It is found that increasing the intracellular calcium concentration 1.5--1.6 time decreases the export of glutathione-S-conjugates by 20 % as against control cells. Different variants of the interpretation of the obtained results are discussed.

*Kabachevskaya E. M., Lyakhnovich G. V., Volotovsky I. D.*

**The influence of light on the activity of phospholipase D in vivo.** pp. 99--103

*Summary:* It is shown that in vivo photoreduction of the oat phospholipase D activity by red light addressed to phytochrome is mediated via G-proteins. It is also found that phospholipase D activities in etiolated and illuminated seedlings differ in their K_{m}, pH-dependence, substrate and ions preferences.

**НАУКИ О ЗЕМЛЕ**

*Bordon V. E., Matveev A. V., Olkhovik E. Т., Anoshko Ya. I., Bordon S. V., Savchik S. F.*
**Clarkes of rock-forming elements in Quaternary deposits of Belarus.** pp. 104--106

*Summary:* The data on the average content of oxides and clarkes of rock-forming elements are defined in different lithological types of Quaternary formations, in surface deposits and in Quaternary thickness as a whole.

*Levykh N. N., Veretennikov N. V., Samodurov V. P.*

**The garhet composition of the volcanic rocks in the Uvarovichi area.** pp. 107--108

*Summary:* Garnets of the volcanic rocks and their xenolites in the paleovolcanic beds and Middle-Jurassic basal horizon of the Uvarovichi area are studied. The garnet chemical and minal composition reveals the low PT-conditions of their forming and, thus, the lack of a garnet and diamond genetic relationship.

*Konishchev V. S.*

**Paleogeodynamics and late Devonian magmatism of the Pripyat--Dnieper--Donets rift zone.** pp. 109--113

*Summary:* It is shown that alkalic ultrabasic, basic, average and silicic rocks of the volcano-pluton complex were formed as a result of cristal differentiation of alkalic ultrabasic magmas.

*Yakubovskaya T. V., Zhukovskaya T. V.*

**The Ludwigia L. genus in the Pliocene of Belarus.** pp. 114--118

*Summary:* The belonging of fossil seeds defined as Hypericum coriaceum Nikit. to some species of Ludwigia L. genus is proved. Two new species of this genus -- L. praepalustris T. V. Jakub. et Zhuk and L. zinovii T. V. Jakub. et Zhuk from the Pliocene of Belarus are described.

*Golberg M. A., Volobueva G. V., Komarovskaya E. V., Kuleshova I. Yu.*

**Main climatic changes in Belarus in the XX century.** pp. 119--123

*Summary:* This article presents the results for air temperature, wind speed and the quantity of precipitations on the territory of Belarus in the 20th century. By the end of the 30s of the 20th century the quantity of precipitations during a year decreased approximately by 10%. Since the 70s of our century there was seen a marked decrease in speed wind by 0.5 m/sec. Since 1989 there was a sharp increase of temperature. An annual temperature for the period 1989--2000 increased approximately by 1° in comparison with the previous period.

/ Издания академии / Научные журналы / К началу страницы

Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *15 ноября 2006 г.*

Создана при участии Игнатия И. Корсака

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