# Доклады Национальной академии наук Беларуси, 2003, Том 47, No.4

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2003, Том 47, No.4

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Uss A. T.*
**Homotopy classification of four-dimensional analogues of the system of the Cauchy-Riemann theorem with real coefficients.** pp. 5--9

*Summary:* A homogeneous system of the four differential equations of order 1 with real constant coefficients in **R**^{4} is called Cauchy-Riemann's analog if each solution's component satisfies Laplace equation in **R**^{4} . It is proved, that the number of homotopic components for set of all Cauchy-Riemann's analogs is 4. The example of Cauchy-Riemann's analog for which fulfill the following properly is carried out. If W Ì **R**^{4} is a region with smooth boundary *d*W then there no exists boundary values do not exist on *d*W so that the boundary-value problem for W satisfies Lopatinskii condition.

*Radyna Ya. M.*

**Mnemofunctions of Egorov type on ***Q*_{p}. pp. 10--14

*Summary:* A new algebra of mnemofunctions of Egorov type is presented. Egorov construction is shown to be natural in case of
*p*-adic domain. Linear space of *P*-adic distributions is embedded into the algebra of mnemofunctions with operations of multiplication and convolution. Thus all distributions (to be exact, corresponding mnemofunctions) can be multiplied. The embedding is in a perfect agreement with operations of multiplication, convolution, and Fourier transform on subalgebra of locally constant functions of Shwartz--Bruhat. Examples of distribution embedding and multiplication are given.

*Yadchenko A. A.*

**On values of complex irreducible characters of finite groups.** pp. 15--16

*Summary:* In this paper, we establish some properties of values of irreducible complex characters of finite groups on elements of the centers of their Sylow subgroups.

*Kilbas A. A., Shchetnikovich E. K.*

**Abelian theorems for the modified Laplace--Hankel transform.** pp. 17--21

*Gabasov R., Kirillova F. M., Kavalionak N. N.*

**Optimal control of linear systems by Lipschitzan controllers.** pp. 22--25

*Summary:* A linear problem of optimal indirect control by Lipshitzan controllers is under consideration. Taking into account specific features of the Lipshitzan controller, optimality conditions and an algorithm for feedback control synthesis are obtained.

*Smazhevskii R., Pylyak D., Sheshko M. A.*

**Inverse of singular integrals with Cauchy kernels in case of infinite domain of integration.** pp. 26--30

*Summary:* In this paper, general decisions in the class of Holder functions are built and the ways of the unique over the simplest singular integral equations with Cauchy kernel are found in case when integral domain is a material positive half axis, material axis, quadrants, or the whole plane of *R*^{2}.

*Monakhov V. S.*

**Remarks on maximal subgroups of finite groups.** pp. 31--33

*Summary:* A new property of maximal subgroups of finite soluable groups is obtained.

*Mironenko V. V.*

**Even integrals of differential systems.** pp. 34--37

*Summary:* We obtain some existence conditions for even in time integrals of nonautonomous differential systems. On the base of this result, we give a sufficient condition for existence and stability of periodic solutions of periodic differential systems.

*Slepchenkov N. L.*

**On nonexistence of entire solutions of semilinear elliptic equation.** pp. 38--41

*Summary:* Semilinear elliptic equation of the form D*u* = *k*(*x*) *f* (*u*). For this equation, we obtained new conditions of nonexistence of entire solutions.

**ФИЗИКА**

*Zhestkov S. V.*
**On existence of soliton solutions of arbitrary-order system of nonlinear Schrodinger equations.** pp. 42--45

*Summary:* For the system of arbitrary-order coupled nonlinear Schrodinger equations, the soliton solutions are constracted. The necessary and sufficient conditions of existence of these solutions are obtaned. It is shown that the maximum number of solitons in nondegenerate case is 4*L*, where *L* is order of the system.

*Bazylev N. B., Lavinskaya E. I., Naumovich S. A., Rubnikovich S. P., Fomin N. A.*

**Laser sounding of living tissues using near-real time dynamic speckle photography.** pp. 46--50

*Summary:* The basic capability of biophysical processes monitoring in living tissues using quasi-real time dynamic speckle photography technique is demonstrated. Simple engineering expressions describing the dynamics of biospeckle images are shown. Some examples of investigations of strained-deformed state in system "cast stump pin -- tooth root" under load and sub-skin blood microcirculation measurements are discussed.

**ХИМИЯ**

*Kozlov G. V., Burya A. I., Sviridionok A. I., Zaikov G. E.*
**Application of autocorrelation function for analysis of the structure of vitreous polycarbonate.** pp. 51--54

*Summary:* Possibility of autocorrelation function application for description of amorphous polymer structure in terms of irreversible aggregation model is shown.

*Ratko A. I., Romanenkov V. E., Krupenkina Zh. V.*

**Effect of bayerite thermal dehydration on phase composition of porous composite Al/Al**_{2}O_{3}. pp. 55--58

*Summary:* It has been established that at the thermotreatment of the porous composite Al/Al(OH)_{3}, thermal dehydration of
bayerite and its conversion into active aluminum oxide leads to increase in penetration of porous cover on the panicles of aluminum for the molecules of water. The cyclic treatment removes diffuse limitations, which complicate synthesis of the composite ceramics, and regulates degree of transformation of aluminum.

*Kolnenkov V. P., Samodurov V. P., Klimza S. V., Tarasyuk D. I.*

**Ion exchange of H**^{+} -- Ca^{2+}, Mg^{2+}, K^{+}, Na^{+} in the clays over tritiated water. pp. 59--62

*Summary:* It has been shown that hydrogen ion selectivity is sufficiently high in case of exchanges of H^{+}/Ca^{2+}, H^{+}/Mg^{2+}, H^{+}/Na^{+} and H^{+}/K^{+} in bentonite, askangel, and palygorskite. Thermodynamic constants of ion exchange affinity to H^{+} in these clays have been calculated. In comparison to normal water, tritiated water as a dissolvent changes selective properties of hydrogen ions in case of exchanges of H^{+}/Ca^{2+} in askangel and H^{+}/Na^{+} in bentonite. In the first case, hydrogen ion selectivity reduces, and in the second case, it increases.

**БИОЛОГИЯ**

*Alekseichuk G. N., Groot S., Bergervoet J.*
**Desiccation tolerance loss in germinating orthodox cabbage seeds: role of cell cycle activation.** pp. 63--66

*Summary:* Simultaneous flow cytometric measurements of chromatin condensation and DNA replication were performed on germinating cabbage (Brassica oleraceae L.) seeds to study the changes in DNA organization associated with desiccation tolerance loss. It was determined that germination of cabbage seeds correlated to gradual decondensation of chromatin. The initiation of DNA replication started in seed axis just before radicle protrusion and is connected to cell water status. Desiccation of germinated seeds resulted in a changed ratio of *G*_{1}/*G*_{2} in the axis only during 'transition' period, when seed became intolerant to desiccation. Increased decondensation of nuclear DNA might be one of factors involved in loss of desiccation tolerance in seeds upon radicle protrusion.

*Titok M. A., Logodich A. V.*

**Molecular and genetic analysis of rep region of the theta-type plasmid pBS72 from Bacillus subtilis.** pp. 67--70

*Summary:* We have scquenced rep region of the theta-type plasmid pBS72 from Bacillus subtilis. The sequenced region (3081 bp.) contains four open reading frames, one of which (orf1) determines the synthesis of an initiation protein. The rep protein of the pBS72 plasmid is unique and shows homology with the DnaA protein of chromosomal origin. Functional analysis has demonstrated that both the rep gene and oriV (origin of vegetative replication) were required for replication of pBS72. We have isolated the mini-replicon of pBS72 which could be utilized for construction of molecular cloning vectors for Gram positive bacteria.

*Bulko N. I.*

**On effect of "interspecies differences" in plants as **^{137}Cs deposition in forest phytocenosis decreases. pp. 71--73

*Summary:* Considered in the paper are influences of interspecies relationships between woody plants comprising main storeys of forest phytocenosis on ^{137}Cs accumulation in principal timber species in Belarus growing in radiation-contaminated mixed two-species forest stands by comparison with single-storeyed stands consisted of the same species. The effect of interspecific distinctions was revealed in woody plants as ^{137}Cs deposition in forest phytocenosis decreased. This effect was governed by the joint action of root systems of trees, the distribution of the available ^{137}Cs along the vertical soil profile and the effect of root exometabolites of the trees.

*Morozov O. V.*

**Selection importance of the hybrid Vaccinium uliginosum L. x Vaccinium vitis-idaea L.** pp. 74--76

*Summary:* Considered in the paper are influences of interspecies relationships between woody plants comprising main storeys of forest phytocenosis on ^{137}Cs accumulation in principal timber species in Belarus growing in radiation-contaminated mixed two-species forest stands by comparison with single-storeyed stands consisted of the same species. The effect of interspecific distinctions was revealed in woody plants as ^{137}Cs deposition in forest phytocenosis decreased. This effect was governed by the joint action of root systems of trees, the distribution of the available ^{137}Cs along the vertical soil profile and the effect of root exometabolites of the trees.

*Hihinyak Yu. G.*

**Water temperature of water bodies and its relationship with the atmospheric pressure.** pp. 77--80

*Summary:* In the paper, a relationship between temperature of upper water layers in water bodies of different types and the atmospheric pressure is shown. The thermobaric relationship is proved by example of the rivers Western Dvina, Vilia, and
Mukhavets flowing in the northern, central, and southwestern part of Belarus. It is shown that a decrease in temperature in water bodies in mid-June ("temperature depression") is observed in all types of native and subjected to anthropic impacts water areas. A "temperature depression" revealed correlates to a change of the atmospheric pressure and some biological processes in biohydrocenosises.

*Brichkova G. G., Maneshina T. V., Zui S. I., Krasovskaya L. I., Hills M., Hill L., Spivak S. G., Kisel M. A., Jones J. J. D., Sorokin A. P., Kartel N. A.*

**Transgenic plants for phytostabilization of metal-contaminated sites.** pp. 81--83

*Summary:* At present, man encounters with a wide range of ecological issues. One of the approaches that can be applied for their solving is to create transgenic plants that would effectively remediate contaminated territories. With the help of rhlA gene, which contributes to the biosynthesis of rhamnolipids, we have created transgenic Nicotiana tabacum plants that demonstrate tolerance to heavy metals. Our plants can grow and produce seeds in soils with copper content exceeding Ig per 1 kg of wet soil. The plants with rhlA gene act as perfect metal excluders. Therefore, they could be used for soil phytostabilization.

*Titok V. V.*

**Bioenergy heterosis conception.** pp. 84--89

*Summary:* A systemic physiologo-biochemical approach to evaluation of breeding material, enabling establishment of cause and effect relationship between bioenergetic parameters and productivity in the heterosis, was realized. Dependence of phenotypic manifestation of morphological traits on the value of integral parameters of energy metabolism was revealed for the first time in various crops that corroborated the relationship between genetic and bioenergetic processes. The regularities revealed point to a key role of macroergic compounds and reducing equivalents in regulation of growth processes, development and formation of productivity in the heterosis in mono- and dicotyledonous plants.
The data obtained are the basis for working out principles of an original conception of heterosis - hypothesis of bioenergy balance.

*Derengovskaya R. A., Kovalevskaya R. Z.*

**Chlorophyll sedimentation in mesotrophic polymictic lake.** pp. 90--95

*Summary:* Data on suspended particle chlorophyll-a sedimentation in the mesotrophic polymictic lake Naroch are given. The vertical flux of paкеiculate chlorophyll-a, settling velocity, loss rate and turnover time of chlorophyll-a due to sedimentation processes were evaluated on the basis of 52 experiments, which were carried out during 8 years in summer months. According to the specific content of chlorophyll-a in seston and sedimenting particulate material, the conclusion was made that the settling suspended matter qualitatively differs from seston by lower content of autotrophic component.

*Zorin V. P., Sosnovskii S. L., Zorina T. E., Khludeyev I. I., Bolotina L. N., Guillemin F.*

**Kinetic characteristics of foskan redistribution in model lipid membrane.** pp. 96--99

*Summary:* The study deals with the redistribution of porphyrin sensitizer meta-tetra(hydroxyphenyl)chlorin (mTHPC) between model membranes. The kinetics of the mTHPC redistribution is shown to be extremely slow as compared to other porphyrin sensitizers. The results obtained are of spesial significance for understanding the pharmacokinetic behaviour of sensitizers introduced within lipid vesicles during for photodynamic therapy.

**НАУКИ О ЗЕМЛЕ**

*Konishchev V. S.*
**Role of mantle, crust, and intramantle faults in formation of the structure of the Pripyat Paleorift.** pp. 100--103

*Summary:* It was proved that 62% of the regional stretching of the Earth's crust in the Pripyat Paleorift was compensated by movements along the mantel faults and only 38% along the crust faults.

*Shkuratov V. I., Makhnach A. S.*

**Paleogeographic conditions of Vendian sedimentation in Belarus.** pp. 104--106

*Summary:* The territory of Belarus in Vilthanian time of the Early Vendian was covered by glaciation. The glaciation caused the accumulation of a thick (up to 483 m) comlex of a continental covering glacial formation with its peculiar series of glacial fluvioglacial and limnoglacial facies.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Vereshchagin M. N., Shepelevich V. G., Ostrikov O. M., Tsybrankova S. N.*
**Influence of isochronous annealing on development of strips of shear in amorphous ferro-alloys.** pp. 107--109

*Summary:* Influence of heat treatment on development of strips of shear in amorphous materials is investigated.

*Kozhevnikova G. V.*

**Fields of lines of sliding with irregular distribution of contact strain.** pp. 110--113

*Summary:* The possibility of application of graphical method of construction of fields of lines of sliding for the solving tasks of metal processing with pressure with irregular distribution of contact strains is proved theoretically.

*Vysotsky M. S., Evgrafov A. N., Romanenko G. A., Ilyin E. V.*

**Influence of aerodynamic screen type on vehicle streamlining.** pp. 114--117

*Summary:* The screen type influence on the automobile testing results in wind tunnel is considered. It is determined that boundary level forming on stationary screen influences essentially on the aerodynamics of the automobile, it is necessary to make corrections taking into account influence of this factor.

*Chichko A. N., Yatskevich Yu. V., Chichko O. I., Sobolev V. F.*

**New approaches in computer modelling of shrinkage porosity for three-dimensional crystallizing castings.** pp. 118--122

*Summary:* The models for calculation of porousity forming at crystallization process of space object with given temperature and thermo-physical properties are offered. Computer calculations of porousity forming in complicated industrial castings crystallizing in metal mould are performed.

/ 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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