# Доклады Национальной академии наук Беларуси, 2005, Том 49, No.4

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2005, Том 49, No.4

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Suprunenko I.D.*

**Unipotent elements of prime order in representations of exceptional algebraic groups: the second Jordan block.** pp. 5--9

*Summary:* Sizes of the second maximal Jordan block in the images of the elements of order *p* in irreducible rational representations of the algebraic groups of types E_{r} and F_{4} over a field of characteristic *p* > 0 are found. These results and similar ones for the classical groups obtained by the author earlier yield a characterization of the standard realizations of such groups in characteristic *p* based on the presence of the elements of order *p* with a big difference between the size of the maximal Jordan block and that of the second maximal one.

*Knyazhishche L.B.*

**Yorke inequalities in the 3/2 stability condition for delay equations.** pp. 10--12

*Summary:* A new version of the 3/2 stability theorem is stated for one-dimensional differential-delay equations. It is supposed that the Yorke conditions are fulfilled on some subset in the space C.

*Martynov I.P., Mozhdzher G.T.*

**Resonances of higher-order differential equations.** pp. 13--16

*Summary:* Some results on the composition of the roots of the resonance equations for higher-order differential equations are obtained.

*Yevkhuta O.N., Zabrejko P.P.*

**New convergence theorems for Krasnoselskij -- Rutitskij approximations of operator equations in Banach space.** pp. 17--22

*Summary:* The article presents some new convergence and error estimate theorems for Krasnoselskij -- Rutitskij approximations for solving the nonlinear operator equations *f*(*x*) = 0 in Banach space.

*Prokopchuk A.V.*

**Relative Brauer groups for the rational function fields of certain genus one curves over the field of rational numbers.** pp. 23--26

*Summary:* Relative Brauer groups of certain series of genus one curves over the field of rational numbers are described.

*Karaliova E.V.*

**Index calculation of Toeplitz operators with discontinuous oscillating coefficients.** pp. 27--30

*Summary:* The article presents the procedure of index calculation of toeplitz operators with discontinuous oscillating coefficients in terms of operators with piecewise continuous coefficients.

*Gabasov R., Kirillova F.M.*

**Optimal state feedbacks: synthesis and realization.** pp. 31--37

*Summary:* Several types of optimal feedbacks (depending on the volume of the used information on states) through the determined and nondetermined linear control systems are under consideration. Using the dynamic programming their synthesis is made, and on-line realizations of optimal feedbacks are described.

*Savchuk V.F., Matysik O.V.*

**Non-explicit iteration method for solution of the operator equations.** pp. 38--42

*Summary:* A non-explicit iteration method for solution of the operator equations in the Hilbert space is proposed. The method convergence obtained is proved in the case of an *a priori* choice of a number of iterations, and the error estimates are obtained. The cases of the nonuniqueness and the approximately given operator are investigated. For the method under consideration, the opportunity of application of the neighboring approximation rule is substantiated.

*Timoshpolsky V.I.*

**Use of the conformal mapping theory for solution of Stefan's problem. Solidification of ingots and square billets.** pp. 43--46

*Summary:* A solution to the heat conduction and thermal plasticity problem for solidifying ingots and square billets with filets under the III kind boundary conditions is obtained using the conformal mapping method. On the basis of the developed algorithm, the time for complete solidification of a 125x125 mm billet cast on a continuous casting machine is calculated, and comparison of the predicted data with the results of full-scale experiment is made, providing the reliability of the developed method.

*Lepeyev A.N.*

**Existence theorems for weak solutions of one-dimensional homogeneous stochastic differential equations and inclusions with unbounded coefficients.** pp. 47--52

*Summary:* One-dimensional homogeneous stochastic differential equations and inclusions with unbounded coefficients are investigated. The existence conditions are given for weak solutions of equations in the sense of the corresponding inclusions and for weak solutions of the inclusions themselves.

**ФИЗИКА**

*Pilipovich V.A., Esman A.K., Goncharenko I.A., Kuleshov V.K.*
**Optical analog-digital converser based on waveguide ring microresonators.** pp. 53--57

*Summary:* The fast method of analog-digital conversion of optical signals with the use of waveguide ring resonators of micron size and its schematic design are proposed. The results of calculation allowing optimizing parameters of such an optical ADC for specific applications are presented. It is shown that the conversion operating speed of the ADC proposed is defined by the time of steady output signal establishing. For a microresonator of 10 µm radius this time is about 10 ps. In this case, as the conversion is performed in parallel, the device operating speed is substantially enhanced. The analysis of the proposed optical method of analog-digital conversion shows that such an optical ADC can operate with the conversion frequencies above 10^{9} counts per second in a wide spectral range with a moderate number of digits.

*Anishchik V.M., Zhukova S.I., Poliak N.I., Vasil'eva L.A.*

**Phase composition evolution of beryllium bronze implanted with 245 MeV krypton ions at the zone aging stage.** pp. 58--61

*Summary:* The change in the phase composition of beryllium bronze implanted with 245 MeV Kr-ions in the range of 5 • 10^{-4} --5 • 10^{-3} d.p.a. damaging doses at the zone aging stage is studied by transmission electron microscopy.

*Nosenko V.A., Dzjuba A.V., Denis A.T.*

**Special information-measure system.** pp. 62--65

*Summary:* In this article the problem for creation of a special information-measure system for industrial and science domain is examined.

**ХИМИЯ**

*Soldatov V.S., Kosandrovich E.G.*
**New equation for isoplestic curves of ion exchangers.** pp. 66--69

*Summary:* A new equation for isopiestic curves of ion exchangers has been derived using the following assumptions: the total amount of water in the polyelectrolyte at a given relative humidity is equal to that in hydrates and in the free state; the only reason for deviation of the polyelectrolyte--water system from the ideal one is the formation of hydrates; the amount of hydrate water is described by the hydration constants, that of free water, by Raul's law. In the most of cases, the experimental data can be described accounting only for one hydrate. In this case the isopiestic equation contains only two easily determinable parameters, those are the number of water molecules in the hydrate and the hydrate stability constant. Applicability of the new equation is illustrated by several representative examples: sulfonic acid ion exchangers, anion exchangers of different types.

*Litvinko N.M., Kuchuro S.V., Rachuba G.N., Skorostetskaja L.A., Kalinichenko E.N., Zhernosek E.V.*

**Action of phospholipase A**_{2} on chimeras substrates created on the basis of phospholipids and components of nucleic acids. pp. 70--73

*Summary:* Synthesis of new conjugates of modified nucleosides with phosphatidylethanolamine and with phosphatidic acid is carried out. Essential changes in a differential spectrum of hemoglobin are found at enzymatic hydrolysis of conjugates obtained by the phospholipase A2 (PLA2) active form. The hydrolysis rate of obtained conjugates by PLA2 is three times lower than that of natural phospholipides.

**БИОЛОГИЯ**

*Palilova A.N., Shaban O.V., Pavlyuchuk N.V., Akhramenko A.D.*
**Peculiarities of inheritance of X-virus resistance in the F1 generation of potato somaclones selected ***in vivo*. pp. 74--76

*Summary:* The inheritance of the X-virus resistance has bien studied in the F1 generation by analyzing the crossings of potato sornaclones from the collection created at the Institute of Genetics and Cytology of the National Academy of Sciences of Belarus. The analysis of this trait is carried out in the natural infectious background and at artificial X-virus infection. At the analyzing crossings, the *in vivo* selected sornaclones are shown to exhibit various types of segregation in the Fl depending on the direction of the crossing and the genotype of the initial cultivar. A reciprocal effect is revealed in the relation of the resistance trait to this virus. Based on the results obtained, it is concluded that the somaclones different in resistance can arise within a cultivar owing to somatic mutations of this trait during vegetative propagation.

*Soltanov V.V., Komarovskaya L.M.*

**Role of ***E. coll* lipopolysaccharide in the mechanisms of humoral control of the sympathetic efferent neurons activity. pp. 77--80

*Summary:* In acute experiments on white rats anesthetized with thiopental sodium (70 mg/kg, intraperitoneally), it is found that after decentralisation of the stomach by transection of vagus and sympathetic nerves there occur, like in control, the inhibition of the efferent activity of the splenic nerve in response to intragastric application of 1 µg lipopolysaccharide *E. coli*. The results indicate the existence of humoral influences from the stomach to sympathetic efferent neurons.

*Titok M.A.*

**Functional analysis of the ***rep*-region of pMT2 plasmid (IncP-9). pp. 81--87

*Summary:* The replication of the pMT2 plasmid (IncP-9) in *E. coli* absolutely requires the presence of the partitioning region in *cis* in addition to the *rep* gene and *oriV*. It is noteworthy that neither the distance between *rep-oriV* and *par* loci, nor their mutual orientation affects the plasmid replication. Mutations in the *parB* gene abolish the replication. In contrast to *E. coli*, in their natural bacterial host *P. putida* the IncP-9 plasmids maintain themselves relatively stably in the presence of *rep* and *oriV* determinants only.

**МЕДИЦИНА**

*Pinchuk S.V., Lobanok E.S., Vorobey A.V., Kucherov I.L, Podolskaya I.A.*
**Intracellular localization and photosensitizing action of ALA-induced porphyrins in blood system cells.** pp. 88--91

*Summary:* The intracellular distribution of endogenic ALA-induced porphyrins in splenocytes, bone marrow cells of rats, Molt-4/8 cells and the mitochondria state of cells after pigment photosensitized action are investigated. It is shown that under the incubation of cells in the presence of ALA for 4 h the significant quantity of formed porphyrins is localized in mitochondria. Illumination of cells accumulated of porphyrin pigments leads to an increase in the binding by the cells of fluorescent probe rhodamine 123. This effect points to the change of the functional state of mitochondria. The extent of mitochondria damage depends on the type of cells, the time of ALA incubation and the conditions of illumination. In comparison with splenocytes and bone marrow cells, Molt-4/8 cells are characterized by the most accumulation of endogenic porphyrins in mitochondria and by the more expressed changes of these organells after illumination.

*Slobozhanina E.I., Kozlova N.M., Kasko L.P., Kutko A.G., Shorokh I.G., Tkachuk T.M.*

**Biophysical parameters of the amniotic fluid under the pregnancy pathology.** pp. 92--96

*Summary:* Some of the biophysical and biochemical parameters of the amniotic fluid for women with the pathology of pregnancy are studied. It is established that at the pregnancy pathology connected with developing anomalies of a fetus and at pregnancy complicated by Rhesus sensitization, there are a substantial growth of the activity of acetylcholinesterase of the amniotic fluid and a decrease of a level of SH-groups of proteins. At the same time, using lipophilic fluorescent probes the changes in the physical state of lipid components in the amniotic fluid are found. The obtained results will be used for developing biophysical tests revealing the mentioned complications of pregnancy.

*Ilyin I.A., Romanovsky D.I., Urban A.S.*

**Hexaminate: the general action on the organism and toxic properties at unitary and regular application.** pp. 97--102

*Summary:* The toxicity and tolerability of Hexaminate -- an original combination of branched chain amino acids, *L*-carnitine and acetyl-*L*-glutamine -- has been studied. The results allow one to conclude that an amino acid composition is untoxic at unitary and chronic enteral introduction. The tested preparation has no immunotoxic and allergenic properties and does not render local irritating action on GIT in the doze surpassing many times a recommended therapeutic doze for the human. On parameters of toxicological safety Hexaminate meets the requirements showed to means of correction of asthenic and hypodynamic conditions.

**НАУКИ О ЗЕМЛЕ**

*Konischev V.S.*
**Halokinesis within the downthrown walls of the Pripyat through faults in the Frasnian saline formation.** pp. 103--107

*Summary:* It was established that salt massifs leant against the end part of uplifted walls of the faults were formed within downthrown walls of high-amplitude faults in Upper-Frasnian saliferous strata due salt laminar flow in thick (more than 70 m) salt beds and to detachment and transportation of blocks of laminated saliferous strata. Salt flowed upward to faults while subsalt deposits were submerged to them. Tectonics was the leading factor of halokinesis.

*Yakubovskaya T.V., Rylova T.B., Litviniuk G.I.*

**Grodno suite of the neogene deposits of Belarus.** pp. 108--114

*Summary:* The lektostratotype of the Neogene deposits of the Grodno suite in the 305^{th} bore (at a depth of 55.0--58.8 m) near the village of Alexandrovo of the Grodno district is described in this article. The Middle Miocene age of the suite is determined from the recent data on the fossil flora.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Zhdanov V.L., Chorny A.D., Kornev N.V., Hassel E.*
**Formation of a field of passive admixture concentration in an axis-symmetrical mixer.** pp. 115--119

*Summary:* The experimental results for the dynamics of passive admixture concentration in an axis-symmetrical jet mixer operating in the turbulent regime with a recirculation zone are presented in the work. The used experimental set-up, measuring equipment and measurement methods are described. A concentration field is characterized by the statistical parameters -- averaged value, fluctuation dispersion as well as by the probability density function (PDF) of a mixture fraction. It is shown that these parameters are affected by changing backflow. Comparison of the experimental PDF and its b-distribution has revealed that the analytical representation of the PDF in the form of the b-distribution widely used for closing the theoretical turbulent mixing models is not valid for the mixing region where asymmetric backflow is realized.

**СОЦИАЛЬНО-ГУМАНИТАРНЫЕ НАУКИ**

*Maroushko D.A.*
**Analysis method and comparative effectiveness assessment of the Internet project.** pp. 120--123

*Summary:* Economic effectiveness assessment of the Internet-project (website) is a very difficult task. As a result, the development of new models, methods and algorithms is a true way to raise the effectiveness of administrative decisions in electronic commerce and electronic government.

/ Издания академии / Научные журналы / К началу страницы

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

Создана при участии Игнатия И. Корсака

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