# Доклады Национальной академии наук Беларуси, 2002, Том 46, No.3

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2002, Том 46, No.3

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Minchenko L. I., Dymkov S. M.*
**Solution suboptimality and differentiability of optimization problem of multistage control system.** pp. 5--7

*Summary:* For the repetitive systems, necessary and sufficient suboptimality conditions are obtained in linear optimization problem with terminal constraints on basis of which classic maximum and e-maximum principles are established, too. In regular case, some differential properties of optimal solutions are also given.

*Radyno E. M., Radyno Ya. V.*

**Change of variables in p-adic and adele integrals.** pp. 8--12

*Summary:* New formulas of changing variables in integrals of real-valued functions of p-adic and adele arguments are obtained. The most general approach involving the Radon and Nikodym theorem is considered.

*Filipuk G. V.*

**On connection between Backlund and Schlesinger transformations for the fifth Painleve equations.** pp. 13--15

*Summary:* For the solutions of the fifth Painleve equations, explicit expression of the Schlesinger transformation in terms of superposition of the Backlund transformations is obtained.

*Tykun A. S.*

**The Conley index and the Poincar index of two-dimensional dynamic systems.** pp. 16--19

*Summary:* An explicit formula for the Conley index of two-dimensional dynamic systems is obtained. This formula allows to evaluate the Conley index for the simply connected isolating neighborhood in terms of the function defined on the boundary of this neighborhood. The relations between the Conley index and the Poincare index (the winding number) are found. Also, analogue of the Hopf theorem for the Conley index is obtained: if two dynamic systems have the same Conley indices with respect to the simply connected isolating neighborhood, then for these systems, there exists an isolating homotopy i. e. homotopy leaving the neighborhood to be isolating.

*Rusak V. N., Starovoitov A. P.*

**On properties of the Pade and Chebyshev tables for entire functions with regular decrease of Taylor coefficients.** pp. 20--23

*Summary:* For some class of entire functions, asymptotic equalities for the Hadamard determinants *D*_{n, m} at *m =m(n)* and *n* ® ¥ are established. It allows investigating behaviour of parabolic sequences of Pade and Chebyshev tables for many known entire functions.

*Bakhtin V. I.*

**Action functional for Perron--Frobenius cascades.** pp. 24--29

*Summary:* The action functional in the probability theory gives a rough exponential asymptotics for probabilities of some very unlikely events. In this paper, the notion of action functional is defined for empirical measures of the Perron--Frobenius cascades. Essentially, it is a functional of two Gibbs distributions. It gives an exponential asymptotics for observation of empiric measure similar to the first Gibbs distribution with respect to the second one. In the case of Bernoulli independent tests, the action functional has avery simple and well known explicit form.

*Zabreiko P. P., Shevelevich K. V.*

**The Hicks and LeChatelier--Samuelson theorems for decomposable nonnegative matrices.** pp. 30--34

*Summary:* The paper deals with analogues of the Hicks and LeChatelier--Samuelson theorems for nonnegative decomposable matrices. In particular, it is proved that the LeChatelier--Samuelson theorem is true for indecomposable matrices (the original statement was for positive matrices).

*Krasovskii S. G.*

**On asymptotic equivalence of linear singular differential systems.** pp. 35--37

*Summary:* For initial and perturbed linear differential systems with positive parameter under derivative, the necessary and sufficient conditions of their asymptotic equivalence are given for all values of the parameter.

*Yanovich L. A., Doroshko V. V.*

**Operator interpolation formulae generated by Abel--Goncharov generalized interpolation polynomials.** pp. 38--41

*Summary:* Interpolation formulae of operator interpolation based on Abel--Goncharov generalized interpolation polynomials are obtained in the function spaces.

*Yablonsky O. L.*

**Stochastic integrals for jump random processes.** pp. 42--46

*Summary:* A new class of stochastic integrals is defined in this paper. Using this integrals limiting behavior of sums of generalized jump processes is investigated.

*Kirillova F. M., Pesetskaya T. I.*

**Efficient algorithm of passive identification of input device parameters of control system.** pp. 47--50

*Summary:* A problem of construction the estimates for an input device parameter of a linear control system is under consideration An algorithm for solving the optimal identification problem for system in question is based on a linear programming method adapted to the dynamic structure of the problem.

*Benyash-Krivets V. V.*

**On free subgroups in generalized triangular groups of (2, 2k, 2) type.** pp. 51--54

*Summary:* The validity of the Tits alternative for generalized triangle groups of (2,2*k*,2) type, where *k* > 4, k ¹ 5,6,10,15,30, is proved.

*Lomovtsev F. E.*

**Complete parabolic odd-order differential-operator equations with variable domains of operator coefficients.** pp. 55--59

*Summary:* Existence and uniqueness of strong solutions of boundary-value problems for complete parabolic odd-order differential equations with variable domains of operator coefficients are proved.

*Bernic V. I., Vasiliev D. V., Dodson M. M.*

**Metric theorems on real numder approximation dy special literal numders.** pp. 60--63

*Summary:* We prove the convergence case for the polynomial generalization of Khintchine theorem with the condition of Harman.

*Matus P. P.*

**On stability of vector-additive schemes.** pp. 64--67

*Summary:* In this paper, the stability of vector additive schemes is studied in the banach grid spases. A priori estimates of stability in the norm С with respect to initial data, boundary conditions, right hand side are obtained.

**ФИЗИКА**

*Zhestkov S. V.*
**On existence of (***l* + 1)-dimensional fundamental dark soliton. pp. 68--70

*Summary:* We give the analytical fundamental dark soliton solutions of the (*l* +1) -dimensional nonlinear Schroedinger equation [(*l* + 1) - D NSE]. The necessary and sufficient conditions of existence of dark soliton are obtained. The results are compared with that obtained by the Hirota's method.

*Goncharenko A. M.*

**Optical ellipsoidal soliton.** pp. 71--72

*Summary:* It is shown that in nonlinear media, the spatio-temporal optical solitons may have ellipsoidal shapes.

*Knyazhishche L. B.*

**Uniform final boundedness conditions of solutions of permanent lag equations.** pp. 73--75

*Summary:* Uniform ultimate boundedness conditions are obtained for equations with time delay on the basis of non-monotone Lyapunov functionals.

**ХИМИЯ**

*Soldatov V. S., Zelenkovskii V. M., Bezyazychnaya T. V.*
**Quantum-chemical modeling of ion relative positions in hydrate structures of carboxylic cation exchangers.** pp. 76--80

*Summary:* The relative positions of carboxylic anion and cations H^{+}, Li^{+}, Na^{+}, K^{+}, Rb^{+} and Cs^{+} in systems containing N molecules of water (N = 0, 1, 2,..., 10) were computed using the non-empirical quantum-chemical calculations in approximation of molecular fragments. Isobutyric acid molecule was used as molecular fragment closely imitate repeated units of the polymeric structure of carboxylic cation exchangers. The results obtained were summarized as follows. In the absence of water, the metal cations are bound to two oxygen atoms of the carboxylic groups. Three atoms of carboxylic group and cation are in the plane. The situations in the systems with successively increasing hydration were considered. At high degrees of hydration, corresponding to the real ion exchangers, the cation is always bound to one of the oxygen atoms of the carboxylic group. Dissociation of COOH-group was not found.

**БИОЛОГИЯ**

*Doroshenko T. M., Chaly Yu. V., Savitskii V. P., Maslakova O. V., Smolnikova V. V., Voitenok N. N.*
**Down-regulation of expression of Interleukin-8 receptors on human neutrophils at phagocytosis.** pp. 81--84

*Summary:* Phagocytosis plays a central role in immune responses. Polymorplionuclear neutrophils (PMN) are the main phagocytes in human body. Interleukin-8 (IL-8), 8 kD chemotactic protein is a key mediator of PMN chemotaxis which induces PMN migration and activation. The action of IL-8 on PMN is mediated via membrane IL-8 receptors CXCR1 and CXCR2, which transmit an IL-8 signal through fast influx of intracellular Ca^{++} in PMN. Since phagocytosis and chemotaxis represent two main functions of PMNs, we studied their interrelations, i. e. the effect of phagocytosis of opsonized yeast cells, opsonized sheep erythrocytes, and zymozan particles on the expression of CXCR1 and CXCR2 in human blood PMN. It was shown that the expression of CXCR1 and CXCR2 on phagocytosing PMN was reduced by 50--80%. Inhibitor of metalloproteinases 1,10-phenantrolin prevented drop of CXCR1 and CXCR2 expression, implying that proteolytic cleavage represents a main mechanism of reduction of IL-8 receptors. Down-regulation of CXCR expression was accompanied by loss of PMN responsiveness to IL-8: intracellular Ca^{++} influx in response to IL-8 was significantly depressed in phagocytosing PMN. Experimental data indicate that phagocytosis induces down-regulation of expression of interleukin-8 receptors on human neutrophils and inhibits their responsiveness to interleukin-8. This phenomenon may play a significant role in physiological regulation of PMN activity and impair their antibacterial functions in pathological conditions.

*Levko A. V., Samoilenko S. G., Rakovich A. A., Konev S. V.*

**Initial stage of calcium response of nerve-endings of rat brain to osmotic swelling.** pp. 85--87

*Summary:* Swelling of isolated nerve-endings of rat brain in hypotonic medium (230 mOsm) causes voltage-independent swelling-induced Ca^{2+} ions entry into synaptosomes from external medium. Using fluorescent Ca^{2+} indicator Fura-2/AM and radioisotopic probe ^{45} Ca^{2+}, it is suggested that Ca^{2+} entry from external medium is an initial stage of intracellular signaling.

*Orlovskaya O. A.*

**Analysis of chromosome conjugation in F**_{1} And F_{4} hybrids during Aegilops L. introgression into genome triticale. pp. 88--91

*Summary:* Chromosome behavior pattern was studied in meiosis MI of F_{1} and F_{4} triticale hybrids during aegilops chromosome introgression into hexaploid triticale genome. Rather high degree of bivalent pairing, exceeding the theoretically expected one, was revealed. This can be caused by using wheat substituted forms, including aegilops genomes, in triticale crosses. As a result, conditions emerge not only for homologous but also for homeologous chromosome conjugation. Such a level of bivalent in F_{1} and F_{4} means possibility of introgression of aegilops genetic material into triticale genome.

*Soklakov V. I., Finin V. S., Voitovich V. A., Savchenko N. E.†*

**Diagnostic capabilities of spin probe method for early detection of diabetic nephropathy and its development.** pp. 92--93

*Summary:* Benzo-g-carboline spin label parameters locating mainly on blood serum lipoproteins reflect changes in protein-lipid metabolism distorted in type I diabetes mellitus patients. The method allows to reveal the group of patients with a higher risk of diabetic hephroangiopathy development and to predict the progression of the given complication.

*Bushmakina I. M., Matus V. K. †, Martynova M. A., Konev S. V., Nikolskaya V. P.*

**Synthesis of liposomal rifampicin by repeated freezing-defrosting.** pp. 94--96

*Summary:* The method of synthesis of liposomal rifampicin by procedure of freezing and thawing of liposomal suspension in the presence of cryoprotectoris is discribed. Relationship between the degree of entrapment of antibiotic into liposomal container and the concentration of overall lipids, the ratio of lipids components, and cryoprotector's nature has been studied. The optimum concentration of overall lipids was 50 mg/ml, the ratio of lipids components phosphatidylcholine from egg yolk : cholesterol : stearic acid, 10:0.5:0.2 mol/mol and 10% cholinchloride solution as cryoprotector.

**НАУКИ О ЗЕМЛЕ**

*Nikolaev V. G., Kovkhuto A. M.*
**Types of Moscow Syneclise faults.** pp. 97--100

*Summary:* The Moscow Syneclise's territory was under influence of different geodynamic conditions during its evolution. Fault systems with different direction and kind of faults were formed in these conditions. Main stages of stress regime were: Riphean, Vendian-Paleozoic (Pre-Carboniferous) and Mesozoic (EarlyMiddle Triassic). Stress regime was stronger during Riphean time when faults were formed. Normal and shift faults predominated at the Riphean stage. Normal and sedimentary faults predominated at the Vendian-Paleozoic stage. Compressional and thrust faults predominated at the Mesozoic stage. Sedimentary faults are interesting in oil and gas prospecting.

*Mamchik S. O.*

**Callovian deposit tectonics within southeastern Belarus.** pp. 101--104

*Summary:* The paper discusses the peculiarities of the Callovian deposit structure within southeastern Belarus: vertical section, facies, thickness variation, structural differences.

*Tolkachikova A. A.*

**Petrogenesis of Kulazhin series rocks of the Pripyat Trough.** pp. 105--109

*Summary:* Petro-geochemical features of the recognized types of metamorphic rocks of the crystalline basement from the easten part of the Pripyat Trough have been considered. These rocks, accumulated under various geodynamic conditions, are shown to be of heterogenous nature. Thermodynamic parameters of metamorphism of Kulazhin series rocks have been determined.

*Pavlovskaya I. E., Murashko L. I.*

**Poozerian Moraine within northwestern Belarus: spreading and lithologic peculiarities.** pp. 110--114

*Summary:* The maximum extent of the Poozerian (Weichselian) Glaciation in north-western Belarus formerly was traced according to morphological features. In this area, the biostratigraphical substantiation of the Poozerian extent is rather impossible due to the lack of interglacial Muravian (Eemian) sediments in situ. The paper considers the occurrence, geomorphological position, mineralogical and petrographical peculiarities of the Poozerian till. Lithostratigraphical and geomorphological evidence suggests that the last glacier in north-western Belarus extended further south than it was confirmed previously.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Zdor G. N., Mamutov A. V., Mamutov V. S.*
**Impulse pressure transformation by mechanical concentrators taking into consideration wave processes.** pp. 115--119

*Summary:* The paper describes the methodology used for computer simulation of ware impulse pressure transformation by mechanical concentrators. To this end, an axisymmetric problem of the ware elasticity theory is solved by a numerical differential method using an inexplicit difference scheme. The use of an elaborated software package is illustrated by an example showing the transformation of a pulsed magnetic field pressure by a movable element of technological arrangement during punching-piercing machining of thin-sheet materials using a magnetic-impulse method with the help of elastic medium. The conditions of optimal transformation obtained allow designing efficient technological devices.

*Lyn'kov L. M., Glybin V. P., Bogush V. A., Borbotko T. V.*

**Structure of cobalt-containing materials synthesized of modified polyacrylonitrile.** pp. 120--122

*Summary:* Results of study of structure and electromagnetic properties of fiber material synthesized of modified polyacrylonitrile (PAN) by chemical reduction of cobalt in aqua solutions are presented in this paper. X-ray diffraction and spectrometry methods were used for structural and element analysis of the synthesized materials. The original technique for synthesis of cobalt material at a temperature of metal reduction of about 55 ± 5 °C is developed. It is shown that the synthesized fibers contain the cubic cobalt and compounds of cobalt with sulfur. Electrical properties and interaction of knitted cloth on the basis of the synthesized materials with electromagnetic radiation were studied. Perspective of using cobalt-containing materials for production of matching layer for microwave absorbers in frequency range of 20 GHz to 118 GHz is shown.

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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *6 сентября 2008 г.*

Создана при участии Игнатия И. Корсака

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