Doklady of the National Academy of Sciences of Belarus, 2002, Vol.46, No.3
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Doklady of the National Academy of Sciences of Belarus, 2002, Vol.46, No.3

DOKLADY OF THE NATIONAL ACADEMY OF SCIENCES OF BELARUS
(Doklady Natsionalnoi Akademii Nauk Belarusi)Published by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Minchenko L. I., Dymkov S. M.
Solution suboptimality and differentiability of optimization problem of multistage control system. pp. 57
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 emaximum 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 padic and adele integrals. pp. 812
Summary: New formulas of changing variables in integrals of realvalued functions of padic 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. 1315
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 twodimensional dynamic systems. pp. 1619
Summary: An explicit formula for the Conley index of twodimensional 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. 2023
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 PerronFrobenius cascades. pp. 2429
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 PerronFrobenius 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 LeChatelierSamuelson theorems for decomposable nonnegative matrices. pp. 3034
Summary: The paper deals with analogues of the Hicks and LeChatelierSamuelson theorems for nonnegative decomposable matrices. In particular, it is proved that the LeChatelierSamuelson 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. 3537
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 AbelGoncharov generalized interpolation polynomials. pp. 3841
Summary: Interpolation formulae of operator interpolation based on AbelGoncharov generalized interpolation polynomials are obtained in the function spaces.
Yablonsky O. L.
Stochastic integrals for jump random processes. pp. 4246
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. 4750
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.
BenyashKrivets V. V.
On free subgroups in generalized triangular groups of (2, 2k, 2) type. pp. 5154
Summary: The validity of the Tits alternative for generalized triangle groups of (2,2k,2) type, where k > 4, k ¹ 5,6,10,15,30, is proved.
Lomovtsev F. E.
Complete parabolic oddorder differentialoperator equations with variable domains of operator coefficients. pp. 5559
Summary: Existence and uniqueness of strong solutions of boundaryvalue problems for complete parabolic oddorder 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. 6063
Summary: We prove the convergence case for the polynomial generalization of Khintchine theorem with the condition of Harman.
Matus P. P.
On stability of vectoradditive schemes. pp. 6467
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.
PHYSICS
Zhestkov S. V.
On existence of (l + 1)dimensional fundamental dark soliton. pp. 6870
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. 7172
Summary: It is shown that in nonlinear media, the spatiotemporal optical solitons may have ellipsoidal shapes.
Knyazhishche L. B.
Uniform final boundedness conditions of solutions of permanent lag equations. pp. 7375
Summary: Uniform ultimate boundedness conditions are obtained for equations with time delay on the basis of nonmonotone Lyapunov functionals.
CHEMISTRY
Soldatov V. S., Zelenkovskii V. M., Bezyazychnaya T. V.
Quantumchemical modeling of ion relative positions in hydrate structures of carboxylic cation exchangers. pp. 7680
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 nonempirical quantumchemical 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 COOHgroup was not found.
BIOLOGY
Doroshenko T. M., Chaly Yu. V., Savitskii V. P., Maslakova O. V., Smolnikova V. V., Voitenok N. N.
Downregulation of expression of Interleukin8 receptors on human neutrophils at phagocytosis. pp. 8184
Summary: Phagocytosis plays a central role in immune responses. Polymorplionuclear neutrophils (PMN) are the main phagocytes in human body. Interleukin8 (IL8), 8 kD chemotactic protein is a key mediator of PMN chemotaxis which induces PMN migration and activation. The action of IL8 on PMN is mediated via membrane IL8 receptors CXCR1 and CXCR2, which transmit an IL8 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 5080%. Inhibitor of metalloproteinases 1,10phenantrolin prevented drop of CXCR1 and CXCR2 expression, implying that proteolytic cleavage represents a main mechanism of reduction of IL8 receptors. Downregulation of CXCR expression was accompanied by loss of PMN responsiveness to IL8: intracellular Ca^{++} influx in response to IL8 was significantly depressed in phagocytosing PMN. Experimental data indicate that phagocytosis induces downregulation of expression of interleukin8 receptors on human neutrophils and inhibits their responsiveness to interleukin8. 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 nerveendings of rat brain to osmotic swelling. pp. 8587
Summary: Swelling of isolated nerveendings of rat brain in hypotonic medium (230 mOsm) causes voltageindependent swellinginduced Ca^{2+} ions entry into synaptosomes from external medium. Using fluorescent Ca^{2+} indicator Fura2/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. 8891
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. 9293
Summary: Benzogcarboline spin label parameters locating mainly on blood serum lipoproteins reflect changes in proteinlipid 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 freezingdefrosting. pp. 9496
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.
EARTH SCIENCES
Nikolaev V. G., Kovkhuto A. M.
Types of Moscow Syneclise faults. pp. 97100
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, VendianPaleozoic (PreCarboniferous) 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 VendianPaleozoic 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. 101104
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. 105109
Summary: Petrogeochemical 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. 110114
Summary: The maximum extent of the Poozerian (Weichselian) Glaciation in northwestern 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 northwestern Belarus extended further south than it was confirmed previously.
TECHNICAL SCIENCES
Zdor G. N., Mamutov A. V., Mamutov V. S.
Impulse pressure transformation by mechanical concentrators taking into consideration wave processes. pp. 115119
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 punchingpiercing machining of thinsheet materials using a magneticimpulse 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 cobaltcontaining materials synthesized of modified polyacrylonitrile. pp. 120122
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. Xray 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 cobaltcontaining materials for production of matching layer for microwave absorbers in frequency range of 20 GHz to 118 GHz is shown.
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