Doklady of the National Academy of Sciences of Belarus, 2001, Vol.45, No.6
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Doklady of the National Academy of Sciences of Belarus, 2001, Vol.45, No.6

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
Gabasov R., Kirillova F. M.
Synthesis of optimal controls of feedforward type. pp. 58
Summary: A method for guaranteed optimization of dynamic systems with the help of compensating controls is under consideration. An algorithm of realization of optimal closable feedforward is justified.
Zalessky B. A.
The efficient minimization of quadratic polynomials depending on integer variables, with quadratic monomials b^{2}_{i,j}(x_{i}  x_{j})^{2}. pp. 911
Summary: The algorithm of efficient minimization of quadratic polynomials, depending on integer variables, with quadratic monomials b^{2}_{i,j}(x_{i}  x_{j})^{2} is presented.
Zhestkov S. V., Zabreiko P. P.
On converse for fixed point principle in theory of Cauchy problem for linear normal systems in partial derivatives. pp. 1216
Summary: For linear partial differential operators L whose coefficients are continuous on t and analytical on x , the existence of the Banach spaces B invariant for L and satisfying the condition L < 1 is proved. Some examples are given.
Dem'yanko S. V.
Solution of integral equations with powerlogarithmic kernels in the space of continuous functions. pp. 1721
Summary: Onedimensional Volterra integral equations of the first kind containing powerlogarithmic functions in kernels, are studied on a finite interval of the real axis. The necessary and sufficient conditions for the solvability of these equations in the space of continuous functions are proved, and their solutions in closed form are constructed.
Anishchenkova N. G., Zverovich E. I., Rasulov K. M.
On the solving of Riemann type generalized boundaryvalue problem for bianalytical functions in the circle. pp. 2225
Dymkov M. P.
Linear quadratic optimization problem in multistage discretecontinuous 2D control system. pp. 2628
Summary: This paper considers a discretecontinuous 2D repetitive processes of both system theoretic and application interest. The minimization problem of the quadratic cost functional is reduced to an extremal problem in appropriate Hilbert space of entire functions. It is proved that the optimal control admits the linear function representation with respect to adjoint variables.
Samsonov Yu. B., Tavgen O. I.
Unipotent representation image F_{2}(x, y) with matrixes from GL(n, C), n = 2, 3, 4, under the condition of mapping generating and primitive elements into unipotent matrixes. pp. 2932
Summary: Let F_{2} = (x, y) be the free group of rank two with generators x and y, r : F_{2} ® GL (n, C), n £ 4 be a matrix representation of F_{2}. Then r(F_{2}) is a unipotent subgroup in GL(n,C) if the images of x, y and of any primitive element from F_{2} are unipotent matrixes.
Borukhon V. T.
Classification of linear reachable discrete systems in the vector space with respect to action of Brunovsky group. pp. 3335
Summary: The parametrization of the orbits of the feedback group (Brunovsky group) acting on the set of the all linear reachable discrete systems defined in the infinitedimensional vector space is established. In the finitedimensional case, the presented parametrization differs from the known results obtained by P. Brunovsky.
Radyno Ya. V., Tuzik S. A.
On de la Harpe problem. pp. 3639
Summary: De la Harpe problem of existance of locally compact metrizable topological group, which includes identity weakly but doesn't include one strongly, is solved. It is proved that the group of unitary fredholm operators with discrete topology is the example of such group.
Pekarskii A. A.
Analogs of the K. Mahler and V. V. Arestov inequalities for rational functions. pp. 4043
Lomovtsev F. E.
Complete hyperbolic highorder differentialoperator equations with variable domains of smooth coefficients. pp. 4448
Summary: Correct strong solvability of boundaryvalue problems for complete hyperbolic differential evenorder equations with variable domains of smooth operator coefficients has been proved.
Bakhtin V. I.
Cramer's theorem with two discrepancies. pp. 4953
Summary: We prove a generalization of the classical Cramer theorem on large deviations. We substitute the usual Cramer condition by some approximation to it. This approximation contains two discrepancies, one being an analytic family of bounded random variables and the other being an analytic function. The weakened condition occures in stochastic systems with fast and slow motions and in some dynamical systems. In the classical case of nonnormalized sum of random variables S_{n} satisfying the usual Cramer condition, our theorem treats deviations of order o(n) as well as O(n) and sometimes even greater.
PHYSICS
Lynkov L. M., Belyatko D. P.
Oxidation of titanium and zirconium films under the influence of pulsed thermal treatment. pp. 5456
Summary: As a result of the research, the annealing technique of such films of Zr and Ti was designed outgoing from by which it was established that for 1 s annealing, Ti has selectivity in relation to Zr. It is explained by the oxide layer on surface of Ti thich derivates the averting oxidation of Ti.
Under these conditions, the research shows the influence of a pulsed annealing on structural barrier thinfilm covers properties of ZrO_{2} and TiO_{2} with the help of a method the Auger of an electronic spectroscopy that film ZrO_{2} and TiO_{2}, obtained by a hyperthermal pulse annealing at 800 °C and 20 s annealing time, have a stoichiometric structure applicable to ZrO_{2} and TiO_{2} accordingly and are a good buffer preventing infiltration of atoms Si from the substrate in overlying layers.
Voitikov S. V., Gribkovskii V. P. †, Khasanov O. Kh.
Carrier transport effect on generation atability of quantumwell lasers with phaseconjugate feedback. pp. 5759
Summary: Carrier transport effect on stability of longwavelength quantumwell lasers with phaseconjugate feedback has been investigated and modeled. It has been shown that structuredependent carrier transport significantly reduces the domain of laser stability and decreases the critical reflectivity of phaseconjugate mirror in » 1.42 times.
Granko S. V., Komarov F. F., Leontiev A. V.
Peculiarities of boron and fluorine atom distribution in photoresist film irradiated by ionized BF_{2}^{+} molecules. pp. 6063
Summary: The results of experimental researches of distribution of boron and fluoride ions in photoresist S1813 irradiated by molecular ions BF_{2}^{+} are presented. The possible reasons for divergences of experimental data and results of theoretical calculations are discussed.
Sirota N. N.
The impulse phase of possible states of monoatomic system and vibration spectra. pp. 6467
Summary: A new method of calculation vibration spectrum of monoatomic system is proposed. The method is based on the investigation of the impulse phase finite and infinite homogeneus and andinhomogeneus space of possible states of monoatomic system.
CHEMISTRY
Starobinets G. L., Rakhmanko E. M., Mechkovsky S. A., Borshchenskaya T. I.
Microstratification of binary waterethanol solutions under nonexchange potassium halogenide sorption by sulfopolystyrene cation exchanger KPC8n(K^{+}). pp. 6870
Summary: The influence of microstratificastion demixture of binary water  ethanol solutions on nonexchange sorption of K^{+} halogenides by sulfopolystyrene cation exchanger KPC8n(K^{+}) hos been studied.
At 298 ± 1 K, the nonexchange sorption of KCl, KBr, KI from binary waterethanol mixtures in all the diapason of their composition by the sulfopolystyrene cationexchanger KPC8n(K^{+}) has been studied.
Abnormally large effects (more greater shan the effect of Donnan) of non exchange sorption of these salts from the broad zone of microstratification of the binary water  ethanol solution (0.8 ³ N_{2} ³ 0.2, N_{2}  is mole fraction of ethanol) has been discovered.
This phenomenon has been explaned by formation of crowded salt ion pairs in the stratification and their passage from the binary solution to individuale ions in the swollen ion exchanger phase (the volume % of water in this phase is greater than one in the binary solution; therefore, the affinity of the ion pairs to the exchanger is great).
This explanation agrees with the following facts: the anomalous distribution coefficients for salts between the two phases are in a linear correlation from the value B^{} / B (volume % of water is in numerator and denominator, the line means the exchanger phase), the maxima of the distribution coefficients and of this value coinside.
Polkhovsky E. M., Mironova T. V., Martinovich V. I., Soldatov V. S.
Acidbase properties and characteristics of ion exchanger structure based on hydrazide nitron. pp. 7174
Summary: The ionexchanger fibres were obtained by the interaction of the copolimer of acrylonitrile, methyl acrylate, itaconic acid with hydrazine hydrate and sodium hydroxide. They were investigated by the method of potentiometric titration. It was established that there are equivalent and overequivalent sorbtion of acid and alkali by carboxylic and hydrazide groups of the ionexchangers. Equivalent ion exchange capacity of hydrazide groups can be defined as degree of cross linkage of the ionexchangers.
BIOLOGY
Potapovich A. I., Kostyuk V. A.
Mechanism of flavonid protection against phagocytic cell injury by asbestos fibers. pp. 7578
Summary: Protective effect of various flavonoids (rutin, dihydroquercetin, quercetin, ECG, EGCG) on phagocytic cell injury caused by asbestos fibers was studied. It was shown that exposure of rat peritoneal macrophages to chrysotile asbestos fibers resulted in TBARS formation, LDG release and lysis. We found that flavonoids were effective in the protection of phagocytic cells against asbestosinduced injury acting as scavengers O_{2}^{}. Rate constants of flavonoids with superoxide were determined from competition kinetics. The results of this study demonstrate that flavonoids exhibited cellular protection in the same order of effectiveness as that observed for the quenching of superoxide: rutin < dihydroquercetin < quercetin < ECG < EGCG.
Orlov P. A., Lenivko S. M., Khotylyova L. V.
Inheritance of pollen embryogenesis parameters in spring wheat dihaploid lines. pp. 7982
Summary: Investigations on developing F_{1} hybrids characterized by a high capacity for embryoid induction and green plant regeneration with application of spring wheat dihaploid lines have been carried out. The highest embryogenic and regeneration potential was shown to have hybrids in developing of which well responsive to in vitro culturing dihaploid lines were used as maternal forms. Additive effect prevailed in inheritance of these traits.
Sushchenya L. M., Semenchenko V. P., Galkovskaya G. A.
Species diversity of pelagian zooplankton of lakes of different types. pp. 8385
Summary: The relationships between zooplankton species diversity (Rotifera, Cladocera, Copepoda) and limnological and hydrobiological parameters of lakes of different types have been studied. Maximal depth of lakes (r = 0.81), phytoplankton biomass (r =  0.69) were the main factors which influenced on species diversity. Relationship between species diversity and zooplankton abundance is a domedtype one (r = 0.71) with maximum at zooplankton abundance of 40 ind. per litre.
Rakovich A. A., Levko A. V., Samoilenko S. G., Konev S. V.
Entry of Ca^{2+} ions into nerveendings of rat brain under osmotic swelling. pp. 8689
Summary: Swelling of isolated nerveendings of rat brain in hypotonic medium (230 mOsm) is coupled with tyrosine kinase activity increase, phosphorylation of membranous proteins and oxidation of tiol groups of proteins cysteine resides that concern Ca^{2+} ion transport. The SHgroup oxidation is a main factor in Ca^{2+} transport. These membranous processes influence considerably on properties of voltagedependent Ca^{2+}channels of Ltype that increase their conductivity to Ca^{2+} ions. The swellinginduced voltageindependent Ca^{2+} entry occurs into synaptosomes from external medium.
EARTH SCIENCES
Kudelsky A. V., Potkin V. I., Lebedeva L. D., Volkova N. P.
Substance composition and ecotoxicological hazard of city waste dumps. pp. 9096
Summary: The results of complex investigations carried out for the first time for substance composition of city waste dumps within Minsk agglomeration have been presented. A chemical composition of solidplastic substratum and water solution (filtrates) including heavy metals and organic compounds has been studied. High ecotoxicological hazard of such objects has been established. It has been shown that the city waste dumps are source of the serious contamination of the underground water of city water intakes with hightoxic metals (cadmium, chrome, etc.) and organic compounds (phenols, amines, trans1,2dichlorethylen, etc.).
Starchik T. A., Aizberg R. Ye.
Listric nature of faults in the Pripyat Trough as reflected in the synrift complex structure. pp. 97100
Summary: A model of formation of liner zones free of intersalt strata in the Pripyat Trough due to the listric nature of stepforming faults has been discussed. A mechanism of relative upwarping and destruction of the stepfrontal parts under general downwarping of the territory during the active rifting phase has been demostrated.
Komarovsky M. E., Rasolko V. V., Litvinyuk G. I.
On structure and origin of the Poozerje deposits of the Late Pleistocene at the Komarishki outcrop (northwestern Belarus). pp. 101105
Summary: On the basis of complex structural, lithologic, palaecarpologic and radiocarbon analyses, it has been established that moraines and an anticline found at the Komarishki outcrop were formed by the LatePoozerje ice sheet. The lower moraine was deposited under conditions of the differentiated plastic flow of ice layers at maximum phase of glaciation, and the upper moraine was formed synchronously with the anticline in an icesheet sole during the SSE ice surge and following deglaciation in front of a local height of the icebed due to a strong local compression of the basal strata.
Aksamentova N. V., Rosen O. M., Trusov A. I., Abbyasov A. A.
Initial composition of the Okolovo ironbearing strata of the crystalline basement in Belarus. pp. 106110
Summary: Initial mineral composition of the rocks from iron ore srata has been calculated on the basis of the lithochemical calculations with help of MINLITH software. It has been suggested that the considered rocks are initial chemogenic ferroussiliceous, tuffaceous sediments and graywackes deposited at the deepwater conditions in the troughlike basin.
Vegera A. I., Lurie M. V.
Modeling of gas escape from underground gas storages in aquifers. pp. 111114
Summary: In this work, such things as results of research of hydrodynamic processes going on when underground gas storages are cyclically operated in aquifers, gas escape, dynamics and stability of gas cavity on time basis are discussed.
On the basis of the analysis of calculations, the hydrodynamic dependence between volume of gas escape on gas cavity, volume and mass of active and buffer gas, minimum pressure in underground gas storages at the end of selection process and maximum of pressure at the end of process of gas filling is found.
With the increase of gas escape from underground gas storages, the volume of buffer gas decreases and the range of volume changes is getting wider. This means that maximum of pressure at the end of gas filling process increases and minimum of pressure at the end of selection process decreases.
The results of the research of hydrodynamic processes going on when underground gas storages are cyclically operated allow to diagnose gas escape from gas cavity in aquifers with the help of control of active and buffer mass changes, and changes of max. pressure of gas filling and min. pressure at the end of selection process.
Matveev A. V., Pavlovskaya I. E.
Glaciomorphological complexes in Belarus. pp. 115118
Summary: Exposed glaciomolphological complexes in Belarus were formed during the Pripyat and Poozerie Glaciations. Pripyat glaciomorphological complexes are subdivided into two main groups belonging to the Dnieper and Sozh Stages of the glaciation (these are Dnieper, Stolin, Mozyr and Chechersk complexes of the Dnieper Stage, as well as Sozh, Slavgorod, Starye Dorogi, Mogilev, Oshmiany and Pleschenitsy ones of the Sozh Stage). Orsha, Lepel and Braslav glaciomorphological complexes are considered to be formed during recession phases of the Late Poozerie Stage of the Poozerie Glaciation.
The paper considers the recent changes in tracing of glacial limits of both the maximum extent and Braslav recession phase of the Poozerie Glaciation. Based on geological and geomorphological data, it is supposed that the Poozerie glacier in NW Belarus extended further south in comparison with the formerly defined limit.
TECHNICAL SCIENCES
Khmyl A. A., Mushovets I. I., Emel'yanov V. A., Dostanko A. P.
Effect of electrolysis conditions on substructure of silversuperdispersed diamond composites. pp. 119121
Summary: Studies influencing fragments of ultra dispersed diamond (UDD) and nonsteady electrolysis conditions on substructure of electrochemical silver covers obtained from ferrocyaniderhodanate electrolyte.
Samoilovich Yu. A., Timoshpolsky V. I., Anisovich G. A., Trusova I. A., Khopova O. G.
Integral method of calculation of solidification an ingot (cast) with square crosssection. pp. 122125
Summary: A method of calculation of solidification process of an ingot (cast) with square crosssection is studied. Interfacing the solidification front of timing parameters KarmanPolhausen method is used. A description of the algorithm of calculation with numerical values e = e(t) and elliptic integrals A_{0}(e), A_{1}(e) is given.
Klubovich V. V., Sakevich V. N.
Some peculiarities of vibration transfer from electroacoustic transducer to instruments in technological ultrasound framed structures. pp. 126128
Summary: In the work, there was presented the theoretical justification of the new principle of development technological ultrasound oscillating systems. It was shown that if the units of the oscillating system were pressed with the static force and there was the resonance vibroimpact regime of oscillations between their edges the amplitude of the instrument oscillations when idling would be not less than one at their hard joining.
A list of articles published in the journal "Doklady of the National Academy of Sciences of Belarus" in 2001. pp. 118122
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