# Доклады Национальной академии наук Беларуси, 2001, Том 45, No.6

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2001, Том 45, No.6

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Gabasov R., Kirillova F. M.*
**Synthesis of optimal controls of feedforward type.** pp. 5--8

*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. 9--11

*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. 12--16

*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 power-logarithmic kernels in the space of continuous functions.** pp. 17--21

*Summary:* One-dimensional Volterra integral equations of the first kind containing power-logarithmic 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 boundary-value problem for bianalytical functions in the circle.** pp. 22--25

*Dymkov M. P.*

**Linear quadratic optimization problem in multistage discrete-continuous 2D control system.** pp. 26--28

*Summary:* This paper considers a discrete-continuous 2-D 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. 29--32

*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. 33--35

*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 infinite-dimensional vector space is established. In the finite-dimensional 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. 36--39

*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. 40--43

*Lomovtsev F. E.*

**Complete hyperbolic high-order differential-operator equations with variable domains of smooth coefficients.** pp. 44--48

*Summary:* Correct strong solvability of boundary-value problems for complete hyperbolic differential even-order equations with variable domains of smooth operator coefficients has been proved.

*Bakhtin V. I.*

**Cramer's theorem with two discrepancies.** pp. 49--53

*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 non-normalized 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.

**ФИЗИКА**

*Lynkov L. M., Belyatko D. P.*
**Oxidation of titanium and zirconium films under the influence of pulsed thermal treatment.** pp. 54--56

*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 thin-film 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 quantum-well lasers with phase-conjugate feedback.** pp. 57--59

*Summary:* Carrier transport effect on stability of long-wavelength quantum-well lasers with phase-conjugate feedback has been investigated and modeled. It has been shown that structure-dependent carrier transport significantly reduces the domain of laser stability and decreases the critical reflectivity of phase-conjugate mirror in » 1.4--2 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. 60--63

*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. 64--67

*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.

**ХИМИЯ**

*Starobinets G. L., Rakhmanko E. M., Mechkovsky S. A., Borshchenskaya T. I.*
**Microstratification of binary water-ethanol solutions under non-exchange potassium halogenide sorption by sulfopolystyrene cation exchanger KPC-8n(K**^{+}). pp. 68--70

*Summary:* The influence of microstratificastion demixture of binary water -- ethanol solutions on non-exchange sorption of K^{+} halogenides by sulfopolystyrene cation exchanger KPC-8n(K^{+}) hos been studied.
At 298 ± 1 K, the non-exchange sorption of KCl, KBr, KI from binary water-ethanol mixtures in all the diapason of their composition by the sulfopolystyrene cationexchanger KPC-8n(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.*

**Acid-base properties and characteristics of ion exchanger structure based on hydrazide nitron.** pp. 71--74

*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.

**БИОЛОГИЯ**

*Potapovich A. I., Kostyuk V. A.*
**Mechanism of flavonid protection against phagocytic cell injury by asbestos fibers.** pp. 75--78

*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 asbestos-induced 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. 79--82

*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. 83--85

*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 domed-type 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 nerve-endings of rat brain under osmotic swelling. pp. 86--89

*Summary:* Swelling of isolated nerve-endings 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 SH-group oxidation is a main factor in Ca^{2+} transport. These membranous processes influence considerably on properties of voltage-dependent Ca^{2+}-channels of L-type that increase their conductivity to Ca^{2+} ions. The swelling-induced voltage-independent Ca^{2+} entry occurs into synaptosomes from external medium.

**НАУКИ О ЗЕМЛЕ**

*Kudelsky A. V., Potkin V. I., Lebedeva L. D., Volkova N. P.*
**Substance composition and ecotoxicological hazard of city waste dumps.** pp. 90--96

*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 solid-plastic 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 high-toxic metals (cadmium, chrome, etc.) and organic compounds (phenols, amines, trans-1,2-dichlorethylen, etc.).

*Starchik T. A., Aizberg R. Ye.*

**Listric nature of faults in the Pripyat Trough as reflected in the synrift complex structure.** pp. 97--100

*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. 101--105

*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 Late-Poozerje 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 ice-sheet sole during the SSE ice surge and following deglaciation in front of a local height of the ice-bed 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. 106--110

*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 ferrous-siliceous, tuffaceous sediments and graywackes deposited at the deep-water conditions in the trough-like basin.

*Vegera A. I., Lurie M. V.*

**Modeling of gas escape from underground gas storages in aquifers.** pp. 111--114

*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. 115--118

*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.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Khmyl A. A., Mushovets I. I., Emel'yanov V. A., Dostanko A. P.*
**Effect of electrolysis conditions on substructure of silver-superdispersed diamond composites.** pp. 119--121

*Summary:* Studies influencing fragments of ultra dispersed diamond (UDD) and non-steady electrolysis conditions on substructure of electrochemical silver covers obtained from ferrocyanide-rhodanate 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 cross-section.** pp. 122--125

*Summary:* A method of calculation of solidification process of an ingot (cast) with square cross-section is studied. Interfacing the solidification front of timing parameters Karman--Polhausen 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. 126--128

*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. 118--122

/ Издания академии / Научные журналы / К началу страницы

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

Создана при участии Игнатия И. Корсака

Копирайт © 2002-2008 Национальная академия наук Беларуси

Копирайт © 2001 Издательство "Беларуская навука"