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Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.2

Homepage / Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.2

(Doklady Natsionalnoi Akademii Nauk Belarusi)

Published by The Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus

Volume 52, Number 2; March-April, 2008

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Demenchuk A. K., Makarov E. K.
Polynomial formulas for Hermitian solutions of the matrix equation AX - XA = C with a normal coefficient. pp. 5--10
E-mail: demenchuk(at), jcm(at)

Summary: Explicit formulas for general solution of the matrix equation AX - XA = C, when A is a simple matrix, as well as for general Hermitian solution of this equation, when A is a normal matrix, are obtained. These formulas are polynomial with respect to A and C .

Knyazhishche L. B.
Nonmonotone functionals for stabilization of delay systems. pp. 11--16
E-mail: klb(at)

Summary: Sufficient nonmonotone functionals based conditions for optimal stabilization of delay systems are proposed. New disturbance estimates preserving the stabilization property of the optimal control stabilizing undisturbed system are obtained.

Zabreiko P. P., Tanyhina A. N.
Implicit description method of solution of the open Leontiev--Ford model. pp. 17--22
E-mail: zabreiko(at), anast-minsk(at)

Summary: The article is devoted to the open Leontiev--Ford model that describes simultaneously two processes: the production of commodities for consumers and the destruction of damages in the environment. From the mathematical point of view this model represents a linear system with a nonnegative matrix. It is shown that in the principal cases the sufficient condition for the considered model that is A-compensating is also necessary.

Kukso O. S., Bernik V. I.
Connection between the value of a discriminant and the behaviour of a polynomial in the neighborhood of a root. pp. 23--25
E-mail: bernik(at), olga_kukso(at)

Summary: In the article the authors demonstrate a connection between the values of the integer polynomial on the fixed interval, the length of this interval and the polynomial discriminant.

Maslov A. S.
Group-theoretic properties of SA-permutations. pp. 26--28
E-mail: maslov(at)

Summary: We have obtained the conditions on SA-permutations, which guarantee that these permutations generate the alternating group. We have also obtained the asymptotic bounds on the conditions for random SA-permutations.

Kostyukova O. I.
Asymptotic expansions of the solution function to parametric nonlinear programming problems. pp. 29--35
E-mail: kostyukova(at)

Summary: Convex parametric mathemetical programming problems are investigated. Regular and irregular situations are considered. Three types of asymptotic expansions of the solution function with respect to the parameter deviation are studied.

Poljakov L. Ya.
Series of finite groups with operators. pp. 36--38

Summary: It is proved that if G is a finite p-soluble group with a operator group A such that (|G|, |A|) = 1, then an A-chief series of G is p-conformal with some A-maximal series of G.



Kushnir V. N.
Multimode phase transition to superconductivity in superconductor/ferromagnet multilayers. pp. 39--42
E-mail: vnkushnir(at)

Summary: The superconductor/ferromagnet multilayer critical states are investigated in the diffusive limit of the superconductivity microscopic theory. The broadening of the transition resistive characteristics is explained in terms of the multimode solution of the boundary problem for Usadel equations.

Goltsev M. V.
Modification of the structure and properties of zirconium on implantation of heavy ions with high energy. pp. 43--46
E-mail: mgoltsev(at)

Summary: By the methods of scanning electron microscopy and mechanical tests the study has been made of the structure and performances of hardening of zirconium presented by a parcel of foils with a thickness of < 25 µm irradiated with ions of neon and argon of high (230 MeV) and superhigh (460 MeV) energy. The indicated method of application has allowed investigating the parcel of samples with a thickness comparable with a magnitude of the projective run of ions and estimating dynamics of progressing of radiation effects at structural damages and introduced ions. The greatest hardening is connected to the accumulation of the introduced ions and is supervised to a greater extent at beaming by ions of higher mass and energy.

Tomilchik L. M.
Quantized action and discrete time in Born's reciprocally-invariant approach. pp. 47--51
E-mail: lmt(at)

Summary: It is shown that the use of M. Born's reciprocally-invariant interval considered as the fundamental SU(3,1) -symmetrical metric invariant of extended phase space leads under some natural assumptions to the operator of action, the eigenvalues of which are multiple of the minimal action value equal to Planck's constant, and to the discreet time nonlinearly dependent on sequential natural numbers.



Zelenkovskii V. M., Bezyazychnaya T. V., Soldatov V. S.
Quantum chemical modelling of sorption of chromate ions by chemosorbent with amino-amide groups. pp. 52--56
E-mail: soldatov(at)

Summary: The quantum-chemical modelling of the structure of complexes of chromate ions and N-(2-amino-ethyl) amide groups of FIBAN AK-22 ion exchanger in the acid environment is made. The structure of sorption complexes is established. It is shown that the fullest linkage of the chromate ion with functional groups occurs in the strong acid environment. The presence of Cl ions essentially does not reduce the size and the velocity of the chromate sorption since they do not form strong complexes with functional groups while SO42- interacts with the N-(2-amino-ethyl) amide groups of polymer, reducing the sorption of CrO42- and slowing down its velocity.

Gilep I. L., Usanov S. A.
Structural polymorphism of the ACE gene of elite athletes. pp. 57--61
E-mail: agilep(at), usanov(at)

Summary: The human physical performance is strongly influenced by genetic factors. The study of the correlation of the physical performance with an expression of certain genes is one of the foreground approach in modern sport practice. One of the most thoroughly studied genetic marker of physical performance of athletes of various ethnic groups is a gene of angiotensin converting enzyme (ACE). Angiotensin converting enzyme is the one of the enzymes of the rennin-angiotensin system, the crucial humoral regulator of arterial pressure. The ACE gene has insertion-deletion polymorphism (I- and D-alleles) with three corresponding types of polymorphs: two homozygous types I/I and D/D, and heterozygous type -- I/D. The performed in this work study showed a significant (P < 0.05) prevalence of the D/D genotype (65%) in the group of athletes specialized in hammer throw and shot-put. Athletes specialized in sprint runners have a prevalence of the genotype with D alleles (D/D and I/D). Team game players and runners (specialized over the distance range 800--5000 m) is authentic (P < 0.05) differed from the control group with prevalence I/I of the genotype. These results support a positive association of ACE polymorphism with the elite physical performance and therefore ACE can be utilized as an athlete abilities diagnostic marker.

Agabekov V. E., Kashevsky B. E, Kashevsky S. B., Manina E. Ju., Kekalo E. A., Prokhorov I. V., Ulashik V. S.
Preparation and properties of nanocrystalline cobalt ferrite for low-frequency ferromagnetic hyperthermia. pp. 62--65
E-mail: ekekalo(at)

Summary: 10--30 nm stoichiometric cobalt ferrite particles and model suspensions on their basis for local thermal therapy of malignant tumors were produced, their toxicity and infiltration in tumor tissues of experimental animals were studied, magnetodynamics and energy dissipation were investigated under the action of a 430 Hz AC magnetic field with an amplitude up to 1250 Oe, nanocrystalline cobalt ferrite potential for creation of nanodisperse of sources heating was shown.



Lobanok E. S., Laurashchuk U. V., Fedulov A. S., Vasilevich I. B., Baida A. G.
5-Aminolevulinic acid-induced porphyrinogenesis in the peripheral blood lymphocytes of multiple sclerosis patients. pp. 66--70
E-mail: krzhes(at)

Summary: The ability of peripheral blood lymphocytes (PBL) of healthy donors and multiple sclerosis (MS) patients to carry out 5-aminolevulinic acid (ALA)-induced porphyrinogenesis and cellular resistance to damages photosensitized by endogenous porphyrins were studied. PBL of MS patients in comparison with the cells of healthy donors characterized by a decrease of the protoporphyrin (PP) formation after 4 and 18 hours of incubation with exogenous ALA (0.8 mM) and a lesser sensitivity to the photodynamic action (PDA) sensitized by endogenous porphyrins were shown. PDA with a dose of 31.6 kJ/m2 in the conditions of excessive porphyrin pigments accumulation (2h, 37 °C) resulted in the 1.2 times increased cellular level of TBA-active products in PBL of sick people, whereas in healthy donors it was elevated 1.9 times. Furthemore, the lymphocytes in MS patients displayed a greater viability right after and at remote time intervals (18h) after the photodynamic treatment.

Lukashenko T. M., Soltanov V. V.
Modification of physiological processes during prolonged soya consumprion. pp. 71--78
E-mail: biblio(at)

Summary: The consumption of ordinary and transgenic soya (30% additions to the diet, 6 months) by rats inverted the reflex responses of gastric smooth muscles after intragastric infusion of 1 ml milk, but the duodenal activity (in most experiments) and the heart rate did not change. No significant differences in the effects of ordinary and transgenic soya were found.

Semenchenko V. P., Razlutskij V. I., Buseva J. F.
Settlement process of artificial macrophytes by zoo-plankton. pp. 79--82
E-mail: zoo23l(at)

Summary: The experimental study of the settlement process by planktonic crustaceans of a new biotope (artificial macrophytes) was carried out. It is established that the average rate of settlement of artificial macrophytes was higher in Cladocera as compared with Copepoda. Most of species invaded to the new biotope from a natural macrophytes bed (rush), but the artificial biotope had its species structure. The sharp changes in the species structure and abundance during a very short time (3 h) can confirm horizontal migrations of zooplankton.

Antanouskaja L. I., Skorb E. V., Sviridov D. V., Belyasova N. A.
Antimicrobial activity of thin-film TiO2 photocatalysts towards gram-positive and gram-negative bacteria. pp. 83--87
E-mail: nl95404(at), sviridov(at)

Summary: The antibacterial activity of thin-film photocatalysts based on titanium dioxide has been investigated using representative strains of gram-negative and gram-positive bacteria: Pseudomonas fluorescens, Escherichia coli, Lactococcus lactis, and Bacillus subtilis. It has been shown that the nanostructured TiO2 films modified with a small amount of photodeposited silver (1--2 monolayers) exhibit the high adsorption capacity towards microorganisms and the excellent antimicrobial response that ensures the radical (70-fold) enhancement of the ultraviolet bactericidal activity. This makes them a promising material for advanced reagent-free disinfection systems. It is shown that the higher susceptibility of gram-negative bacteria to the photocatalyst action as compared to the gram-positive ones is due to the comparative morphologies of their cell envelopes.



Romanov A. V., Okhrimenko A. E., Shaliapin S. V., Semashko P. G.
Devices of coherent compensatuion and decorrelation of two-layer background returns. pp. 88--93
E-mail: alevkurp(at)

Summary: In the work a tracking compensator of two-layer background returns is synthesized. This includes the development of a functionally justified structure of two-channel interperiod subtracter as well as discriminators of error signals of circuits forming optimal weighting coefficients in delay channels. The processes of cancellation and decorrelation of background returns are analyzed. It is made for two theoretically justified and practically significant shapes of the correlation function of jitter, namely, exponential and exponentially parabolic shapes. The validity of the superposition principle in the case under consideration is proved, and the efficiency of coherent compensation of background returns is estimated.

Greated C. A., Cosgrove J. A., Fomin N. A.
Monitoring of ultrasound waves by digital laser speckle interfer-ometry. pp. 94--98
E-mail: fomin(at)

Summary: Digital Laser Speckle Interferometry has been applied to the visualization and quantitative measurement of an acoustic standing wave in water. The acoustic standing wave has been generated in a glass tube filled with salt water submerged in a rectangular tank filled with the same salt water matched in refractive index to the glass of the internal tube. Propagation of the sound wave through the water causes fluctuations in the refractive index which produce minute deflections of the collimated laser beam passing through the measurement volume. This results in a diffraction pattern modulated by the dynamic speckles at the far side of the measurement volume which is recorded using a high resolution digital CCD camera.



Garetsky R. G., Tolstosheyev V. I., Kudriavets I. D.
Structures suitable for underground gas storages in the Pripyat Trough. pp. 99--105
E-mail: igig(at), belgeo(at)

Summary: Three types of local structures described in the article that could be used as underground gas storages in the Pripyat Trough are as follows: traps of exhaused oil pools, salt uplifts of the Upper-Famennian saliferous strata and interdome uplifts of turtleback type. The third type structures have been described in more detail. Deposits of the Mytva suite of the Moscow stage of the Middle Carboniferous and of the Korenev suite of the Indian stage of the Lower Triassic are of particular interest as reservoirs. Clayey formations of the Gulevichi suite of the Moscow stage of the Middle Carboniferous and Dudichi suite of the Tatarian stage of the Upper Permian serve as a caprock for the Mytva sandstones. The Korenev sandstones are a reference horizon, and the overlying rocks of the Mozyr suite of the Olenek stage of the Lower Triassic serve as an additional caprock. Seismic investigations using the reflection method by CDPS 2(D) and 3(D) and drilling works are suggested to be performed within six interdome uplifts.



Kulesh I. V., Malashko V. V.
Morphology of the skeletal muscles of pigs acted upon by low-intensity laser radiation. pp. 106--109
E-mail: science(at)

Summary: The morphology of the skeletal muscles of pigs under the influence of laser radiation is investigated. Laser radiation boosts the myogenesis and the functional activity of the ultrastructural components of the muscles.

Khochenkov A. A., Khodosovsky D. N.
Heat balance of stock buildings for weanling piglets. pp. 110--114
E-mail: belniig(at)

Summary: The most effective version of the reconstruction of a weanling piglets building is a combination of the fence construction heat rehabilitation (coefficient of heat transfer resistance for walls -- 3.2, for floors -- 3.7 m2 °C/Wt, respectively) and air feeding without active inducement. The ventilation system with air feeding from special ventilation rooms allows one to utilize the essential part of the animal's biological heat in winter and transition periods and to reduce the heat expenditure for 45 wt per hour for one weanling piglet.



Prokopenko T. K.
Analysis of the effectiveness of Intercorporate communications. pp. 115--119
E-mail: t-prokopenko(at)

Summary: The article touches upon the problems of launching and further controlling the process of intercorporate information exchange between the enterprise that produces manufactured products and its customers using modern technologies and the Internet. The suggested method of management of intercorporate communications is the Internet resource of the enterprise -- the Internet site with the option of differential access to its levels, and also the statistics that shows the customer's awareness of the information on the site and that is based on the analysis of special program files. The emphasis is laid on the effectiveness measurement of the above-mentioned method and on the possibility of its automatization. The model of the effectiveness measurement of marketing communications is based on the following elements of the system of intercorporate information exchange: the exact time of receiving information, the degree of the customer's awareness of the information (high/low), technical pecularities of the customer's working place (the degree of the customer's computerization).

Zaitsava N. V.
Development of the system of social security of the rural population of Belarus. pp. 120--123
E-mail: lockaut(at)

Summary: The article is devoted to the problems of improvement of social consumption fund of collective-farmers 1965-1975. The main achievments in the economic development, including its agricultural sector in that period, are made the necessary possibilities for modernization of the social consumption fund of collective-farmers. For studying the social and living conditions of Belarusian collective-farmers, the questions of development of the social consumption fund are general at that time.

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