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Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.1

Homepage / Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2008, Vol.52, No.1

(Doklady Natsionalnoi Akademii Nauk Belarusi)

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

Volume 52, Number 1; January-February, 2008

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Tikhonov S. V.
Generalized Severi--Brauer varieties over real fields. pp. 5--8
E-mail: tsv(at)

Summary: A reality criterion of function fields of generalized Severi-Brauer varieties defined over the real fields is obtained.

Usnich A.V.
Alternative presentation of the thompson group T. pp. 9--11
E-mail: ausnich(at)

Summary: The Thompson group T is an infinite simple group with the known presentation in terms of generators and relations. This paper derives a new presentation of this group which is much simpler and intuitive.

Dmitruk N. M.
Construction of optimal feedbacks by incomplete and inexact measurements of states of linear systems. pp. 12--17
E-mail: dmitruk(at)im. bas-net. by

Summary: The article deals with an optimal control problem for a linear time-varying system with constrained states and inputs subject to bounded disturbances on incomplete measurements. For the problem in question a notion of a solution that closes the system at one fixed future time instant is introduced. Based on this notion of the solution a method for closed-loop optimal feedback control in real time is suggested.

Shafransky Ya. M.
Computational complexity analysis of discrete optimization problems with hard computable objective functionals. pp. 18--21
E-mail: shafr(at)

Summary: A new approach for proving the NP-hardness of discrete optimization problems is proposed. The approach is illustrated by a scheduling problem for parallel machines and identical jobs with processing times dependent, in particular of the machine state at the moment when the machine starts the job processing. The main obstacle in the NP-hardness proof of this problem is the absence of a possibility to use the standard scheme for proving the NP-hardness of discrete optimization problems. The proposed approach may be also used for the complexity analysis of “usual” problems.

Mirotin A. R., Romanova M. A.
Parts of the spectrum of the algebra of generalized analytic functions. pp. 22--26
E-mail: amirotin(at), kazubomarina(at)

Summary: For positive semicharacters the criteria for the Gleason equivalence with respect to the algebra of generalized analytic functions is given.

Antonevich A. B., Dolichanin Ch., Reshich S.
Convergence of the trajectories of vector subspaces: the case of a single eigenvalue. pp. 27--32
E-mail: antonevich(at), dolicanin(at)ptt.yu

Summary: The sequence of the form Vn = An(V), where V is a given subspace of a finite-dimensional space L and A is a linear operator in L, is studed. Under the condition that A has only one eigenvalue, it is shown that the limit of Vn exists for arbitrary V and an expression of this limit is obtained.

Matysik O. V., Savchuk V. F.
Convergence of a method of simple iteration with a variable-alternating step for solution of the operator equations in the Hilbert space. pp. 33--37
E-mail: matysik(at)

Summary: An implicit iteration method with a variable-alternating step for solution of the operator equations in the Hilbert space is proposed. Convergence of the method is proved in the case of an apriori choice of a number of iterations, аnd apriori estimations of an error are obtained. For the iteration method the opportunity of application of a rule residual stop is studied. The case of the nonuniqueness of solution of the equation is investigated. The offered method solves the inverse problem of the potential theory.

Kostyukova O. I., Tchemisova T. V., Yermalinskaya S. A.
Explicit optimality conditions for convex semi-infinite programming problems. pp. 38--43
E-mail: kostyukova(at), tatiana(at), lanalex(at)

Summary: The article deals with convex Semi-Infinite Programming (SIP) problems. On the basis of the notion of immobile points, new first and second order optimality conditions are obtained. The obtained results are compared with some known optimality conditions for SIP. It is shown that in the case of the convex SIP problem not satisfying the Slater condition the proposed optimality conditions are more efficient.

Xiaolan Yi., Kovalev A. L., Shemetkov L. A.
Group classes defined by local functions. pp. 44--47
E-mail: shemetkov(at)

Summary: New criteria for existence and conjugacy of F-covering subfgroups in finite groups are obtained. An information on minimal non-F-groups (F is a partially saturated formation) is obtained. Proofs are not given.



Yearchuck D. P., Yerchak E. D., Kirilenko A. I., Popechits V. I.
Optical analogue of magnetic spin wave resonance. pp. 48--53
E-mail: dpy(at)

Summary: A new phenomenon is experimentally identified: electrical spin wave resonance (ESWR) consisting in characteristic splitting of vibration levels in optical spectra of interacting localized centers. Spectral positions of ESWR lines are determined in the linear approach by the quadratic dispersion law. It is found that the values of resonance mode amplitudes are inversely proportional to mode numbers (by a low excitation level). The prediction that Raman-ESWR and IR-ESWR are characterized by splitting constants with different values has been confirmed. Their ratio is approximately equal to two (by the frequencies of zero modes reduced to the same value). It is a key moment for ESWR identification. ESWR is the first stationary optical analogue of effects and phenomena accompanying magnetic resonance. It was established by the example оf carbynoids studied that the condensed state of the matter possessing simultaneously by ferroelectric and ferromagnetic properties can exist.

Matsevich I. G., Strekal N. D., Nowicky J. W., Maskevich S. A.
Application of surface enhanced Raman scattering for studying the interaction of berberine with DNA. pp. 54--57
E-mail: imotevich(at)

Summary: Spectra of UV-VIS, fluorescence and SERS spectra of berberine and complex berberine-DNA adsorbed on silver hydrosol are presented. Possible sites of intercalation of a molecule of berberine into a double chain of DNA are revealed.

Zhaunyak O. G., Borzdov V. M., Borzdov A. V., Podnyakov D. V., Komarov F. F.
Monte Carlo simulation of electron transport in SOI-MOSSETS. pp. 58--60
E-mail: zhevnyakol(at)

Summary: The numeric model of electron transport in SOI-MOSFETs is elaborated. By Monte Carlo simulation the dependences of an electron drift velocity on the channel length as well as the channel depth are calculated. The peak of the curves of the electron drift velocity as a function of channel depth is observed.

Goltsev M. V.
Synthesis of multicomponent ion-plasma coatings on the basis of nitrides of transition metals. pp. 61--64
E-mail: mgoltsev(at)

Summary: It is established that the method of mating plasma streams shapes coatings with adjustable composition, structure and properties depending on a value of an ion current, energy of ions and pressure of a reactive gas. It is revealed that the composition-complex structure of coatings based on chemical combinations of transition metals with nitrogen is characterized by fine dispersion and high texture in direction (311), and separate alloys of the Ti-Cr-N system are characterized by the two-phase state, including the amorphous state. The arguments of synthesizing triple nitrides having superhigh hardness and wear-resistance reaching the values of 40--50 HPa are stated.



Mozheiko F. F., Shevchuk V. V., Rydakovskaya T. G., Zhdanovich I. B.
New reagents for rust protection of road concrete products. pp. 65--69
E-mail: secretar(at)

Summary: A perspective method of increasing the longevity and resistance to attack by corrosive (salt) media for road concrete products by the use of impregnation of a composition based on inorganic salts and water-repelling agents is developed.

Lakhvich F. A., Litvinko N. M., Kuchuro S. V., Skorostetskaya L. A., Rakhuba G. N., Gerlovsky D. O., Rubinov D. B., Zheldakova T. A.
Phospholipolytic reactions as a model of detection of pesticide safety. pp. 70--74
E-mail: nata(at)

Summary: Lipolysis in vitro after preincubation of pancreatic phospholipase A2 with trаlkoxydim and its derivatives by the sensitive hemoglobin-used method was investigated.

Solomyansky A. E., Zhavnerko G. K., Agabekov V. E., Gracheva E. A.
Local adsorption of hydroxyapatite on the silicon surfase. pp. 75--78
E-mail: zhavn(at)

Summary: Adsorption of hydroxyapatite (HA) on the silicon surface modified by polyelectrolytes films and the tribological behavior of the formed coatings have been studied. The method of local modification of a solid surface by an HA particle using its adsorptions on the surface activated by microcontact printing of polyelectrolytes has been developed. This method of HA adsorption on the solid surface can be used for produсtion of implants.

Halauko Yu. S., Ivashkevich O. A., Matulis Vadim E.
5-Nitroimidazoles: quantum chemical investigation and quantitative of the structure -- biological activity relationship. pp. 79--83
E-mail: hys(at)

Summary: Quantum chemical calculations within the framework of DFT were carried out for a set of 5-nitroimidazoles. A physically interpretable QSAR model was developed, and a relationship between the biological activity and structural properties was obtained using the multiple linear regression method. Crucial properties of compounds and their relationship with the mode of action are discussed.



Gapeeva T. A., Rukavtsova E. B., Shulga N. Ya., Buryanov Ya. I., Volotovsky I. D.
Obtaining and characterization of transgenic potato plants synthesizing the surface antigen of hepatitis B virus. pp. 84--87
E-mail: gapeeva(at), ruk(at)

Summary: Transgenic potatoes of the Belarusian variety Vetraz expressing the gene of the surface antigen of hepatitis B virus (HBsAg) under control of the double promoter of 35S RNA of cauliflower mosaic virus (CaMV 35SS) have been obtained. The biochemical analysis of plants obtained has been carried out. The HBsAg amount in leaves, microtubers, and tubers of transgenic potatoes growing in vitro and in vivo was 0.005--0.035% of the total soluble protein. The HBsAg content in leaves and tubers amounted to 300--1500 ng/g of plant tissue. The obtained plants can be used as producers of vaccine against hepatitis B virus.

Orlovskaya O. A., Sakovich V. I., Lemesh V. A., Khotyleva L. V.
Callusogenesis and organogenesis features in intervarietal flax hybrids F1 (Linum unsitatissimum L.). pp. 88--91
E-mail: o.orlovskaya(at)

Summary: Conditions affecting the regeneration of shoots from hypocolyl segments of intervarietal flax hybrids F1 were estimated and optimized for developing accelerated methods of vegetative propagation of valuable genotypes as well as for carrying out genetic transformation of this crop. The data obtained have shown that the processes of callusogenesis, regeneration and acceleration in the culture in vitro depend on the genotype of the starting material. Hypocotyl segments from different parts of a seedling were revealed to exhibit a different capacity for regeneration. Application of explants from the upper part of hypocotyls allows production of the highest number of regenerants. A nutrient medium containing major mineral elements in half concentration, saccharose in 10 g/l concentration and agar -- in 8 g/l concentration is the most effective for accelerating shoots as compared with other media studied by us.



Hancharou A. E., Titov L. P.
Functional characteristics of monocyte-derived dendritic cells in patients with pulmonary tuberculosis. pp. 92--96
E-mail: andrei.hancharou(at), leonidtitov(at)

Summary: Impaired differentiation of monocytes into dendritic cells (DC) under influence of GM-CSF and IL4 has been found in the pulmonary tuberculosis. Expression of a costimulatory molecule CD86 was significantly reduced on DC derived from the patients with tuberculosis, while CD80 expression values were normal. The process of maturation of DC derived from the patients with tuberculosis under the influence of TNF-a was significantly impaired, as it was revealed by a decreased expression of CD80, CD86 and CD83. Production of proinflammatory pro-Th1 cytokine -- IL12p70 by DC in tuberculosis was not impaired, but production of antiinflammatory pro-Th2 IL10 was reduced significantly.

Kirillov V. A., Gladyshev A. O., Demidchik E. P.
Assessment of the significance of qualitative features of cell atypia in cytologic diagnosis of thyroid diseases. pp. 97--99
E-mail: kirillov(at)

Summary: Formulas for transformation of qualitative features of cell atypia to a quantitative form and for a diagnostic index have been derived. These formulas have made a basis for the developed technology of creating an expert system for diagnosis of malignant neoplasms on the base of a set of qualitative features of cell atypia.



Dyakonov O. M.
Numerical calculation and optimization of operating parameters of a muffle furnace. pp. 100--105
E-mail: deaconco(at)

Summary: The numerical solution algorithm of the mathematical model of the metal chip heating process in a continuous muffle furnace and a computer calculation program that allow one to determine the heat and mass transfer parameters have been worked out. The numerical modeling has been performed for three different lubricant-coolant compositions and six different furnace heights (all together 18 variants) at a furnace productivity of 2000 kg of chip per hour. The main characteristics of the chip heating process have been calculated. It is determined that the optimum furnace height at the point of its highest energy efficiency equals 4.5 m.

Kheifetz M. L.
Fractal parametrization of the formed interface of layers at synthesis of materials. pp. 106--109
E-mail: mlk-z(at)

Summary: Principles of transformation of fractals at the interfaces of structures, phases and layers of a composite material are offered.

Chorny A. D.
Application of the mixing models for determining an averaged rate of the chemical reaction in a homogeneous isotropic turbulent flow. pp. 110--115
E-mail: anchor(at)

Summary: In the present article the model for mixing with chemical reacting in a homogeneous isotropic turbulent flow is stated using both the method of statistical moments for calculation of hydrodynamic characteristics and the method of probability density function (PDF) of mixture fraction for the closing of unknown correlations responsible for chemical reacting. The multizone model is compared with the micromixing models (linear mean square estimation model and the binominal Langevin model), which are used in the equation for PDF with objectives to find out how their application affects a calculated averaged rate of the chemical reaction.



Aksamentova N. V., Nosova A. A., Tolkachikova A. A.
Mineral composition and genesis of paleoproterozoic ultramafites of the central part of Belarus. pp. 116--123
E-mail: aksam(at), tolk(at), nosova(at)

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