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Doklady of the National Academy of Sciences of Belarus, 2009, Vol.53, No.4

Homepage / Publications / Scientific Journals

Doklady of the National Academy of Sciences of Belarus, 2009, Vol.53, No.4

(Doklady Natsionalnoi Akademii Nauk Belarusi)

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

Volume 53, Number 4; July-August, 2009

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Demidenko V. M.
Conditions of effective solvability of the quadratic problem of selection. pp. 5--9
E-mail: demidenko(at)

Summary: The cone, for which strong resolvability of the quadratic problem of selection is guaranteed, is described in the four-index matrixes space.

Matalytski M. A., Koluzaeva E. V.
Markovian queuing networks of arbitrary topology with incomes. pp. 10--17
E-mail: koluzaeva(at)

Summary: Methods of finding expected incomes for Markov queuing networks of arbitrary architecture with incomes are considered. Examples of application of such networks as mathematical models of various objects are obtained.

Erovenko V. A., Marton M. V.
Generalization of Kato stability theorem to essentially semiregular operators. pp. 18--22
E-mail: erovenko(at)

Summary: The stability properties of bounded essentially semiregular operators in Banach space as generalizations of semi-Fredholm operators are discussed. This article is devoted to the proof of generalization of Kato theorem for essentially semiregular operators at commuting perturbations.

Shamukova N. V.
Diophantine approximations by monic polynomials and nonmonotonic right-hand side. pp. 23--26
E-mail: shamukova_n(at)

Summary: In the article it was proved that integral monic polynomials of arbitrary degree and with the convergence limitation of some series can approximate zero with a given order on a set of zero measure and nonmonotonic right-hand side.

Usnich A. V.
Non-commutative cluster mutations. pp. 27--29
E-mail: ausnich(at)

Summary: In the work non-commutative cluster mutations are defined and studied. For a particular mutation matrix it is proved that the iteration of cluster mutation is assigned by non-commutative Laurent polynomials, and this gives an independent proof of the Laurent phenomenon in the commutative case.

Kilbas A. A., Zhukovskaya N. V.
Closed solution of linear inhomogeneous differential equations of Euler type with fractional derivatives. pp. 30--36
E-mail: anatolykilbas(at)

Summary: Linear inhomogeneous differential equations with a finite number of the Riemann--Liouville fractional derivatives, being analogues of Euler-type ordinary differential equations, are investigated. Using the direct and inverse Mellin transforms and the residue theory, partial solutions of the considered equations are established in terms of the generalized hypergeometric function and of the Euler psi-function.

Demenchuk A. K.
Control problem of a spectrum of strongly irregular periodic oscillations. pp. 37--42
E-mail: demenchuk(at)

Summary: The linear control periodic system with reverse communication is considered. The control problem of a spectrum of irregular oscillations is solved.



Gusak N. A.
Nonreciptocity effect in kinetic phenomena in photorefractive crystals. pp. 43--46
E-mail: rectorat(at)

Summary: It is shown that in a photorefractive crystal with a low concentration of acceptors a time of transition to the excited stated (and inversely) decreases with increasing the light intensity. In this case, the decrease of time of the direct process appears to be larger.

Malik A. A., Satsunkevich I. S.
Production of the (t-t+)-atom at VEPP-4M. pp. 47--51
E-mail: aliasimmalik(at); satsun(at)

Summary: Basic properties of a possible bound state of t+ and t- are given in this article. A total cross section of (t-t+) production in electron positron annihilation taking into account radiative corrections and experimental widths of initial beams is calculated. It is shown that modern experiment is able to observe (t-t+).

Zhestkov S. V., Romanenko A. A.
Constructing and analysis of soliton-like solutions of (1 + 1), (2 + 1), (3 + l)-dimensional Schrodinger equations with the third power nonlinearity law. pp. 52--57
E-mail: zhestkov_s(at)

Summary: The problem of existence of soliton-like solutions of (1 + 1), (2 + 1), (3 + 1 )-dimensional Schrodinger equations with the third power nonlinearity law is investigated. The numerical-analytical method of constructing solitons is developed.



Anishchenko I. V., Andrianov A. M.
Study of the conformational mobility of the HIV-1 subtype A V3 loop for the rational structure-based drug design. pp. 58--63
E-mail: anishchenko.ivan(at); andrianov(at)

Summary: Molecular dynamics simulations were implemented for the HIV-1 subtype AV3 loop on the basis of its static 3D structure followed by determining the rigid V3 segments and evaluating by molecular docking methodology the masking effect that can occur due to interaction of the V3 loop with the two virtual molecules constructed previously by tools of computational modeling and named CycA and FKBP peptides. As a result, the V3 segments preserving their structural parameters during the molecular dynamics computations were defined to present the universal targets for anti-AIDS drug researches. From the data on molecular docking, synthetic analogs of the CycA and FKBP peptides were suggested being suitable frameworks for making a reality of the V3-based anti-HIV-1 drug projects.

Babenko A. S., Sinelyov V. A., Britikov V. V., Tutubalina E. A., Gilep A. A., Usanov S. A.
Expression of CYP19A1, CYP1B1 and ERBB2 genes in human breast cancer tissues. pp. 64--67
E-mail: usanov(at)

Summary: This article is devoted to the study of a relative expression level of CYP19A1, CYP1B1, and ERBB2 genes in samples of human breast tumors. The aim was to detect a possible relationship between relative expression levels of these genes using correlation analysis. A relative gene expression level of ERBB2, CYP19A1, CYP1B1 was determined in 50 tumor samples of human breast tissue in real-time PCR. These quantitative data were normalized to GAPDH. We found a statistically significant correlation between the relative expression level of CYP19A/CYP1B1 (rs = - 0.508, P < 0.001). Between ERBB2/CYP19A1 (P = 0.638) and ERBB2/CYP1B1 (P = 0.438) a statistically significant correlation of the relative expression level was unable to identify what can be explained to different mechanisms of initiation and development of tumors caused by either the distortion of biosynthesis and metabolism of steroid hormones (CYP1B1, CYP19) or ERBB2-proxy tumors.

Matrunchik Ju. V., Vorobieva E. V., Krutko N. P., Basalyga I. I.
Influence of different-nature surfactants on the properties of polyacryl acid-based polymer hydrogel. pp. 68--72
E-mail: secretar(at)

Summary: The article presents the results of investigation of the colloid-chemical properties of dispersion of polyacryl acid-based polymer hydrogel (PHG) in aqueous solutions of surfactants depending on the surfactant type and concentration. It is shown that a cation-type surfactant evolves absorbed water and a non-ionic surfactant practically does not exert any influence on the rheological properties of hydrogel dispersion. Results of comparison of anion-type (soldium dodecylsulfate and sodium oleate) surfactants have revealed essentially higher values of rheological characteristics for the structure of PHG with soldium oleate. The cross-linking, when hydrogel interacts with sodium oleate, yields a product with new properties differing from those of the initial components.

Gerlovskij D. O., Litvinko N. M., Kuchuro S. V., Gros N. N.
Anticonpetitive inhibition of the activity of pancreatic phospholipase under the action of 2-propanoil-5-(2,4,6-trimethylphenyl)-cyclohexane-1,3-dione. pp. 73--76
E-mail: al_h(at)

Summary: The kinetics of the inhibiting action of 2-propanoil-5-(2,4,6-trimethylphenyl)-cyclohexane-1-3-dione (compound I) on the activity of pancreatic ФЛA2 is investigated. The Linuiver-Berk graphical method in double reverse coordinates has defined the inhibiting mechanism of phospholipase with the participation of ФЛA2 in type of conjugating or anticompetitive deceleration by this 5-mesityl-substituted cyclohexane b-triketone (Kmi = 1.6 • 104 M, KSi = 1.3 • 10-2 M, Ki = 5.3 • 10-3 M) and without it (Km = 3 • 10-4 M, KS= 1.0 • 10-4 M), Vmax &#gt Vmaxi, 1.7 • 10 and 0.74 • 10 µmole • min-1 • mg-1 respectively. In experiment the action of compound I upon phospholipolysis can be made in succession due to the interaction of mesithyl or ketone fragments with hydrophobic sites and agrinyl residues of enzyme necessary for participation in catalysis.



Moroz I. V., Eryomin A. N., Mikhayilova R. V., Lobanok A. G.
Comparative characterization of catalases synthesized by Penicillium piceum F-648 A3 under different cultural conditions. pp. 77--81
E-mail: enzyme(at)

Summary: In the studies of the influence of mono- and polyalcohols on biosynthesis of extracellular catalase by P. piceum F-648 A3 it was found that ethanol serves as an activator of catalase synthesis. Introducing 4% (v/v) ethanol into the nutrient medium ensures an increase in the enzyme production and fungal mycelium productivity 4.5 and 7.6 times, respectively. Under the above-mentioned conditions the fungus synthesizes catalase with an elevated initial rate and H2O2 decomposition efficiency -- 4.1--4.9 times and 2.6--3.4 times respectively. The enzyme is characterized by high operational stability and specific activity exceeding 1.5--19.2 times this parameter in other catalases.

Kulesh V. F.
Growth and survival of larvae of the freshwater shrimp Exopalaemon modestus (Heller) in liquid wastes of a thermoelectric power station. pp. 82--87
E-mail: victor_kulesh(at)

Summary: The growth and survival of larvae of the freshwater shrimp Exopalaemon modestus (Heller) were analyzed under the temperatures 16--19°C, 20--22°C, 25--26°C in liquid wastes of the Berezovskaya electric power station (Belarus). It is shown that the larval period consists of two stages of zoea and continues 5--10 days depending on the temperature. The survival comes to 54--100%. An average length of zoea I, II and postlarval is 4.08 ± 0.12 mm, 4.47 ± 0.23 mm and 4.70 ± 0.26 mm respectively, and an average mass is 0.54 ± 0.11 mg, 0.80± 0.15 mg and 1.02 ± 0.24 mg respectively.

Galinousky D. V., Evtushenkov A. N.
Expression of b-carotene synthesis genes in different strains of gram negative bacteria. pp. 88--91
E-mail: dimgal200(at)

Summary: A plasmid based on a broad host range vector is harboring genes of synthesis of b-carotene. The plasmid was transferred to different strains of gram negative bacteria by conjugation. The obtained strains collected b-carotene and had yellow pigmentation of bacterial colonies. Strain Psedomonas stutzeri B975 harboring the plasmid produced the maximum yield of pigment. This strain collected b-carotene 3.2 as much as wild-type bacteria Pantoea agglomerans 206. We revealed the optimal growth temperature and the maximum pigment collecting temperature of Ps. stutzeri B975 caring the b-carotene synthesis genes.



Chakova N. N., Mikhalenka A. P., Shloma E. N., Chebotareva N. V., Kruglenko S. S., Shelkovich S. E., Krupnova E. V., Demidchik Yu. E.
Gene polymorphism of biotransformation enzymes in ovarian cancer patients. pp. 92--96
E-mail: XTRO_8127(at)

Summary: The aim of this research was to study the polymorphism of GSTT1, GSTM1 and NAT2 in ovarian cancer patients. The highest odd ratio for an ovarian cancer risk reached 3.60 (95% CI 0.85--15.29) in the GSTT1(-)/GSTM1(+) genotypes.



Astapenko V. N.
Crustul anomalies of the electrical conductivity and paleotrougs of the East European platform. pp. 97--101
E-mail: astapenko(at)

Summary: A map of crustal anomalies of electrical conductivity of the East European Platform is presented. It is shown that a great many anomalies are situated in troughs of the Platform. Most of the good conductors (S > 1000 S) occur in the upper crust (0--15 km) of aulacogen and troughs.



Vityaz P. A., Sosnovskiy L. A., Sherbakov S. S.
New approaches in mechanics of deformable systems. pp. 102--110
E-mail: sersher(at)

Summary: New approaches to mechanical and mathematical modeling of tribo-fatigue systems simultaneously subject to complex loading are considered. A new method of comprehensive study of the mechanical state of a deformable system and its elements including the statement and solution of stress-strain state, damage and limiting state problems is presented. Results of a roller/shaft type system research by such a method are given.

Pinchuk L. S., Bannyi V. A., Goldade V. A.
Effect of radio absorption intensification by nanosize components of polymer composites. pp. 111--114
E-mail: mpri(at); bannyi(at)

Summary: Radiophysical characteristics of polymer composite materials filled with metals and ferrites have been studied as dependent on the intensity of physical-chemical processes at the interfaces between the polymer binder and filler particles during thermal molding of a composite. The kinetics of these processes controlled by varying time and temperature regimes of the composite formation and dispersivity of the filler is shown to be a determining factor in the structure formation of new phases at the polymer-filler interface and the probability of appearing colloidal particles in the polymer matrix affecting much scattering and absorption parameters of the energy of SHF radiation.

Sychevskij V. A.
Mathematical simulation of the technological process of wood drying. pp. 115--119
E-mail: vas(at)

Summary: A mathematical model for heat and mass transfer and stress-deformed state of material is presented for description of the technological process of wood drying. The performed calculations have shown that maximum stresses appear near the sample surface. A detailed study of the development of stresses with time has made it possible to determine maximum mechanical load zones. In view of this information, the technological process of drying is calculated using GOST 19773-84 "Carving Materials of Soft and Hardwoods. Drying Regimes in Chambers of Batch Operation". The analysis of the results obtained has shown that in principle, the developed mathematical models and the numerical calculation methods can describe drying processes.



Tsyganov A. R., Sheliuto B. V., Sheliuto A. A.
Agroeconomic efficiency of forage crops cultivation for green mass and raw in crop rotation. pp. 120--124
E-mail: kancel(at)

Summary: The article shows the results of research on estimation of the agroeconomic efficiency of forage crops cultivation in crop rotation for green mass and raw in the conditions of Belarus. The efficiency of crop rotation for green mass and raw was estimated according to the structure of gross produce and economic usage. We have established an advantage of pasture and hay types of crop rotation on the basis of perennial grasses. Among the crops examined, the most productive and economically efficient are alfalfa for sowing as single crop and in combination with Festuca orientalis.

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