Doklady of the National Academy of Sciences of Belarus, 2005, Vol.49, No.2
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Doklady of the National Academy of Sciences of Belarus, 2005, Vol.49, No.2

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
Zabreiko P. P., KirsanovaEvkhuta O. N.
Method of minimal residuals in Banach spaces. pp. 510
Summary: The new result on the convergence of the minimal residual method for nonlinear operator equations in Banach spaces with the Bynum inequality is presented.
Malyutin V. B.
Approximate evaluation of functional integrals over of spine variables. pp. 1116
Summary: The article presents the method of approximate evaluation of spine variable functional integrals and matrixvalued functional integrals. Moreover, to evaluate integrals we simulate the random time of trajectory changing, not the random values of trajectory in fixed time.
Grinko A. P.
Abeltype integral equation and local fractional integrals and derivatives. pp. 1721
Summary: The Abeltype integral equation is considered in the neighborhood of a real line. For it the solvability conditions in the space of summable functions are proved and its solution in closed form is constructed. On the basis of the results obtained, local fractional integrals and derivatives are introduced and some of their properties are investigated. In particular, local fractional derivatives of power and logarithmic functions are evaluated.
Lepin V. V.
Algorithm for finding the independence number of a recursively constructed hypergraph. pp. 2225
Summary: Informally, a recursive hypergraph class is the one, in which any sufficiently large member in the class can be formed by smaller successively joining members in this class at specific vertices called terminals. Letting the maximum allowable number of terminals be k, we sometimes refer to these as kterminal hypeigraphs. We give a lineartime algorithm for finding the independence number of a kterminal recursively constructed hypergraph.
Evtukhova S. M., Monakhov V. S.
Finite groups with subgroup core factor orders free of squares. pp. 2629
Summary: Study is made of finite groups, whose orders of subgroup core factors are not divided into squares of simple numbers. Some properties of such groups are revealed. In particular, it is proved that their derivative length does not exceed 4.
Karaliova E. V., Lebedev A. V.
Index of singular integral operators with discontinuons oscillating coefficients. pp. 3034
Summary: The paper presents the procedure of index calculation of singular integral operators with discontinuous oscillating coefficients in terms of operators with piecewise continuous coefficients.
PHYSICS
Vereshchagin M. N., Komarov F. F., Shepelevich V. G., Ostrikov O. M.
Influence of the implantation of N_{2}^{+} ions on the inhomogeneous plastic warp of an amorphous alloy FeCrMoVBSi. pp. 3537
Summary: The influence of the implantation of differentdose nitrogen ions on the regulari ties of the inhomogeneons plastic warp of an amorphous FeCrMoVBSi alloy is studied. It is found that the ion implantation decreases the number of shift bands in the region of local surface warp. In this case, the length of shift bands in the form of semirings decreases and in the form of beams  increases. The flaking of warp regions in the ion  implanted amorphons strips is revealed.
Demidtchik V. I., Kornev R. V., Koukharchik P. D.
Mathematical modeling of scattering properties of wire particles of arbitrary configuration and composite materials on their base. pp. 3841
Summary: A numerical technique of polarizability tensors calculation for thinwire elements is developed. This method is based on the numerical solving of Poklington's integral equation. Using the known polarizability tensors, calculations of the effective properties of artificial composites based on these particles have been made.
Kudryashov V. V., Tomilchik L. M.
Phenomenological approach to description of intragalactic motions. pp. 4246
Summary: The proposed dynamical model is described by the Hamiltonian which is the simple function of the spherically symmetric oscillator Hamiltonian. The elliptic motions in this model reproduce the characteristic features of the intragalactic motions. The empirical rotation curves of the typical spiral galaxies are well approximated by means of the obtained universal threeparameter formula.
CHEMISTRY
Bil'dyukevich A V., Fen'ko L. A.
Critical solution temperatures in polysulphonepolyethyleneglycoldimethylacetamide system. pp. 4749
Summary: The upper critical solution temperature and the lower critical solution temperature for the polysulphonepolyethyleneglycol (PEG400)  dimethylacetamide ternary polymer system have been established using the cloudpoints method.
BIOLOGY
Alekseichuk G. N., Zadvomova J. V., Groot S. P. C., Bergervoet J. H. W.
Peculiarities of cell cycle activation at germination and desiccation of Brassica Oleracea L. seeds of different physiological quality. pp. 5053
Summary: Flow cytometric evaluation of cell cycle activation was done on axis nuclei of white cabbage seeds to study the changes associated with seed physiological quality and depending on desiccation tolerance. The initiation of DNA replication started in seed axes just before radicle protrusion and related to the cell water status. Progression in the cell cycle from G_{1} towards G_{2} negatively correlated with seed quality. Desiccation of highquality seeds in 24 h and in 48 h of imbibition resulted in progressing the nuclear activities under subsequent rehydration. Desiccation of lowquality seeds with a high amount of chlorophyll in 48 h of imbibition (just before radicle protrusion) decreased their germination performance.
Soltanov V. V., Lukashenko T. M.
Changes in the efferent activity of the cervical sympathetic nerve after the introduction of endotoxin E. colii onto the jejunum and ileum. pp. 5456
Summary: In experiments on thiopentalanesthetized rats it was found that introducing lipopolysaccharide E. coli (10 mkg) into the distal ileum decreased the efferent firing rate in the cervical sympathetic nerve while injecting the preparation into the jejunum was accompanied both by activating and inhibitory effects in the nerve, thus pointing to possible actions of endotoxins on brain structures by an interoceptive sympathetic reflex mechanism.
Sachok G. I., Kamyshenka H. A.
Vegetative substance and its carbon equivalent in the regional geoecosystem of Belarus. pp. 5761
Summary: The methods and means used in the informationmodelling system "Biogeocenosis variety of Belarus" allowing one to carry out ecological diagnostics of geoecosystems and also the results of modelling calculations are given in brief.
Derengovskaya R. A., Ostapenya A. P.
Zooplakton accumulation in sediment traps and the evaluation of the settling matter flux. pp. 6268
Summary: In studies of the processes of sedimentation of suspended matter by sediment traps installed in the pelagial zone of Lake Naroch, considerable concentration of zooplankton was observed. It accounted for 20% of the dry weight of collected matter. While practically absent in the pelagial plankton, the dominant species in traps was represented by littoral crustacean Sida crystallina, which accounted for more than 80% of the total biomass of the zooplankton collected. High values of the weight of crustaceans brought about an error into calculations of the vertical flux of settling matter, thus increasing it during summer months by 1320%. The results obtained suppose the necessity of the quantitative assessment of zooplankton in sediment traps in investigations of sedimentation processes in lakes.
Lobanok E. S., Kvacheva Z. B., Votyakov V. I., Sbukanova N. A., Vorobei A. V., Nikolaeva S. N.
Inhibition of herpesvirus infections in continuous cultures of cells under photodynamic influence. pp. 6972
Summary: The photoinhibition of reproduction of variants of herpes simplex virus type 1 (HSV 1) sensitized by endogenous porphyrins is examined. The selective ability of herpes infected cells Vero and C6 to the increased synthesis of photodynamic active porphyrin pigments in the presence of 8aminolaevulinic acid (ALA) is revealed. Optimum conditions of photodamage virus z infected cells are determined (ALA0.6 mM, incubation of a cellular monolayer with ALA1.5 h, illumination dose  19.5 kJ/m^{2}, influence on the early stages of development of an infection). The photodynamic influence sensitized by porphyrins is most expressed to acyclovir resistant variant of HSV 1.
Nikandrov V. N., Polukoschko E. F., Lukashevitch V. S., Lukashevitch I. B., Balaschko S. I., Ostrovsky Yu. P., Sidorenko G. I.
Peculiarities of the development of myocardial cellular elements of newborn rats in culture. pp. 7376
Summary: Monolayer cultures of heart tissue cellular elements (including fibroblasts, endotheliocytes, smooth muscle cells, nervous cells and cardiomyocytes) were preparated. The dynamics of development and fading of these cultures during 30 days was described and compared with the ^{3}Hthymidine incorporation, extracellular lactate dehydrogenase activity, creatine kinase activity of cells. Two types of the functional activity of cardiomyocyte groups were demonstrated, and effect of plasminogen on the cardiomyocytes contractile ability was established.
Bushmakina I. M., Martynova M. A., Drozdova N. I., Konev S. V.
Cholesterol effect on the lipid state in liposomal rifampicin. pp. 7779.
Summary: The cholesterol effect on lipid bilayer microviscosity and lipid peroxidation in liposomal rifampicin was studied. It was found that the lipid bilayer is stabilized and lipid peroxidation is inhibited by cholesterol. Cholesterol has a property of "structural antioxidant" only up to its definite content in liposomal membranes.
Semenchenko V. P., Buseva J. F.
Formation of aggregations on zooplakton. pp. 8082
Summary: Spatial patterns of Crustacea (Cladocera and Copepoda) have been studied in pelagic and littoral zones in eutrophic Lake Obsterno (Republic of Belarus). Aggregations make the cladocerans which are typical for the littoral zone. The macrophytes lead to the increasing of the aggregation coefficient. In the most cases, aggregation coefficients are higher in midnight time as compared with midday. In the pelagic zone aggregations are observed only for Diaphanosoma brachyurum and Chydorus sphaericus. The adults, copepodit and nauplial stages of Copepoda are distributed randomly.
MEDICINE
Volosheniuk A. N.
Endoprosthetics of the hip joint in nonstandard clinical situations. pp. 8385
Summary: The author presents a new concept of endoprosthetics of a hip joint in nonstandard clinical situations (displastic osteoarthrosis, idiopathie coxartrosis, hip tumors, etc).
EARTH SCIENCES
Konischev V. S.
Types of the UpperFrasnian salt uplifts in the Pripyat trough. pp. 8688
Summary: Six types of UpperFrasnian salt uplifts were revealed using the present knowledge about an extent of halokinesis in the UpperFrasnian salt strata a, correlation of UpperFrasnian salt massifs with highamplitude faults and overlying internal and uppersalt Famenian deposits.
Taran L. N., Varaksa V. V.
Composition of the Grodno complex in the crystalline basement of the northwestern part of Belarus. pp. 8993
Summary: The present study of the gabbrodioritegranodioritegranite assemblage in the crystalline basement of the northwestern part of Belarus has resulted in revealing a specific suite (Grodno complex) with AMCG affinity. Fractional crystallization favoured the continuous evolution from mafic to acidic rocks. A latecollisional/postcollisional tectonic setting may account for the geochemical features of the Grodno rocks.
TECHNICAL SCIENCES
Sheleg V. K., Pyatov V. V., Kovchura A. S.
Extrusion of an isotropic material. pp. 9496
Summary: The problem of the presence of an intense condition in a powder is solved at its extrusion through a conic matrix with a cylindrical part. The material is squeezed out through a backlash formed by an internal surface of a matrix and an external surface drift, moving together with a powder. The drift necessary for the formation of tubular products represents a cylindrical core. The effort of expression is supposed distributed in the crosssection of a matrix homogeneously. The problem is shown to the solution of the differential equation with divided variables. Boundary conditions on the friction surface are set as Coulomb's law, and the condition of plasticity in a conic part of a matrix looks like s_{r}  s_{z} = s_{s}. As a result of the solution of this equation the distribution of pressure in conic and cylindrical parts of a matrix is found. Substitution into the obtained ratios of a zero boundary condition (external friction is absent) allows one to develop the ratio wellknown in the theory of pressure processing of metals.
Pochtennyi E. K.
Calculation of the design service life under accidental loading. pp. 97102
Summary: The numerical method of design resource determination at the random loading is considered. This method provides for: calculation of fatigue curve parameters at pulsating and symmetrical loads; construction of load blocks with regeard to the nonregularity and multifrequency as descending blocks of stresses; summing of fatigue damage by nonregular stresses and combined damage by blocks of the multifrequency random loading.
Timoshpolskiy V. I., Postolnik U. S., Ratnikov P. E., Kalinevich E. V.
Mathematical simulation of prim heating in the counterflow (in rolling heating furnaces). pp. 103107
Summary: The solution of the heat conduction problem for heating of prism ingots under counterflow heat transfer conditions is presented for the first time. The mathematical model proposed by the present authors enables one to calculate temperature fields in terms of ingot cross  sections in travelling sole and bar furnaces where ingots are placed with a clearance, and allsided heating takes place. The calculation results are compared with the unique experimental data obtained at the Republican Unitary Enterprise "Belarusian Metallurgical Works".
Yashcheritsyn P. I., Kheifets M. L., Klimenko S. A., Vasiliev A. S.
Technological and operation inheritance of quality indices in the service cycle of products of mechanical engineering. pp. 108113
Summary: A mathematic model for the inheretance of quality indices of mechanical engineering products describing different behavior regimes at the production and usage of engineering systems was derived.
SOCIAL SCIENCES AND HUMANITIES
Nikitenko P. G., Platonova L. A.
Estimation of the connection between enterprise work indices and export volume. pp. 114116
Summary: The enterprise work indices influence on the export volume has been investigated by the example of different enterprises of the Republic of the Belarus textile industry. The distinctions of the partial derivative function between initial indices and competitiveness coefficient, initial indices and export volume have been shown.
Beryozkina N. Yu.
Role of the book in dissemination of scientific knowledge in Belarus in XVIXVII centuries. pp. 117120
Summary: Activities of Belarus printing pioneer Frantsisk Skorina, his followers Symon Budny, brothers Mamonichi, Spiridon Sobol, fraternal and reformation printing houses and their role in the dissemination of scientific knowledge in Belarus in XVIXVII centuries are considered. Libraries were of great importance for the development of science.
Vashtomov G. V.
Civilized priorities of Belarus in the frontier area cooperation. pp. 121123
Summary: The introduction of scientifically grounded priorities in the frontier area cooperation in XXI century into the socialcultural practice that cover all aspects of the life of the society  economics, politics, law, culture is analyzed. It is emphasized that the specific character of the model for the consistent development of the Republic of Belarus is connected with reviving the best traditions of the socialcultural creation of the East Slavic community and is determined by the national interests of the intrapolitical stability and external security, preservation and development of the values of the material and spiritual culture of the Belarusian people.
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