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

/ Publications / Scientific Journals

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

## CONTENTS

### MATHEMATICS

Zabreiko P. P., Kirsanova-Evkhuta O. N.
Method of minimal residuals in Banach spaces. pp. 5--10

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. 11--16

Summary: The article presents the method of approximate evaluation of spine variable functional integrals and matrix-valued 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.
Abel-type integral equation and local fractional integrals and derivatives. pp. 17--21

Summary: The Abel-type 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. 22--25

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 k-terminal hypeigraphs. We give a linear-time algorithm for finding the independence number of a k-terminal recursively constructed hypergraph.

Evtukhova S. M., Monakhov V. S.
Finite groups with subgroup core factor orders free of squares. pp. 26--29

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. 30--34

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 N2+ ions on the inhomogeneous plastic warp of an amorphous alloy Fe--Cr--Mo--V--B--Si. pp. 35--37

Summary: The influence of the implantation of different-dose nitrogen ions on the regulari ties of the inhomogeneons plastic warp of an amorphous Fe--Cr--Mo--V--B--Si 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 semi-rings 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. 38--41

Summary: A numerical technique of polarizability tensors calculation for thin-wire 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 intra-galactic motions. pp. 42--46

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 intra-galactic motions. The empirical rotation curves of the typical spiral galaxies are well approximated by means of the obtained universal three-parameter formula.

### CHEMISTRY

Bil'dyukevich A V., Fen'ko L. A.
Critical solution temperatures in polysulphone-polyethyleneglycol-dimethylacetamide system. pp. 47--49

Summary: The upper critical solution temperature and the lower critical solution temperature for the polysulphone-polyethyleneglycol (PEG-400) -- dimethylacetamide ternary polymer system have been established using the cloud-points 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. 50--53

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 G1 towards G2 negatively correlated with seed quality. Desiccation of high-quality seeds in 24 h and in 48 h of imbibition resulted in progressing the nuclear activities under subsequent rehydration. Desiccation of low-quality 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. 54--56

Summary: In experiments on thiopental-anesthetized 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. 57--61

Summary: The methods and means used in the information-modelling 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. 62--68

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 13-20%. 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. 69--72

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 8-aminolaevulinic acid (ALA) is revealed. Optimum conditions of photodamage virus z infected cells are determined (ALA-0.6 mM, incubation of a cellular monolayer with ALA-1.5 h, illumination dose -- 19.5 kJ/m2, 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. 73--76

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 3H-thymidine 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. 77--79.

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. 80--82

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 non-standard clinical situations. pp. 83--85

Summary: The author presents a new concept of endoprosthetics of a hip joint in non-standard clinical situations (displastic osteoarthrosis, idiopathie coxartrosis, hip tumors, etc).

### EARTH SCIENCES

Konischev V. S.
Types of the Upper-Frasnian salt uplifts in the Pripyat trough. pp. 86--88

Summary: Six types of Upper-Frasnian salt uplifts were revealed using the present knowledge about an extent of halokinesis in the Upper-Frasnian salt strata a, correlation of Upper-Frasnian salt massifs with high-amplitude 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 north-western part of Belarus. pp. 89--93

Summary: The present study of the gabbro-diorite-granodiorite-granite assemblage in the crystalline basement of the north-western 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 late-collisional/post-collisional tectonic setting may account for the geo-chemical features of the Grodno rocks.

### TECHNICAL SCIENCES

Sheleg V. K., Pyatov V. V., Kovchura A. S.
Extrusion of an isotropic material. pp. 94--96

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 cross-section 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 sr - sz = ss. 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 well-known in the theory of pressure processing of metals.

Pochtennyi E. K.

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 non-regularity and multifrequency as descending blocks of stresses; summing of fatigue damage by non-regular 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. 103--107

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 all-sided 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. 108--113

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. 114--116

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 XVI--XVII centuries. pp. 117--120

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 XVI--XVII centuries are considered. Libraries were of great importance for the development of science.

Vashtomov G. V.
Civilized priorities of Belarus in the frontier area co-operation. pp. 121--123

Summary: The introduction of scientifically grounded priorities in the frontier area cooperation in XXI century into the social-cultural 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 social-cultural 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.