# Доклады Академии наук Беларуси, 1997, Том 41, No.2

/ Издания академии / Научные журналы

Доклады Академии наук Беларуси, 1997, Том 41, No.2

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Gaishun I.V.*
**Axiomatic approach to the notion of fuzzy vector space.** pp. 5--9

*Summary:* The system of axioms that single out the class of *F*-spaces, is suggested. The *F*-space has the set *O* of unit elements. The set *O* is equipped by the structure of partial order which consistent with the algebraic structure. The interconnection of *F*-space with the fuzzy vector spaces in the conception of L. Zadeh is established and the properties of *F*-space are investigated.

*Glaeske H.-J., Kilbas A.A., Saigo M., Shlapakov S.A.*

*L*_{v,r}-theory of integral transforms with *H*-function as kernels. pp. 10--15

*Summary:* Integral transforms (Hf)(x) = Int{ H^{m,n}_{p,q}[xt]f(t)dt} (x>0) involving *H*-function as the kernel are studied in the spaces *L*_{v,r} of functions f such that Int{t^{vr-1} |f(t)|^{r}dt} < inf (1 <= r < inf, v ª R). Results are given on the boundedness and one-to-one correspondence, various representations and ranges of the transforms *H*.

*Vignoli A., Zabrejko P.P., Moroz V.B.*

**Critical values of bounded from below functionals and Hammerstein equations.** pp. 16--21

*Summary:* A new variant of The Three Critical Points theorem is obtained. The authors prove that (under suitable quite simple hypotheses) either the functional in question has at least three distinct critical values or, its set of minimum points is noncontractible in itself. As application, the problem of nontrivial solutions of nonlinear integral Hammerstein equations with lack of compactness is considered.

*Yegorov A.D.*

*L*_{2}-isomorphic Gaussian models for a class of functional integrals with respect to non-Gaussian quasimeasures. pp. 22--26

*Summary:* Isomorphism between a subspace of square integrated functionals with respect to nongaussian quasimeasure defined by characteristic functional and the subspace of square integrated functionals w.r.t. corresponding gaussian measure is established.

*Belko I.V.*

**Transversal continuations of foliated Lie groupoids.** pp. 27--29

*Summary:* The author introduces the notion of a foliated Lie groupoid and its transversal continuation of the *k* order. He constructs the transversal continuations of the action of a foliated Lie groupoid on a bundle. The transversal connections of *k* order are the examples of transversal structure. For the foliated Lie groupoid continued the Sh. Ehresmann theorem about its Lie algebroid is proved.

*Tretiakova N.N.*

**Fourier type multidimensional integral transforms.** pp. 30--36

*Summary:* The paper studies the Fourier type integral transforms, connected with the representations of Euclidean rotation group *SO(n)* and motion group *M(n)*. The theorems about a convergence of these transforms are proved here. These theorems generalize some known results of analysis to the fields of arbitrary qualities (scalar, vector, tensor, spinor and others) in Euclidean space *E*_{n}.

*Alekhno A.G.*

**On solvability of the homogeneous Riemann's boundary value problem with infinite index.** pp. 37--44

*Summary:* A discussion of basic results concerning the theory of homogeneous Riemann's boundary value problem with infinite index of arbitrary power order in the case of multilateral vorticity is given.

**ФИЗИКА**

*Sirota N.N., Soshnina T.M.*
**Density distribution of electron kinetic and exchange energy in interatomic bond range according to the atomic statistical model.** pp. 45--49

*Summary:* Density distribution of electron kinetic and exchange energy in the range of interatomic bond which is formed by additive superposition of electronic density of two neutral atoms in a ground state is calculated according to the atomic statistical theory.

*Gurinovich V.A., Kononyuk I.F., Korshunov F.P., Makarenko L.P.*

**The influence of vacuum annealing on properties of Bi(Pb)-2223 superconductor after gamma-irradiation.** pp. 50--54

*Summary:* Preliminary gamma-ray irradiation has been found to enhance oxygen out-diffusion and degradation of Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{y} ceramic superconductor under vacuum annealing. Recovery of initial characteristics of this material takes place by annealing at 400°C in air. It is suggested that degradation of Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{y} ceramic superconductor under gamma-ray irradiation is due to the radiation enhancement of gas change with environment.

*Makovetsky G.I., Smolik Ch.K.*

**Determination of intensities and positions of overlapping peaks by the extrapolation method. I.** pp. 55--59

*Summary:* The technique for separation of the intensities of the overlapping diffraction peaks by the extrapolation method algorithms with the high order of precision has been presented. The optimum conditions for carrying out the diffraction experiment have been reported for separation of the intensities of the peaks.

*Novikov V.P., Dymont V.P.*

**Synthesis of diamond-like carbon at low temperature.** pp. 60--63

*Summary:* A new method of carbon synthesis has been suggested and realized using acetylene solution in liquid ammonia through acetylene oxidation by transitive metal ions. The conclusion was made that the substance obtained was a new diamond-like carbon modification.

**ХИМИЯ**

*Matusevich V.V., Khirsanova I.F., Lukashevich L.I., Soldatov V.S.*
**The influence of acidity and nutrient solution concentration on biozones of ionite substrates.** pp. 64--67

*Summary:* The biozones of anion and cation exchange components of fibrous nutrient substrate BIONA-F for growing plants have been obtained. There have been derived 4 biozones of anion exchanger FIBAN AK-22-1 at two total nutrient solution concentrations 0.017N and 0.00425N and at two pH values 6.5 and 5.5. The biozone of fibrous cation exchanger FIBAN K-1 has been obtained at the total nutrient solution concentration 0.017N and pH = 6.5.

*Krut'ko N.P., Ovseenko L.V., Starostina O.I.*

**Interactions in mixed solutions of ionogen surfactants.** pp. 68--72

*Summary:* The interaction of even homologs of primary aliphatic amines having the length of the C_{12} -- C_{18} hydrophobic radical with anionic and ampholitic surfactants have been investigated by the conductometric method. According to summary length of the surfactant hydrophobic radical the equimolar complexes are shown to be formed in solution the existence of which are confirmed by IR-spectroscopy.

*Makarevich N.A.*

**Average mass and average numerical characteristics of surfactant associative solutions.** pp. 73--78

*Summary:* Critical analysis of known definitions for aggregation degree a, aggregation number *n* in solutions of nonionic surfactants and binding degree of counter ions by associative complexes beta in solutions of ionic surfactants was carried out on the basis of the laws of mass action and conservation of mass and charge. When studying colligative properties of surfactant solutions and the properties dependent on surfactant aggregate sizes in solution, differentiation of definitions for a, b and *n* between numerical a, *n* and b, and mass a_{w}, *n*_{w} and b_{w} values was given. There are represented expressions for equilibrium constants of quasi-chemical reaction *K*_{asw} and *K*_{a s} and ratios between a, *n*, *K*_{as}, and a_{w}, *n*_{w} and *K*_{asw} with the methods for determining these characteristics shown. Definitions for a_{i}, *n*_{i}, b, b_{w}, a_{iw}, *n*_{iw}, for ionic surfactant solutions are given. Corrections taking account of molecule association in an adsorption layer in terms of a and electrolyte effect in terms of isotonic coefficient *L*_{s} = *v* / (*v* - 1 + b), where *v* -- ion number into which surfactant dissociates are shown to be required for ionic surfactant solutions in Gibbs and Van der Waals' equations of state, adsorption isotherms of Gibbs, Hill -- de Boor, Frumkin -- Guggenheim -- Fauler *etc*.

*Polikarpov A.P., Valendo A.Ya.*

**Thermomechanical properties of irradiated ultrahigh molecular polyethylene.** pp. 79--83

*Summary:* Thermomechanical properties of ultrahigh molecular-weight polyethylene films gamma-irradiated in air and in argon were studied. Irradiation in the medium of argon causes significant increase in heat stability due to creating of covalent bonds.

**БИОЛОГИЯ**

*Titok V.V., Yurenkova S.I., Tsebrikov Yu.V., Khotyljova L.V.*
**Comparative estimation of bioenergetic process activity in fiber flax seedlings.** pp. 84--87

*Summary:* Comparative analysis of the peculiarities of biomass accumulation and of bioenergetic processes in fiber flax seedlings with the differences in economically valuable traits was carried out. High positive correlation between potential capacity of bioenergetic processes in cotyledons of etiolated seedlings and productivity traits in different varieties was revealed.

*Melnikova A.M., Matus V.K., Konev S.V.*

**Formation of respiratory activity-stimulating factor by yeast ozonization.** pp. 88--91

*Summary:* Low doses of ozone were shown to stimulate the respiratory activity of yeasts at the stationary growth phase. This is caused by the accumulation in the medium of low molecular thermostable factor(s) capable of biological activity. No formation of substances with similar physico-chemical properties and biological activity was observed under other conditions of incubation, without O_{3} treatment. This indicates an important role of oxidative stress in the induction of the factor. A cooperative decrease in the plasma membrane permeability for endogenous metabolites of low molecular mass (nucleotides) as well as a rise in the cell sedimentation rate were observed at the concentrations of the factor stimulating bioenergetic processes. Therefore, the biological effect of the factor is probably mediated by its membrane-modifying action. This effect is not species-specific because the stimulation of respiration by the yeast factor was discovered in other cells (bacteria).

*Gorbunova N.B., Kalyunov V.N.*

**Effect of psychosocial stress on concentration of nerve growth factor (beta-NGF) in blood serum.** pp. 92--95

*Summary:* Using the bicentral radioimmunoassay it was found that a psychosocial stress-induced elevation of the nerve growth factor level was prolonged and determined by the duration of preceding isolation and stress interaction and showed a long dynamics of recovery in the post-stress period.

*Domansky V.P., Shantarovich A.M., Fradkin L.I.*

**Induction of active photosystem 2 formation in barley etiolated leaves without light participation.** pp. 96--99

*Summary:* The influence of exogenous chlorophyllide (Chlide) and NADPH on the ability of etiolated leaves to emit delayed luminescence (DL) of photosystem 2 (PS2) was examined. Infiltration of Chlide into 6-day-old etiolated leaves of barley and subsequent dark incubation for an hour promotes an increase in DL under illumination. Infiltration of etiolated leaves with acetone extract from green leaves deprived of lipids and pigments, or with Chlide and 3 mM NADPH resulted in the appearance of DL just at the beginning of illumination in contrast to normal etiolated leaves where PS2 DL was detectable after about 10 min of continuous light. It is concluded that Chlide infiltration into etiolated leaves promotes PS2 light formation and infiltration of Chlide jointly with NADPH, furthermore induces dark formation of functionally active PS2 in etiolated leaves.

*Maslova I.V., Vismont F.I.*

**Cholinergic activity in rat brain structures under animal immobilization-induced stress.** pp. 100--103

*Summary:* ACh metabolism in rat brain has been studied under conditions of emotional stress caused by the immobilization of animals. Reciprocal changes in ACh metabolism have been observed in cortex and subcortex brain structures. The changes are characterized by the decrease in cholinergic activity in cortex and the increase of this activity in brain stem and hypothalamus. Changes in striatum bear the phase effect. Initially, there occurs transmitter release. Later, transmitter content is decreasing against the background of weaker ACh synthesis.

**НАУКИ О ЗЕМЛЕ**

*Arkhipova A.A.*
**Average contents of macro- and microelements in the main rock types of gneissic-migmatite complexes of Belarus crystalline basement.** pp. 104--108

*Summary:* The average macro- and microelements contents (regional clarkes) of intermediate and acidic rocks from gneissic and migmatitic complexes of Belarus crystalline basement are presented. The distinctions in geochemical specialization of rocks from different structural zones of the region basement have been revealed.

### Kozhemyakina N.A.

**Admixture elements in potassium feldspars from Precambrian granitoids of Belarus.** pp. 109--113

*Summary:* The distribution of admixture elements in potassium feldspars from granitoids of Belarus has been discussed. It is suggested to use these elements as additional indicators when revealing the genetic nature of granitoids.

*Makhnach N.A., Gulis L.F.*

**Special distribution of the ground water saturation index by calcite in Belarus.** pp. 114--118

*Summary:* Schematic map of the saturation index of ground waters by calcite is given and analysed in the paper. Correlation between the saturation index value and geomorphological, lithological, landscape peculiarities and technogenic effect was revealed.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Vantsevich V.V., Vysotsky M.S., Kharitonchik S.V.*
**Combination of rolling regimes for elastic wheel.** pp. 119--122

*Summary:* The new problem was formulated and solved - control of tractive and power characteristics of wheel by combining rolling regimes and, correspondingly, by changing purposefully its force, kinematic and power parameters. The carried out research is basic for developing a new theory for mobile vehicles motion aimed at solving problems for controlling their service properties.

/ Издания академии / Научные журналы / К началу страницы

Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: *6 сентября 2008 г.*

Создана при участии Игнатия И. Корсака

Копирайт © 1997-2008 Национальная академия наук Беларуси

Копирайт © 1997 Издательство "Беларуская навука"