# Доклады Национальной академии наук Беларуси, 2002, Том 46, No.2

/ Издания академии / Научные журналы

Доклады Национальной академии наук Беларуси, 2002, Том 46, No.2

## СОДЕРЖАНИЕ

**МАТЕМАТИКА**

*Zabreiko P. P.*
**On Poincare index of essentially singular points of analytic functions.** pp. 5--8

*Summary:* The article deals with isolated essentially singular points of analytic functions. The basic result states that if an essentially singular point z_{0} of an analytic function *f* is an isolated singular point of the corresponding plane vector field, then the function can be represented in the form *f*<(z) = (z - z_{0})^{n} g (z) exp *h* ((z - z_{0})^{-1}) where *n* is an integer (coinciding with the Poincare index of z_{0}), *g* is an analytical function in a neighborhood of z_{0} with g (z_{0}) ¹ 0, and *h* is an entire function with *h*(0) = 0. The similar representation for arbitrary isolated singular points is also given.

*Lipnitsky A. A.*

**2-torsion of Brouwer groups of elliptic curves with multiplicative reduction over field of real formal power series.** pp. 9--12

*Summary:* The description of an abstract structure of 2-torsion part of Brauer groups of elliptic curves with multiplicative reduction defined over real power series has been obtained. The presentation of the elements of Brauer groups by products of quaternion algebras is provided.

*Komrakov B. B.*

**Four-dimensional homogeneous insoluble Einstein spaces.** pp. 13--17

*Summary:* This paper presents the complete local classification of four-dimensional homogeneous spaces of non-solvable Lie groups with an invariant Einstein metric of arbitrary signature and the complete local classification of four-dimensional homogeneous spaces of nonsolvable Lie groups with an invariant pseudo-Riemannian metric of arbitrary signature and the metric not satisfying the Einstein equation *R* - l*g* = 0 where *g* is a metric, *R* is the Ricci tensor, l is an arbitrary real number.

*Bushuev I. A., Yanchevskii V. I.*

**On algebras of exponent two which are trivial in all real closures of their centers.** pp. 18--20

*Summary:* Possible ramification of finite dimensional central simple algebras of exponent two over **R**((*t*))(*x*) which are trivial in all real closures of their centers is described. The proof of the local Pfister conjecture is given in cases where either points of ramification defined by quadratic polynomials or polynomials with roots which are not squares in corresponding extensions of the field of constants.

*Gabasov R., Kirillova F. M.*

**Synthesis of optimal feedforward-feedback controls.** pp. 21--24

*Summary:* A principle of optimal feedforward-feedback for linear lime-varying systems with disturbances at using both inputs and outputs is justified. An algorithm suggested to functioning optimal controller represents the procedure of correcting elements of open-loop solution for a current position by fast algorithms.

*Monakhov V. S.*

**On soluble finite groups with Sylow subgroups of small rank.** pp. 25--28

*Summary:* A finite soluble group *G* with Sylow subgroups of ranks £ 3 is considered. It is proved that the nilpotent length of the group *G* 5 and *p*-length does not exceed 2.

*Tishchenko K. I.*

**On simultaneous approximation of two real numbers by literal numbers.** pp. 29--33

*Summary*

*Suprunenko I. D.*

**Irreducible linear groups containing matrixes with small number of Jordan blocks.** pp. 34--39

*Summary:* Irreducible semisirnple Zariski closed connected subgroups of a general linear group over an algebraically closed field of characteristic ¹ 2 containing matrixes with at most 5 Jordan blocks are classified. In particular, if *G* Î *GL*_{n} (*K*) is such subgroup of rank > 2 and *n* > 97, it occurs that *G* is one of the classical groups of degree *n* or a tensor product of the standard realization of a classical group and an irreducible semisimple linear group of degree at most 5.

*Erovenko V. A., Severenchuk N. B.*

**Semi-Browder spectra of analytic functions of bounded operators.** pp. 40--43

*Summary:* In this paper, the necessary and sufficient conditions of validity of analogues of the Weyl's theorem for semi-Browder essential spectra of analytic functions of operators are obtained. It is proved that quasi-hyponormal operators and analytic functions of quasi-hyponormal operators obey the Weyl's theorem for semi-Browder essential spectra.

*Vasilets S. I., Kilbas A. A.*

**Action and representations of Riesz potentials with power-logarithmic kernels in weight L**_{p}-spaces. pp. 44--47

*Summary*

*Egorov A. D.*

**On operator representation of multiple stochastic integrals for quasi measures.** pp. 48--52

*Summary:* An operator representation of multiple stochastic integrals in the space of white noise nonlinear functionals with Gaussian quasi measures is obtained. Application to multiple stochastic integrals in the spaces with non-Gaussian measures is considered.

*Kovalevskaya E. I.*

**Diophantine approximations of points of the same class of space curves over Z**_{p}. pp. 53--56

*Summary:* We prove the *p*-adic analogues of the convergence part of Khintchine's metric theorem (1924) for the linear Diophantine approximations to the points of the same class of the space curves having the non-zero second curvature almost everywhere over *Z*_{p}.

*Yadchenko A. A.*

**Finite p-separable linear groups and their normal subgroups.** pp. 57--58

*Summary:* In this paper, a finite p-separable complex irreducible linear group *G* is investigated. The conditions under which the *S*_{p} -subgroup is normal in *G* and abelian subdroup are determined. The result is a solution of the well-known Isaacs problem in some particular cases.

*Ringel D. E.*

**Algebraic and linear-analytic properties of mnemonumbers.** pp. 59--61

*Summary:* The study of mnemonumbers continues. The mnemonumber roots of polynomial with coefficient in the basic field have been determined. Also, we have established that mnemonumbers were classical quotient field. Finally, we consider analogs of linear algebra and linear functional analysis.

**ИНФОРМАТИКА**

*Selyaninov M. Yu.*
**Application of numerically-analytical modular computing technique for performing additive and multiplicative operations on signals in spaces of orthogonal projections.** pp. 62--66

*Summary:* On the basis of a new numerically-analytical modular technique of parallel calculations in spaces of orthogonal projections original fast methods of adding, subtracting and multiplying of discrete signals are offered. Their productivity is evaluated.

**ФИЗИКА**

*Knyazev M. A.*
**Kink in self-excitation system.** pp. 67--69

*Summary:* One-kink and one-antikink solutions for equation of motion of the scalar field theory with fourth-ordered potential in absence of driven force and accounting of the linear dissipation and nonlinear quadratic self-excitation effects are considered.

*Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K.*

**Optical logical elements based on fiber Bragg reflectors.** pp. 70--73

*Summary:* The basic parameters (signal-to-noise ratio, switching energy, operation time) of optical logic elements "AND" with three inputs are estimated. The logical elements are based on complex fibre Fabry-Perrot resonators, formed by two Bragg reflectors and one end mirror. Such a logical element producing function of half-adder in a oneswitching tact can be used for algorithmic acceleration of optical computing.
Considered optical logic elements can be used for preliminary information processing in fibre interconnections between chips or blocks of computing systems.

**ХИМИЯ**

*Frolova E. V., Ivanovskaya M. I., Azarko I. I., Sviridov V. V.*
**Formation of paramagnetic centers under thermal dehydration of zirconium hydroxide.** pp. 74--77

*Summary:* ESR technique has been used lo study the nature of the paramagnetic centers (PC), which were obtained by thermal dehydration of zirconium hydroxide xerogels and precipitates. The occurrence of Zr^{3+}, O^{-} , and F-centers was established in the ZrO_{2} samples heated at 150 to 900 °C in the air. The mechanism of PC formation was considered and correlation between thermal treatment conditions in redox gas media and concentration of PC was found.

**БИОЛОГИЯ**

*Voluevich E. A., Buloichik A. A., Mikhno A. M.*
**Effect of alien plasmon on expression of defeated wheat genes of resistance to brown rust.** pp. 78--80

*Summary:* Expression of defeated resistance genes Lr10 and Lr23 was studied at the seedling stage in 5 new series of common wheat alloplasmic lines by inoculation with two brown rust clones different in virulence genes. The mean spore-forming pathogen capacity per 1cm^{2} of leaf area was evaluated. Expression of the defeated genes was detected to depend on nuclear and cytoplasmic background of host plant and gene pool of fungus genotypes.

*Samoilenko S. G., Rakovich A. A., Levko A. V., Konev S. V.*

**Activation of intracellular calcium depots in nerve endings of rat brain under osmotic swelling.** pp. 81--83

*Summary:* Swelling of isolated nerve endings of rat brain in hypotonic medium (230 mOsm) induces activation of ryanodin- and inositol-1,4,5-trisphosphate -- sensitive Ca^{2+} depots. It is established that the inositol-1,4,5-trisphosphate -- sensitive Ca^{2+} depots provides basic contribution to intracellular Ca^{2+}-induced reactions. Calcium-dependent reduction by 50% of energetic potential of the nerve endings is observed. The calcium response of the synaptosomes to osmotic swelling has energeticaly irreversible nature.

*Mazhul V. M., Shcherbin D. G., Zaitseva E. M., Kalitukho L. N., Kabashnikova L. F.*

**Room temperature tryptophan phosphorescence of plant rootlet.** pp. 84--87

*Summary:* The ability of the rootlet cells of mono- and dicotyledons (wheat, rye, barley, tritikale, fiber flax, oil flax) to emit room temperature tryptophan phosphorescence (RTTP) has been discovered. Spectral and kinetic parameters of RTTP of plant cells have been defined. The absence of considerable difference in the dynamic properties of the RTTP-capable membrane proteins for various species and variety of seedlings of different age has been demonstrated.

**НАУКИ О ЗЕМЛЕ**

*Aizberg R. E., Karabanov A. K., Vishnevsky V. N., Kadol V. M., Aronov A.G.*
**The latest geodynamics of the Central fault zone within the Starobin potash deposit.** pp. 88--92

*Summary:* The aggregate displacement amplitude of the Central fault within the territory of the Starobin potash deposit varies from 200 to 500 m. The value of neotectonic vertical movements (late Oligocene-quarternary) runs up to 20 to 25 m. The signs of horizontal slide movement are simultaneously established. The possibility of present-day activization of the Central fault under the combined influence of natural and man-caused factors is shown.

*Konishchev V. S.*

**Development of faults of Pripyat Trough during the late Famennian.** pp. 93--97

*Summary:* It is proved that speed of movements along thrusts of the Pripiat depression during the late famenian phase of rift stage was rather small at the Western and Central segments (0 -- 41 m/mln year) and rather high at the Eastern segment (52 - 160 m/mln year), but it was ten times less than that during principal middle Famenian phase of rift stage.

*Nalivaiko V. F.*

**Reconstruction of neotectonic stresses of the earth's crust within the eastern part of the Starobin potash deposit based on structure and geomorphological data.** pp. 98--101

*Summary:* The stress condition in the eastern part of the Starobin potash deposit was studied using the method of the secondary disturbances. The block structure of the study area was recognized. The axes of compression and tension as well as fault cinematic types of it were reconstructed.

*Korzun V. P.*

**The nature of volcanic ashes in oversaline Devonian deposits of the Starobin depression.** pp. 102--104

*Summary:* Volcanic ashes from the Late-Famennian supersalt deposits of the Starobin Depression of the Pripyat Trough are products of eruption of Late Famennian volcanos situated in the northwestern margin of the Dnieper-Donets Depression.

**ТЕХНИЧЕСКИЕ НАУКИ**

*Pochtenny E. K.*
**Analysis of construction elements fatigue.** pp. 105--107

*Summary:* The assay techniques are esteemed and synthesizing of a fatigue of members of designs which one includes: the analysis of transport process, analysis and synthesizing of a fatigue of members at standard modes of exploitation, synthesizing of fatigue damages at multiplemode loading and estimation of resource of designs.
The possibility of using the technique for maintenance of resource of designs on preparation stage of series production of machines and increase of a technological level of their exploitation is rotund.

*Chigarev A. V., Miklashevich I. A.*

**On influence of composite material heterogeneity on crack trajectory.** pp. 108--110

*Summary:* Onset of stochastic regime by the crack growth is investigated for the crack trajectory equation which is found on the basis of optical-mechanical analogy. Conditions of deterministic chaos initiation in the crack behaviour are obtained.

*Susin A. A., Rudenko S. P.*

**Bending fatigue, structure, and submicrostructure of chemically and thermally hardened construction steels.** pp. 111--114

*Summary:* The essential influence of compressed stresses of the hardened stratum on limit of bending fatigue life of case-hardened and carbonitriding steels and defining role of an effective thickness of a stratum up to microhardness of 750 HV and 700 HV is shown.
Based on X-ray diffraction, metallographic, and electron microscope studies, it is established that the origin and propagation of fatigue cracks starts at surface of products of non-martensite type and on boundaries of plates or racks of marten-site. The consequent fatigue crack propagation at cyclical loading depends on structure of these structural components, magnitude of a grain, and magnitude and sign of residual stress. The following parameters should be provided at chemical and thermal hardening to ensure high limits of bending fatigue life, such as 1000 to 1100 MPa: the hardness of the hardened stratum 750--800 HV, effective thickness up to this hardness not less than 0.05 of the module, compressed of stresses of 750--500 HV at this depth at magnitude of grain that is not lower than 8 to 10 steps.

*Dorozhkin N. N., Kashitsin L. P., Abramovich T. M., Khudolei A. L.*

**Compression kinetics of powder layer by force activation of sintering process.** pp. 115--118

*Summary:* Equation of compression kinetics of a powder layer by force activation of sintering process is obtained on the basis of the evaluation method of the average on layer volume speed deformation. The technological schemes for coatings deposition on external surfaces of details are considered.

*Kashevsky B. E., Prokhorov I. V., Kuzmin V. A., Rusalovich A. A.*

**Influence of dissipative electromagnetic texturing of conducting particles on filled polymer electric conductivity.** pp. 119--121

*Summary:* The experimental investigation of the electric conductivity of epoxy polymer -- Ni particles compound is carried out. A new technique of polymerising mixture treatment with the use of spatially arranged alternating electromagnetic field is applied. The treatment provides the formation of "dissipative" conductive structures and leads to the notorious increment of the material bulk conductivity. The increment is singularly high (7 to 9 orders of magnitude as compared with the conductivity of the non-treated samples) in case of small particle concentrations (<10 vol. per cent).

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

Создана при участии Игнатия И. Корсака

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Копирайт © 2002 Издательство "Беларуская навука"