Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2003, No.4

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2003, No.4

Proceedings of the National Academy of Sciences of Belarus
(Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICAL-MATHEMATICAL SCIENCES
Published by The Institute of Mathematics of NASB, Minsk, Republic of Belarus

Number 4, 2003

TO 75TH ANNIVERSARY OF THE FOUNDANTION OF THE NATIONAL ACADEMY OF SCIENCES OF BELARUS

Makarov E. K.
On main trends of investigation in the Institute of Mathematics of the National Academy of Sciences of Belarus. pp. 5--21

Summary: Main trends of investigation at the Institute of Mathematics of the National Academy of Sciences of Belarus are discussed.

Belyi V. N., Kazak N. S., Khilo N. A.
Quasi-riondiffracting light beams: properties and methods of formation. pp. 22--33

Summary: The results of theoretical and experimental investigations of the properties of Bessel quasi-nondiffracting light beams are presented. In detail various types of superposition of Bessel beams are analyzed which exhibit such new properties as the suppression of lateral rings, the periodical reconstruction of transversal spatial structure in the process of propagation, the diffractionless of nonmonochromatic beam et al. An intermediate class of beams (between Gaussian and Bessel), the so-called few-ring light beams is predicted. It is shown that using the few-ring beams allow to enhance the efficiency of nonlinear-frequency conversion in comparison with the Gaussian beams. The schemes for forming Bessel beams by conical and toroidal lenses as well as by the anisotropic crystals are discussed. Some polarization properties of vector Bessel beams and possibility of their experimental realization are investigated.

Goncharenko A.M., Sinitsyn G. V., Apanasevich S.P., Lyakhnovich A. V.
Transfer and multiplexing of optical signals in bistable planar semiconductor structures. pp. 34--43

Summary: Principles of formation and controlled propagation of switching autowaves in optically bistable interference structures are considered. On this basis a number of all-optical methods and devices are proposed and developed for read-in, storing, read-out, switching (multiplexing/demultiplexing) as well as for transfer of information light signals in the plane of 2D-arrays of nonlinear optical elements of micron size. A peculiarity of these methods is the possibility to shift data laterally in the array's plane in a direction that is perpendicular to the direction of incident light beams without its interim transformation into electrical signals. This distinctive feature enables developing new architecture concepts of optical information processing systems. Examples of numerical simulations and experimental realization are presented of optical digital devices with a wide range of functional applications such as Boolean logic elements, shift registers, multiplexers/demultiplexers, basic planar ring processors, etc.

Gurskii A. L., Lutsenko E.V., Yablonskii G.P.
Lasers and light emitting diodes based on nano-dimensional InGaN/GaN and ZnMgSSe/ZnSe heterostructures for spectral range from ultraviolet to green region. pp. 44--53

Summary: The achieved results, the perspectives of development, and applications together with the physical and technical problems of creation of the coherent and incoherent radiation sources for ultraviolet-green spectral region based on quantum-dimensional InGaN/GaN and ZnMgSSe/ZnSc heterostructures are discussed. The main results obtained during the last 7 years by authors and their colleagues from the laboratory of semiconductor optics of B.I. Stepauov's Institute of Physics of the National Academy of Sciences of Belarus at investigation of the optical and laser properties of heterostructures have been reviewed. The research WHS carried out in a collaboration with scientific groups of Technical University of Aachen (Germany), of the firma AIXTRON AG (Germany), and of Ioffe Physical-technical Institute of RAS (Russia), where all technological work on creation oi heterostructures has been done. The regularities of the spontaneous and stimulated emission of all types of heterostructures under study have been established in a wide range of excitation intensities, wavelengths and temperatures, in interrelation with the. growth parameters. A couple of results, for example, the creation of lasers on InGaN/GaN heterostructures grown on sapphire for the spectral region of 450 - 470 nm. the achievement of laser action in epitaxial layers and InGaN/GaN heterostructures grown on silicon substrates, the creation of green lasers based on ZnMgSSe/ZnCdSe heterostructures pumped by radiation of blue InGaN/GaN heterostructure lasers, has the world priority.

Fedosyuk V. M.
Magnetic Nanomaterials. pp. 54--63

Summary: Mechanism formation, structure, magnetic and magnetoresistive properties of some magnetic materials are discussed.

Kravchenko V. M., Mukchurov N. I., Chaplanov A.M.
On the development of investigations in Microelectronics. pp. 64--75

Summary: Results of researches of Institute of Electronics of the National Academy of Sciences of Belarus are submitted in the field of microelectronics.

Ablameyko S. V., Mahnach V. I., Anishchanka V. V.
Scientific center on Informatics in Belarus. pp. 76--83

Summary: The paper describes an activity of the United Institute of Informatics Problems -- the main organisation in the Republic of Belarus in the area of informatics. Main research areas, theoretical and practical results, and their usage in industry, medicine, and other applications are shown.

MATHEMATICS

Levakov A. A.
Existence theorems for stochastic differential inclusions. pp. 84--89

Summary: Different definitions of the weak and strong solutions fot non-stationary stochastic differential inclusions are introduced. Existence theorems for these inclusions are proved.

Korzyuk V. I.
A conjugation problem describing the longitudinal vibrating string. pp. 90--97

Summary: This work focuses on the conjugation problem for a second order linear differential hyperbolic equations. The considered conjugation problem is a mathematical model describing longitudinal vibration after impact. For the mentioned problem the existence and uniqueness of the strong solution are proved using mollifying operations with a variable step and functional analysis methods on the base of the previously proved energy inequality.

Borodich R. V.
About intersections of the set maximal subgroups of finite groups. pp. 98--102

Summary: The intersections of the given systems of maximal subgroups of finite groups are investigated.

Vasilyeva T. I.
On the properties of projectors of subgroups' products of finite soluble groups. pp. 103--106

Summary: For Schunck class X the conditions of embedding in X-projectors of a finite soluble group G = AB X-projectors of subgroups are studied.

Kosenok N. S.
Criterions of p-closelity and p-nilpotency of finite groups. pp. 107--110

Summary: It is proved that if every maximal subgroup of every Sylow subgroup of a finite group G has a p-closed supplement in G, then G is p-closed.

PHYSICS

Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K.
Electrooptic adder with spectral compression in input/output channels. pp. 111--116

Summary: Functional diagram of single-digit optoelectronic adder is proposed. In the adder the transfer into i+1 digit is developed with spectral shift with regard to carrier wavelength of the input/output i-th digit. Controlled fibre Bragg cells are used for electrooptic conversion on different wavelengths. Frequency characteristics of electrooptic Bragg cells and entire adder are estimated. The proposed adder structural diagram permits to reduce the number of cascades of optical conversion and signal branching and perform the real time data processing with performance 10¹³ bit/s in single fibre assuming the same performance of optic operands input/output.

INFORMATICS

Dovzhenok T. S.
On insensitivity conditions of the stationary state probabilities for the networks with the rounds and negative customers. pp. 117--122

Summary: Open queueing networks with negative customers, rounds and EPS service discipline are considered. Customers arrive network according to a Poisson process. Service duration has general distribution for the nodes with the rounds and an exponential distribution for the nodes with negative customers. It is shown that the stationary state probabilities doesn't depend on the service time distribution with fixed expectations.

SHORT NOTES

Senko D. V.
The model of a stochastic process with dependence on previous values. pp. 123--125

Summary: A model of a stochastic process with special type of dependence on previous values is presented in form of a stochastic difference equation. The type of dependence on previous values is derived from the common techniques of time series technical analysis in finance. The process paths are simulated, the parameters are estimated by the method of simulated maximum likelihood.

ABSTRACTS OF DEPOSITED PAPERS

Shved O. L.
On plasticity condition during finite strains for two-dimentional stress-strain state. p. 126

Pashkevich M. A.
Robust modelling and forecasting for clustered binary data. pp. 126--127

SCIENTISTS OF BELARUS

Nikolai Nikolaevich Sirota (On the occasion of the 90th birthday). pp. 128--130
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