Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2003, No.2
/ Publications / Scientific Journals
Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2003, No.2

Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICALMATHEMATICAL SCIENCESPublished by The Institute of Mathematics of NASB, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Beresnevich V. V., Vasilyev D. V.
On prime number generation. pp. 510
Summary: The improvement of some methods for generating prime number is proposed.
Bazylev D. F.
Indices of Walgebras with special ramification. pp. 1113
Summary: It is proved that any Walgebra over the field R((t))(x) have the index which do not exceed 2.
Bazylev D. F., van Geel J., Yanchevskii V. I.
A special case of the local Pfister conjecture. pp. 1416
Summary: Finitedimensional central simple algebras of exponent 2 over the field R((t))(x) which are trivial at all real closures of their centers are considered. For special ramification point of such algebras the local Phister conjecture is proved.
Romanovskii Yu. Ya.
Invariant metric structures on homogeneous spaces, which are generated by proper Poincare group. pp. 1721
Summary: The global pare (G, G) for proper Poincare group B_{+}^{} is constructed. G is universal covering group of B_{+}^{} and G is a semigroup of automorphisms of G. Homogeneous spaces which are generated by the global pare (G, G) are isomorphic to the spaces of figures in Minkowski space R^{1}_{4} . The problem of finding of invariant metric structures on such spaces has been solved.
Vorobei L. A.
On the properties of the lattice of transitive regular subgroup functors. pp. 2224
Summary: The construction of group G is studied in case when width of lattice Reg_{tr} (F) with F = form G do not exceed of the number of prime divisor of the group G.
Gal'mak A. M.
nAry subgroup of identityes. pp. 2530
Zherelo A. V.
Approximation formula of one class of continual integrals on quasimeasure in cylinder domain. pp. 3136
Summary: The approximation formula for the some class of continual integrals on the quasimeasure in the cylinder domain is constructed.
Al'sevich V. V.
On the presentation of the solution of differential equations with the variable delay argument of the neutral type. pp. 3744
Summary: The form of the presentation of solutions for the linear neutral differential system with the variable delay is given.
Levakov A. A.
Application of the method of Lyapunov functions of constant signs for the investigation of the stability of the semidynamical systems. pp. 4551
Summary: It is proved that systems which are generated by the functional and generalized differential equation, evolutionary parabolic equations are socalled Gsystems. Gsystems are some class of the semicontinuous and semidynamical systems. The asymptotic stability criterion for the Gsystems is derived. It is proved that from the asymptotic stability of the Gsystem follows the asymptotic stability of the any system which tends to the given Gsystem as
t ® + µ.
Rasol'ko G. A.
The direct method of the approximate solution of singular integral equation with Cauchytype kernel using the Chebyshev polynomials. pp. 5258
Karandzhulov L. I., Stoyanova Ya. P.
Boundary value problem for singular perturbed impulse systems in a critical case. pp. 5965
Summary: The asymptotic expansion for the linear singular perturbed differential equations with impulse actions effects and linear boundary conditions in a critical case is constructed.
PHYSICS
Pilipovich V. A., Esman A. K., Goncharenko I. A., Kuleshov V. K.
Parallel optical calculations in binary sign bit system. pp. 6669
Summary: The algorithms of parallel performing of basic arithmetic operations in optical computers on the base of spectrally sensitive fibre Fabry  Perrot resonators in binary sign bit system with twochannel binary coding of digits has been considered. The proposed algorithms make it possible to perform the operations of adding, subtraction, multiplication without ripplethrough carries and in parallel both on digits, and on operand matrices. Peak performance of data processing could be as high as 10^{12} operations per second.
Red'kov V. M.
Linear representations of spinor coverings of the full Lorentz group and intrinsic spacetime parity of a fermion. pp. 7076
Summary: The known ambiguity in determining intrinsic fermion parities is considered on the base of investigating possible linear singlevalued representations of spinor coverings of the extended Lorentz group, describing in accordance with Cartan approach by matrix operations without complex conjugation. It is shown that every of four different groups, coverings of the full Lorentz group, has only two nonequivalent, 4component, complex, spinor representations, which can be related to certain two sorts of physical fermions. In is shown that spinor coverings of partly extended Lorentz groups L_{+}^{} and L_{+}^{¯} have only one type of nonequivalent representations, therefore in the framework of such partly extended spinor symmetry any determination for an intrinsic fermion parity cannot be found. It is established that only one group from four coverings of the full Lorentz group can be reduced by a similarity transformation to a realvalued form and therefore just this covering permits existence of Majorana fermions.
Tunyak U. M.
On the gravitational theory with tensor tetrahedronlike potential. pp. 7779
Summary: The gravitational field in Minkowski space is described in terms of tensor tetrahedronlike potential. The expression for the metric energymomentum tensor of gravitational field and nongravitational matter is obtained.
Sinitsyn G. V., Khodasevich M. A.
Entropy analysis of informationrate density of passive optical communication systems. pp. 8085
Summary: Informationrate densities in optical communication systems are investigated on the base of the numberstate model. Results of numerical simulation show that the considered characteristics increases monotonically with increasing signal power, reducing passband width and environment temperature. For wideband optical communication channels quantumstatistical peculiarities of information carriers should be taken into account at small enough signal powers when fluctuations can not be neglected.
Brinkevich D. I., Prosolovich V. S., Yankovskii Yu. N.
Interaction of oxygen impurity with rareearth elements in silicon. pp. 8689
Summary: The processes of interaction of oxygen with rareearth elements (Er, Yb, Gd, Ho, Lu, Dy) in Si have been studied by the methods of scanning electron microscopy, photoluminecence as well as of Hall effect measurements and infrared absorption. Two types of rareearth elements inclusions were detected for all lantanoids: aggregations of cell structures with dimensions > (1  5) µ having well defined boundary and blurred inclusions of less diameters. Oxygen concentration increases with the approaching to the inclusion boundary meanwhile the correlation versus the change of lantanoid concentration.
Petrashko V.V., Shishonok N. A., Gatal'skii G.V., Leusenko A. A., Kurochkin L. A., Vyshatko N. P.
Properties Bi_{1.6}Pb_{0.4}Sr_{2x}K_{x}Ca_{2}Cu_{3}O_{y} superconductor which obtained in the different synthesis conditions. pp. 9093
Summary: The influence of different synthesis conditions on phase composition and superconducting properties of Bi_{1.6}Pb_{0.4}Sr_{2x}K_{x}Ca_{2}Cu_{3}O_{у} superconductor are investigated. The maximum value of critical current is reached with using of high pressure treatment of precursor on the appointed stage of synthesis process. Potassium input in content of started mixture improves of intergrain boundaries and critical current increase.
Akimov A. I., Savchuk G. K., Rubzov V. A., Letko A. K.
Rietveld method refinement of the crystal structure of the ceramic titanate prepared by the method of the cold compacting under a high pressure. pp. 9498
Summary: The influence of the high pressure of cold compacting on the change of crystal structure parameters of lead titanate ferrielectric ceramics is investigated. The decrease of the value of the displacements of titanium atoms as well as of the volume and tetragonality degree of the unit cell, and the increase of the distortion of the oxygen TiO_{6}octahedra with increasing high pressure of cold compacting were established. It is shown that the increase of the high pressure of cold compacting causes the monotonic decrease of the temperature of the ferrielectric phase transition.
Shipilo V. B., Dutov A. G., Shipilo N. V., Komar V. A., Azarko I. I.
Crystallization of diamonds in a melt of metal at use of annealed graphite in the carbonic gas atmosphere. pp. 99103
Summary: It is established that the bakeout of graphite in atmosphere of carbonic gas (470  1070 l) diminishes a degree and speed of transformation of graphite in diamond in a system Mn  Ni  C at P = 5.5 GPa, T = 1620 K and t = 180 s. It is shown that a bakeout of graphite up to ~ 470 K reduces the contents in diamonds of manganese and nickel, augments their durability and density of paramagnetic imperfections N_{p1} and N_{pp}. The obtained experimental data are considered from a point of view of the colloidal theory of diamonds synthesis and contact with change at a bakeout in a crystallizing melt of the contents CO_{2} or products of its interaction with components of a melt.
INFORMATICS
Tiunchik A. A.
Finegrained systolic implementation of discrete logarithm problem. pp. 104108
Summary: Pure systolic array (suitable for VLSI or FPGA implementation) such that the whole procedure of the Pollard's rmethod can be carried out entirely by the single systolic unit is constructed.
Demidenko V. M., Metelskii N. N.
Quadratic assignment problem and packing graphs. pp. 109112
Summary: The approach to construction of new heuristic algorithms for the quadratic assignment problem is developed. The approach is based on the results about packing graphs and shortest trees under constrains on their configuration.
Matskevich A. N.
Mathematical models of the determined nonstationary perturbations in the class of regular processes. pp. 113119
Summary: The techniques of synthesis and mathematical models of the determined nonstationary perturbations in the class of regular processes are developed.
ABSTRACTS OF DEPOSITED PAPERS
Lukshin E. V.
On noninteger vertices of a class of threeindex axial transportation polytopes. p. 120
SCIENTISTS OF BELARUS
Boris Ivanovich Stepanov (On the occasion of the 90^{th} birthday). pp. 121123
Click here to read this article in Russian (Windows 1251)
/ Publications / Scientific Journals / Back to Top of Page
Designed and maintained by Dr. Nikolai N. Kostyukovich. Last updated: October 14, 2003
Created with assistance of Dr. Ignatii I. Korsak
Copyright © 2003 The National Academy of Sciences of Belarus
Copyright © 2003 The Institute of Mathematics of NASB