Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2001, No.1
/ Выданні акадэміі / Навуковыя часопісы
Весці Нац. акадэміі навук Беларусі. Сер. фіз.-матэм. навук, 2001, No.1
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Весці Нацыянальнай акадэміі навук Беларусі
СЕРЫЯ ФІЗІКА-МАТЭМАТЫЧНЫХ НАВУКВыдавец: Інстытут матэматыкі НАН Беларусі, Мінск, Рэспубліка Беларусь |
Нумар 1, 2001
ЗМЕСТ
МАТЭМАТЫКА
Beresnevich V.V., Vasilyev D.V.
An analogue of a theorem of Khintchine for curves in 3-dimensional complex space. pp. 5--7
Summary: A full analogue of Khintchine's theorem for Diophantine approximation on analytic curves in C3 is proved.
Beniash-Kryvets V.V.
Representation varieties of a group SL2(Z). pp. 8--11
Summary: The representation variety of the group SL2(Z) is studied. All irreducible components of Rn(SL2(Z)) is found. Their rationality and smoothness are proved.
Bobr V.V., Yadchenko A.A.
About p-solvable irreducible linear groups of relatively small degree. pp. 12--17
Summary: The invariant tests of Sp-subgroup H of p-solvable irreducible complex linear group of degree less then 2|H| are obtained.
Mirotin A.R.
On the extentions of finite dimensional representations of Lie semigroups. pp. 18--21
Summary: It is shown that a finite dimensional representation of a generating quasiinvariant Lie semigroup S extends to a local representation of the Lie group generated by S. The conditions of a global extandability have been given.
Kenko M.V.
About w-composition formations with length 3. pp. 22--25
Summary: A description of w-composition formations with length 3 is obtained.
Galmak A.M.
Theorems describing isomorphisms of polyadic groups. pp. 26--31
Summary: New versions of theorems describing isomorphisms of polyadic groups are given.
Monastyrny P.I.
On calculation algorithms of hybrid type for grid and boundary problems. I. pp. 32--36
Summary: The new approach to the problem of the solution of grid equations is proposed. It is based on the hybrid principle of the joining of various calculations algorithms which are local adapted to the characteristic of equations. The method is provided by constructive using of the mechanism of closing of the calculations in boundary zones.
Shvakel N.A.
About the optimal stabilization of two-parameter discrete systems with a shift operator of the infinite order. pp. 37--42
Summary: The linear quadratic optimal control problem for discrete two-dimensional (2-D) systems with a shift operator of the infinite order is studied. The problem of optimal stabilization by means of a feedback optimal control is considered. The conditions of the optimal control stabilizing given system is determined.
Malyutin V.B.
Interpolation formula for functional integrals defined by a first degree differential equation with noncommutative values. pp. 43--46
Summary: Interpolation formula for functional integrals defined by a first degree differential equation with noncommutative values is constructed.
Jovanovich B.S., Shchehlik V.S.
On the convergence of one difference scheme for the nonlinear heat equation with generalized solutions. pp. 47--50
Summary: Implicit non-iterative difference scheme for the nonlinear one dimensional heat equation with unbounded nonlinearity is considered. Solution of the initial differential problem is supposed to belong to the Sobolev space of functions W23,3/2(QT). The coefficient of heat conductivity is a Lipschitz continuous function in the neighborhood of the domain of the exact solution. Estimates of the following form are obtained.
Kalinin A.I.
Asymptotic minimization of quadratic functionals on trajectories of linear singularly perturbed systems. pp. 51--56
Summary: The algorithm of the calculation the asymptotic solution for the singularly perturbed linear-quadratic terminal control problem with conditions on control functions is proposed.
Blinova E.I., Zalesky B.A.
The sizes of clusters, arising in the maximum a posteriori estimates in Gibbsian models. pp. 57--62
Summary: The maximum a posteriori (MAP) estimates properties in the case of a special type Gibbsian distribution for binary images degraded with independent Bernoullian noise is studied. It is shown that MAP estimates of the black image do not contain large clusters of white points with great probability. The MAP based consistent estimate for real black-and-white images is constructed.
Kurenok V.P.
Existence of solutions of stochastic equations controlled by stable Levy processes. pp. 63--67
Summary: Stochastic equations Xt = x0 + ò0tB (s, Xs-) dZs where x0 is an arbitrary initial value, Z is an one-dimensional stable Levy process of the index a Î (1,2] and В: [0, ¥) x R ® R is a measurable coefficient are studied. Sufficient conditions for the existence of weak solutions are given. Results of P. A. Zanzotto for the homogeneous case with 1 < a < 2 are generalized. New sufficient conditions for the case with a = 2 are found.
ФІЗІКА
Goncharenko A.M.
Approximated theory of optical solitons. pp. 68--72
Summary: Gaussian's functions are used to consider properties of optical solitons. It is shown that transverse dimensions and temporal duration of the solitons oscillate in inhomogeneous nonlinear medium.
Sirota N.N.
The phonon spectra of elements of cubic structures with using of Born potentials. pp. 73--77
Summary: The phonon spectra of monoatomic crystals (V, Nb, Mo, Cu, Ag, Au, Pd, Pt) with cubic lattices (FCC, VCC) using Born potential and Mie--Gruneisen potential are calculated.
Hoang Quoc Khanh, Komarov L.I.
Operator method in the theory of atoms. pp. 78--81
Summary: Within the framework of one-particle approximation the model of atom is offered. The model based on introduction of individual potential fields for the description of electronic states, allowing as against Hartree--Fock method to present energy of atom as the sum one-electron energies and giving analytical expressions for one-particle wave functions.
Goncharenko I.A., Esman A.K., Pilipovich V.A.
The method of analysis of apodized fibre gratings structures. pp. 82--86
Summary: The method for calculation of parameters of apodized fibre gratings is proposed. The analysis of the gratings with different apodization functions based on this method is carried out.
Korshunov F.P., Kyuregian A.S., Zhdanovich N.E., Marchenko I.G.
Deep levels determination in the spase charge region at silicon p - n-junction avalanche breackdown. pp. 87--90
Summary: The analysis of the differential resistance (Rd) temperature dependence (80 -- 300 К) of the gamma-irradiated Si p--n-junctions in breakdown avalanche region have been fulfilled, The possibility of determination of the defect deер level ionization energy in the p--n-junction space charge region based on the Rd(T) experimental dependency measured at different avalanche currents have been shown.
Petrova E.S., Khilo N.A.
Quasicircular polarized Bessel light beams. pp. 91--94
Summary: Vectorial Bessel light beams with quasicircular polarization are investigated. It is shown that the circular polarization of beams is retained for angles of a conicity up to 20 deg that considerably exceeds a paraxial limit. The azimuth component of the energy flow vector is calculated and its connection with polarization state and the order of Bessel function is established. The spin-orbit coupling inside a Bessel beams is discovered and the connection between polarization state and transverse spatial structure of the field is also founded.
Goncharenko E.A.
Coupled states of three kinks for the system of two scalar fields. pp. 95--98
Summary: The model of two real scalar fields with the fourth order interactive potential is considered on. The field configuration corresponding to the coupled states of three soliton-like objects are described which based on numerical calculations.
Kramoreva L.I., Khilo P.A.
Polarization self-action in process of II-type second harmonic generation in KTP crystal. pp. 99--102
Summary: The phase self-modulation of the fundamental wave in the conditions of nonsynchronous second harmonic generation is investigated. It is shown that the optimal transmission coefficient is realized for the case of linearly polarized fundamental output radiation.
Kostko V.S., Kostko O.V., Makovetskii G.I., Yanushkevich K.I.
Light-sensitivity of thin-film SnI2 -- Sn - glass structure and phase composition of SnI2 -- Cd - glass structure. pp. 103--106
Summary: The results of experimental research of light-sensitive properties of the SnI2 -- Sn - glass structure and phase composition of SnI2 -- Cd - glass structure are presented. The conclusion about the dependence of photosensitivity of the structure upon the thickness of metal and semiconductor layers is made. The modification of phase composition of the SnI2 -- Cd - glass structure during the light radiation is considered.
Tochitskii T.A., Dmitrieva A.E.
On mechanism of formation structure nanocrystalline electrolytically deposited nickel films. pp. 107--111
Summary: The mechanism of formation structure nanocrystalline electrolytically deposited nickel films has been investigated.
Novysh B.V., Dorozhkin N.N.
The calculation algorithm of the crystal defect potential. pp. 112--114
Summary: The algorithm of calculation of crystal defect potential has been developed based on Lippmann -- Schwinger equations in coordinate space. The algorithm allow to take into account non-spherical components of electron densities and potentials inside MT-spheres of defect atoms.
ІНФАРМАТЫКА
Pilipovich V.A., Esman A.K., Goncharenko I.A., Kuleshov V.K., Solonovich I.F.
Optical logic elements on the base of the effect of self-induced transparency in optical fibres with resonance impurities. pp. 115--119
Summary: All-optical logic elements of the "control delay" type on the base of the effect of self-induced transparency (SIT) in erbium-doped optical fibres have been considered. The use of the preliminary pumping erbium doped fibres for decreasing the peak power of the SIT-solitons down to the levels comparable to the peak power of the solitons, propagating in usual fibres, has been proposed. The dependence of the SIT pulses delay time in fibre from concentration of the erbium ions has been calculated. It has been shown that the delay times difference obtained by use of the SIT effect more than on the order exceeds the ones received on the basis of the other nonlinear optical effects. By this, the length of the logic element operated on the clock frequency 1100 GHz is about 10 cm, and time of performing the logical operation of addition is ~ 0.5ns .
Kravtsov M.K., Krachkovskii A.P.
Polynomial algorithm for multicriteria multi-index axial problem of choice. pp. 120--123
Summary: Polynomial algorithm for multicriteria multi-index axial problem of choice is proposed.
Andreev G.V., Sotskov Yu.N.
Brunch and bound method for mixed graph vertex coloring. pp. 124--129
Summary: A mixed graph coloring is an assignment of positive integers (colors) to vertices of a mixed graph such that, if two vertices are joined by an edge, then their colors have to be different and if two vertices are joined by an arc, then the color of the startvertex has to be not greater than the color of the endvertex. A brunch and bound algorithm is developed for mixed graph coloring based on conflict resolution strategy and adding some arcs. Computational results for randomly generated mixed graphs of order n £ 150 are given.
Ignatenko I.I.
The non-assortment cutting problem with rectangles of equal width. pp. 130--133
Summary: The guillotine cutting problem of dissecting a rectangle sheet is considered. It is shown that the problem can be reduced to a pseudo-polynomial time algorithm of the knapsack problem.
ВУЧОНЫЯ БЕЛАРУСI
Владимир Антонович Пилипович (К 70-летию со дня рождения). С. 134--135
Націсніце тут, каб прачытаць артыкул
Віктар Сямёнавіч Буракоў (Да 70-годдзя з дня нараджэння). С. 136--137
Націсніце тут, каб прачытаць артыкул
Лев Митрофанович Томильчик (К 70-летию со дня рождения). С. 138--139
Націсніце тут, каб прачытаць артыкул
/ Выданні акадэміі / Навуковыя часопісы / Да пачатку старонкі
Распрацавана і падтрымліваецца Мікалаем М. Касцюковічам. Апошняе абнаўленне: 8 снежня 2006 г.
Створана пры ўдзеле Ігната І. Корсака
Капірайт © 2001-2006 Нацыянальная акадэмія навук Беларусі
Капірайт © 2001 Інстытут матэматыкі НАН Беларусі
