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21.
22.
For a ? R\alpha \in \mathbf{R}, the class of a-\alpha -order spherical harmonic functions in an open set W í\Omega \subseteq Sn-1\mathbf{S}^{n-1}, Ha(W)H^{\alpha }(\Omega ) is defined as the C2-C^{2}-solutions of Dau=0\Delta _{\alpha }u=0; where Da=Ds+a(n+a-2)\Delta _{\alpha }=\Delta _{s}+\alpha (n+\alpha -2) is the spherical Laplace--Beltrami operator of order a\alpha and Ds\Delta _{s} is the radially independent part of the Laplace operator. We obtain a Green's integral formula for the functions in Ha(W)H^{\alpha }(\Omega ) with kernel expressed as a Gegenbauer function. As generalizations, higher order spherical iterated Dirac operators are defined in a polynomial form. Integral representations of the null solutions to these operators and an intertwining formula relating these operators on the sphere and their analogues in Euclidean space are presented. 相似文献
23.
A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime. 相似文献
24.
25.
Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties)
polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with
the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes
for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken
into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional
case provides interesting classes of groups.
Received: 13 December 2001 / Revised version: 24 June 2002
The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107
Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20 相似文献
26.
王巨平 《中国科学A辑(英文版)》2002,45(7):827-835
This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions
for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-typeL-series. 相似文献
27.
Soliton interaction under the influence of higher-order effects 总被引:6,自引:0,他引:6
In this paper, we present exact N-soliton solution by employing simple, straightforward Darboux transformation based on the Lax pair for Hirota equation, a higher-order nonlinear Schrödinger (HNLS) equation. As examples, one- and two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one can adjust frequency shift for each soliton appropriately. Further, we obtain the approximate eigenvalues by employing two-soliton solution and discuss analytically the interaction between neighboring solitons under the influence of the higher-order effects. It is shown that the combined effects of the higher-order effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically. 相似文献
28.
It is explicitly shown that if phase transition occurs at the core of a newborn neutron star with moderately strong magnetic
field strength, which populates only the electron’s Landau levels, then in the β -equilibrium condition, the quark core is
energetically much more unstable than the neutron matter of identical physical condition. 相似文献
29.
We derive an explicit autocorrelation function (ACF) formula of state of polarization for a fiber transmission system with polarization mode dispersion (PMD) and polarization dependent loss (PDL), which is found to agree well with Monte Carlo simulation. Then we use the new ACF to investigate the combined effect of PMD and PDL on the polarization multiplexed scheme. We find the performance of the polarization multiplexed scheme can be deteriorated more severely than the case without PDL. 相似文献
30.
Dimitar I. Pushkarov 《Central European Journal of Physics》2004,2(3):420-455
Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon
are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they
turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but
by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation
formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison
with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan
theory is shown. 相似文献