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21.
A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP 总被引:2,自引:0,他引:2
朱理 《数学物理学报(B辑英文版)》2002,22(3)
In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group. 相似文献
22.
Milan Medved? 《Journal of Mathematical Analysis and Applications》2002,267(2):643-650
A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality. 相似文献
23.
24.
Johan Helsing 《BIT Numerical Mathematics》2006,46(2):307-323
A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come
from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating
distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar
to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that
of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with
up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners
of otherwise similar construction, and especially so when the preconditioners are very sparse.
AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30 相似文献
25.
Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture
By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems. 相似文献
26.
Zhao Hanzhong 《Acta Mechanica Solida Sinica》2002,15(2):156-162
A finite difference/boundary integral procedure to determine the acoustic reflected pressure from a fluid-loaded bi-laminated
plate is described. The bi-laminate is composed of a piezoelectric layer and an elastic layer in contact with the fluid, and
is held by an acoustically hard baffle. In the numerical model, the fluid pressure at fluid/solid interface is replaced by
a continuum of point sources weighted by the normal acceleration of the elastic plate, and the governing equation system is
solved in the solid domain. With the normal acceleration found, the reflected pressure in the fluid is determined by an integral
expression involving the Green's function. It is demonstrated that an appropriate applied voltage potential across the piezoelectric
layer has the effect of cancelling either the reflected or scattered pressure of the plate at any chosen field points in the
fluid.
Project supported by the National Natural Science Foundation of China (No. 10172039). 相似文献
27.
Mehdi Dehghan 《Numerical Methods for Partial Differential Equations》2002,18(2):193-202
Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040 相似文献
28.
V. B. Bekezhanova 《Fluid Dynamics》2006,41(3):343-350
The problem of the stability of steady convective viscous incompressible fluid flow in a vertical layer with boundaries at different temperatures is considered in the presence of transverse blowing through the layer. The complete spectral problem is solved for a silicon melt. The neutral curve is constructed and the critical Grashof number is found. The numerical calculations show that the presence of transverse blowing significantly affects the flow stability. As compared with the Oberbeck-Boussinesq model, in the microconvection model the instability develops at lower wavenumbers. 相似文献
29.
一类积分不等式的推广 总被引:1,自引:0,他引:1
对一些基本的积分不等式进行了推广,给出了含有n个无关变元的更广泛的非线性积分不等式.利用所得的不等式讨论了某些非线性积分方程解的有界性. 相似文献
30.
The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itself, it is proved that the maximal singular integral is bounded from L∞to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions. 相似文献