In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z,...In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).展开更多
Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface condi...Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.展开更多
Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in te...Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.展开更多
Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a ...Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.展开更多
The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The el...The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.展开更多
文摘In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).
基金The project is supported by the Natural Science Foundation of China.
文摘Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.
文摘Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.
基金Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. Y2008A23)
文摘Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.
基金supported by the National Natural Science Foundation of China(Nos.90305023 and 11172332)
文摘The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.
文摘探究了含有多个椭球夹杂的双材料和半无限大空间的稳态传热解.双材料的界面由包含连续性条件的双材料空间格林函数考虑,通过调整参数,该函数可退化为半无限大空间或者无限大空间格林函数.利用Eshelby等效夹杂法(equivalent inclusion method,EIM),将椭球夹杂等效为基底材料和夹杂内连续分布的本征温度梯度场.基于含多项式密度的椭球积分,椭球夹杂的扰动作用由本征温度梯度场和双材料格林函数域积分精确描述.本征场由夹杂形心展开的泰勒级数,并通过各个夹杂形心建立的多项式等效热流方程求解,求解精度由有限元法(finite element method,FEM)验证,实现了无网格求解双材料和半无限大空间中多个椭球夹杂的稳态传热问题.
