Application of asymptotic iteration method to the Khare-Mandal and its PT-symmetric QES partner potential

We study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for certain values of potential parameters, its PT-symmetric partner exhibits real energy eigenvalues in all cases.      

Indestructibility under adding Cohen subsets and level by level equivalence

We construct a model for the level by level equivalence between strong compactness and supercompactness in which the least supercompact cardinal κ has its strong compactness indestructible under adding arbitrarily many Cohen subsets. There are no restrictions on the large cardinal structure of our model (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Additive preconditioning, eigenspaces, and the inverse iteration

We incorporate our recent preconditioning techniques into the classical inverse power (Rayleigh quotient) iteration for computing matrix eigenvectors. Every loop of this iteration essentially amounts to solving an ill conditioned linear system of equations. Due to our modification we solve a well conditioned linear system instead. We prove that this modification preserves local quadratic convergence, show experimentally that fast global convergence is preserved as well, and yield similar results for higher order inverse iteration, covering the cases of multiple and clustered eigenvalues.     

Asymptotic Speed of Wave Propagation for A Discrete Reaction-Diffusion Equation

We deal with asymptotic speed of wave propagation for a discrete reactlon-diffusion equation. We find the minimal wave speed c★ from the characteristic equation and show that c★ is just the asymptotic speed of wave propagation. The isotropic property and the existence of solution of the initial value problem for the given equation are also discussed.     

二阶微分方程反周期边值问题解的存在性

在这篇文章中,我们考虑了一类非线性二阶常微分方程反周期边值问题．利用上下解方法结合单调迭代技巧,我们得到了解的存在性结果．     

求n阶实方阵A的全部模最大的特征值及其相应特征向量的幂法

本文给出并论证了 ,当 n阶实方阵 A具有 i ( 1≤ i≤ n)个 (即任意多个 )模最大的特征值时 ,用幂法求出这些模最大的特征值及其相应特征向量的方法 .该方法是对幂法理论的进一步完善     

Variational iteration method for elastodynamic Green’s functions

In this study, a new application of the variational iteration method is presented. We use this method to obtain approximations to 3D Green’s function for the dynamic system of anisotropic elasticity. The numerical results obtained from convolution of Green’s function and data of the Cauchy problem are compared with the exact solution for cubic media.     

逃逸时间法生成M集中控制变量B的确定

逃逸时间算法是生成Mandelbrot集(简称M集)最常用的算法,本文针对非线性复映射f(z)=zm c为迭代函数的情形进行讨论.首先,根据逃逸时间算法的基本原理给出相应的算法步骤;然后,对迭代函数f(z)=zm c进行了详细研究,从而合理地确定了算法中需要控制的变量B(参数值c0的取值范围)的取值,这样就大大地减少了迭代次数,从而提高了算法的运算效率.     

有限个严格压缩映像隐迭代格式的逼近

假设E为一致凸的Banach空间,对偶空间E*有Kadec-Klee性质,K为E的非空闭凸子集{Ti:i=1,2,…,N}:K→K为Browder-Petryshyn意义下的严格伪压缩映像且F=∩Ni=1F(Ti)≠0.{αn}n∞=1满足0相似文献