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461.
孙越  田贵花  董锟 《中国物理 B》2011,20(6):61101-061101
We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s = 1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen- functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.  相似文献   
462.
In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the (k + 1)th eigenvalue in terms of the first kth eigenvalues independent of the domains.  相似文献   
463.
考虑了混合气体线性化Boltzmann算子的特征值与特征函数问题.通过对算子中核函数的分析得出了更一般的混合气体线性化Boltzmann算子的特征值与特征函数.而且结论还适用于单一气体情况.  相似文献   
464.
In this paper, we propose a method to improve the convergence rate of the lowest order Raviart-Thomas mixed finite element approximations for the second order elliptic eigenvalue problem. Here, we prove a supercloseness result for the eigenfunction approximations and use a type of finite element postprocessing operator to construct an auxiliary source problem. Then solving the auxiliary additional source problem on an augmented mixed finite element space constructed by refining the mesh or by using the same mesh but increasing the order of corresponding mixed finite element space, we can increase the convergence order of the eigenpair approximation. This postprocessing method costs less computation than solving the eigenvalue problem on the finer mesh directly. Some numerical results are used to confirm the theoretical analysis.  相似文献   
465.
分别研究了一类带有Hamiltonian路和带有Hamiltonian圈的有向图的基本有圈性(essential cyclicity),给出了这种有向图的Laplacian谱,表明这些图具有全实的Laplacian谱.  相似文献   
466.
讨论了抽象算子方程F(λ,u)=0的局部分歧问题,其中F:R×X→Y是一个C~2微分映射,λ是参数,X,Y为Banach空间.利用Lyapunov-Schmidt约化过程及偏导算子F_u(λ~*,O)的有界线性广义逆,在dim N(F_u(λ~*,0))≥codim R(F_u(λ~*,O))=1的条件下,证明了一个广义跨越式分歧定理.当参数空间的维数等于值域余维数时,应用同样的方法又得到了多参数方程的抽象分歧定理.  相似文献   
467.
We consider an infinite Hermitian positive definite matrix M which is the moment matrix associated with a measure μ with infinite and compact support on the complex plane. We prove that if the polynomials are dense in L2(μ) then the smallest eigenvalue λn of the truncated matrix Mn of M of size (n+1)×(n+1) tends to zero when n tends to infinity. In the case of measures in the closed unit disk we obtain some related results.  相似文献   
468.
469.
Graphs with second largest eigenvalue λ2?1 are extensively studied, however, whether they are determined by their adjacency spectra or not is less considered. In this paper we completely characterize all the connected bipartite graphs with λ2<1 that are determined by their adjacency spectra. In addition, we prove that all the connected non-bipartite graphs with girth no less than 4 and λ2<1 are determined by their adjacency spectra.  相似文献   
470.
Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.  相似文献   
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