The first eigenvalue of Finsler p-Laplacian

The eigenvalues and eigenfunctions of p-Laplacian on Finsler manifolds are defined to be critical values and critical points of its canonical energy functional. Based on it, we generalize some eigenvalue comparison theorems of p-Laplacian on Riemannian manifolds, such as Lichnerowicz type estimate, Obata type theorem and Mckean type theorem, to the Finsler setting. Not only that, the Lichnerowicz type estimate we obtained is even better than the corresponding one in Riemannian geometry.     

Exact constants in Poincaré type inequalities for functions with zero mean boundary traces

In this paper, we investigate Poincaré type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd.     

关于Jacobi矩阵的特征值反问题可解的充分必要条件的一个注记 (英)

本文讨论一类具有特殊结构的Jacobi矩阵的特征值反问题,该问题由描述变截面杆的微分方程离散化得到．我们得到了这个问题有解的一些必要条件,并且通过一些数值例子,说明了L．Lu和K．Michael给出的充分条件和算法在矩阵的阶数高于3的时候是错误的。     

The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems

In this paper we prove a double order for the convergence of eigenfrequencies in fluid-structure vibration problems. We improve estimates given recently for compressible and incompressible fluids. To do this, we extend classical results on finite element spectral approximation to nonconforming methods for noncompact operators.

     

MULTIPLE POSITIVE SOLUTIONS FOR A FOURTH-ORDER NONLINEAR EIGENVALUE PROBLEM

In this paper, by using the Guo-Krasnoselskii’s fixed-point theorem, we establish the existence and multiplicity of positive solutions for a fourth-order nonlinear eigenvalue problem. The corresponding examples are also included to demonstrate the results we obtained.     

Biorthogonal Rational Functions and the Generalized Eigenvalue Problem

We present some general results concerning so-called biorthogonal polynomials of R_II type introduced by M. Ismail and D. Masson. These polynomials give rise to a pair of rational functions which are biorthogonal with respect to a linear functional. It is shown that these rational functions naturally appear as eigenvectors of the generalized eigenvalue problem for two arbitrary tri-diagonal matrices. We study spectral transformations of these functions leading to a rational modification of the linear functional. An analogue of the Christoffel–Darboux formula is obtained.     

主特征值估计的新故事

本文介绍主特征值估计的两种通用方法，着重于两个侧面：来自黎曼几何的第一种方法如何应用于概率论；来自概率论的第二种方法如何应用于黎曼几何。此外，还将概述若干基本结果。     

板几何中一类具抽象边界条件迁移算子的谱

在LP（1≤P〈∞）空间上，研究了板几何中一类具抽象边界条件下各向异性、连续能量、非均匀介质的迁移方程，证明了这类方程相应的迁移算子的谱在右半平面中仅由有限个具有限代数重数的离散本征值组成等结果．     

Nuclear fusion rate for ddμ muonic molecule

A variational approach using a new wave function to ddμ muonic molecular ion is proposed. This approach requires four terms in the total three‐body wave function. The formation and fusion take place by the reason of the existence of the both Coulomb potential and nuclear absorption. The nuclear fusion rates and eigenvalues related to such levels below dμ(1s) + d threshold are calculated with a good accuracy and a short computation time. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008