谱半径

In this paper,the estimates of upper bounds for the spectral radius of the iterative matrix M~(-1)N for some generalized diagonally dominant matrix M are presented.

对几类广义对角占优矩阵M，给出了迭代矩阵M~(-1)N谱半径的上界估计式，所得结果较已有结果适用于更加广泛的矩阵类。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

Using the Genetic Algorithm to solve a difficult problem –searching the eigenvalue and the eigenvector of a matrix.

对正矩阵和正对称矩阵的谱半径的下界作了修正。(2)应用遗传算法解决矩阵特征值和特征向量问题。

Irreducible matrix. A probabilistic proof is proposed, together with

对不可约的非负方阵，其谱半径和诱导的无穷-范数之间满足

Our paper is mainly about the ordering of the connected graphs with thesmallest Laplacian spectral radii.

本文主要是对连通图的最小Laplace谱半径的排序问题的研究。

In the case of discrete systems, some simple stability criteria are given in terms of matrix norm and the spectral radius of matrix, which are delay-independent and are therefore valid for any large delay.

对带滞后的线性定常离散广义系统，则通过矩阵的范数与谱半径建立了一些形式简单的稳定性判据，用它们判别系统的稳定性时，不会因滞后的增大而明显地增加计算量。

In recent years, domestic and foreign scholars have made particular progress onthe research of it.

近年来，对图的Laplace谱半径问题的研究，国内外都取得了一定的进展。

For solving the linear system with the iterative method, it is very important to estimate the spectral radius of the iterative matrices.

在用迭代法解线性方程组时，迭代矩阵的谱半径估计在迭代法的收敛性分析中起着重要的作用。

The eigenvalue and the spectral radius of linear completely continuous operators are very important and significant indexes.

线性全连续算子的特征值和谱半径是非常重要的、具有实际意义的指标。

In the first chapter, we have introduced the research background and someresearch achievements of Laplacian spectral radius, and we also introduce somebasic conceptions on algebraic graph.

在第一章中，我们介绍了图的Laplace谱半径的研究背景以及近年来国内外学者的一些研究成果，也介绍了代数图论中的一些基本概念。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。