具有密度依赖的Monod-Haldane反应项捕食模型的动态分歧和跃迁

本文研究具有密度依赖的Monod-Haldane反应项捕食模型在齐次Dirichlet边界条件下的动态分歧和跃迁.利用中心流形约化以及动态分歧理论,在两种不同情形下分别得到跃迁类型及其判据,给出吸引域的刻画,补充和完善相关文献中的已有结果.最后通过数值模拟验证理论分析的正确性并给出生物学解释.     

浅谈考研题中特征值和特征向量的计算

本文首先回顾了矩阵特征值的相关概念和性质,给出了一类特殊矩阵特征值和特征向量的简便计算方法,并结合全国硕士研究生入学统一考试的数学试题实例进行了讨论.最后讨论了特征值和特征向量的一个具体应用.     

利用矩阵的初等行变换对矩阵的特征值与特征向量同步求解

利用矩阵的初等行变换对矩阵的特征值与特征向量同步求解刘国琪，王保智（河北电力职工大学０７１０５１）一般教科书中介绍的求矩阵Ａ的特征值与特征向量的方法是：首先，求问ＩＡＥ—Ａｌ＝０，得特征值Ａ。；然后，对每一个人，间方程组（Ｇ怎一Ａ）Ｘ—。，得特征向量...     

具有内部构造安全保障体系的冗余机器系统的特征值的问题

对具有内部构造安全保障体系的冗余机器系统中的特征值的存在性进行了分析求解,给出了实例,并对该系统的特征值进行了一个特征值对应一个特征向量的求征.     

具有四个状态的系统特征值的存在性

针对具有四个状态的系统所建立的模型,得出了系统算子一个特征值对应一个特征向量的结论,并证明了除0特征外还存在另外非零实特征值.     

特征值与特征向量

特征值与特征向量的两种不同定义是一致的：线性变换/A与其对应的n阶矩阵A有相同的特征值,而n阶矩阵A的特征向量x是/A的特征向量ξ在基ε1,…εn下的坐标。     

矩阵特征值、特征向量的确定

首先对由 A的特征值、特征向量求 A- 1 ,AT,A* ( A的伴随矩阵 )、P- 1 AP以及 A的多项式φ( A)的特征值和特征向量的结论作了个归纳 ;对相反的情形 ,我们给出了部分已有的结果 ,并通过四道例题着重讨论了如何由 φ( A)的特征值来求 A的特征值 .     

Jacobi矩阵的逆特征问题

本文研究了两个Jacobi矩阵的逆特征问题：I给定实数λ,μ(λ＞μ）和n维非零实向量x,y,求n阶Jacobi矩阵J,使Jx=λx,Jy=μy,且λ＞λ2（J）＞…＞λi-1（J）＞μ＞λi＋1（J）…＞λn（J）,或λi（J）＞λ2（J）＞…＞λi－1（J）＞λ＞λi＋1（J）＞…＞λn-1（J）＞μ·II给定实数λ,μ（λ＞μ）和n维非零实向量x,y,求n阶Jacobi矩阵J,使Jx＝λx,Jy＝μy,且λ1（J）＞λ2（J）＞…＞λi－1（J）＞λ＞μ＞λi＋2（J）＞…＞λn（J）．文中给出了问题I;II有唯一解的充要条件,并给出了解的表达式．     

d-d跃迁谱强的三参数拟合方案

本文推广Judd-Ofelt的closure近似于对主量子数n''的求和,提出了在晶场等效点荷模型和能量拟合基础上,用三参量拟合静奇宇称晶场诱导的d-d电偶跃迁强度的方案,并成功地拟合了金绿宝石低温偏振吸收谱强的12个大小相差5个量级的实验数据。对金绿宝石晶体的激光微观机理进行了分析。     

特征值反问题的唯一性

证明了由特征值及特征向量反求矩阵时,特征值在对角矩阵中的排序可以是任意的,只须将对应特征向量作相应排序,所得矩阵唯一。对于重特征值的线性无关的特征向量可任意选取,所得矩阵唯一。     

Stratified random walks on the n-cube

In this paper we present a method for analyzing a general class of random walks on the n-cube (and certain subgraphs of it). These walks all have the property that the transition probabilities depend only on the level of the point at which the walk is. For these walks, we derive sharp bounds on their mixing rates, i.e., the number of steps required to guarantee that the resulting distribution is close to the (uniform) stationary distribution. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 199–222, 1997     

Homogenization of eigenvalue problems in perforated domains

In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet: λ_ε = ε⁻² λ + λ₀ +O (ε), Stekloff: λ_ε = ελ₁ +O (ε²), Neumann: λ_ε = λ₀ + ελ₁ +O (ε²). Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in the case of Neumann eigenvalue problem.     

Nearest q-Flat to m Points

Recently, Bradley and Mangasarian studied the problem of finding the nearest plane to m given points in ⁿ in the least square sense. They showed that the problem reduces to finding the least eigenvalue and associated eigenvector of a certain n×n symmetric positive-semidefinite matrix. We extend this result to the general problem of finding the nearest q-flat to m points, with 0qn–1.     

一类三对角矩阵任意正整数幂的计算

给出一类带有一个零行或两个零行的三对角矩阵的任意正整数幂的一般表达式.本文所用的方法较Leonaite和Rimas的方法简单,而结果既简洁又更具一般性.     

乘幂法的改进算法

本文提出了一种改进的乘幂法,一方面大大加快了收敛速度,另一方面可以方便地计算全部的特征值,最后给出一个计算的特征值通用算法。     

On the Randomized Error of Polynomial Methods for Eigenvector and Eigenvalue Estimates

In this paper we consider the problem of estimating the largest eigenvalue and the corresponding eigenvector of a symmetric matrix. In particular, we consider iterative methods, such as the power method and the Lanczos method. These methods need a starting vector which is usually chosen randomly. We analyze the behavior of these methods when the initial vector is chosen with uniform distribution over the unitn-dimensional sphere. We extend and generalize the results reported earlier. In particular, we give upper and lower bounds on the _pnorm of the randomized error, and we improve previously known bounds with a detailed analysis of the role of the multiplicity of the largest eigenvalue.     

On a special basis of approximate eigenvectors with local supports for an isolated narrow cluster of eigenvalues of a symmetric tridiagonal matrix

Let $ \tilde \lambda Let be an approximate eigenvalue of multiplicity m _c = n − r of an n × n real symmetric tridiagonal matrix T having nonzero off-diagonal entries. A fast algorithm is proposed (and numerically tested) for deleting m _c rows of T− I so that the condition number of the r × n matrix B formed of the remaining r rows is as small as possible. A special basis of m _c vectors with local supports is constructed for the subspace kerB. These vectors are approximate eigenvectors of T corresponding to . Another method for deleting m _c rows of T− I is also proposed. This method uses a rank-revealing QR decomposition; however, it requires a considerably larger number of arithmetic operations. For the latter algorithm, the condition number of B is estimated, and orthogonality estimates for vectors of the special basis of kerB are derived. Original Russian Text ? S.K. Godunov, A.N. Malyshev, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 7, pp. 1156–1166.     

A Computational Approach for Fluid Queues Driven by Truncated Birth–Death Processes

In this paper, we analyze fluid queues driven by truncated birth-death processes with general birth and death rates. We compute the equilibrium distribution of the content of the fluid buffer by providing efficient numerical procedures to compute the eigenvalues and the eigenvectors of the associated real sign-asymmetric tridiagonal matrix. We illustrate the effectiveness of the procedures through tables and graphs.     

Leading students towards the formal world of mathematical thinking: a mathematician’s reflections on teaching eigentheory

ABSTRACT

In this study, we analysed a mathematician’s teaching journals on eigenvalues and eigenvectors in a first-year linear algebra course. The research team employed Tall’s [How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge University Press] three-world model of embodied, symbolic and formal as a framework for understanding the mathematician and teacher’s pedagogical reflections as he led the class to the formal world. In order to reach the formal world, he used a sequence of tasks that emphasized embodied and symbolic, as well as formal thinking. The analysis of the journals showed that the mathematician faced challenges in leading the class towards the formal world. The study also revealed that the mathematician strived to build a concept image, that, while perhaps mirroring his own, did not resonate with the students.