矩阵负特征值的上下界估计

矩阵是一类特殊矩阵,R.L.Smith在文献中证明了它有且只有一个负特征值,并利用N0矩阵谱半径给出了N0矩阵负特征值的一个粗略上界和下界估计.而本文仅仅利用N0矩阵本身的元素给出了一个更加实用且计算简单的上界和下界估计.     

基于高阶辛算法的纳米器件本征问题仿真

研究精确和高效的数值方法是现代纳米器件建模和优化的重要目标之一,而分析大部分纳米器件特性的切入点是确定器件结构的能量本征值和能量本征态。本文提出了一种新的算法—高阶辛时域有限差分法(SFDTD(3,4): symplectic finite-difference time-domain)求解含时薛定谔方程。在时间上采用三阶辛积分格式离散,空间上采用四阶精度的同位差分格式离散,建立了求解含时薛定谔方程的高阶辛时域有限差分算法。将高阶辛算法SFDTD(3,4)用于一维量子阱中盒中粒子和谐振子的仿真中,实验结果表明SFDTD(3,4)法比传统的时域有限差分算法以及高阶时域有限差分算法更加准确,适用于对纳米器件本征问题的长时间仿真。     

Morse临界群在椭圆方程组中的应用

应用Morse临界群讨论了如下的变分型的非线性椭圆方程组的非平凡解的存在性：（P）{-△u=λ（m11（x）u m12（x）v） n1（x）|u|^q-2u Fv(x,u,v) x∈Ω；-△v=λ(m21(x)u m22(x)v) n2(x)|v|^q^-2v Fv(x,u,v) x∈Ω；u|2Ω=v|2Ω|=0这儿，q∈(1,2),ni(x)可允许变号，这使得本文的结果是新的。     

对称正交对称半正定矩阵逆特征值问题

对给定的特征值和对应的特征向量，提出了对称正交对称半正定矩阵逆特征值问题及最佳逼近问题，通过分析对称正交矩阵和对称正交对称半正定矩阵的结构，利用矩阵的奇异值分解，导出了这种逆特征值问题的最小二乘解的表达式，以及这种逆特征值问题相容的充要条件和通解表达式，利用矩阵的极分解，导出了逆特征值问题的最佳逼近解，最后，通过数值算例说明了如何计算矩阵逆特征值问题的最小二乘解及最佳逼近解。     

地震属性方法在油田开发阶段薄砂体识别中的应用——以印尼苏门答腊盆地Gemah油田M油层为例

印度尼西亚南苏门答腊盆地Jabung地区西北部油区的Gemah油田Lower Tanglang Aka油层组储层砂体厚度较薄,一般为5~10 m,部分小于5 m,且横向变化快。找准这些储集砂体是油田开发取得油气产量的关键因素;应用地震属性确定砂体分布既是油气开发的关键之一,也是难题之一。将地震波形分类、本征值相干体属性分析等新技术,应用于薄层砂体的识别,据此部署钻井5口,实钻与预测吻合良好,实践证实,结合测井资料,进行地震属性综合分析,是油田开发中识别薄层砂体的有效方法。     

基于回归模型的溶液浓度测定方法的研究

针对目前电厂水中铜离子浓度测量方法操作繁琐的问题,提出了一种快速检测方法,并基于各颜色特征值的变化规律和朗伯-比尔定律建立了硫酸铜溶液浓度、颜色特征值和光程长的计算模型。实验结果表明,该方法及模型可以准确地计算铜离子溶液浓度,而且方法简洁,造价成本低,精度高,实用性强。     

On a class of generalized eigenvalue problems and equivalent eigenvalue problems that arise in systems and control theory

Systems and control theory has long been a rich source of problems for the numerical linear algebra community. In many problems, conditions on analytic functions of a complex variable are usually evaluated by solving a special generalized eigenvalue problem. In this paper we develop a general framework for studying such problems. We show that for these problems, solutions can be obtained by either solving a generalized eigenvalue problem, or by solving an equivalent eigenvalue problem. A consequence of this observation is that these problems can always be solved by finding the eigenvalues of a Hamiltonian (or discrete-time counterpart) matrix, even in cases where an associated Hamiltonian matrix, cannot (normally) be defined. We also derive a number of new compact tests for determining whether or not a transfer function matrix is strictly positive real. These tests, which are of independent interest due to the fact that many problems can be recast as SPR problems, are defined even in the case when the matrix D+D^∗ is singular, and can be formulated without requiring inversion of the system matrix A.     

Output regulation for linear singular systems using dual-observer based compensators

In this article, the output regulation problem is solved for singular systems by using dual observer-based compensators. This has the advantage that output regulation can be achieved under weak conditions. Namely, different from previous approaches, an implementable compensator can be directly determined in form of a classical state space model without a transformation into Weierstrass–Kronecker canonical form. Furthermore, the impulse controllability and observability of the singular system is not required and the output to be controlled needs not be measurable. The results of the article are demonstrated by means of a simple mechanical system.     

EIGENPAIR SENSITIVITY OF MEMBRANE WITH RESPECT TO PERTURBATION OF BOUNDARY SHAPE

This paper presents a method to evaluate the eigenpair sensitivity of a membrane with respect to perturbation of the boundary shape. Analytic expressions for eigenpair sensitivity are obtained. Treatment of the boundary condition is facilitated by using a δ-function. An example of a rectangular membrane is given to illustrate the method and its validity.