浅谈行列式的几种计算方法

行列式是线性代数中的一个重要内容,行列式的计算具有一定的规律性和技巧性,本文结合实例,归纳出了几种求行列式的计算方法。     

An evaluation of limited‐memory sparse linear solvers for thermo‐mechanical applications

We consider the performance of sparse linear solvers for problems that arise from thermo‐mechanical applications. Such problems have been solved using sparse direct schemes that enable robust solution at the expense of memory requirements that grow non‐linearly with the dimension of the coefficient matrix. In this paper, we consider a class of preconditioned iterative solvers as a limited‐memory alternative to direct solution schemes. However, such preconditioned iterative solvers typically exhibit complex trade‐offs between reliability and performance. We therefore characterize such trade‐offs for systems from thermo‐mechanical problems by considering several preconditioning schemes including multilevel methods and those based on sparse approximate inversion and incomplete matrix factorization. We provide an analysis of computational costs and memory requirements for model thermo‐mechanical problems, indicating that certain incomplete factorization schemes can achieve good performance. We also provide empirical evaluations that corroborate our analysis and indicate the relative effectiveness of different solution schemes. Our results indicate that our drop‐threshold incomplete Cholesky preconditioning is more robust, efficient and flexible than other popular preconditioning schemes. In addition, we propose preconditioner reuse to amortize preconditioner construction cost over a sequence of linear systems that arise from non‐linear solutions in a plastic regime. Copyright © 2007 John Wiley & Sons, Ltd.     

Towards an accurate sleep apnea detection based on ECG signal: The quintessential of a wise feature selection

A wise feature selection from minute-to-minute Electrocardiogram (ECG) signal is a challenging task for many reasons, but mostly because of the promise of the accurate detection of clinical disorders, such as the sleep apnea. In this study, the ECG signal was modeled in order to obtain the Heart Rate Variability (HRV) and the ECG-Derived Respiration (EDR). Selected features techniques were used for benchmark with different classifiers such as Artificial Neural Networks (ANN) and Support Vector Machine(SVM), among others. The results evidence that the best accuracy was 82.12%, with a sensitivity and specificity of 88.41% and 72.29%, respectively. In addition, experiments revealed that a wise feature selection may improve the system accuracy. Therefore, the proposed model revealed to be reliable and simpler alternative to classical solutions for the sleep apnea detection, for example the ones based on the Polysomnography.     

Bifurcation solutions in the diffusive minimal sediment

This paper is concerned with the diffusive minimal sediment model with no-flux boundary conditions. The steady-state bifurcation with two-dimensional kernel is firstly obtained with respect to this model by the space decomposition and the implicit function theorem. The existence of the Hopf bifurcation is next attained, and the direction and the stability of the Hopf bifurcation are analyzed in detail. Numerical simulations are done to support and complement the theoretical results.     

一类离心调速器的Hopf分岔及其混沌控制

研究了受外部扰动的离心调速器系统的复杂动力学行为。通过系统运动的拉格朗日方程和牛顿第二定律,建立了离心调速器系统的动力学方程,应用Lyapunov直接方法分析了该系统平衡点的稳定性。利用相图分析了系统超混沌吸引子的特性,通过Poincaré截面和Lyapunov指数研究了系统的超混沌行为,通过仿真系统的分岔图和相图分析了系统通向混沌的道路,并且验证了该系统的分岔图与Lyapunov指数谱是完全吻合的。通过对系统施加非线性反馈控制器,并选取合适的反馈系数,可以获得各种不同的所需的稳定周期轨道。对受外部扰动的离心调速器系统施于此控制,计算机数值模拟结果表明,这种控制方法简便有效,控制范围广。     

WKI方程族的扩展可积系统

通过构造特殊的等谱矩阵U和V以及构造的一个维数为5的loop代数,得到了WKI方程族的可积耦合系统,即WKI的一类扩展可积系统。我们所选取的V中既含有位势函数,又含有a,b或c关于x的偏导数项,所构造出来的扩展可积系统与已有结果不同。     

一种新型的混合Petri网建模及其分析方法

提出一种新型的混合Ｐｅｔｒｉ子网建模和描述方法,离散化这种混合子网后,利用双子代数理论推出其线性代数方程组,在代数框架下研究混合系统的可达性,实践证明了该方法的可行性。     

C^＊-Structure of Quantum Double for Finite Hopf C^＊-Algebra

Let H be a finite Hopf C^＊ -algebra and H′be its dual Hopf algebra. Drinfeld＇s quantum double D（H） of H is a Hopf^＊-algebra. There is a faithful positive linear functional θ on D（H）. Through the associated Gelfand-Naimark-Segal （GNS） representation, D（H） has a faithful^＊ -representation so that it becomes a Hopf C^＊ -algebra. The canonical embedding map of H into D（H） is isometric.     

简单电力系统的局部分岔数值计算分析

运用延拓法对一个简单电力系统的鞍结点分岔和Ｈｏｐｆ分岔进行计算分析,并与其它文献的计算方法和进行了比较,不难看出,延拓法是对电力系统非线性行为进行局部分析的一种较为严谨和准确的数值计算方法,能满足电力系统分岔计算的要求。     

浅谈工科线性代数的教学

该文介绍了作者在工科线性代数课程教学实践中的尝试和想法:针对该课程定义、定理多、概念抽象难懂的问题,提出了重视直观背景,由具体看抽象的方法。而对于现行教材理论联系实际不够、与后继课程有所脱钩的弊病,提出了加强数学建模训练、将为后继课程留伏笔与线性代数相关内容有机结合起来的方法。