加权算术平均与几何平均关系式的新证法

利用函数极小点的性质,得到了若干个正数的加权算术平均与几何平均关系式的新证法     

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete‐time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi‐Sugeno (T‐S) fuzzy model to represent a discrete‐time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on‐line optimization paradigm that utilizes the closed‐loop state feedback controller and is solved using the standard semi‐definite programming (SDP). To reduce the on‐line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

利用分部积分法巧解二次积分

根据被积函数的特征分四种情形分别进行讨论,给出了不需转换积分区域D类型交换积分次序而使用分部积分法计算二次积分的方法,首次将分部积分法成功地引入到二重积分的计算中。     

矩阵在不等式证明中的妙用

矩阵是一种重要的数学方法,在数学领域有其独特的作用。根据正定实对称矩阵的一个重要不等式及均值不等式在矩阵方面的一个重要性质,对国际数学竞赛和不同书刊中有关不等式进行探讨。通过对比,体现了在解某类不等式问题时运用矩阵解题的优势。     

中介语中英语定冠词误用分析及其启示

对比分析了英语和汉语中的定指表达,提出中国学生在英语定冠词使用中的错误多集中在定指表达,揭示了定冠词误用与其不同语义表达的相关性,提出对定冠词教学和学习策略的启示。     

一类矩阵方程的算法研究

研究了矩阵方程X+A*X-1A+B*X-tB=I的正定解,通过构造单调有界迭代序列求得方程正定解.提出的新算法收敛速度有所提高.并通过算例进行算法比较.     

周期黎卡提微分方程正定解的存在性

讨论了标准的周期黎卡提微分方程,给出了其存在埃尔米特周期正定（HPPD）解的一个完整的充分必要条件。准确地说,在经过一个适当的状态空间基底变换后该条件通过能稳性和能检测性概念表述。结果表明,当HP－PD解存在时,它或者是唯一的,或者有无限多个。这一结果可以看作是Richardson和Kwong的结果对周期时变情况的扩展。     

Applications of the Conjugate Gradient method in optimal surface parameterizations

This paper concerns the solutions of very large symmetric semipositive definite (singular) linear systems involved in the problem of optimal surface parameterizations using inverse curvature mapping. Two approaches are presented that transform the singular linear systems into two kinds of symmetric positive definite linear systems, so that the famous Conjugate Gradient (CG) method can be used for solving them. Numerical experiments are run on two practical large problems to illustrate that the CG algorithm works very efficiently.     

Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X+A T X −2 A=I

Necessary and sufficient conditions for the matrix equation X+A ^T X ^?2 A=I to have a real symmetric positive definite solution X are derived. Based on these conditions, some properties of the matrix A as well as relations between the solution X and A are derived.