关于四元数矩阵乘积迹的几个定理

本文得到四元数矩阵乘积迹的几个重要不等式,进而在四元数体上推广了文[1]、[2]、[5]的主要结果。     

A new set of orthogonal functions and its application to the analysis of dynamic systems

The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f(t) of Lebesgue measure.     

冷弯薄壁型钢畸变屈曲的研究进展

新材料和先进加工技术的进步使得钢材的屈服强度不断提高,为了取得更好的经济效益,冷弯钢材的厚度变得越来越薄。作为控制冷弯薄壁型钢承载能力的几种屈曲模式之一,畸变屈曲正逐步受到重视。本文总结了国内外对畸变屈曲研究的主要成果,并对几种常见荷载下的畸变屈曲计算进行了归纳。     

关于任意体上矩阵方程AXB+CYD=E

求解任意体与环上矩阵方程是近年来矩阵方程研究的一个热点问题,特别是四元数体上矩阵方程的研究。本文利用任意体上的双矩阵分解的方法,讨论了任意体上矩阵方程AXB＋CYD=E,并给出了其一个实用的解法和它的通解表达式。     

Implementation of approach to compute the Lyapunov characteristic exponents for continuous dynamical systems to higher dimensions

A general method for accurately computing the Lyapunov characteristic exponents (LCEs) of continuous dynamical systems has been developed in [10]. In this paper, this method is extended to implementations on systems of arbitrary dimensions. An accurate implementation of the extension of the method to compute LCEs that uses available numerical techniques is presented for systems of arbitrary dimensions. Previously in [10], the original approach had only been implemented for general systems of up to dimension three. Closed form expressions for the exponential of skew symmetric matrices of order 4 and 5 will be presented. These formulas are used to obtain an accurate and efficient implementation of the method for dynamical systems of dimensions 4 and 5. Numerical examples illustrating the accuracy of the implementations are presented.     

一类广义压缩型映象的不动点

本文在完备度量空间中讨论了一类广义压缩型映象不动点的存在及唯一性,是Ｂａｎａｃｈ压缩原理的一种推广。     

用细胞跟踪系统确定在外细胞间质(ECMs)上的细胞迁移(英文)

大部分哺乳动物具有细胞迁移容量.细胞迁移对于生命中的许多生物学现象有重要作用.在胚胎形成中,细胞迁移是在重要的形态形成过程中重复出现的主题.在成年人的组织中、在正常的生理学以及病理学中,细胞迁移都有其重要性.在炎症反应中,白血球迁移到受伤区域,在哪里它们进行吞噬细胞和实现免疫功能.虽然在现在已有创伤愈合细胞迁移测定等几种方法,但是这些细胞迁移的测定方法对于各类问题并不是总有效的[1-6].我们发展了一种由计算机辅助的时间流逝显示微观复制系统,它包括影象形成过程软件,其程序编制含有自动影象分析和自设计CO2微小细胞培育器,它的功能是在一个倒置显微镜平台上对于细胞迁移进行迅速而精确的分析从而形成细胞的培育.我们运用这一计算机辅助系统计算了外细胞间质(ECMs)覆盖表面的细胞迁移.     

块对角占优阵与广义块对角占优阵Kronecker积的性质

讨论了块对角占优阵与广义块对角占优阵的Kronecker积的性质，得到了几个新的有意义的结果。     

面对数据丢包的船舶航向保持网络预测控制器

针对网络控制系统中存在的数据丢包问题,使用一种带有常值补偿机制的广义预测控制(Generalized Predictive Control,GPC)算法设计船舶航向保持的网络预测控制器.首先,利用TrueTime工具箱仿真使用传统GPC算法设计的船舶航向保持的网络预测控制器.然后,考虑数据丢包对船舶航向保持的网络控制系统造成的影响,使用带有常值补偿机制的GPC算法设计一种新的船舶航向保持的网络预测控制器并进行仿真.仿真结果表明,在数据丢包情况下,采用新方法设计的控制器可以减少船舶航向调节时间,从而改善船舶航向保持的网络预测控制器的控制效果.     

加权广义逆矩阵的若干性质

文章讨论了关于权为可逆阵的加权广义逆矩阵的一些性质。利用矩阵的运算及秩的变化的相关结论,结合矩阵的加权广义逆存在时的充要条件与表示式,给出了复数域上两个及三个矩阵乘积的加权广义逆的几个表达式。