关于矩阵的Perron根

设A是实数域上的n×n完全正矩阵,B是A的镶边矩阵,且是完全正矩阵,给出B的Perron根与A的Perron根之间的关系．     

求一类特殊二重循环矩阵逆矩阵的方法

给出了一类特殊二重循环矩阵逆矩阵的求法。     

A generalization of Kempe＇s linkages

A new, general type of planar linkages is presented, which extends the classical linkages developed by Kempe consisting of two single-looped kinematic chains of linkages, interconnected by revolute hinges. Together with a locking device, these new linkages have only one degree of freedom （DOF）, which makes them ideal for serving as deployable structures for different purposes. Here, we start with a fresh matrix method of analysis for double-loop planar linkages, using 2D transformation matrices and a new symbolic notation. Further inspection for one case of Kempe＇s linkages is provided. Basing on the inspection, by means of some novel algebraic and geometric techniques, one particularly fascinating solution was found. Physical models were built to show that the derivation in this paper is valid and the new mechanisms are correct.     

矩阵的广义相合的若干性质

本文引进了广义相合的概念,得到如下结论:当A、B是同阶方阵时,矩阵的相合、嵌入相合、{1}-相合、{d}-相合、{s}-相合彼此等价.当A、B不是同阶方阵时,其秩数相等,且有与二次型的矩阵相当的性质.     

How autonomy support mediates the relationship between self-efficacy and approaches to learning

Abstract

The significant interplay between self-efficacy, autonomy support and approaches to learning in adolescent students is widely recognized. However, less is known about whether substantial differences exist between early and middle adolescent students from schools with different environments. To close this research gap, this study used latent mean comparison and multigroup structural equation modeling with questionnaire data from a sample of German adolescent students (N?=?1153; M_AgeT1?=?13.97, SD = 1.37; M_AgeT2?=?14.27, SD = 1.25) in two waves. Multigroup structural equation modeling reveals that autonomy functions as a mediator in the association between self-efficacy and approaches to learning only for students from schools with a student-centered learning environment based on competence-matrices in contrast to a teacher-directed learning environment, particularly for early adolescent students. More specifically, adolescents’ approaches to learning can be enhanced through autonomy-supportive learning independently of their self-efficacy.     

迹为零的几类特殊本原矩阵的本原指数

对本原矩阵指数集研究中的另一方面是研究一些特殊的本原矩阵类的本原指数.邵嘉裕先生和李乔先生在这一领域取得了一些令人满意的结果[1].邵嘉裕先生[2]给出了一个特殊的本原矩阵--对称本原矩阵类的指数集合En={m∈Z |存在某个n阶对称本原阵A,使γ(A)=m},并且给出了En的完全刻划.我们考虑一个特殊的本原矩阵类:对角元为零的几类特殊本原矩阵类的指数集.记对角元为零的本原矩阵集为T0n.证明一类对角线为零的最小圈长n-d 1的特殊本原有向图的指数集.这里的d是满足:大于等于2但小于(n)/(2)的偶数,且gcd(n,n-d 1)=1.     

几类分块矩阵的行列式

利用Laplace展开定理的特例一分块三角阵的行列式，研究了几类分块矩阵的行列式，得到了三个结果。并利用得到的结果计算一些特殊的行列式，能达到简化计算的目的。     

四元数矩阵方程AXB＝C的中心对称解

利用体上双矩阵分解，给出了实四元数据阵方程AXB＝C有中心对称解的充要条件及其解的通式。     

基于DSM的模块化产品创新价值分析

模块化具有分解复杂性创新系统的作用,提高了产品创新系统的战略柔性.一方面,模块化分解丰富了模块之间的组合方式,体现为模块化的分割价值;另一方面,模块内部平行研发团队的竞争产生了模块化的替代价值.本文归纳了模块化创新的基本特征,并基于DSM方法分析模块关联结构对模块化创新价值的影响,发现:在模块之间存在联系的情形下,模块化产品创新的替代价值和分割价值下降;单平台模块关联结构下的模块化创新价值最高,双平台情形下的模块化创新价值居中,无平台情形下的模块化创新价值最低.     

图K(5m,5)的自同态幺半群

本文研究了循环完全图K(5m,5)的自同态幺半群,得到循环完全图K(5m,5)的自同态幺半群是一个正则半群.