The Criterion-Related Validity of the Sit and Reach Test: Replication and Extension of Previous Findings

Abstract

The purposes of this study were to (a) examine the stability and consistency of the Caltrac accelerometer (Hemokinetics, Madison, WI) and an activity record to assess physical activity in children and adults (Experiment 1), and (b) to determine if there is a relationship between parents and their children in physical activity level (Experiment 2). Thirty 5–9-year-old children and their biological parents wore Caltrac accelerometers for three consecutive days (including one weekend day). At the same time, parents completed a Caltrac Activity Record (CAL REC) for themselves and their child. Dependent variables were counts per day for the Caltrac and minutes of light activity and activity for the CAL REC. Between-day correlations for the Caltrac ranged from r = .73 to .87 for the parents (p < .001) and from r = .38 (p < .04) to .79 (p < .001) for the children. An analysis of variance with repeated measures indicated no significant differences for the Caltrac between days for parents and children. Between-day correlations for CAL REC ranged from r = .67 to .91 (p < .05) for parents and r = .36 to .72 (p < .05) for children, and there were no significant differences between days. In Experiment 2, χ² analyses were used to examine familial resemblance in physical activity. Using the Caltrac, familial resemblance occurred in 67% (father and child) and 73% (mother and child) of the families. Using the CAL REC, familial aggregation was present in 70% (father and child) and 66% (mother and child) of the families. Thus, children of active and less active parents exhibited physical activity patterns similar to their parents.     

Linear Algebra Students' Understanding of Similar Matrices and Matrix Representations of Linear Transformations in a MATLAB-Assisted Learning Environment

Abstract

The purpose of this research study was to understand how mathematics majors make sense of similar matrices, a linear algebra topic that is rich in internal and external connections, in a series of in-depth qualitative interviews in a technology-assisted (MATLAB) learning environment. The study was also an attempt to develop a cognitive theory in mathematics majors’ treatment of similar matrices and matrix representations of linear transformations in a computer-assisted learning environment by drawing primarily on three aspects of the experimental mathematics methodology, made possible by using modern digital tools to enhance learning: testing conjectures, suggesting proofs, and, computing lengthy hand derivations (Borwein &; Bailey, 2003 Borwein, J. M., &; Bailey, D. H. (2003). Experiments in mathematics: Computational paths to discovery. Natick, MA: AK Peters. [Google Scholar]). The analysis revealed a diversity of innovative ways by which research participants coordinated analytic and computational (MATLAB) methods for understanding matrix similarity and its connections to the rest of linear algebra. The paper concludes by offering pedagogical implications and recommendations for further research.     

基于电压闭环控制的矩阵变换器仿真研究

针对矩阵变换器开环控制碰到扰动输出电压波形不能自动调节的问题,采取电压闭环的控制方式,通过坐标系变换将输出电压采样变换得到空间矢量,与目标电压矢量进行比较得到偏差量,以此来进行反馈控制,并运用MATLAB软件进行器件建模及控制策略、电压闭环控制方法的仿真。通过对两种典型干扰仿真研究,表明电压闭环控制方法对于输入干扰抑制的有效性。     

拟酉矩阵及其性质

利用共轭次转置矩阵和可逆Hermite矩阵的概念,提出了拟酉矩阵的概念,从而推广了准正交矩阵,并研究了拟酉矩阵的若干性质。     

关于一个矩阵秩等式的注记及其应用

从一个简单的对任意矩阵都适用的矩阵秩恒等式出发,对一个对合矩阵秩等式进行修正,结果表明它是对任意矩阵都成立的恒等式;作为应用,还推广一个已有的幂等矩阵的秩等式。     

Unwrapping and stereo rectification for omnidirectional images

Omnidirectional imaging sensors have been used in more and more applications when a very large field of view is required. In this paper, we investigate the unwrapping, epipolar geometry and stereo rectification issues for omnidirectional vision when the particular mirror model and the camera parameters are unknown in priori. First, the omnidirectional camera is calibrated under the Taylor model, and the parameters related to this model are obtained. In order to make the classical computer vision algorithms of conventional perspective cameras applicable, the ring omnidirectional image is unwrapped into two kinds of panoramas： cylinder and cuboid. Then the epipolar geometry of arbitrary camera configuration is analyzed and the essential matrix is deduced with its properties being indicated for ring images. After that, a simple stereo rectification method based on the essential matrix and the conformal mapping is proposed. Simulations and real data experimental results illustrate that our methods are effective for the omnidirectional camera under the constraint of a single view point.     

线性流形上实对称矩阵的左右逆特征值问题

讨论了线性流形上实对称矩阵的左右特征值反问题解存在的充分必要条件,并给出了通解表达式.对于给定的矩阵,得到了它的加权最佳逼近解的表达式.     

反矩、合矩及几个基本公式的证明(Ⅰ)

以将拉普拉斯变换推广到高阶为出发点,提出反矩、合矩概念及其作用法则,证明了与之相关的几个基本公式。     

语言判断矩阵解决决策问题的新方法

研究了语言判断矩阵的加性一致性及方案排序问题.在给出有关语言判断矩阵和模糊互补判断矩阵的概念的基础上,提出语言判断矩阵的加性一致性的定义,然后通过引进导出矩阵将语言判断矩阵转换为数值判断矩阵.通过判定现有的数值判断矩阵的一致性方法.对导出矩阵进行一致性判断,得到给予语言判断矩阵的一致性的判定方法,最后通过一个算例说明文中提出的分析方法.     

关于环上两个特殊分块矩阵的相似性

设R为一个有单位元1的环.如果A,B均为R上的幂等矩阵,则R上矩阵(A D0 B)与(A 00 B)相似当且仅当AD+DB=D.如果A,B均为R上的对合矩阵,则R上矩阵(A D0 B)与(A 0