Mediation Effects In 2-1-1 Multilevel Model: Evaluation Of Alternative Estimation Methods

We compared six common methods in estimating the 2-1-1 (level-2 independent, level-1 mediator, level-1 dependent) multilevel mediation model with a random slope. They were the Bayesian with informative priors, the Bayesian with non-informative priors, the Monte-Carlo, the distribution of the product, the bias-corrected, and the bias-uncorrected parametric percentile residual bootstrap. The Bayesian method with informative priors was superior in relative mean square error (RMSE), power, interval width, and interval imbalance. The prior variance and prior mean were also varied and examined. Decreasing the prior variance increased the power, reduced RMSE and interval width when the prior mean was the true value, but decreasing the prior variance reduced the power when the prior mean was set incorrectly. The influence of misspecification of prior information of the b coefficient on multilevel mediation analysis was greater than that on coefficient a. An illustrate example with the Bayesian multilevel mediation was provided.     

Degeneracy cases of generalized inverse function-valued Padé approximation

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application. Project supported by the National Natural Science Foundation of China (Grant No. 10271074)     

“科教兴国”必须落实教育优先发展

把教育摆在优先发展的战略地位,是贯彻党的十六大提出的“大力实施科教兴国战略”的基础和前提。优先发展教育,必须真抓实干,落实措施。本认为落实教育优先发展战略,必须强化思想认识;必须建立科学的运行机制,真正体现政策优惠、投入优先、待遇优厚的导向;必须建立健全教育法规,实现依法治教,保证教育优先发展。     

线性方程组和矩阵的中数式教学提纲

本文以中学数学的陈述方式引入《高等代数》课程的线性方程组和矩阵的重要概念和相关的运算法则,从实例出发将抽象的定义、法则具体化和通俗化。     

三对角逆M-矩阵性质的探讨

本文研究一类特殊的逆M-矩阵:三对角逆M-矩阵.用图论的方法完全刻划了三对角逆M-矩阵的结构特征和性质,给出了三对角非负矩阵是逆M-矩阵的充要条件.最后,证明了具有唯一路M-矩阵的逆在Hadamard乘积下的封闭性.     

具有单面完整约束的力学系统的Noether理论

研究具有单面完整约束的力学系统的Noether对称性与守恒量，首先，建立了系统的运动方程；其次，基于Hamilton作用量在r参数有限变换群Gr的无限小变换下的不变性，给出了系统的广义Noether定理及其逆定理；最后,举例说明结果的应用。     

Continued Fraction Algorithm for Matrix Exponentials

A recursive rational algorithm for matrix exponentials was botained by making use of the generalized inverse of a matrix in this paper.On the basis of the n-th convergence of thiele-type continued fraction expansion,a new type of the generalized inverse matrix-valued pade approximant(GMPA)for matrix exponentials was defined and its remainder formula was proved.The resuts of this paper were illustrated by some examples.     

循环矩阵的逆问题

本文对循环矩阵的逆问题进行了探讨，提出了求解循环矩阵的逆的两个方法，文中所提方法比现有的方法简单实用。     

To Read or Not to Read: A Qualitative Study of Students’ Justifications for Document Selection in Task-Oriented Reading

When navigating through the vast amount of information that we encounter in our everyday lives, we constantly make decisions concerning what information to read more closely and what information to disregard. Consideration of the relevance and trustworthiness of information sources facilitates those decisions. In the present study, we interviewed 25 upper-secondary students after they had selected documents to use in completing a task, and we asked them to justify their selections. A qualitative analysis of the interview data showed that students’ justifications could be related to (1) content relevance, (2) source features, and (3) prior topic knowledge. The results demonstrate that students are able to evaluate content relevance and source features as part of their document selection strategies but that perceived prior knowledge seems to influence both selections and justifications.     

求逆矩阵与广义逆矩阵的统一方法

首先给出同时用初等行变换与初等列变换求可逆矩阵的逆矩阵的方法,然后将此方法推广,得到求一般矩阵广义逆矩阵的具有实用性的方法。