不可压磁流体方程在柱坐标下的表示及其基本能量估计

在考虑方程解的适定性时,解有有限能量总是一个最基本要求。因此,对方程做基本能量估计是非常有必要的,也是考虑解的适定性的前提。本文给出了磁流体力学方程在柱对称条件下的解的基本能量估计,这为后续的解的存在唯一性,正则性等,提供了一个保障。首先运用微积分的知识,将直角坐标系下的梯度算子和拉普拉斯算子换算成柱坐标系下的情形,进而求得柱坐标系下的磁流体力学方程表达式,而后求该方程在无旋情形(所有变量关于角变量是固定的)的基本能量估计。     

Empirical Performance of Covariates in Education Observational Studies

This article summarizes results from 12 empirical evaluations of observational methods in education contexts. We look at the performance of three common covariate-types in observational studies where the outcome is a standardized reading or math test. They are: pretest measures, local geographic matching, and rich covariate sets with a strong theory of treatment selection. Overall, the review demonstrates that although the pretest often reduces bias in observational studies, it does not always eliminate it. Its performance depends on the pretest's correlation with treatment selection and the outcome, and whether preintervention trends are present. We also find that although local comparisons are prioritized for matching, its performance depends on whether comparable no-treatment cases are available. Otherwise, local comparisons may produce badly biased results. In cases where researchers have a strong theory of selection and rich covariate sets, observational methods perform well, but additional replication studies are needed. Finally, observational methods that rely on demographic covariates without a theory of selection rarely produce unbiased treatment effects. The article concludes by offering education researchers empirically based guidance on covariate selection in observational studies.     

一阶非线性具偏差变元的微分方程的振动准则

研究了一类一阶非线性具偏差变元的微分方程解的性质，获得了其解的有关振动性质的一些新的结果，所用的方法也适用于时超微分方程，所得结果推广了文献中的相应结果．     

时标上的一类中立型非线性动力方程的稳定性

讨论了时标上的一类中立型非线性动力方程的稳定性,得出了该方程一致稳定的充分条件.     

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。     

一类椭圆型方程广义解的有界性

本文考虑方程: integral from n=G to {▽v·A(x,μ,▽μ)+vB(x,u,▽u)}dx=0 (?) v∈W_(pi)~1(G)∩L_∞~(G)在适当条件下,证明解的整体有界性。     

二元算子方程组的唯一解

利用锥理论和半序方法,对Banach空间上一类二元算子方程组的求解进行了探讨,利用较简捷的条件,得出方程组的唯一解及其迭代逼近式及误差估计式,并推广到n元算子方程组的情形,改进了许多有关结果.     

一类二阶迭代微分方程的周期解

利用Ｓｃｈａｕｄｅｒ不动点定理,首次研究了一类二阶迭代泛函微分方程ｘ″（ｔ）＝ｃｏｓｔｆ（ｘ〈ｎ〉（ｔ））满足所给条件周期解的存在性     

超越代数方程图像解法的程序实现

超越代数方程只能用数值解法或图像解法近似求解．笔者给出一个实用超越方程图像解法TRUEBASIC程序．     

一类时滞中立型微分方程的振动性

研究时滞中立型微分方程的正解的振动性,给出了方程的所有正解振动的新的充分条件,改进了已有的结果．证明了一个猜想的正确性．