Two-grid method for characteristisc mixed finite-element solutions of nonlinear convection-diffusion equations

A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.     

A study of the effect of HyperCard and pen-paper performance assessment methods on expert-novice chemistry problem solving

This study investigated HyperCard as a tool for assessment in science education and determined whether or not a HyperCard assessment instrument could differentiate between expert and novice student performance (balancing stoichiometric equations) in science education. Five chemical equations were presented by traditional pen-paper and by a HyperCard (Hyperequation) program. Thirty honors (expert) and 30 regular (novice) chemistry students were randomly divided into HyperCard and traditional pen-paper groups of 15 students each. Scoring was based on five dependent variables: performance scores, number of attempts, rate of attempts, time on task, and correctness. Correlation results indicated that students with high performance scores correctly balanced more equations, required fewer attempts to balance equations, and required less time per attempt than did students with low performance scores. MANOVA results showed that performance scores and correctness scores for both experts and novice were significantly higher on HyperCard compared to pen-paper assessment; the novice scores on HyperCard nearly equaled the expert pen-paper assessment scores. Significant interactions were found for time on task and for correctness. The results suggest that HyperCard can be a suitable tool for assessment in science education and that such an instrument can differentiate between expert and novice student performance.     

脉冲条件下具周期时滞的竞争模型的周期正解

使用Mawhin重合度理论的连续性定理和拓扑度理论，对脉冲条件下具周期时滞的竞争模型进行研究，得到了该模型周期正解存在的充分必要条件．     

关于Lucas猜想的简洁初等证明

利用简洁初等方法证明了Lucas方程x(x 1)(2x 1)=6y^2仅有正整数解（x,Y)=(1,1),(24,70),获得了丢番图方程x(x 1)(2x 1)=2py^2有正整数解的充要条件。     

有疾病潜伏期的传染病动力学模型

从不考虑种群动力学因素和添加种群动力学因素两种情形出发,在双线性发生率、标准发生率和βNαSI/N(α位于0.03和0.07之间)发生率下,建立了有疾病潜伏期的等各种传染病动力学模型。     

一类半线性二维积分微分方程

考虑线性粘弹性板振动所引出的半线性积分微分方程的初边值问题，通过解的先验估计利用Leary-schauder不动点定理在某些条件下得到了初边值问题锵的存在唯一性。     

三分量开边界Bariev模型的基本对易关系式及多粒子态波函数

运用三分量开边界Bariev模型的monodromy矩阵,T,T-1,U-,作用到真空态上的值、Yang-Baxter关系及反射方程,给出了该模型的基本对易关系式,并给出了模型的递推的多粒子态波函数,从而为进一步运用嵌套的代数Bethe ansatz方法求解该模型的多粒子解Betheansatz方程以及系统的能谱奠定了基础。     

关于丢番图方程x2±y4=z3

利用数认方法,获得了丢番图方程x2±y4=z3的全部整数解公式.     

由“一句话“巧记热力学函数关系式

本文通过一句日常英语对话"How are you? Fine. Thanks.",在总结前人资料基础上,提炼出了用"一句话"的简便记忆热力学函数关系的方法.该方法经过在课堂上教学实践,取得了很好的效果.