二元一次方程组在实际问题中的应用

本文以实际案例为依托,着重从解题思路和解题过程中折射出运用二元一次方程组解决实际问题的五大步骤。通过这种定型化思维的培养,使学生养成用数学建模思想和方程思想来解决生活中的实际问题的思维过程,这也是本文的价值和目的所在。     

非线性二阶边值问题解的存在性

利用上下解方法讨论了一类二阶边值问题解的存在性问题 ,并给出了一种求解方法。     

非线性热传导方程的渐近理论

本文采用整体迭代法,研究非线性热传导方程Cauahy问题的渐近理论,在Sobolev空间中,空间维数n 1时,证明了初值问题的适定性和形式近似解的合理性。     

R—模线性方程组

本文给出了只一模线性方程组解的唯一性条件以及R—模线性方程组的Cramer规则。     

一类具有可变时滞的高阶非线性中立型差分方程正解的存在性

本文研究了一类具有可变时滞的高阶非线性中立型差分方程的正解,得到了这类差分方程最终正解的存在判据．     

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。