By using travelling wave reduced form method, the nonlinear partial differential equation of wave propagation in a functionally graded beam was transformed into an ordinary differential equation. 运用行波约化法将非线性波动方程化为常微分方程，然后利用位移形函数的系数待定法求出了非线性波动方程的位移孤波解。
As preparation, we first investigate the graded differential operators on a path algebra and the associated graded Lie algebra. Thirdly, we study the first cohomology of admissible algebras which can be seen as a generalization of basic algebras. 作为准备，我们首先讨论了路代数上的分次微分算子和相应的分次李代数。第三，我们研究了容许代数的一阶上同调，容许代数可以看做基本代数的推广。
Objective To detect the differential item functioning ( DIF ) using Item Response Theory graded model between the gender of college freshmen on a measure of emotion adaptation, witch is a subscale of Student Adaptation to College Questionnaire, and then discuss the impact of DIF. 目的探讨项目功能差异（DIF）在研究大学新生情绪适应性性别差异中的作用。
The differential equation with varied coefficient of the SH-wave in the functionally graded materials is established. 建立了功能梯度材料中SH波的变系数微分方程。
Based on the classical theory of plate, the equilibrium differential equation was derived for the buckling analysis of thin elastic plate with functionally graded structure considering small deflection. The functionally graded material properties obeyed a power law across the thickness. 假设梯度材料的弹性参数为板厚度方向坐标的幂函数，基于经典板理论，导出了功能梯度弹性薄板小挠度屈曲平衡微分方程。
