基本解释：几何差分方程
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We also proved that the problem of solving BAE can be transformed into the problem of finding the roots of a hypergeometric polynomial,which was much simpler.在具体求解过程中,利用超几何微分方程十分有效地简化了计算。
First,it introduces a first-order energy functional,then minimizes it to derive a second-order geometric partial differential equation(GPDE) in the level-set formulation.首先引入一个一阶能量范函,然后通过对其极小化诱导出一个水平集形式的二阶几何偏微分方程,从而将曲面变形过程转化为一个三维体上的隐式模型的演化过程。
On the basis of the hypothesis of straight normal line, geometrical equations about finlte deformation analysis of shells with small shear are exactly derived by means of continuum mechanics methods.对壳体只采用直法线假设，应用连续介质力学方法，严格地推证有剪切的壳体有限变形的几何方程。
The paper deduced geometric equation based on the physical concept of engineering linear and shear strain and the characteristics of "axial symmetry" and "large deformation".从工程线应变和工程切应变的物理概念出发,根据"轴对称"和"大变形"的特点,推导出相应的几何方程,另导出大变形条件下的体积不变定律。
In the frame of quantum mechanics,the equation to describe the particle motion was reduced to the hypergeometric equatin by this potential.在量子力学框架内,把电子的Schrodinger方程转化为超几何方程,用系统参数和超几何函数严格地求解了电子的本征值和本征函数,并以Ga1-xAlxAs-GaAs-Ga1-xAlxAs量子阱为例计算了电子的带内跃迁。
In the frame of quantum mechanics, Schrodinger equation to describe the particle motion is reduced to the hypergeometric equatin by this potential.鉴于“方形”势阱描述量子阱中的空穴运动行为过于简单、理想,引入了反比相关的双曲余弦平方势,并在量子力学框架内,利用这个相互作用势把空穴的Schrodinger方程化为了超几何方程,用系统参数和超几何函数严格地求解了空穴的本征值和本征函数,并以Ga1-xAlxAs-GaAs-Ga1-xAlxAs量子阱为例,计算了阱内的空穴跃迂。
confluent hypergeometric differential equation合流型超几何微分方程
The Partial Differential Equations Based Geometric Technique in Image Processing;基于偏微分方程的图像几何处理方法
RKMK Geometric Integration of Non-linear Partial Differential Equations;非线性偏微分方程的PKMK型几何积分方法
overdetermined system of partial differential equations偏微分方程的超定组
topological differential geometry拓扑微分几何(学)
Methodology for Ultra Deep Sub-micro Integrated Circuit Interconnect Geometric Variation Extraction超深亚微米集成电路互连线几何变异提取方法
Solutions to Several Classes of Nonlinear Differential Equations and Integral Equations;几类非线性微分方程和积分方程的解
the Differential Geometry Method of Support Vector Regression Machines;支撑向量回归机（SVRM）的微分几何方法
Several Methods in Discussing Real Number s Radical of Equations in Differential Calculus;微积分中讨论方程实数根的几种方法
Dynamical Behaviors of Some Differential, Difference Equations;几类微分、差分方程动力学性质的研究
Qualitative Analysis on Several Kinds of the Second Order Nonlinear Differential Equations;几类二阶非线性微分方程的定性分析
Some Questions on the Application of Differential and Difference Equations Theory;微分差分方程理论应用中的几个问题
Study on Oscillations of Several Kinds of Difference and Differential Equations;几类差分方程和微分方程的振动性研究
A NEW METHOD FOR THE EXPECTATION AND VARIANCE OF SUPER GEOMETRY DISTRIBUTION;超几何分布的期望和方差的一种新求法
a differential equation involving a functions of more than one variable.含有超过一个变量的函数的微分方程。
OSCILLATION CRITERIA OF A CLASS OF ADVANCED TYPE DIFFERENTIAL EQUATIONS;一类超前型微分方程的振动准则(英文)
Oscillation of the Solutions of the Second-order Super-linear Impulsive Equations二阶超线性脉冲微分方程解的振动性
Exitence of Positive Solutions of Boundary Value Problems for Nonlinear Differential Equations;几类非线性微分方程边值问题的正解
