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The transformed value function is proved to satisfy dynamic programming partial differential equation with the coefficient of risk aversion.

给出了值函数和风险规避系数的定义，并通过对值函数进行非线性变换，证明了变换后的值函数满足带有风险规避系数的动态规划偏微分方程。

With Eulerian formulation the partial differential equations of curve evolution are given and the two curves will stop on the desired boundary.

利用欧拉公式，得到曲线演化的偏微分方程。那两条曲线将在想得到的边界停止。

Because the equation is a various coefficients second-order parabolical partial differential equation,explicit difference formats usually have high condition for stability. Implicit difference formats have good stability,but they must calculate a set of algebraic equations,which are too complex.

由于泥沙扩散方程是一个二维变系数的抛物型方程，对于多维的方程，显格式往往稳定性要求很高，而隐格式虽然稳定性较好，但它要解大型的代数方程组，工作量也非常大，为了克服这两种格式的不足，常用ADI法求解，但仍存在一些计算量偏大等不足之处，因此构造出更好的差分格式是有必要的。

At last, an application of this problem in partial differential equation is also discussed.

最后，给出了上述问题在偏微分方程方面的一个应用。

Partial differential equation is widely used in problems of science and engineering.

偏微分方程在科学和工程上有着广泛的应用。

It has been more than 300 years since people first did the research on partial differential equation.

人们对偏微分方程的研究已经有近 300 年的历史。

In recent years, many partial differential equation problems are also appeared in life science and economics.

近年来，在生命科学、经济学中也出现了大量的偏微分方程问题。

The main objective of this course is to supply different methods to analyze partial differential equation and its applications.

本课程主要目的是介绍偏微分方程式与机械系统，电路系统的关系，并教授各种分析偏微分方程式的方法。

It is well known that the method of separation of variables is an efficient way to solve linear partial differential equation.

众所周知，分离变量的方法是研究线性偏微分方程的最实用、最有效的工具之一。

This technique based on nonlinear partial differential equation is a kind of promising image smoothing method.

本文详细介绍了五个基于非线性偏微分方程的平滑模型的形式和控制平滑速度的机理，并给出了实验结果。

You can do some assertiveness training.

你可以进行一些自信训练。

We were well on the path to making a rear-wheel-drive global platform," says Mays."

我们正致力于建立一个后轮驱动的平台，"Mays这样说道。"