微分几何

The paper have two parts, one is numerical solution of partial di?erential equation,another is submanifold.

本文分两部分，第一部分是偏微分方程数值解内容，第二部分是子流形几何内容。

We also showed that the value of the third critical field is higher for a superconductor with edges and conners.

我们的工作揭示了区域几何对偏微分方程的解的重要影响。

Dynamical Systems Theory: Dynamical systems theory is also known as the geometric theory of differential equations or global analysis.

动力系统理论：动力系统的理论也被称为微分方程或全球性的分析，几何理论。

The constructing process of the algorithms itself indicate that they are brevity and have definite geometric meaning, scientific iterative terminal criterions and no strict requirement to function. Finally, some digital experimentation is presented to indicate the algorithms application in solving the problem of maximum of function, transcendental equation,integer programming and so on. The results indicate that the algorithms have more global and more adaptability compared to traditional algorithms and have more calculating efficiency and more scientific iterative terminal criterions compared to some present popular artificial intelligence algorithms.

算法的构造过程本身表明了该算法简单明了、几何意义明确、迭代终止准则科学、对函数的要求较低；最后举了几个数值试验的例子以说明该类算法在求函数的最值，解超越方程以及整数规划等问题中的应用；数值试验的结果标明该算法比单纯由"微分"思想演化而来的传统算法有更好的全局性和对问题的更广泛的适应性，比现在流行的一些人工智能方法有更高的运算效率和更适当的迭代中止准则。

In the first place, the normal flexible body dynamics modelling method of continous system is built based on hamilton principle. And then taking the flexible beam tunning in the horizontal plan for example, in the assumption of Euler-Bernoulli beam,the identical linearilized vibration differential equation is deduced according to geometry constraint conditions .

首先基于Hamilton原理建立起一般柔性体连续系统的动力学建模方法，进而以水平面内作大范围回转运动的柔性梁为例，在Eu1er-Bemoulli梁模型的假设前提下，根据轴向不可伸长的柔性梁的几何约束条件，推导出作大范围刚体运动的柔性梁连续系统的一致线性化振动微分方程。

Secondly, European option pricing problem is discussed when price of stocks follows geometric Brown motion and return of stocks follows Ornstein-Uhlenbeck process. Using Arbitrage-free principle, we give a partial differential equation with which option price is satisfied and using Fourier inverse transformation, the closed-form solution to European Call option pricing formula is given.

其次，讨论了股票价格服从几何布朗运动，股票收益服从Ornstein-Uhlenbeck 过程的欧式期权定价问题，利用无套利原理给出了期权价格满足的偏微分方程，并运用傅立叶逆变换，求出了欧式看涨期权定价公式的封闭解。

Some applied examples show that the differential relationship not only contains fundamental content in geometrical optics, such as the three laws of geometrical optics, imaging formula of single spheric face, but is another form of differential equation of the light ray.

通过应用示例可见，此微分关系式包含了几何光学的3个实验定律和球面镜成像公式等，而且是光线方程的另一种表达形式。

Here we take the characteristic functions of Laplace operator as coordinate functions, then a standard Galerkin method naturally leads to a semidiscrete scheme with structure preserving property for the continuous system.

这样的离散化模型含有原连续模型的几何与物理特征，用它能够更好的模拟发展型微分方程的长时间的和全局的动力行为。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。