微分

This paper studies a class of cubic system with planar polynomial.We use the qualitative theory of ordinary differential equations method of analysis, reached the following conclusions of four parts: First, we analyze the quality of all critical points of the system,and draw the conditions of existence of singular integrals for the system , in front based on the analysis, using Pioncare form series method to calculate the focal value of o(0,0). Finally, we also study the behavior of critical points at infinity.

中文摘要：本文研究了一类平面三次多项式系统，我们采用常微分方程的定性理论的分析方法，得出如下四个部分结论：第一部分，分析系统所有奇点的性态，并得出系统存在奇异积分直线的条件；在前面分析的基础上，用Pioncare形式级数法，计算出了系统在奇点o(0，0)的三个焦点量；最后，研究了系统无穷远奇点的性态。

Chapter 2 introduces some propaedeutics of classic differential geometry, which include the first basic form, the second basic form, normal curvature, main curvature, mean curvature, Gauss curvature, unit normal vector, main vector, etc.

第二章介绍一系列的预备知识，主要是关于古典微分几何中第一，第二基本形式的定义，法曲率，主曲率，平均曲率，Gauss曲率，单位法向量，主方向等的定义。

It is based on the discrete model of finite analysis to get curvature ,normal vector, direction and geodesic curve,then to analyze and design the structure.

基于有限元分析的离散模型，将离散微分几何领域的最新成果运用于膜结构设计，求解曲面曲率，法向量，主方向及测地线，进行结构分析设计。

The shape-form analysis and load analysis were done by nonlinear FEM. On the basis of surface FEM grid nodes, geometry property research of structure curved surface was progressed, including normal vector, GAUSS curvature, mean curvature and principal direction vector. In this process, the approximate expression of surface didn't need to he known.

采用非线性有限元法进行了膜结构的形态分析和荷载分析，得到了曲面有限元网格；通过离散微分几何方法，研究了薄膜结构曲面的几何性质，包括曲面的法线向量、高斯曲率、平均曲率和主方向矢量，避免了复杂的曲面拟合过程。

We propose a unified method to approximate important geometric attributes, including normal vector, gauss curvature, mean curvature, principal curvatures and principal directions on point sampled surface. Based on MLS projection our method is robust to noise and stable to the sampling density.

曲面的微分性质包括法向量和切平面、高斯曲率、平均曲率、主曲率和主方向，在计算机图形学、机器视觉和计算机辅助设计等领域发挥了重要的作用，比如曲面绘制、内外测试、曲面重建、曲面简化、去除曲面噪声和模型分割等。

It has built-in programs for solving differential equations, curve fitting, and signal analysis.

其中有内建的程式可以解微分方程、曲线拟合、及信号分析。

And then, the theory of curve evolution, how to solve the PDEs model based on level set method and its calculation methods are expatiated.

其次详细介绍了曲线演化理论、偏微分方程模型的水平集方法求解以及数值计算方法。

The pressure correction method is used to calculate the two-dimensional turbulent flow in general curvilinear coordinates.

按照进气箱对称面的形状，给出一种简化的二维进气箱几何模型，用微分方程法生成贴体的曲线网格，在任意曲线坐标系下采用压力修正法数值模拟了其内部二维湍流流动。

Geometrically nonlinear strain-displacement relations, the total potential functions and equilibrium equations of the tires are derived with respect to the orthogonal curvilinear coordinates for details.

以轮胎的内轮廓曲面为参考面，用正交曲线坐标描述轮胎的几何变形，详细推导了正交曲线坐标系下轮胎的几何非线性的应变—位移公式和平衡微分方程。

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。