微分几何

Moreover, multivariate splines are closely related with some topics in pure mathematics, such as, abstract algebraic, algebraic geometry and combinatorics.

另一方面，多元样条与基础数学的一些领域，如：抽象代数、代数几何、微分方程及组合数学等，亦有着密切关联。

Manifolds occur in algebraic geometry, differential equations, and classical dynamics..

流形出现于代数几何、微分方程式和经典动力学中。

The technique of boundary-fitted coordinate system is used to overcome the difficulties resulting from the complicated shapes of natural river boundaries;the method of alternating direction implicit finite difference scheme is used to solve the partial differential equations in the transformed plane;and the technique of moving boundary is used to deal with the river bed exposed to water surface.

用适体坐标技术克服天然河道复杂的几何边界给有限差分法所带来的困难；用交替方向隐式有限差分格式求解变换平面上的偏微分方程；用动边界技术处理河床的淹露。

The paper deals with curvature line and curvature characteristic of developable surface based on differential invariant of developable surface and it details curvature line and curvature characteristic of cone and tangent surface .

本文通过可展曲面的微分不变量，导出可展面的曲率线与曲率特征，并以锥面和切线曲面为例阐明这些特性的几何意义。

According to that characteristic and based on the differential equation of the deformed surface of the orthotropic plate, with one principal direction size fixed, changing another principal direction size linearly, maintaining elasticity coefficient the same as in the first principal direction and Poisson ratio equal to the geometric mean of two principal Poisson ratios, the original orthogonal plate is equivalent to an isotropic plate. Results obtained show that the deflections of the equivalent isotropic plate are the same as the deflections of the original orthotropic plate at the corresponding points, the forces of the correspondent points have simple relations.

根据这一特性、从正交各向异性板挠曲面的偏微分方程出发，保持一个主方向尺寸不变，另一主方向的尺寸做线性缩放，保持弹性模量与第一主方向相同，泊松比取2个主方向泊松比的几何平均值，将这类正交各向异性板等效为一块各向同性板；通过分析得到：各向同性板任意点的挠度就是原正交各向异性板对应点的挠度，各对应点内力之间存在简单的比例关系，该文的方法将为工程技术人员提供方便，同时可以更加直观的认识正交各向异性板的受力。

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。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

For example, we study the properties of the"centroid curve" and the"auxiliary curve", and identify two planes in which these two curves are defined respectively; we also use the idea of homotopy method to prove a fact that the orbit of a differential system has no triple contact point with the line we considered. Another key technique, which we use several times, is deformation argument.

例如研究由Abel积分之比定义的"质心曲线"和"辅助曲线"的几何性质，并把这两条在不同平面上定义的曲线放在同一坐标系中考虑；利用拓扑中同伦的思想来证明微分系统的轨线不可能与某条直线三重相切；利用几何方法与分析计算相结合证明了某一曲线是正则的；以及连续变动参数的技巧。

According the experiential formulas of headbox to design the stepped diffuser headbox's geometry parameters. Supposing Paper suspension flow as potential flow and basing on hydrokinetic and computational fluid dynamics theories, we can solve the elliptoid partial differential equations which are followed by the flow functions and the potential functions by finite element method and simulate the flow's speed distribution with pde toolbox of matlab software. The simulate results and the flow analysis have good precision.

按照流浆箱的经验设计公式，设计阶梯扩散式流浆箱的各组件几何参数，以流体动力学、计算流体力学等理论为基础，假定浆流的流动为势流，采用有限元法求解浆流流动时其流函数和速度势函数所符合的椭圆型偏微分方程，应用matlab软件的偏微分方程工具包pde toolbox，模拟出所设计的流浆箱各组件内的浆流的流场流速分布，模拟结果与数值计算流动分析结果吻合。

Curvature is the result of geometric structure in image; a new third order partial differential equation is proposed which transports curvature information along isophotes. The third order POE is morphologically invariant. Helmholtz vorticity equation which annihilates vorticity and third order POE which forward transports curvature information are coupled to be a new model.

曲率是图像几何特征作用的结果，本文提出沿等照度线方向传输曲率信息的三阶形态学不变偏微分方程，并将抑制涡量的无粘亥姆霍兹方程和正向传输曲率信息的三阶偏微分方程耦合。

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。