曲率

There have been many good results when M is minimal sub manifold. In the first section we will introduce the context and make a general description on the recent researches. In the second we will introduce the complexion of the development for this problem. In the fourth we\'ll discuss the second gap on special conditions using similar methods when the mean curvature is constant, and find the second gap.

关于极小子流形的间隙问题已经有了很多好的结果，第一节引言中我们将介绍本文的研究背景及这些主要结果，第二节中我们来介绍具有常平均曲率情形的间隙问题的发展现状，在第四节中我们用类似的方法讨论平均曲率为常数的紧致超曲面的第二间隙问题，得到了第二间隙δ=？

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Firstly, quadric surface is approximated with the vertex and its neighboring vertexes of the triangle mesh model, and the first and the second basic quantity are calculated, then estimating the normal and curvature of the mesh vertexes, lastly OpenGL technique is used in realizing the graphics display of the triangle mesh model.

首先根据三角网格模型中的顶点及其邻接点逼近二次曲面，并计算其第一、第二基本量，然后据此估算网格顶点的法失和曲率，最后利用OpenGL技术实现三角网格模型法矢和曲率的显示。

In 1986, R.D.Cook proposed differential geometry to assess local influence of minor perturbations of linear statistical models. Poon and Poon(1999) constructed a conformably invariant curvature , the conformal normal curvature, for the same purpose.

Cook(1986)用微分几何的方法评估了线性统计模型微小扰动的局部影响，Poon and Poon(1999)改进了Cook提出的统计曲率概念，定义了保形法曲率。

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高复杂曲面多坐标数控加工精度和加工效率为目的，在对国内外研究现状进行深入分析的基础上，对数控编程中各环节的关键技术问题进行了深入研究，主要内容包括以下几方面： 1 分析了复杂曲面各种造型方法的优缺点，给出了根据各种边界条件所确定自由曲面的NURBS表示方法以及三次NURBS曲线曲面反算算法；用微分几何理论推导了NURBS曲面的偏导矢及法曲率计算表达式；对曲面不同曲率特性区域的几何特征进行了深入分析，为建立复杂曲面的数控加工刀位计算模型奠定了理论基础。

The first and second derivatives of the coordinates of a cam profile are calculated using numerical differentiation method,and substituted with curvature radius formulas in calculus,thus obtaining its curvature radius.

应用数值微分法计算凸轮廓线坐标的一、二阶导数，代入微积分学中曲率半径公式，即得凸轮廓线的曲率半径。

The numerical approach consists of an operator split technique,which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains.

针对接触表面变曲率的特点，引入局部坐标系，构造出局部坐标下残余应力应变场的分布状态，建立了变曲率连续啮合过程中安定状态残余应力的计算方法。

One is based on the B-spline fitting to the contours;the other computes the curvature directly taking advantage of the relation of curvature and osculating circle.

一是基于轮廓的B样条拟合，通过计算拟合B样条曲线在各采样点处的曲率估算轮廓点的曲率

By the solution method of the principal curvature and Boussinesq problems, the equations of the contact characteristics of the contact points on the face gear are developed.

利用曲面上任意点处主曲率的计算方法，得到了传动中圆柱齿轮和面齿轮上接触点处主曲率的变化规律。

Dolomite reservoir fracture system, which was structural fracture,was studied by these two methods in Anpeng area of Biyang Depression.The results show that the principal curvature method has obvious deviation when used for a gentle structure latitude district.

研究结果表明，在凹陷内部构造变形幅度相对平缓的地区，采用主曲率法预测构造裂缝时存在较大偏差，而高斯曲率法的应用结果与地质解释、钻井和测井资料吻合较好。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。