曲线的曲率

Curve C at the spot P(x0, y0) curvature is the maximal circle of the curve C tangency at the spot P(x0, y0). Contrail curve G of the center D of curvature circle entitles evolute of curve C.

曲线C在点Px0，y0）曲率圆是与该曲线C相切于点P(x0，y0的最大圆，曲率圆的圆心D的轨迹曲线G称为曲线C的渐屈线。

Degree B-Spline curve is chosen to fit the longitudinal settlement curves, which solves the problem of curvature continuum for joint notes due to its continuous second derivative vector and overcomes the efficiency and accuracy of computing curvature with 3 points by hand.

选取三次B样条方法对隧道纵向累计沉降曲线进行拟合，利用三次B样条曲线二阶导矢连续的特性，解决了拟合曲线在曲线连接点处曲率的连续性问题，克服了以往人工计算隧道曲率半径在效率和准确性方面的缺陷；并在此基础上，推导了隧道纵向变形曲率与纵向螺栓拉应力、相对弯曲与纵向螺栓剪应力之间的关系； 3。

Under this flow, the convex initial curve will preserve its perimeter, enlarge the enclosed area and make its curvature to be positive definitely. And as the time lasts, it will become more and more circular, and finally, as the time goes to infinity, the curve will converge to a circle in the Hausdorff metric.

本文证明在这种新的曲线流之下，闭凸曲线周长保持不变、所围区域的面积不断增大而曲率保持恒正，并且，随着时间的推移曲线变得越来越圆，最终当时间t趋向于无穷大时，曲线在Hausdorff度量意义下收敛到一个圆周。

A curve coordinate system which is suitable for variable height curved box-girder were established. The flexure, torsion and distortional warping displacement functions were established, and the strain-deformation equations were obtained, a spatial finite element analysis method of trapeziform cross section variable-curvature box-girder with vertical symmetrical axis was also presented.

建立适合于变高度曲线箱梁的曲线坐标系，推导了变曲率、变高度箱梁弯曲、翘曲扭转和畸变的位移方程和应变-位移关系式，提出了具有一个竖直对称轴的变高度变曲率曲线箱梁的薄壁曲梁空间分析有限元方法。

Next, what have double input and variable of 2 dimension appearance in the light of a kind is nonlinear system, used opposite curvature concept and curve to design controller of contract of appearance of 2 dimension plane by basic theorem, the curve of contrail of appearance be accusinged that controller of contract of this kind of appearance can assure a system and referenced contrail curve have identical figure.

梗概： 针对一般控制系统，利用微分几何中的曲线理论提出了外形变量、被控外形轨迹曲线和外形合同控制等概念。然后，针对一类具有双输入及二维外形变量的非线性系统，利用相对曲率概念和曲线论基本定理设计了二维平面外形合同控制器，这种外形合同控制器能够保证系统的被控外形轨迹曲线和参考轨迹曲线具有完全相同的外形。

Based on this property, by solving a series ODEs we construct a two-parametric family of helicoidal surfaces under cubic screw motion with prescribed mean curvature or Gauss curvature and solve an open problem left by Beneki.

基于这一点，当螺旋面的平均曲率或Gauss曲率为给定光滑函数时，本文选取伪正交标架，使得两类螺旋面的平均曲率和Gauss曲率的表达式相对简化，通过求解一系列的非线性常微分方程，即可确定一族生成曲线，从而最终确定平均血率或Gauss曲率为给定光滑函数的双参数族螺旋面，并在这一过程中解决了Beneki等人留下的一个公开问题。

The line of curvature is relation to many basic conception with curve and surface, by which normal curvature and principal curvature are easier.

曲率线将曲线与曲面中的许多基本概念有机地联系起来，使得法曲率和主曲率的求解简单化。

Finally, a method is developed for detecting feature points of the fragment con-tour based on total curvature.

将曲率和挠率相结合得出轮廓曲线上各点的全曲率，然后由全曲率值来检测碎片轮廓的特征点。

This paper establishes cubic spline function, analyzes subsection curve function and curve slope and curvature, at last decides to place the curve especial points which can be obtain easement curve length and other line parameters, such as the ZH point (end of line and beginning of transition curve), the HY point (end of transition curve and beginning of circular curve), the QZ point, the YH point (end of circular curve and beginning of transition curve), the HZ point (end of transition curve and beginning of line).

针对公路平面线形的8种组合类型，其线形元素特征则由最基本的直线、圆曲线、缓和曲线组成的特点，解析三次样条函数模型，得分段曲线函数、曲线斜率、曲率，从而确定曲线特征点（直缓ZH点、缓圆HY点、曲中QZ点、圆缓YH点、缓直HZ点）位置，进而得到曲线缓和曲线长度及其他线形参数。

In the case of loadingalong curved strain path,the author discovered that the instability mentioned aboveoccured only if the curvature changed from large to small.The drop and recovery instress obviously depend on the curvature and its rate.

对曲线应变路径的情形，本文发现只有在曲率由大向小变化时才出现上述瞬时软化响应，且曲率改变变化趋势时曲率的大小及路径弧长对应力大小的降低和重新强化的程度及变化率的影响较为明显。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。