曲线的曲率

Let be the center of Curvature at.

设已知曲线的方程是，且其二阶导数在点不为0，则曲线在对应点的曲率中心的坐标为

This paper used a method of curvature circle replacing general curve,the authors obtain twouniversal formulas calculating the inherent frequency of relative oscillation in miniamplitude be-tween columns that have general section curve.

本文应用曲率圆弧近似一般曲线的方法，导出了具复杂截面曲线的等截面柱体在另一柱体上微幅摆动时固有频率的一般计算式。

If singular value curve is convex in the coordinates 'k' of maximum peak of curvature spectrum, then the number of effective singular values is k; if singular value curve is concave in the coordinates 'k', then the number of effective singular values is k-1, and this rule is tested by the signal processing examples.

如果奇异值曲线在曲率谱最大峰值的位置坐标k处是凸出的，则有效奇异值的个数为k；如果奇异值曲线在k处是凹进的，则有效奇异值的个数为k-1，通过信号处理实例证实了这种结论。

A method for interpolating global curvature continuity curves with conic segments is presented in this paper.

提出利用有理二次样条曲线插值整体曲率连续的曲线的一种方法。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

If the change of step-size is controlled by the value of curvature of integral curve, the result can avoid such an error accumulation.

定步长的缺点在于不管是积分曲线的各个点的曲率如何都取一样的步长，这样肯定会在曲率大的一些点带来比较严重的误差，这种误差将在每一步的计算中积累。

The weakness of fixed step-size is that step-size is not variable regardless the curvature of each point of the integral curve change or not, which will affirmatively bring serious error in these points that the value of curvature is bigger. And, this kind of error will accumulate in calculating process.

定步长的缺点在于不管是积分曲线的各个点的曲率如何都取一样的步长，这样肯定会在曲率大的一些点带来比较严重的误差，这种误差将在每一步的计算中积累。

Consider a plane curve with parametric equation.

设平面曲线的参数方程为，则曲率为

In this paper a framework is built for differential quantity calculation on spatial curves of point cloud and a new matching method for given point curves is proposed.

建立了点云几何分析的相关理论框架，即定义和计算点云潜在曲线的几何微分量，包括Frenet标架、曲率、挠率等；在此基础上提出一种新的点云空间曲线匹配方法。

According to the spline theory we presented a shape matching algorithm based on the similarity matrix of curvature and torsion values of 3D curve, we reduced the 3-D curve matching task into a 1-D string matching problem, which makes the matching more veracious and can be used on the 2D or 3D curve matching.

周期性离散曲率函数具有和原有曲率相似的位移、旋转、缩放等特性，为提高匹配的准确度，利用高斯函数进行平滑处理，取得了较好的结果，同时该方法具有直观、速度快等优点，在2D轮廓曲线的匹配中，具有实用可靠的用途。

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。