曲线的曲率

This paper gives a mathematical definition to that two open planar curves have the same shape based on curvature representation, therefore, a new kind of shape distance is proposed. It is concluded that the problem of computing the shape distance between two open planar curves can be changed to the problem of a functional extremum, and the differential equation is given, which can be used to figure out the shape distance.

本文为基于曲率表示的两条平面开曲线的等形下了严格的数学定义，从而找到了一种新的形状距离度量，并且证明了这种形状距离的计算问题可以转化为一个泛函的极值问题，同时给出了求解形状距离的微分方程。

In section 4.2, we study the rescaled WLC model which is equivalent to Langer and Singer's theory of elastica because the Gauss curvature equals zero in three-dimensional Euclidean space.

我们首先讨论了Feoli 等人的结果，将之作为自由能仅为曲率的泛函的特例纳入普遍形式理论中来；并研究了Langer 和Singer 提出的关于弹性曲线的理论(即重新标度的WLC模型)，与当前理论符合得很好。

Inequality Constraint and κref Selection: The kurtosis value corresponding to a target is related to many factors, such as the abundance of the target component contained in a pixel, the target size relative to the image size, and the number of spectral bands.

不平等限制和κ裁判员选择：或然率曲线峰值的曲率度对一个目标符合的数值被讲到被包含在一个图素的许多因数，像是目标的丰富元件，目标与影像大小相关的按规定尺寸制作，和光谱能带的数目。

Four main types of spatial binary links are investigated in details for kinematic synthesis both in precision-position synthesis and multi-position synthesis. In terms of the invariants of spherical curve and cylindrical curve, the mathematical models of adaptive fitting sphere and cylinder are constructed by means of the saddle-point programming.

再次，根据常见空间机构运动副组合的约束曲线与约束曲面的曲率理论，阐述了空间机构运动综合的基本要素及其不变量拟合理论与方法，研究了有限位置和多位置情况下，自适应综合方法在空间S-S、C-S、C-C和S-C四类二副杆组运动综合中的应用，实现了自适应综合方法从平面到空间的扩展。

In this program, the declining segment of the stress-strain relation of the concrete, the restriction effect of hooped reinforcement and the bond-slip problem of the reinforcement are considered, as the same time the optimized arithmetic is applied to accelerate calculation procedure. Though the appropriate experiment arrangement, the influential factor such as the strength of concrete, the ratio of hooped reinforcement, the ratio of axial compression and the loading angle are researched, some available rules of carrying ability and ductility of the special-shaped column can be attained.

程序中考虑了混凝土应力应变曲线的下降段及箍筋对混凝土的约束影响，采用了合适的算法加速计算过程并考虑了纵筋锚固滑移的影响，通过正交试验分析了混凝土强度、体积配箍率、轴压比和荷载角对异形柱截面抗弯承载能力及截面曲率延性比的影响。

The residual stress in bent pile can be ignored. The curvature of batter pile has important influence on additional moment to bent pile under vertical load on top. When the radius of curvature on the upper segment of pile is small, the additional moment can not be ignored.

得到以下结论：桩体由于施打而发生的弯曲在桩体中产生的残余应力可以忽略不计；桩顶竖向荷载作用下桩身的弯矩同桩的偏斜曲线有重要关系，桩顶处的曲率较大时，桩身的弯矩在工程中是不能忽视的。

According to the curvature and convex-concave characteristic of the fitting curve, inrush current and fault current of power transformers can be distinguished.

该方法利用初始5ms内差电流的数据（5ms数据窗），将其拓展为长10ms的数据窗，然后通过最小二乘算法拟合差电流波形得到其近似表达式，再根据拟合曲线在各点处的曲率和凸凹特性来区分变压器励磁涌流和内部故障。

Utilizing the sample data within 5ms after fault initiation and extending the date windows from 5ms to 10ms, the approximate current formula can be extracted from fault current or inrush current using least square fitting method. According to the curvature and convex-concave characteristic of the fitting curve, inrush current and fault current of power transformers can be distinguished.

该方法利用初始5ms内差电流的数据（5ms数据窗），将其拓展为长10ms的数据窗，然后通过最小二乘算法拟合差电流波形得到其近似表达式，再根据拟合曲线在各点处的曲率和凸凹特性来区分变压器励磁涌流和内部故障。

According to the objective of second-order derivative related to curvatures, it is proved that there is no difference whether we insert a knot or not. And it presents a characteristic of cubic Hermite interpolation curves.

如果以与曲率有关的二阶导数为目标，证明插入节点与不插入节点的情形是一样的，体现三次Hermite插值曲线的一种特性。

In this way it is easy to establish the parallel frame of curves in any dimension space.One of the application of the parallel frame is that it can prove the equivalence between the vortex filament equation and the non-linear schrodinger equation.

建立曲线的平行标架的一个应用是可以证明Vortex filament方程和非线性Schrodinger方程表示的是同一个方程。1906年，Leivi-Civita的学生da Rios写了一篇硕士论文，关于漩涡在粘稠液体里以曲率大小的速度沿着副法线的方向运动的模型。

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。