有理曲线

For anelliptic curve E over a number field K,the set of K-rational points of it forma group Evia a special kind of"addition".This group is a finitely gener-ated abelian group,and is named Mordell-Weil group of E/K.

数域K上的椭圆曲线E的K-有理点全体，通过特别的"加法"构成一个群E，这是一个有限生成的阿贝尔群，称为莫代尔-威伊（Mordell-Weil）群，其结构是椭圆曲线研究的中心课题。

The rational points of an elliptic curve forms an additive group. The discrete logarithm problem of this group is called elliptic curve discrete logarithm problem.

椭圆曲线上的有理点会形成一个加法群，此加法群上的离散对数问题称为椭圆曲线离散对数问题(elliptic curve discrete logarithm problem)。

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。

Some new formulae for the derivative bounds of parametric curves, such as the general polynomial curves and rational polynomial curves in CAGD, are presented.

对CAGD中常见的多项式曲线和有理多项式曲线的导矢的界提出了新的估计公式。

We decompose curvature signal with wavelet at first and then use its low frequency coefficients as new smooth curvature signal, which is used to construct a G^2 continuous piecewise rational cubic Bezier curve with (Geometric Hermite Interpolation, GHI) GHI method subsequently.

针对在逆向工程的实践中常见的轮廓线的光顺问题，给出了一种先对曲率图进行小波分解，提取其低频部分作为新的曲率图，并利用几何Hermite插值方法，生成G^2连续的分段三次有理Bézier曲线，从而重建出光顺的产品轮廓曲线的新方法。

By constructing local affine coordinate system , the geometric construction and properties of end vertices for rational cubic uniform B splines are studied.

给出了有理三次均匀 B样条曲线的几何形状修改法，使对该样条曲线的修改更加灵活、方便

The stuff in between, including the internal Lemma, is there only to prove there exists an injective map from the group of rational points on an elliptic curve to the group of points over each finite field of prime order not dividing 2D where D is the discriminant.

证明中间的引理，主要是证明椭圆曲线上有限阶有理点到有限域上椭圆曲线的点之间的嵌入映射的存在性，其中点的阶不整除两倍的判别式2D。

If the method is combined with the subdivision method of curve,the rational spline curve with higher-order continuity is presented which is the approximation of offset curve.

该方法与离散算法相结合，可得到等距曲线的高阶连续的有理样条逼近曲线，最后，通过数值实例与已有方法作了比较。

The re-parameterization by Mbius transformation maintains both the same shape and the same control points of rational Bézier curve, only changes the distribution of the parameter.

Mbius变换能够保持有理Bzier曲线的控制顶点和形状不变，仅仅改变曲线的参数分布情况。

A necessary and sufficient condition for the curve being torsion curve in every sub-interval is given.

当张力参数趋于零或趋于无穷大时的极限曲线，分别是等距节点的有理三次B样条曲线和其控制多边形，故张力参数可用于调节曲线的光顺性。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。