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The characteristic of a trefoil knot is: three independent faces becoming a linked closed curve, or single side curve.

该展品是拓扑研究的课题之一，具有单侧曲面特征。

But the design of complex curve and curve surface is the core in the CAD of vehicle body.

汽车车身是复杂的空间自由曲面，在汽车设计开发过程中，车身设计是直接影响设计成功与否的重要因素，而在车身的计算机辅助设计当中，复杂曲线和曲面的设计又是一个核心的问题。

By combining OLE control-ware with OLE automation technology in visual basic, not only any complex curve can be made, but also data in the curve can real-timely be refreshed.

将VB提供的OLE控件与OLE Automation技术相结合，不仅可实现任意复杂曲线的制作，而且可实现曲线数据的实时刷新。

In this paper, the waved-edge force model is deduced on the basis of straight edge force model by use of the curve integral principle. This method is suited to the case for the complex 3-D grooves of random curve edge.

在直线刃铣刀片模型的基础上，利用曲线积分原理，建立了波形刃铣刀片铣削力数学模型，该方法可适用于任意曲线刃的三维复杂槽型的情况。

The most important idea is that over the complex numbers, an elliptic curve looks like a torus, and the points of finite order in the group of the curve have a very simple geometric description.

最重要的思想是复数域上的椭圆曲线是一个环面，曲线簇中的有限阶点有简单的几何描述。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

Moreover, the curve of mixing energies△G_m at different surface compressure vs molar fraction of nervonic acid appeared a positive deviation comparing to the ideal mixing surplus energies△G_M~1 curve, which indicated a phase separation phenomena in the mixed monolayer.

此外，在不同表面压下的混合自由能ΔG_m对神经酸摩尔分数曲线与理想的混合过剩自由能ΔG_M~1曲线相比出现相似的正偏差，说明这种混合单分子膜出现了相分离现象。

The results showed that the cubic curve, inverted U-shaped EKC and the concave curve could be used to describe the relationship between environmental change and economic development in Henan province.

结果表明：河南省环境状况和经济发展之间呈现三次曲线、倒U形和"凹函数"和3种形式。

This blade has a gentle, sloping convex curve to the point versus the concave curve of the clip blade.

相对于回形刀刃的凹曲线而言，这种刀刃具有一条延伸到刀尖的、温和的凸斜率曲线。

It can be seen from the long time asymptotic solutions, that the pressure curve is a concave curve and ...

注稠化水等措施是改造这种油层的方向，但最终界限目前还不好确定。浊层研究、油田开发和各种油井工程措施应当考虑相对流动比这一因素。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。