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However, due to the complex of computation and the need of the design, sometime we need to use polynomial approximation for a rational curves and surfaces.

然而由于计算的复杂性和设计的需要，有时我们还需要用多项式函数来逼近有理曲线和曲面。

Two new approaches are proposed for a polynomial approximation of Bezier offset curves.

提出了Bezier曲线等距线的两种多项式逼近新思路。

Because only two points a straight decisions, and in between the two curves can be used an infinite number of cubic polynomial approximation.

因为，两点只能决定一条直线，而在两点间的曲线可用无限多的三次多项式近似。

The rocking curves of different area have been measured by high resolution X-ray diffractometry. The reflections were indexed, furthermore the polytype structures were identified. The results are consistent with those of Raman spectroscopy analysis. It is demonstrated that Raman spectroscopy is a simple and powerful method for the determination of SiC polytypes.

同时采用高分辨X射线衍射测量了该晶片不同区域的摇摆曲线，将不同多型体的计算衍射角与实验值加以比较，对SiC晶片中的多型进行了标注，所得结论与激光Raman光谱测定结果相一致，说明Raman光谱是一种简单、快速地鉴定多型结构的强有力的工具。

The model of programmed crystallization of SPM was proposed based on the moment transformation of the population considering the agglomeration. The optimal temperature-time curves in a batch crystallizer which maximized the terminal mean size and mean weight size can be determined from the application of the Pontryagin Maximum Principle. The calculated crystallization results heating under optimal temperature were compared with ones under linear or natural heating temperature.

根据第四章所得到的螺旋霉素晶体二次成核和晶体生长和布朗扩散引起的聚集动力学，利用第六章所描述的晶体尺寸分布的各阶矩对时间的一阶导数所构成的自封闭的一阶常微分方程组，采用庞得里亚金极大值原理，以温度为控制变量，在满足某些约束条件下，以最大平均尺寸和最大晶体重量平均尺寸为性能指标，计算出了螺旋霉素间歇结晶的最优温度—时间曲线，并同线性加热和自然方式进行了比较。

Algorithm in computer graphics presentation systems, including drawings, curves, straight lines, etc.

计算机图形学算法演示系统，包括各种绘图，曲线，直线，变换等等算法，较实用。

Therefore,a series studies of ice-pier vibration are performed from different aspects in this paper.The main work of this his thesis is summarized as follows:(1) Ice response spectra is proposed based on the idea of a seismic response spectra analysis of str .. uctures.Firstly,ice response spectra on the basis of power spectra density function is established;Secondly,based on the assumption of quadratic parabolic interpolation method,the nonlinear interpolation analysis method of ice response spectra is studied from both theoretical and practical points of view,and the successive computation formulas including ice displacement,velocity and acceleration response spectrum are deduced by Duhamel integral.Furthermore,to analyze the effectivity and applicability of the method, the real temporal curves of ice pressure are used to be studied.The results show that the presented method is more convenient and accurate to study the structural response induced by ice force,also it can be effectively applied in the design of ice resistance.

鉴于此，本文针对冰激桥墩结构振动问题从不同方面展开了一系列与之相关的研究，主要研究内容如下：(1)根据结构抗震反应分析思想提出了冰振反应谱，首先建立了基于功率谱密度函数的冰振反应谱；其次借鉴地震反应谱内插法的思想从理论和实际观点出发，假定在等距离微小时间间隔内冰荷载按二次抛物线规律变化，由Duhamel积分推导出冰振位移、速度以及加速度反应谱的一系列连锁公式，建立了基于非线性内插法的冰振反应谱，并利用实际冰压力时程曲线进行了冰振反应谱数值分析，为以后冰激结构振动的研究提供一种方便、简捷、精确的分析方法，也能够将其有效地应用到结构的抗冰计算中。

This paper describes the Atkin's elliptic curves primality proving algorithm and discusses all implementation details of this algorithm. Finally it gives the implemention of this algorithm by software and exhibits an example explicitly. This algorithm is implemented with software and this software is used to test some general large integers and acquire a good testing result.

文章给出了由Atkin提出的一种非常有效的素性测试方法即椭圆曲线素性证明算法，详细讨论了具体实施该算法的所有细节，而且通过在计算机上编程获得了其软件实现，并用该软件来测试一般的大整数的素性，取得了很好的效果。

Building elliptic curves over large prime field whose orders contain two or more large prime factors, and which have no subgroups with smooth orders.

椭圆曲线密码体制近几年来已成为密码学界的一个研究热点，有望在某些领域替代RSA等现行密码体制，不管在理论界还是应用领域都已引起了极大关注。

Building elliptic curves over large prime field with nearly prime orders or prime orders.

构造大素域Z〓上素数阶或近乎素数阶椭圆曲线。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。