计算多项式

From our results, it can be known that the weakly asymptotic order of the information-based algorithm whose recover function is the classical Bernstein interpolation sequence is below that of the corresponding minimal information radius whose permissible information operator is function value.

通过我们的结果可以知道，以经典的Bernstein多项式算子列作为计算恢复函数的信息基算法，其在Wiener空间(或1-重积分Wiener空间)下的的平均误差的弱渐近阶均低于相应的以函数值计算为可允许信息算子的最小平均信息半径的弱渐近阶。

Secondly, the asymptotic series are used to evaluate the density function of heavy-tailed Rayleigh distribution, and an efficient three-step method is proposed using the interpolating polynomial fit.

其次， 本文使用渐近级数计算拖尾Rayleigh分布的概率密度函数，基于插值多项式拟合，提出了高效计算密度函数的三步方法。

We try to use a modified Bernstein polynomial to reduce the number of variables when calculating the circle array. Finally we use PSO to optimize the circle array and obtain a beam form with a flat top which is needed in the practical design.

在计算圆环阵时尝试引入了修正的波恩斯坦多项式以减少需要优化的变量，并结合工程上的需要，用粒子群优化算法给圆环阵赋行计算得到了主波瓣是平顶的方向图。

Two main aspects of the research work are as follows:(1) The paper introduces the experimental ice forces on semi-circular breakwaters which is made by State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology and calculate the ice value for different radius semi-circular component, based on which it speculates on that horizontal ice value and water level accord with biquadratic polynomial function, meanwhile, the paper analyses incidence of ice heap to horizontal ice value of semi-circular component.

论文的主要工作有三部分：(1)主要介绍大连理工大学海岸和近海工程国家重点实验室所做的物理模拟试验，应用水平冰力计算公式计算了不同半径半圆型构件的冰力值；根据这些数值的分析，推测半圆型构件水平冰力与水位符合四次多项式函数关系；同时分析了碎冰堆对半圆型构件水平冰力影响。

In the single and double integral terms of Green function, the kernel function of wave-making resistance expression, Special function expansion method and Chebyshev polynomial approach method have been adopted respectively, which greatly increase the calculation speed.

对作为兴波阻力计算核函数的Green函数的单、双积分项分别采用特殊函数展开、切比雪夫多项式逼近的方法进行计算，提高了计算速度。

Introducing the user algorithm of the broadcast ephemeris, the algorithms are explained on principle, which are Lagrange Interplation and Chebyshev polynomial simulation. Then comparisons of calculating of satellite coordinate with broadcast ephemeris and with precise ephemeris are made.

推导了广播星历用户算法，对GPS数据处理中常用的拉格朗日内插和切比雪夫多项式拟合从原理上进行了阐述，并对广播星历卫星坐标计算和精密星历卫星坐标计算进行了分析比较。

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。

The linear extrapolation technique was the most practical and suitable method because of its relative high correlation with a wide range of chlorophyll content, relative simple algorithm, relative high sensitivity to chlorophyll at high or low content and application to more wider bandwidth spectra.

四点线性内插法计算的红边位置往往偏大，最大一阶导数法与叶绿素含量的关系存在着明显的不连续性，拉格朗日内插法、倒高斯模型法在一定程度上存在着对高叶绿素含量的饱和现象，多项式拟合法对拟合波段区间、最高项次及光谱分辨率等比较灵敏而导致结果不够稳定，而线性外推法计算出的红边位置对叶绿素含量最为敏感，预测的准确度最高，且计算相对比较简单，并能适用于较宽波段的遥感数据。

Compared with tranditional methods, it is not too optimistic or pessimistic, fit for the exact timing of high-speed circuit design. Anda retiming scheme based on the above method is also presented to optimize the timing behavior of sequential circuits.

同传统方法相比，本方法计算出的最小周期既能保证电路的正确计算，又不至于保守，而且能同时计算出组合逻辑部分的延迟；然后从时序电路的波形多项式出发，进一步给出了多周期敏化的最小时钟周期确定方法，适用于有苛刻定时要求的环境。

This kind of parallel processing hugely improves the computational speed, and can change some NP problems that cannot be accomplished by classical computers, i.e., the complexity of the problems exponentially increases with the increase of bits, to P problems, i.e., the complexity of the problems polynomially increases with the increase of bits. In 1994 Peter Shor at Bell Laboratory proved that quantum computers could efficiently solve the problem of Large Number Factorization, which was the security footstone of nowaday classical cryptosystems, while none of any classical computers could implement this.

这种并行处理极大地提高了计算速度，可以把一些经典计算中无法计算的NP问题即问题的复杂度随着比特位数的增长而指数上升，变成P问题即问题的复杂度随着比特位数的增长以多项式上升。1994年，Bell实验室的Peter Shor证明量子计算机可以有效解决经典计算机所不能解决的大数因子分解问题，而这恰恰是目前经典密码的安全性基础。

I use an example quoted by Hu Jiaqi:"It is reported that America separates the DNA of a kind of virus by making use of genetic technology and combines it with another kind of DNA. Finally, they get a kind of virulent biological agent called a "pyrotoxin". Someone discloses in private that 20 grams of such a kind of biological agent could result in the global death of 6 billion people due to infection."

我在这里例举胡家奇所引用过的例子："据报道，美国利用转基因技术，将一种病毒的DNA分离出来，与另外一种DNA进行结合，拼结成一种剧毒的"热毒素"生物战剂，且私下有人透露，这种生物战剂只需20克，就可以导致全球60亿人全部感染死亡。"

Waiting, for the queers and the coons and the Reds and the Jews.

等待着疯子和黑人还有红色共产主义者还有犹太人