查询词典 order of polynomial

Qiu-Ming Luo, Yun-Xin Ma, Feng Qi, The relations between higher order Bernoulli polynomial and higher order Euler polynomials , Shuxue Zazhi Journal of Mathematics (Wuhan 25 (2005), no.

雒秋明，马韵新，祁锋，高阶Bernoulli多项式和高阶Euler多项式的关系，数学杂志 25 (2005)， no。

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 method includes steps: each point in sequence x with length L, i=0, 1, 2,apostrophe L-1 is served as a independent variable of k order polynomial; changing coefficient of polynomial to generate multiple sequence f with length L, where k is nonnegative integer; operation in polynomial is carried out in Galois Field GF, where Q=pm, p as a prime number, and m as nonnegative integer; assigning generated sequences to multiple sectors to set of create biased sequences for each sector; it is different in constant terms of polynomial, and identical to other coefficients of coefficients corresponding to sequence assigned to same sector; creating corresponding time - frequency pattern unit from biased sequences of the sector; repeating TFP unit with equal interval in frequency domain so as to obtain integrated TFP.

本发明涉及一种时频资源的分配方法，所述方法包括：把一个长度为L的序列{x，i＝0，1，2，…L-1}中的每一点作为一个k次多项式的自变量，改变多项式的系数生成多个长度为L的序列{f}，其中k是非负整数，多项式中的运算在伽罗华域GF中进行，其中Q＝p m ，p是一个素数，m是非负整数；把生成的序列分配给多个小区，生成各小区的偏置序列集合，其中分配给同一个小区的序列所对应的生成多项式的常数项不同，其他项的系数都相同；由所述小区的偏置序列生成对应的时频图案单元，将时频图案单元经过频域等间隔重复，得到完整的时频图案。

At last, we gets the coefficients of rectifying curve ploynomial through the curves fitting of three order Hermite interpolation polynomial, second order interpolation polynomial, and presents a fitting methods of small current working.

本文对高压电动机测量用电流互感器在小电流工作时电流比值误差和角度误差进行了研究，通过对引起误差的各参数的深入分析，得到误差与电流的关系，并通过三次Hermite 多项式插值法、二次多项式插值法的曲线拟合，得到曲线多项式的各系数，提出一种小电流工作时的拟合方法。

Adopting Hermite polynomial in stead of Taylor expansion has greatly decreased the order of the high-order cross sensitivity.

利用埃 尔米特插值逼近函数代替泰勒展开式，使目标函数对几何参数高阶交叉灵敏度的阶数大为降低，减小了计算代价。

Based on in comparison of all statistical criteria and behavior of estimated parameter the RRM with a fifth-order Legendre polynomial for both fixed effects and additive genetic effects, a seventh-order Legendre polynomial for permanent environment effects is equally well equipped to model all effects, which is the best model among different RRMs.

通过各种统计指标和估计参数行为的比较，确定固定效应和加性遗传效应镶嵌5阶Legendre多项式，永久环境效应镶嵌7阶Legendre多项式的随机回归模型为最优模型。

These algorithms can get very high precise mapping together with high speed of convergence, because the mapping error is able to reach zero and the computational complexity is at order of polynomial.

新算法有很高的精度及较快的运算速度，这是由于映射误差可以为零，其计算复杂性是多项式阶。

The results show that, with the increasing order of polynomial chaos, the probability density curve of a response approaches the results from Monte Carlo simulations.

结果表明：随着随机多项式次数的增加，随机响应面所得到的响应概率密度曲线愈加趋近于由蒙特卡罗方法所得到的概率密度曲线。

REPs extracted by polynomial fitting technique were unstable due to its high sensitivity to the spectral resolution, waveband range and the highest order of polynomial.

结果表明，叶片红边位置的计算结果对选择方法的依赖性很大，几种计算方法提取的红边位置与叶绿素含量的相关性均较好。

In order to make up the deficiency of ordinary trigonometric polynomial curves in aspect of shape adjustment, then in view of polynomial spline cannot represent some transcendental curves, a new kind of parametric trigonometric polynomial spline with a shape parameter is constructed by linear singular blending technique.

为了弥补普通三角多项式样条曲线在形状调整方面的不足，同时又考虑到多项式样条曲线不能精确表示一些超越曲线，我们利用奇异混合的思想构造了一种新的带有形状控制参数的三角多项式样条曲线。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失