查询词典 degree of a polynomial

Under weighted squared error loss, it is showed that a least favorable prior, when estimators are restricted to be polynomials of X with degree no more than k, exists and has at most (k+2)-point support, and its Bayes solution, under above restriction, is a k/sup th/ polynomial minimax estimator.

是观测值X的期望值，在X的多项式函数中，於加权平方误差损失之下，本文考虑使其最大风险最小化的多项式大中取小估计式。

To factor a polynomial of degree n over Fq, the number of arithmetic operations in Fg isO(n1.8010111405662083logq) or On2+o(1 +n1+o(1) log q or On (1,3/4,3/4+ n1+o(1) logq, of which the first one is less by 0. 00433886 than the previous record.

具体地说，为了分解有限域F~q上一个次数为n的多项式，该算法的时间开销为 On~(1.8010111405662083logq或On~(2+o(1)+n~1+o(1logq或On~(ω(1，3/4，3/4)+n~I+o(1logq个F_q中算术运算，其中第一个开销的指数比已知的最好结果降低了

Also the constructed curve is a shape-preserving curve for the original curve. We can also adjust the shape of curves by parameters of trigonometric uniform polynomial curve to approach the polygon closer. The general trigonometric polynomial curves with m degree and C(superscript 2m-1)(m=1, 2, 3) continuity are further presented.

除了通过切点参数，还可以通过三角均匀多项式曲线参数来调整曲线形状，使所得曲线更加逼近多边形，并可进一步、类似地可构造与给定多边形相切的C(上标 2m-1)(m=1， 2， 3)连续的m次三角多项式曲线。

Dixon method was adopted to construct a 22×22 Dixon matrix and then the greatest common divisor of two columns was extracted. After expanding the determinant of the matrix, a 64 degree univariate polynomial equation was obtained and 6 extraneous roots were canceled in the process of solving the other 3 variables.

结合矢量法和复数法建立了4个几何约束方程式，使用Dixon结式构造22×22的Dixon矩阵，对两列提取公因式后展开矩阵的行列式得到一元64次多项式方程，回代过程中去掉6组增根后得到58组解。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

And the self-shrinking generator is a typical model of the clock-conctolled During the past ten years or more, some researches have been done on the period and linear complexity of the self-shrinking sequence obtained from an m-sequence which is generated by a primitive polynomial f over GF(2), degree=n , in the related academies.

近十余年，国际上已对由n级m-序列导出的自收缩序列的周期和线性复杂度做了研究，给出周期的上下界，其中所给的下界为2~([n/2])，由此也给出了线性复杂度的下界为2~([n/2]-1)+1。

Using the estimates of character sums over Galois rings and the trace de scription of primitive sequences over Zpe, we obtain an estimate for the frequency of the occurrences of any element in Zpe in one period of a primitive sequence, which is better than Kuzmin's results[1] if n ＞ 4e, where n is the degree of the generating polynomial of the primitive sequence.

范淑琴 ，韩文报文研究了Zpe上本原序列的元素分布。利用Ga，lois环上的指数和估计和本原序列的迹表示，得到了Zpe中各元素在本原序列的一个周期中出现频率的一个估计。当n＞4e时(n为本原序列生成多项式的次数)。我们的估计优于Kuzmin的结果[1]。

The matrix inhomogeneous eigenvalue problem is widely applied in mathematics and many other fields,for instance,the studies of the stability of solutions of linear differential equations and the stationary values of a second-degree polynomial on the unit sphere,and the constrained eigenvalue problem and so on.

矩阵非齐次特征值问题在数学和其他领域里有许多应用，如线性微分方程组解稳定性研究，球面上二次函数的稳定点求解及约束特征值问题等。

Relative contents of four main cellular proteins corresponding to MALDI-TOF-MS peaks m/z 4466, m/z 6455, m/z 6514, and m/z 7772 were all found to be close correlated with the concentration of melamine, although their up- and/or down-regulations showed different patterns when the concentration of melamine changed. Support vector regression leave-one-out method, with the optimized polynomial kernel function and a poly-degree of 3, was chose to evaluate the correlation between the alteration of Tetrahymena pyriformis main proteins'relative contents and the concentration of melamine in the culture medium.

支持向量机软件中支持向量回归support vector regressi(来源：A3cBC17论b1文网www.abclunwen.comon， SVR留一法预报结果表明，选用幂指数为3的多项式核函数进行建模，相对误差的平均值为7.238%，说明梨形四膜虫主要蛋白质相对含量的变化与培养基中三聚氰胺浓度变化相关。

After much effort, such a formula was indeed found for quartics — but since then it has been proven that such an approach dead-ends with quartics; they are the highest-degree polynomial equations whose roots can be expressed in a formula using a finite number of arithmetic operators and n-th roots.

自然，人们为了找到这些根做了许多努力。就像其它多项式，有时可能对一个四次方程分解出因式；但更多的时候这样的工作是极困难的，尤其是当根是无理数或复数时。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。