计算多项式

Each weight function is a composite function of a generalized Chebyshev polynomial and a linear function, only algebraic calculation is needed, and no requirement is involved for the calculation such as the steepest descent-like algorithms or matrix calculation.

权函数是广义Chebyshev多项式和线性函数的复合函数，只需要通过代数计算就可以求得，不需要梯度下降计算或者矩阵计算。

Each weight function is a composite function of a generalized Chebyshev polynomial and a linear function, only algebraic calculation is needed, and no requirement is involved for the calculation such as the steepest descentlike algorithms or matrix calculation.

权函数是广义Chebyshev多项式和线性函数的复合函数，只需要通过代数计算就可以求得，不需要梯度下降计算或者矩阵计算。

Combining the definition of CWT and the derivative property of convolution, we constructed a general method to calculate the approximate derivative of signal through CWT by using the first and second derivative of Gaussian function, Haar, and the first derivative of three-order-Spline function as wavelets. As compared with the other approaches of calculating derivative, which include the numerical differentiation, polynomial filters, Fourier transform, and the recently proposed DWT method, fast calculation and simple mathematical operation were remarkable advantages of CWT method. For the signal corrupted by severe noise (Signal-toNoise Ratio=5), the satisfactory results could also obtained via CWT method through appropriately adiusting the dilations.

在此基础上，(1)结合连续小波变换的特点和卷积的微分性质，提出了使用Gaussian函数的一阶和二阶导数，Haar和三次样条函数的一阶导数作为小波函数的连续小波变换计算信号近似导数的一般性方法，与其他导数计算方法(包括数字微分法，多项式滤波法，Fourier变换法和离散小波变换法)相比，本法简单便捷，计算速度快，对于噪声含量较高的信号(S/N为5)，只要适当调节尺度即可获得比较满意的结果。

In addition, an experimental system using C language is established, including modules such as representation of waveform polynomial, decision of path senstization, delay computing, clocking based on single-period sensitization, clocking based on multi-period sensitization, test generation considering noise and transformation from bit-level waveform polynomial to word-level polynomial model. They respectively used to test models and techniques proposed in this paper.

另外，：基于C语言本人设计开发了一个实验软件系统，该系统包括波形多J一贞式表示模块、敏化通路判定模块、延时计算模块、单周期敏化的最小时钟周期精确确定模块、多周期敏化的最小时钟周期确定方法模块、考虑噪声的测试生成模块和位级波形多项式描述转化成字级多项式描述模块，分别用于对本文各章中提出的自动化设计的模型和方法进行实验验证。

All the sub-plans are described by a group of general mathematic formulae. The computation of the sub- plan can be decomposed into two sub-problems by relaxing the constraint that production level at production period of a sub-plan must be more than zero. Based on the properties of an optimal solution, two polynomial algorithms are devised to solve sub-problems and reintegrate the relaxed constraint. Finally, a dynamic programming algorithm with complexity O(T^4) is developed to solve the global problem, where T is number of periods in planning horizon.

给出了所有子计划的通用数学描述，并通过松弛正生产量约束将子计划的计算分成两个子问题；依据子问题和子计划最优解的性质，设计了求解子问题和重新集结松弛约束的多项式算法；在此基础上提出了一个复杂性为O(T^4)的求解整个规划问题的多项式动态规划算法，这里T是规划时段上的周期数。

PID controllers based on the interval polynomial stabilization theorem;2. Not only the H ∞ norm calculating guestion of the robust stability of the mixed-type perturbation in the interval polynomial family is studied, but also the range which can be done is enlarged to that of the more general linearly dependent cofficients perturbation.

本文讨论了不确定性系统的鲁棒稳定性分析问题，不仅研究了区间多项式族混和摄动的鲁棒稳定性中H∞的计算问题，而且将研究的范围从区间多项式族扩展到更具一般性的线性相关系数摄动的系统，以值域断面的几何性特为基础，提出了一种形象直观，简便实用的混和型摄动系统鲁棒稳定性的分析方法。

The first line of the input is a positive integer T. T is the number of test cases followed.

给出了多项式和变量的值，你的任务是计算值的多项式第一行输入的是一个正整数T 。

Most of previous segmentation approachs make use of the surface curvatures or the approximative polynomial coefficients which are very sensitive to noise, but the mathematical morphological operations are robust, so another main advantage of our scheme is its good noise immunity.

以前的大多数分割方法都使用表面的曲率或近似多项式的系数，表面的曲率或近似多项式的系数的计算对噪声很敏感，而数学形态学运算具有较好的抗噪声性，因此我们的方法的另外一个优点是它具有良好的抗噪声性能。

N algorithm for close approach determination was developed by Alfano and Negron （1993） based on polynomial splining techniques.

lfano—Negron（1993）提出的空间目标接近分析算法将最小相对距离及其对应时刻和进出误差椭球时刻的求解问题均转化为插值多项式求根问题。A—N算法在判断三次多项式根的存在性、筛选合理实根时存在缺陷，可能导致多余计算。

In the first chapter, general ideas and basic concepts about homotopy method, polynomial equations and the multi-homogeneity are introduced.

第一章，给出多项式及多项式方程组的一些基本定义，简单介绍了同伦方法，并给出了m-Bezout数的定义及计算方法。

This is not an ordinary box, which is used as a background picture of the dialog box, very pretty.

详细说明：这可不是一个一般的对话框，它是用图片作为背景的对话框，非常好看。

Conceal me what I am,and be my aid for such disguise as haply shall become the form of my intent.

遮掩我的身份，帮助我，我的面具将成为我的目的。