多项式的阶

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 this paper ,on one hand ,we establish the weakly asymptotic order of the classical Bernstein interpolation sequence approximate functionin the Wiener space(or 1-fold integrated Wiener space),on the other hand,we discuss the asymptotically order for the average error of Lagrange interpolation sequence, Hermite-Fejer interpolation sequence and Hermite interpolation sequence based on the Chebyshev nodes on the 1-fold integrated Wiener space.

本文一方面确定了经典的Bernstein多项式算子列逼近函数时在Wiener空间(或1-重积分Wiener空间)下的平均误差的弱渐近阶；另一方面确定了基于第一类Chebyshev多项式零点的Lagrange插值算子列、Hermite-Fejer插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差的弱渐近阶。

Prove the formulas with related the Bernoulli polynomials of higher order and Euler polynomials of higher order.

证明了与高阶Bernoulli多项式和高阶Euler多项式相关的无穷积分的计算公式。

Because the characteristic equation of fractional order system is a pseudo-polynomial function with exponential-type fractional orders of complex variable, the control of integer orders cannot be directly applied to it.

分数阶系统的特征方程是一个具有复变量的分数阶指数的伪多项式，因此不能直接应用整数阶系统的控制方法。

For different polynomials g, if the characteristic polynomial of a n matrix A is irreducible, then we get some theorems to determine matrix equations g =A solvable; if it is reducible, then, to see n-dimension space vectors M over a field F as F-module, we use module theory to determine these equations solvable such that it is simpler and clearer to investigate these questions.

对于不同多项式g，当n阶矩阵A的特征多项式为不可约的，我们给出了矩阵方程g=A有解的判定定理；当A的特征多项式为可约的，把域F上的n维线性空间M作为由A导出的F -模，我们利用模论知识来决定矩阵方程g=A有解性，从而使这一问题变了简单，研究思路更加清晰。

The state space forms of all these predictive PID control system are given, and their characteristic polynomial are derived by augmentation approach and Laplace expansion. At the same time, the performances of robust stability, close-loop response, and anti-disturbance of these control systems are compared with other control systems.

同时，给出了一阶加纯滞后对象、二阶加纯滞后对象、非最小相位加纯滞后对象和高阶滞后对象的预测PID控制算法，推导出了它们的状态空间形式，并通过状态增扩方法和Laplace展开方法，求出了系统的特征多项式。

Secondly, we embedded a Legendre polynomial of 5 orders into fixed effects, additive genetic and permanent environment effects were characterized by using Legendre polynomials with from three to eight orders.

其次，固定效应镶嵌5阶Legendre多项式，加性遗传效应和永久环境效应分别镶嵌3到8阶的Legendre多项式。

In the temperature sensing, the theory of fiber Bragg grating temperature sensing has first been proposed, the characteristic of the FBG temperature sensing was analyzed, it was deduced that the sensitivity coefficients of first-order and second-order ,and experimental findings was protracted, the gained polynomial better inosculate with the theory value. The experiment was processed in the low temperature , the thermo-optic coefficient was emended in the polynomial of the normal temperature ,the result was accorded with the sensing character of the normal and low temperature ,and it was resolved that the theory account of the normal and low temperature did not accord with the experiment.

在温度传感方面，主要从光纤布拉格光栅的温度传感模式出发，对光纤布拉格光栅的温度传感特性进行了分析，推导出了光纤光栅的一阶与二阶温度灵敏度系数，并对实验数据进行了拟和，所得多项式和理论值吻合的很好，并对低温传感进行了实验，将在常温下得出的多项式进行了热光系数的修正，所得的结果同时符合常温与低温的传感特性，解决了低温与常温情况下的理论计算与实验的不一致性。

A bstract: This paper focus on virtual instrument design of modal parameters identification with curve fitting theory based on rational fraction orthogonal polynomials. Using Forsythe orthogonal polynomials solves the coefficient equation instead of normal power polynomials in order to decrease the morbidity of it, making the orders of coefficient equation reduce to half and increasing computing efficiency.

本文基于有理分式正交多项式曲线拟合理论对振动系统的模态参数辨识进行了虚拟仪器的设计，为了减少系数矩阵的病态，采用 Forsythe 正交多项式代替普通的幂多项式进行求解，使系数矩阵阶次降低近一半，提高了运算速度。

In this paper,the rational approximation of the offset curve of Bézier curves is obtained when a polynomial of symmetric power basis is used to approximate the norm of parametric speed of Bézier curves.

等距曲线逼近技术的关键在于参数速度的逼近，文章用S幂基多项式逼近平面Bézier多项式曲线的参数速度模长，得到Bézier多项式曲线的等距曲线的有理逼近曲线，所得有理多项式逼近曲线与等距曲线在端点处能够达到高阶插值。

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。