多项式级数

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理，将一致概周期函数与有限三角多项式联系起来；第二，在恒同定理的基础上，给出了一致B~2概周期函数的Fourier级数，并且级数是唯一的；第三，讨论了一致B~2概周期函数的Parseval方程，建立了函数与其Fourier级数的系数之间的联系；接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

Let Un the Chebyshev polynomials of the second kind and the associated functions In this paper we discuss the approximations of the partial sums for the biorthogonal series based on and the corresponding conjugate series.

记Un是第二类Chebyshev多项式，伴随函数，这里讨论基于的双正交级数和其共轭级数的部分和逼近问题。

This paper is generaly devided into three parts,The first prepare knowledge,introduceing some conceptions asssociated with the polynomial ring and ring of power series such as power-zero element,inverse element and primitive polynomia and so on,prepare to introduce characters of power series.

本文主要分为以下三部分：首先介绍与环、多项式环、幂级数环密切相关的一些概念，如幂零元、可逆元、本原多项式等，为接下来介绍幂级数环的定义及其性质做下铺垫；然后着重讨论了环的性质，加深对多项式环与幂级数环的理解；最后讨论了多项式的性质，并将这些性质推广到幂级数环中，这也是本文的重点所在。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

In this thesis we propose an orthogonal polynomials adaptive filter and perform theoretical convergence analysis of residual echo power which proves its faster convergence rate owing to the reduced eigen spread of the input signal.

在传统上，多项式采用次方级数展开的形式；而在本篇论文中，为了提升非线性适应性滤波器的收敛速度我们使用正交多项式的非线性适应性滤波器。

The theory of rings is an important content of Modern Algebra, while the polynomial rings is an important part of the rings. Polynomial ring is similar with power series ring, and it is a subset of the power series.

摘要环论是近世代数中的重要内容，而多项式环的性质又是环论理论中的重要组成部分，多项式环是幂级数环的子环且与幂级数环形式相近。

Through comparing the ring and polynomial ring to power series, the defition and theorem of the ring and polynomial ring can be extended into power series.

通过对比环、多项式环与幂级数环，将环、多项式环中的性质推广到幂级数环中。

Furthermore,the stability behavior and accuracy characteristics of the algorithmare proven by a spectral decomposition method.

在前人工作的基础上，提出了一种新的用于解决结构动力分析问题的时间积分方法——Taylor级数方法；建立了求解线性问题和非线性项可以表示为多元多项式形式的非线性问题的Taylor级数方法的理论，并给出递归求解通式；阐述了该方法的程序实施过程，给出了计算流程图，并在非线性有限元分析平台NFAP中嵌入了Taylor级数方法的计算模块；利用谱分解的方法分析了该方法的稳定性和精度特性，以封闭的解析形式给出了描述积分法特性的周期延长率和振幅衰减率的表达式；通过对该方法的理论分析和特性研究，阐述了该方法的可行性和高效性。

The solution is proved that it can be written as the sum of limited polynomial series.

通过所做的非线性函数变换，得出了考虑雷暴活动的全球电模式的近地稳态解析解，并证明其能展开为有限多项式级数之和。

As one of the leading branches of the modern statistics, the riouparametric regression analysis is widely applied to explore the relationship between the the response variable y and the covariable A'.

对于非参数回归人们提出了许多估计方法，如核估计，局部多项式估计，光滑样条估计，级数估计(傅里叶级数估计，小波级数估计)等。这些方法本质上讲都是局部估计或局部光滑，当回归变量X为一维变量时，非参数回归函数用这些方法一般都能得到很好的估计。

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。