代数空间

Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra and functional analysis .

向量空间的一个中心主题在现代数学，因此，线性代数被广泛使用在抽象代数和功能分析。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

Linear space linear algebra is the most important subjects, one of the most basic concepts.

线性空间是线性代数最主要的研究对象、最基本的概念之一。

Therefore, the property, of Pascal line is important for both algebraic curve and singularity of spline space The aim of this paper is to find common properties among conic curves which have the same Pascal line and compute the track of Pascal lines.

所以，对于Pascal线性质的讨论，对于代数曲线以及多元样条空间的结构方面的研究也起着重要作用。

Lagrange Interpolation; Osculatory Interpolation; Dimension Of Interpolation; Algebraic Curve And Surface; Bezout's theorem

Lagrange插值；切触插值；插值空间维数；代数曲线曲面； Bezout定理

Quantity and space both play a role in analytic geometry , differential geometry , and algebraic geometry .

数量和空间在解析几何，微分几何和代数几何中都发挥作用。

One has its origin in algebraic geometry, whereas the other one comes from differential geometry.

借助于它们上面的Hermitian度量我们可以定义两个模空间：一个联系着代数几何；一个联系着微分几何。

For implementing the encryption/decryption and information hiding for digital multimedia, and aiming to generate enough large cipher key space, the accurate period of high dimension random matrix scrambling transformation is studied with the help of number theory and algebraic theory.

为了适合数字多媒体特性，实施多媒体加密与信息隐藏，生成充分大的密钥空间，使用了数论、近世代数、算法分析等工具，对高维随机矩阵置乱变换的精确周期进行了研究。

Based on an introduction to the robust control of uncertain linear systems and a survey on the past and recent contributions to the related polynomial algebraic method, state space method and frequency domain method, this dissertation focuses on the robust control problem of uncertain linear systems in frequency and time domain.

本文首先就不确定线性系统的鲁棒控制问题作一扼要的介绍和概括，并分多项式代数方法、状态空间方法和频率域方法对其历史发展及其研究现状进行了比较全面的综述。

Furthermore, people found that the relationship between intrinsic properties of planar algebraic curves and the singularity ofbivariate spline spaces is m-ore and more important.

尤其是经过近年来的研究，人们发现多元样条空间的奇异性问题与代数曲线的内在性质有着越来越重要的关系。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了