代数空间

The theory of vector space is an important and extensively applied algebraic branch of which matrix is one of the most important tools.

一个重要的有广泛应用的代数分支是线性空间理论，矩阵是其中最重要的工具。

This method is the combination of Simulation results are presented that demonstrates the performance of the new methods and compare it with two recently developed methods: Cumulant Enhancement and the All Vector Orthogonal Subspace.

本文提出了一种新的线性代数方法—累计量增强全矢量正交子空间方法，用于非最小相位滑动平均模型的建模。

In this doctorial dissertation,we study the stabilization,strong stabilization and estimation problem in the framework of nest algebras in Hilbert space.

本文我们是在套代数框架下，研究Hilbert空间中线性系统的稳定化、强稳定化以及一般估计问题。

One studying collaborative product design system was established, including: the structure and function of framework, self-study, self-adaptive, and self-organized collaborative design unit, Assistant Design Agent , communicative agent are discussed.

3分析了协同设计中知识表示和共享的研究现状，提出了将术语分为概念的内涵与外延，建立了术语含义一致化体系，包括概念内涵树和基于布尔代数的属性空间，解决协同设计中术语含义不一致的问题。

From the Maxwells equations in integral form directly, the Maxwell Grid Equations are derived through discretization of the solution space and the equations, and thereout the common equation of arbitary structures. Secondly, the solution uncertainty of a common electro-magnetic equation is proved and a strategy is advised to get the unique solution of the finite integration equation.

直接从积分形式麦克斯韦方程组出发，通过空间离散与方程离散得到麦克斯韦网格方程组，由此得到任意结构的一般方程；深入分析了麦克斯韦网格方程组的代数特性，论证了其解的不确定性，并指出了一种可避免解不确定性的措施。

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。

Firstly, by using Clifford algebra, we get the general expression of n-dimensional hyperbolic transformations.

首先，我们以Clifford代数为工具，得到了n维空间中双曲变换的一般表达式。

In the same time, after shortly review the Halclanes description of the quantum Hall effect on 2-sphere S2, we obtain the corresponding noncommutative algebra An and the Moyal structure of the Hilbert space.

同时在回顾了Haldane在二维球面S~2上对量子Hall效应的描述，我们构造了S~2的非对易代数及其Hilbert空间的Moyal结构。

Our results show that 2-local isomor-phisms of JSL algebras must be isomorphisms; local derivations and 2-local derivationsof JSL algebras must be derivations.

证明了J子空间格代数上的2-局部同构一定是同构；局部导子和2-局部导子一定是导子。

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