代数空间

We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition , substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

Specify what status the spatial operator algebra locates at in many methods of multibody systems dynamics formulations and what the relations are between the spatial operator algebra and other dynamics formulations.We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition, substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

Keywords: Hecke algebra; quantum affine algebra; Fock space

中文关键词：黑克代数；量子仿射代数； Fock空间

Determinants and their properties are also introduced. After review of the algebraic structure of the Euclidean space, the algebraic vector space then will be studied.

再复习欧几里德空间的一些代数性质与几何，然后学习向量空间与向量空间的性质。

In this paper, we have made a systemic theoretic research on modelling and reshaping several types of spline curves/surfaces in CAGD. And some creative productions are given as follows. At first, the uniform C-B-spline basis is proved to be a normalized totally positive basis, and can be extended to a normalized B-basis. C-B-spline and C-Bézier basis, similar to B-spline basis and Bézier basis in algebraic space, are two bases in algebraic trigonometric space.

本文围绕着CAGD中常用的几种曲线曲面造型和形状调整进行了深入的研究，主要获得了以下一些成果：首先，证明了代数三角空间中的n次均匀C-B-spline基是一组标准全正基，并进一步扩充为一组标准B基。C-B-spline基与C-Bézier基是多项式与三角混合空间中的两组基，是适应工程实践中设计特殊曲线曲面的需要而产生的，类似于多项式空间中的B-spline基与Bézier基，是CAGD中重要的造型工具。

Although many results have been obtained, there are still a number of very interesting questions about composition operators unsolved. There is much more to be learned about the collective compactness and convergence of composition operator sequences, compactness of various product of composition operators, cyclicity, closed range and spectra of composition operators in various settings. Commutants of composition operators seem to be very difficult to characterize. Only a little is known about their reducing invariant subspaces. There has been no work on C〓 algebras generated by composition operators.

尽管已取得如此丰富的结果，但是关于复合算子仍然有大量非常有意义的问题值得研究，例如：复合算子序列的总体紧性及收敛性、复合算子的各种乘积的紧性、复合算子的闭值域问题、复合算子在各种解析函数空间上的谱的描述、换位复合算子的刻画、复合算子诱导的不变子空间问题、循环复合算子的研究、由复合算子生成的C〓-代数的研究、不同解析函数空间之间的加权复合算子及复合算子半群等等问题。

The research of this thesis focuses on spectral complements of operator matrices, the Moore-Penrose inverse and Drazin inverse of projections in a C~*-algebra, Weyl theorem and infimum and generalized infimum of quantum effects on a Hilbert space.

本文研究内容涉及Hilbert空间中算子矩阵的谱补、C~*代数上投影算子的Drazin逆及Moore-Penrose逆、Banach空间上算子的Browder定理和Weyl定理、Hilbert空间中量子效应的下确界和广义下确界四个方面的内容。

Vector is an important mathematical tool for the study, the method is the use of vector algebra vector solution to the issue of three-dimensional geometry of a convenient method, space vector as the new content, in dealing with space issues have considerable advantages space than the original problem to deal with more flexibility.

向量是数学研究的一种重要工具，向量的方法是使用向量的代数方法去解决立体几何问题的一种便捷的方法，空间向量作为新加入的内容，在处理空间问题中具有相当的优越性，比原来处理空间问题的方法更有灵活性。

So, in this paper, a circular cavity witha large radius is used to replace the straight boundary of thehalf space, then the half space problem can be changed tothe scattering problem of two circular cavities to the steadyincident P-wave . Having the aid of the mature cylinderfunction theory, the general solutions of the wave functionscan be given, and an infinite linear algebraic equations ofthe unknown coefficients in the wave functions can be gottenwith the boundary conditions and the Fourier complex seriesexpansion technology, the infinite linear algebraic equationscan be approximately solved by the finite trunction withsatisfying some definite precision, at the basis of thissolution of the equation, the variations and the lay-outs ofthe DSCF at the circular cavity boundary vs. the differentincident angles, the different embedded depths of thecircular cavity as well as the different dimensionless wavenumber of the incident P-wave.

为此，本文采用一个半径很大的圆孔来代替半空间的直边界，将该半空间问题转化为一无限大空间中两个圆孔对稳态P波的共同散射问题，借助于成熟的柱函数理论，通过写出问题波函数的一般形式解，利用问题的边界条件，并采用复数傅立叶级数展开技术将其化为一个仅包含问题波函数中未知系数的一无穷线性代数方程组，在满足一定计算精度的前提下，通过有限项截断进行近似求解，进而讨论了圆孔边界处的动应力集中系数随不同入射角、不同的圆孔掩埋深度、入射波的不同无量纲波数以及介质的泊松比变化和分布情况。

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

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