仿射群

In terms of subshifts of finite type determined by an irreducible marrix, affine maps of compacted connected metric abelian group and continuous maps of tree, the two concepts of topologically ergodic map and topologically transitive map are identical.

指出对于由不可约方阵所决定的符号空间有限型子转移而言，或紧致交换群的仿射变换及树上连续自映射而言，拓扑遍历与拓扑可迁这两个概念是一致的。

After a historical motivation of the definition of a Lie group we shall develop basic manifold theory, vector fields, tangent spaces leading to the Exponential mapping for an affine connection.

在简单介绍了李群的定义的历史来源之后，我们将讨论关於流形理论、向量场和切空间，进而引出仿射联络的指数映射的基本知识。

Proves by matrix technique and ways that affine Unitary groups have double transition on the affine maximal and deseribes the total isotropic subspaces over affine Unitary geometry and their orbits and the use of affine maximal and total isotropic subspaces to construct several classes association scheme and PBIB designs, and the calculation of all parameters as well.

利用矩阵的技巧和方法，证明了仿射酉群双可迁地作用在仿射酉几何中的仿射极大全迷向子空间上，并且给出了轨道的明确表示。作为该理论的一个应用，利用仿射酉几何中的极大全迷向子空间的全体作为处理集构作了一个多个结合类的结合方案和PBIB设计，并计算了所有的参数。

Description and recognition of plane has been processed depend on the geometry model of continental group and affine group anciently, with the development of the computer vision application, people attaches importance to the investigation of the perspective invariants, thus the investigation of perspective invariants gradually become an important problem in the computer vision.

以往人们对曲线的描述和识别大都是在欧氏群和仿射群的几何模型下进行的，近几年随着计算机视觉应用的发展，射影群下不变量的研究开始受到人们重视，所以射影变换下几何不变性的研究是计算机视觉中的一个重要的研究课题。

Symplectic group research is enlarged in the fi nite field to the affine Symplectic group by studying the transition of affine Symplectic group.

把有限域上的辛群的研究推广到仿射辛群并对仿射辛群的可迁性进行了研究。

They include:collinearity--an invariance under the projective transformation group;Parallelisminvariance under the affine transformation group;the direction of angles--aninvariance under the rotation transformation group.

这些几何不变性质包括共线性——在射影变换群下的不变性；平行性——在仿射变换群下的不变性；角的方向——在欧氏平移变换群下的不变性。

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

Thismethod adopted affine transformation model and a Lie derivative-based analytical algorithm.We introduced the process and characters in extracting information of biological visionsystem, studied the feasibility of the generalized Gabor function used as receptive fieldfunction in extracting information and analyzed affine transformation group and Liederivatives. Finally, we deduced the mathematical denotation for Lie derivatives, i.e. theinfinitesimal generator of the geometric distortion in affine transformation.

对生物视觉信息提取的过程及特点进行了介绍，其中主要研究了广义Gabor函数作为感受野函数提取初级视觉信息的可行性；对仿射变换作为外界图像信息在视觉成像系统上的投影模型的原理进行了初步讨论；对Lie变换群微分算子用于提取仿射变换不变量的分析方法作了剖析，并推导了该方法中关键部分——仿射变换Lie微分算子的具体表达式，也就是几何变形无限小微分算子的计算表达式，使下一步编程实现该方法成为可能。

In this paper we define the concept of Projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. We prved that if M be a complete projective Blaschke n-sphere and its universal covering manifold is isometric to a complete (n+1) dimensional parabolic, elliptic or hyperbolic affine hypersphere, then M is a quotient space of E^n, S^n or D^n by a isometric subgroup of its corresponding spaces.

在这篇文章中我们定义了射影Blaschke流形的概念，将等仿射微分几何的理论推广到了射影Blaschke流形，并证明：如果n维完备射影Blaschke 超球面 M 的通用覆盖流形分别是完备的抛物型、椭圆型或双曲型仿射球，则M分别是n维欧氏空间、n维超球面或n维单位圆盘关于各自空间的一个等距离散子群的商，从而对完备射影Blaschke 超球面进行了分类。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐