仿射空间

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。

That is that information processing of neural networks is viewed as the composition of the two steps: field organization and field action, in which, field organization transformation converts input pattern into relevant structure representation, extracting the underlying architecture features and forms a architecture representation in action transformation space; The field action transformation converts the features representation into expected output. In strategies, we use the dual affine coordinates in dual flat manifold as way of representation of field organization system and field action system, which established a theoretical framework of analysis the coupling mechanism of information processing from the view of point of structure representation and model generation.

在具体人工神经网络结构描述的策略上，利用对偶流形空间上的对偶仿射坐标概念分别表示场组织变换系统和场反应变换系统，建立起从问题的结构表示和模型生成两种观点来分析信息处理的理论框架；分析了有监督和非监督学习人工神经网络模型在神经场变换机理下的形式化描述。

The nonlinear mapping is realized by modelling the Local Generative units in the input space and a Global Affine transformation in the feature space.

这个非线性映射是由在输入空间中建立局部生成单元模型并且在特征空间中构建全局仿射变换来实现的。

3D reconstruction is one of the most challenging problems in computer vision. This project uses CAD model to increase the accuracy,robustness and speed of 3D reconstruction and five different works are conducted: 1 research on space curve 3D reconstruction method based on high curvature point nad turning point; 2 free-form curve 3D reconstruction based on B-spline and BURBS; 3 Active surface affine reconstruction based on single frame; 4 Matching and reconstruction of 3D sparse points; Data fitting method based on the iteration of nearest point.

三维重建是计算机视觉中公认的难题，本项目使用CAD模型来提高三维重建的精度、稳健性和速度的思路，围绕着空间曲线和曲面的三维重建和匹配开展了以下五个方面的研究：1）基于高曲率点和拐点分割的空间曲线三维重建方法研究；2）基于B样条和NURBS表示的空间自由曲线三维重建方法研究；3）基于单帧图像的有源曲面仿射重建；4）三维离散数据的匹配与重建；5）基于迭代最近点的数据拟合方法。

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。

The author also investigates Geo~coordinate transformation and similitude/affine transformation. Having accomplished the design of functions of spatial reference system, the author defines and designs the interfaces, component classes and then implements the component framework.

研究了关于大地坐标系转换和平面坐标的相似和仿射变换理论，在完成空间参照系统的功能设计的基础上，定义了空间参照系统的接口和组件对象，并设计和实现了这一系统。

For example, a line is affinely infinite while an oval space curve is affinely finite.

如空间中一条直线是仿射无限的，而一条卵形曲线是仿射有限的。

This chapter provides a mathematic model for the transformation between two images obtained from the same scene. Based on pin-hole camera model, the relationship between the coordination of two images is discussed using two camera models, and it is proved that geometric relationship of two images obtained from one scene satisfies affine transformation.

论文在透视投影成像模型基础上，用两个不同相机在不同位置对空间中同一点成像，推导出对应点在不同图像中像素坐标之间的解析表示形式，证明了像素坐标之间满足仿射模型，同时分析了图像之间满足仿射模型时应具备的条件。

This chapter provides a mathematic model for the transformation between two images obtained from the same scene. Based on pin-hole camera model, the relationship between the coordination of two images is discussed using two camera models, and it is proved that geometric relationship of two images obtained from one scene satisfies affine transformation.

论文在****投影成像模型基础上，用两个不同相机在不同位置对空间中同一点成像，推导出对应点在不同图像中像素坐标之间的解析表示形式，证明了像素坐标之间满足仿射模型，同时分析了图像之间满足仿射模型时应具备的条件。

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