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Also prove that every bounded linear approximately local Hilbert space representation of a abelian von Neumann algebra is a representation,every bounded linear approximately 2- local Hilbert space representation of a von Neumann algebra is a representation.

同时证明了交换von Neumann代数的有界近似局部表示是表示,每个von Neumann代数的有界近似2—局部表示是表示。

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。

Nothing, however, is capable of being universally communicated but cognition and representation so far as appurtenant to cognition. For it is only as thus appurtenant that the representation is objective, and it is this alone that gives it a universal point of reference with which the power of representation of every one is obliged to harmonize.

除了知识和属于知识的表象外,没有什么是可普遍传达的,因为如果知性和属于知性的表象只单纯是客观的,并且由此拥有了一个普遍的结合点,通过它所有人的想象力都被强制协调一致。

Based on the discussion about perceptional representation, natural language representation and scientific knowledge representation, it is showed that the constructive form has significant influence on the systematic function of representation and the basic aspects it possesses as a representative system.

通过对知觉表征:自然语言表征和科学知识表征三个系统的讨论,可以看到构造方式对表征系统功能的重要影响,以及作为一个表征系统所必备的一些基本方面。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上,使用非流形几何模型作为理想材料零件几何拓扑模型的基础,并在半边数据结构基础上,针对理想材料零件的非流形特征局限内部边界上的特点,给出了一个半面数据结构来表述零件的几何拓扑信息;对于理想材料零件的材料模型,本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手,将材料信息表述为(n-1)维单纯形,然后通过对三维几何区域的单纯剖分,以插值的方式表述零件材料分布特征;在此基础上,根据功能梯度材料零件分层制造中对CAD数据处理的要求,给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法;而对于文中所定义的理想材料零件,本文将其材料信息表述分解到细观和宏观两个尺度进行,首先给出了细观尺度上参数化的周期性功能细结构概念,以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料;把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组,以表达零件的细观材料特征;对于零件宏观的材料变化特征,则同样在几何区域单纯剖分的基础上,通过对细观尺度上周期性功能细结构控制参数的插值来完成;通过理想材料零件CAD数据处理的算例,验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上,使用非流形几何模型作为理想材料零件几何拓扑模型的基础,并在半边数据结构基础上,针对理想材料零件的非流形特征局限内部边界上的特点,给出了一个半面数据结构来表述零件的几何拓扑信息;对于理想材料零件的材料模型,本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手,将材料信息表述为(n-1)维单纯形,然后通过对三维几何区域的单纯剖分,以插值的方式表述零件材料分布特征;在此基础上,根据功能梯度材料零件分层制造中对CAD数据处理的要求,给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法;而对于文中所定义的理想材料零件,本文将其材料信息表述分解到细观和宏观两个尺度进行,首先给出了细观尺度上参数化的周期性功能细结构概念,以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料;把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组,以表达零件的细观材料特征;对于零件宏观的材料变化特征,则同样在几何区域单纯剖分的基础上,通过对细观尺度上周期性功能细结构控制参数的插值来完成;通过理想材料零件CAD数据处理的算例,验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

A problem of representation. In the 19th century, Courbet led fine arts to leap beyond representation of the visual forms into representation of social realities. Shortly after, in the field of literature, Lukacs posed a higher requirement for Realism: the duty of art is to give a truthful representation of the real world.

在此之前,关于艺术与现实的关系的思考一直停留在视觉层面,即再现的问题上,而库尔贝使美术从视觉再现意义上的真实走向了社会表征意义上的现实,之后,在文学领域中,卢卡奇对现实主义又提出了更高的要求:"艺术的任务是对现实整体进行忠实和真实的描写。"

Since representation of the subclass object starts out like the representation of a superclass object, the circle can always pretend to be a point — at the initial address of the circle's representation there really is a point's representation.

因为子类的表示开始于一个非常像其父类的结构,所以圆可以把自己伪装成一个点——圆的物理表示的地址的前面部分就是一个点的表示。

Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.

空间曲线是造型中最基本的几何元素之一,对其有效的表示是造型的基础,而特征参数化表示是其中一种包含语义信息的高层次表示,本文对空间自由曲线的特征参数化表示进行研究,建立了一种针织物线圈的特征参数化几何模型,采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系,并将该模型与能量极小化的方法相结合,得到了一种能较好地预测针织物缩水率的新模型,对随机选取的一些针织布缩水预测实验表明了算法的可行性。

Supported by the National Science Foundation of China, this thesis concentrates on the image sparse representation theories, methods and the image processing applications based on sparse representation. We make deeply study for the applications based on multiscale geometry analysis, theories of overcomplete sparse image representation and its applications, theories of sparse image representation via combined transforms and its applications.

本文在国家自然科学基金项目&联合基图像稀疏表示理论研究及其应用&的资助下,针对图像稀疏表示理论、方法以及基于稀疏表示的图像处理应用问题,重点围绕多尺度几何分析在图像处理中的应用、基于冗余字典的超完备图像稀疏表示理论及应用、组合变换图像稀疏表示理论及应用等内容进行了探索性的研究。

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The difference between him and the others forced me to be less partial.

也这是因为这种区别,让我在他和其他孩子之间没有偏爱任何人。

I decided to be frank in rejecting the proposal.

他说,他准备直率地拒绝接受这个建议

One downside: the iPhone doesn't have a built-in slot for a stylus.

不过,还有一个问题:iPhone没有内置的手写笔槽。