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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。

On the basis of Earth surface space using reference ellipsoid as height basis, map space using Gauss-Kruger projection plane as height basis, a viewpoint is proposed that map projection actually establishes corresponding relationship between the height bases of two different spaces above. From the viewpoint of projection and visible representation, the relationships among earth surface space, RS imagery space and map space are analyzed; the differences among different representations of earth surface space are identified theoretically; virtual reality is applied to the representation of land surface space, and a prototype of real 3D virtual reality system based on spatial information is developed. By means of digital simulation, virtual reality representation of land surface space in visual image space is realized.

在以参考椭球面为高程基准面表征地表空间、以高斯-克吕格地图平面为高程基准面表征地图空间的思想基础上，提出了地图投影实质上是建立两个空间的高程基准面之间关系的观点；从投影和可视表达的角度，分析了地表空间、遥感图像空间、地图空间之间的关系，从理论上区分了对地表空间的不同表达方式之间存在的差别；将虚拟现实技术应用于地表空间的表达，研制了空间信息三维虚拟现实系统原型，利用数字模拟技术在视像空间实现了对地表空间的真三维虚拟现实表达。

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。

For example, U-space is uniformly regular and which makes it has fixed point property, U-space is uniformly non-square and thus super-reflexive, uniformly convex space and uniformly smooth space are U-spaces, and an Banach space is an U-space iff its dual space is U-space, etc. In1990s, a lot of work had been done on U-space theory, e.g., Tingfu Wang and Donghai Ji introduced the concepts of pre U-property and nearly U-property. Under the structure of Orlicz space, they made systematic investigation of these properties, and gave the criteria for an Orlicz space to have U-property.

U-空间具有一致正规结构进而具有不动点性质；U-空间是一致非方的，进而也是超自反的；一致凸空间和一致光滑空间是U-空间；Banach 空间为U-空间的充要条件是其对偶空间为U-空间，等等。20世纪90年代，国内外学者对U-空间理论做了很多工作，王廷辅，计东海等人先后引入了准U-性质与似U-性质的概念，并在Orlicz空间框架下对有关性质进行了系统研究，完整给出了Orlicz空间具有各种U-性质的判据。

By describing Pythagorean theorem, the first time-space view explain the plane-line thought which impacts human's thinking manner; the second time-space view is absolute time-space theory of Newton and three-dimensions space-time view intersected by space-time; the third space-time view is curve space-time view which is generated from Einsteinian relative theory. The fourth space-time view is the directional, irreversible entropy time-space thought; the fifth time-space view is dense time-space view of cracked fractal generated from chaos-fractal theory.

第一时空观是通过对勾股定理的描述来说明影响人们思维方式的平直时空观；第二时空观是牛顿的绝对时空理论，是时空分割的立体三维时空观；第三时空观是爱因斯坦的相对论理论所带来的弯曲时空观；第四时空观是具有方向不可逆的熵时空观；第五时空观是混沌与分形理论所带来的破碎分形的稠时空观。

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。

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。

In this paper,the nonstandard analysis theory is used for inducing a metric space by a Loeb measure space.On this basis,a metric space is induced by a internal finitely additive measure space.The close relationship between the metric space induced by a Loeb measure space and the metric space induced by a internal finitely additive measure space is illustrated with the concepts and some properties of Loeb measure.Then,some properties of the metric space that induced by a internal finitely additive measure space are studied.In the first two chapters,we first Succinctly present the origin,development and research states of the nonstandard analysis.Then,the theoretical foundation of nonstandard analysis as well as the axiomatic nonstandard analysis are given.Finally, the nonstandard model and the saturation model are discussed,as well as some natures of the nonstandard model and several equivalent conditions of saturation model are given.

本文利用非标准分析理论，在由Loeb测度空间导出度量空间的基础上，由内有限可加测度空间导出了度量空间，并借助Loeb测度的概念和若干性质证明了由标准的测度空间导出的度量空问和由内有限可加测度这个非标准的测度空间导出的度量空间有着密切的关系，在此关系的基础上还研究了由有限可加测度这个非标准的测度空间导出的度量空间的性质在第一、第二章里，我们首先简单介绍了非标准分析的产生、发展及研究现状，接着给出了非标准分析的理论基础以及公理化的非标准分析，进而讨论了非标准模型和饱和模型，并给出了非标准模型的一些性质和饱和模型的若干等价条件。

Regarding (6) type, when tradition Time variable t is two spatial vectors (+ psi 1i) and (- psi 2j) Crossed products v also is not 0, it (x1, x2, x3) differs 90 compared to on speed with the three-dimensional space in the space by the pure imaginary number attribute, I=e^I pi, therefore it Number space has in the physical property with the dot product constitution the difference, because Crossed products psi 1i (X psi 2j extremely small visible it is equal to zero under the conventional speed, but is very big in the object movement speed time, Crossed products psi 1i (X psi 2j in the physical quantity and for the quantum mechanics in may not to the easy quantity, its space and the conventional space is different, the performance is intrinsic or the interior space If the definition vector (+ psi 1i) and (- psi 2j) the dot product constitutes the three-dimensional space (x1, x2, x3) is exterior space, but the three-dimensional space which (+ psi 1i) and (- psi 2j) Crossed products constitutes by the vector is the internal space, contrasts its component

对于⑥式，传统时间量t为两个空间矢量(+ψ1i)与(-ψ2j)的叉积比上速度v且不为0，其与三维空间(x1，x2，x3)在空间上相差90度以纯虚数表征，I=e^Iπ，故其与点积构成的实空间有物理性质上的不同，因为在常规速率下叉积ψ1i(Xψ2j非常小可视其等于零，而在物体运动速率很大时，叉积ψ1i(Xψ2j之中物理量与则为量子力学中的不可对易量，其空间与常规空间不同，表现为一个内在或内部性空间。若定义矢量(+ψ1i)与(-ψ2j)点积所构成的三维空间(x1，x2，x3)为外部空间，而由矢量(+ψ1i)与(-ψ2j)叉积而构成的三维空间为内部空间，对比其分量

Bob Eckert has been chairman and chief executive of Mattel for eight years.

美泰董事长兼首席执行官鲍勃·埃克尔特在任已8年。

The outlook for honors and disgraces carries on and surpasses the traditional outlook for honors and disgraces theoretically, and carries on and develops the theory of construction of socialist mora...

社会主义荣辱观的提出在理论上是对传统荣辱观的一次继承和超越，是对社会主义道德建设理论的继承和发展，在实践上有利于形成良好的社会风尚。