集合

In this paper, firstly, it is stated that, an intuitionistic fuzzy sets is a L-fuzzy set, and a set of all intuitionistic fuzzy sets over X is a complete lattice.

首先指出一个直觉模糊集是L-模糊集且X上所有直觉模糊集的集合是一个完备格。

We have also shown that the collection of prime event structures on N can be endowed with the structure of a complete metric space, and in this space the collection of all universal homogeneous prime event structures is topologically large: it is the complement of a meager set.

我们也表明，集的主要事件结构对N可以赋予一个完整的度量空间结构，在该空间的主要活动是普遍均匀结构拓扑大：它是相辅相成的微薄的集合。

One of Hutchinson's basic results is: If {S〓,…, S〓} is a family of contract operators on a complete metric space, then there is a unique nonempty compact set K, such that K=〓.

Hutchinson的一个基本结论是：对于完备距离空间上的任一族有限压缩映射{S〓，…，S〓}，存在唯一的不变非空的紧集合K，〓。

The soundness and completeness theorem of this method were proved at last. 5. The a-automated reasoning method based on the a-resolution principle of LP was discussed, the author given a method to describe the set of simple generalized clauses (veriables and non-subregular 1 - IBSFs are only contained) by using a matrix, and translated the a-resolution of two clauses to column operations of this matrix.

最后，证明了该方法的可靠性和完备性； 5、对格值命题逻辑系统LP中基于α-归结原理的α-自动推理方法进行了研究，给出了用符号矩阵表示一类简单的广义子句集合(只含命题变元和非正则1-IESF广义文字)的方法，把α-归结原理转换成矩阵的列变换。

The soundness and completeness theorem of this method were proved at last. This part consists of the following points: 1. The properties of the indecomposable extremely simple form of LP were discussed, the theorem shown that every logical formula of LP was equals of a generalized conjunction normal form. 2. The method for judging a logical formula is a indecomposable extremely simple form or not was discussed, the necessary and sufficient conditions of a logical formula with not more than three implicative connective being a indecomposable extremely simple form was given. 3. The α-resolution fields of the indecomposable extremely simple form of LP were discussed, some elementary results were obtained. 4. The automated reasoning method based on the resolution principle of classical logic was discussed, the author given a method to describe the set of clauses by using a matrix, and translated the resolution of two clauses to column operations of this matrix.

二、关于格值命题逻辑系统LP中α-自动推理方法的研究 1、对LP中不可分极简式的性质进行了研究，证明了LP中任何一个格值逻辑公式等值于一个广义合取范式； 2、对LP中不可分极简式的判定方法进行了研究，讨论了含有不超过3个蕴涵运算的格值逻辑式为不可分极简式的充分必要条件； 3、对LP中不可分极简式的α-归结域进行了研究，得到了一些基本结果； 4、对经典逻辑中基于归结原理的自动推理方法进行了研究，给出了用符号矩阵表示子句集合的一种方法，把不同的归结过程转换成矩阵的列变换。

In this thesis, we will mainly do research on the novel scheme for Digital image Steganography, Digital Image Secret Transmission in network and the development of the information hiding device for application. The main contributions of this thesis are as following: The novel conversion method for mapping image to complex number is proposed, and the plus, minus, multiply and complex conjugate operation of image are defined based on Positional number systems and complex number system. Following new results have been gotten: 1 The suitable complex number basis to be used to express integers is a big set. 2 Any image can be mapping into a one-to-one point. 3 Lots of image processing problem can be considered based on geometric theory.

在本论文中，研究工作集中在数字图像伪装算法的新模型、图像在网络中的加密传输的新方案和信息伪装设备的研发等三个方面，主要包括：基于位值制记数法和复数系理论，提出利用复数作为基底的数字图像新的表示方法，用复数运算定义了图像和图像间的"加"、"减"、"乘"、"共轭"等运算关系；得到理论结果： 1、能表示任何整数的复数基是很大的一个集合。2、任何一幅图像，都能和复平面上的一个点一一对应。3、可以将图像问题化归为平面几何问题处理。4、复数系下的图像表示适合用于信息伪装。

The result obtained by J.V.Neumann about the coherent states of unit lattice on complex plane constructing a set of complete states is generalized.

推广了J.V.Neumann关于用复平面上单位方格点的相干态构成完备态集合的结果(他们的结果相当于A=1的情形)。

More relevantly, it is doubtful that fulfilling any set of functions is conceptually sufficient for life.

更贴切地说，这是可疑的：完成任何功能的集合，就概念上充分于生命。

The market is where all insurance companies operate. Only by concertedly taking care of the market, building up the market and developing the market, and seeking mutua ...

市场是保险同业人赖以生存的基础，只有大家齐心协力爱护市场、建设市场、发展市场，集合各种形式所有制的保险主体共同发展，才能挖掘保险业潜力，为和谐社会建设贡献自己的力量。

The market is where all insurance companies operate. Only by concertedly taking care of the market, building up the market and developing the market, and seeking mu ...

市场是保险同业人赖以生存的基础，只有大家齐心协力爱护市场、建设市场、发展市场，集合各种形式所有制的保险主体共同发展，才能挖掘保险业潜力，为和谐社会建设贡献自己的力量。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。