集代数

In chapter 2, the concept of ""isolated point"" is defined, whose influence on algebraic structure of rough set is demonstrated.

孤点不会位于任何粗糙集的边界上，它对粗糙集的代数结构产生特殊影响。

Finally, the equivalence properties between Boolean matrix representation and algebra representation of attribute reduction are proved.

建立了布尔矩阵与逻辑方程组的解和决策表中的属性集之间的关系；然后在此基础上给出了决策表中的粗糙集理论的布尔矩阵表示；最后证明了属性约简在布尔矩阵和代数两种不同表示下是等价的。

Chapter one: Provide the simple introduction to basic conceptions and properties used in the article about MTL-algebra; prove the set of all the filters form a complete distribution lattice in MTL-algebra; Discussion some property characteristics of Boolean filter, at the same time introduce the conceptions of positive implicative filter and obstinate filter, receive some properties of them, discuss the relation between the important filters and their equivalent condition.

第一章：对文章中用到的关于MTL-代数的基本概念和性质给出简单的介绍，证明了MTL代数中的全体滤子之集构成一个完备的分配格；讨论了布尔滤子的一些性质特征，同时引入和固执滤子的概念，得到它们的一些性质，探讨了几类重要滤子之间的关系。

Zadeh put forward, make MTL-algebra"s filter conception fuzzified, provide the conceptions and properties of fuzzy filter, obtain the structure of all fuzzy, filters, prove that the set of all fuzzy filters forms a complete distribution lattice; Provide several fuzzy Boolean filter"s equivalent forms, introduce fuzzy positive implicative filter, fuzzy obstinate filter and fuzzy ultra filter, discuss some property characteristics and terms that transform each other under certain terms to obtain them.

Zadeh提出的模糊集思想使MTL-代数的滤子概念模糊化，给出了Fuzzy滤子的概念和性质，得到了全体Fuzzy滤子的结构，证明了全体Fuzzy滤子之集构成完备的分配格；给出了Fuzzy布尔滤子的若干等价形式，并且引入了Fuzzy正蕴涵滤子，Fuzzy固执滤子和Fuzzy超滤的概念，得出了它们的一些性质特征以及在一定条件下之间相互转化的条件。

Random sets ; Data fusion ; Fuzzy sets ; Conditional event algebra

随机集；数据融合；模糊集；条件事件代数

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

The study of lattice-valued propositional logic system based on lattice implication algebra.On the bases of previous study, by using the concepts and methods of T algebras we established the lattice-valued propositional logic system LP , whose truth values domain is a lattice implication algebra, and discussed systematically the semantical and syntactical properties of LP , proved the soundness theorem 、consistency theorem、deduction theorem and the decidability of validity of the system when the truth values lattice is finite. We also discussed the relationship between the α-theorem of some premise, say A, and the closed sets that contain A.

本文在前人研究工作的基础上，利用T代数的概念与方法，建立了真值取于格蕴涵代数的格值命题逻辑系统LP，对它的语义及语法性质进行了较系统的研究，得到了它的可靠性定理、协调性定理及演绎定理等，证明了值格有限时系统"有效性"的可判定性并讨论了某一前提A下的α定理与包含A的闭集之间的关系。

In chapter 3, we give a unifying proof for some known difference sets by using Gauss sums, and we construct a new family of divisible difference sets.

在第三章中，我们用Gauss和给出了几个已知差集的统一的代数证明，它们原有的证明要么是用组合设计的方法，要么是用很技巧性的计数方法得到的。同时我们构造了一族新的可分差集。

The article applies the multivector algebra which is isomorphism with the real Dirac algebra in the real space-time adopted by Venzo de Sabbata to the contact number of set pair analysis, and consequently, t...

试图将VenzodeSabbata教授所采用的与Dirac代数同构的实时空中的多重向量代数应用于集对分析中的联系数，从而相应地推广了联系数的范畴。

For detail,we studied the Incidence Algebra I defined by finite Partially Ordered Set X,and sheaf F based on the topology T_x defined by the partial order;By studying the relation between finite module category mod I and the sheaf category Sh_x A,we proved that they are equivalent.

特别的，对给定的有限偏序集X确定的Incidence代数Ⅰ，及由X的序关系定义的拓扑结构T_X上的层F，通过考查有限模范畴modⅠ与层范畴Sh_XA之间的关系，证明了Incidence代数上的模范畴与层范畴的等价性。

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。