代数

The Laplace matrix is an active and important subject in Algebra Graph Theory. It is a discrete form of the Laplace operator on the compact Rimannian manifold acting on the graphs. It has been widely used in many fields such as Physics, Chemistry, Biology, Computer net science and Information theory ,etc. Some results on the Laplace matrix are given in this thesis.

本文主要研究了代数图论中的一个课题：单圈图的Laplace谱，它是黎曼流形上的拉普拉斯算子在图上的离散形式，Laplace矩阵在物理、化学、生物和计算机通信网络研究等学科中有着广泛的应用。

The compactness theorem of model theory has an extensive application in algebra.

模型论中的紧致性定理在代数中有很广泛的应用。

Also, I wrote the compiler for ALTRAN, a language and system for symbolic calculation.

同样的，我也写了ALTRAN语言的代数编译器，那是用于符号计算机的一种语言和系统。

In Chapter 4, we define the induction of divisors and prove the existence of Galgebras of complete induction; through the analysis of Mackey formula, we give an equivalent characterization of the relationship between Green correspondence and free projectivity.

在第四章中，我们定义了除子的诱导，证明了完备诱导的G-代数的存在性；通过分析Mackey公式，给出了Green对应和自由投射关系的等价刻画。

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。

A fuzzy conditional expectation with respect to sub σ-algebra of for a fuzzy random variable is introduced in the complete probability space, and the fact that such a fuzzy conditional expectation exists uniquely is proved and its some properities are discussed.

在完备的概率空间中引进一个模糊随机变量关于■的一个子σ代数■的模糊条件期望，并证明这样定义的模糊条件期望存在且唯一，还就其某些性质作了讨论。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

By defining restricted representation,we get the necessary andsufficient condition for all restricted representations of a restricted Liesuperalgebra to be completely reducible.

最后，通过定义限制表示，得到了一个限制李超代数的所有限制表示是完全可约的充要条件。

The details of proving the completeness theorem of formula system L~*, which is given by Prof. Wang, are reviewed, and the proving of strong completeness about L~* is analyzed and revised.

考察了形式系统*完备性的现有证明过程，并对其中所涉及的R0代数同构问题进行了研究，分析了关于*系统强完备性证明中的错误并给出了一个全新的修正证明。

Because Horn-clause logic theory is of significance in both respects of theory and application, We especially studied lattice-valued Horn-clause logic with truth-value in lattice implication algebra, and the soundness and completeness theorem have been proved.

经典逻辑中，Horn子句逻辑理论具有广泛的应用，因而，本文中特别建立了基于格蕴涵代数的格值-类Horn子句逻辑，并证明了可靠性和完备性定理，这为建立一类基于格值逻辑这种非经典逻辑的人工智能语言将产生重要的作用。

They go to town. Would you just ask them?

他们在城里你能问他们吗？

Ossein pretreated for a2 weeks period exhibited the maximum% yield incase of bone gelatin, while the yield from intact skin was higher than that realized incase of de-scaled skin.

预处理时间达2星期的骨胶原表现出最高的骨明胶百分产量，然而从未处理鱼皮中得到的产率比去鳞的鱼皮得到的要高。