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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。

We introduce the notion of fuzzy-valued continuous function on a compact set K in a metric space, and discuss its properties; On this base, we study the uniformly d∞-convergence of a sequence of fuzzy-valued continuous function on K. We prove that the space of fuzzy-valued continuous functions on K, i.e. C(K, E1), is a complete metric space with respect to the metric D.

引入了定义在某度量空间的紧子集K上的模糊数值连续函数和水平连续函数的概念，讨论了它们的某些性质；在此基础上，研究了K上模糊数值连续函数列的一致d∞-收敛性，证明了K上模糊数值连续函数空间C(K， E1)关于度量 D 构成一个完备的度量空间。

We establish the equivalent integral equations to these problems, and prove that the defined operator is completely continuous.

建立了与这些问题等价的算子方程，并证明了所定义的算子是全连续的。

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。

At last, we give two simplified proof for the necessary lemma in order to prove the completeness theorem of PI resolving.

第二部分：基于均匀概率的思想，给出了Godel和Kleene三值命题逻辑系统中公式的真度理论。

Compared with Plotkin's work, a reduction closed CPS language is defined in which all continuations are explicitly expressed as functional encodings and it is simpler to prove both the soundness and completeness directions of simulation theorem.

与Plotkin的工作比较，工作特点在于，给出了一个CPS归约闭语言，该语言中所有继续都可以用函数形式表达，且模拟定理的可靠性和完备性方向证明更为简单。

Finally, we prove the frame completeness of DC with respect to the frame conditions as well.

最后，我们证明DC相对这些框架条件也是框架完全的。

Robots that mimic this complex group behavior could prove useful in a number of human applications.

机器人模拟这个复杂的群体行为，可以证明是有用的，在一定数量的人也是适用的。

Robots that mimic this complex group behavior could prove useful in a number of human applicati**.

模仿这种复杂的群体行为的机器人可以证明在很多人类应用中是有用的。

By mean of the method of upper and lower solutions, we will obtain a existence theorem like Kazdan-Warners. Using this theorem, we will study the vortex equation in holomorphic line bundle over complex manifold and prove a theorem of existence of Hermitian metric with a prescribed holomorphic section.

在本论文的最后部分，我们在紧复流形上讨论一类Kazdan-Warner型方程，用上下解方法得到了光滑解存在的Kazdan-Warner型定理，并将其用于研究全纯线丛的涡旋方程，得到了一个具有预定全纯截面的厄米度量的存在定理。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。