明了

Since bounded closed sets in infinite dimensional space are notcompact generally,in order to employ Horn's fixed point theorem the compactness of operator Pis initially proved in section 3 in this chapter.

由于无限维空间的有界闭集一般不具备紧性，为了应用Horn不动点定理，我们先证明了Poincare算子P的紧性。

Finally,an example of comparative analysis shows that the proposed method is effective and feasible.

最后的算例对比分析说明了算法的可行性和有效性。

Whether it was the heart which dictated this system of complaisance and humility adopted by our Rebecca, is to be proved by her after history.

至于丽贝卡表现出来的谦虚有礼是否是出自内心的行为，我们只有等待时间来证明了。

The author also changes theproportion of Fe~(3+)、Cu~(2+) in total ions to study the complementariness of Fe~(3+)、Cu~(2+) in thesystem and proves that the replacement of the single catalytic ions with the complicatedSystem Fe~(3+)/Cu~(2+)/H_2O_2 has a good ability of the ability of counter assault against thechanges of pH value.

通过改变Fe~(3+)、Cu~(2+)在总离子中的不同比例，研究了Fe~(3+)、Cu~(2+)在体系中的相互补充、相互促进的作用，证明了用Fe~(3+)／Cu~(3+)／H_2O_2复合体系代替单一的催化离子能有效的对pH的变化起到很好的抗冲击的作用。

The article analysed economy of complementary motion function and negative function, explained complementary to economy function has the way of the operation.

本文分析了经济互补运动的正功能和负功能，说明了对经济互补功能进行操作的途径。

It is proved that MADST belongs to NP complete class, thus can not be solved by some polynomial algorithm.

文中证明了MADST问题是NP完全问题，不能用有效的多项式算法求解。

Based four-level forecast model, this paper presented an improved complete graph algorithm and derived analysis formula of computational amount of algorithms to prove improvement in algorithm performance.

以四级预测模型为基础，提出改进的完全图算法，并推导出该算法计算量的解析式，从理论上证明了改进的完全图算法性能上的提高。

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。

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 show that the whole space IF~*(R, d_∞~* is complete metric space, and when K is a nonempty compact subset of R, the metric space IF~*(K,d~* and IF~*(K,d_p~* are complete.

我们证明了当K是R上的非空紧子集时，紧支撑包含在K中的所有区间值模糊数所成之集TG~*

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。