等价的

of transitive closure based on equivalence relation, method of maximum fuzzy spanning tree based on fuzzy graph, and algorithm Fuzzy C-Means based on partition are more deeply investigated. Respectively, this thesis proposes an algorithm for document fuzzy clustering based on methed of transitive closure and an algorithm for document fuzzy clustering based on methed of maximum fuzzy spanning tree. Moreover, FCM is particularly studied from data standardization method, metrics method, and selection method of initial clustering prototype.

较深入地讨论了基于等价关系的传递闭包法、基于模糊图论的最大树法以及基于划分的模糊C-均值算法，分别提出了基于传递闭包法的文本模糊聚类方法ATCFC和基于最大树法的文本模糊聚类方法ATCMT；重点从改变规格化方式、改变度量方式、改变初始聚类原型选择方式三方面对FCM算法进行研究。

Note that this completes the first Hexagon and as this equals 127months,shows why some campaigns will run 10years and seven months,or until they reach asquare of the Hexagon,or the important last angle of 45*.

如上所讲的那样，这样就结束了第一个六边形的循环，这可以等价于127个月，这就解释了为什么一段大行情会运行10年零7个月，或者直到价格达到了6边形的方形，或者重要的最近的45度角才结束。

Note that this completes the first Hexagon and as this equals 127 months , shows why some campa igns will run 10 years and seven months , or until they reach a square of the Hexagon ,or the impor tant last angle of 45*.

如上所讲的那样，这样就结束了第一个六边形的循环，这可以等价于 127 个月，这就解释了为什么一段大行情会运行10 年零7 个月，或者直到价格达到了6 边形的方形，或者重要的最近的45 度角才结束。

The dissertation includes:◆General research of canonic VSC The contents are following: the cause and eliminating approach of chattering; Invariance property; the relation between VSC and high-gain linear feedback control.

讨论了产生不变性的条件；揭示了VSC与大增益线性反馈控制的等价关系；提出了用切换面邻域内的稳定性来分析抖动起因的方法。◆研究了不确定系统的VSC设计分别针对满足匹配条件但集总不确定部分上界不确知、不满足匹配条件但满足广义匹配条件、不满足广义匹配条件等情况，研究了其VSC设计问题。

We get the sufficient and necessary conditions for the reaction process to be stochastic monotonic under certain conditions e.g.

第三部分推广了[29]中的结果，对较广的有限系统证明了若干泛函不等式与底过程对应的泛函不等式的等价性以及不等式常数之间的关系。

We also provide the ergodic convergence theorems for semitopological nonexpansive type mappings in the reflexive Banach in Chapter 3. By this theorem we can get the main results in [13]14[15][16], and we should notice that their methods do not extend beyond Lipschitzian mappings.

本文第三章在自反的Banach空间中给出了一般拓扑半群上渐近非扩张型半群的遍历收敛定理与其殆轨道情形的等价性，从而利用本章中的定理可以直接推得文[13][14][15][16]中的主要结果。

In addition, we improve Nivens method and our new method to solve the equation more quickly.2 Complete Solution Structure: We obtain that the whole solutions of real quaternionic polynomial equation are just composed of some quaternion equivalence classes and some isolated points.

另外，从新方法及四元数带余除法理论出发，进一步改进了新方法和Niven的传统方法。 2解的完整结构：由求解的新方法得到四元数多项式方程全体解的完整结构为四元数等价类与孤立点的集合，以往的结果成为其自然推论。

In 1987, the notion of a splicing system was introduced by Tom Head in [3] as a mathematical model of restriction enzyme digestion and subsequence religation in the recombination of DNA molecules.

摘要1987年，Tom Head发表了一篇论文，引入拼接系统的概念作为限制酶与DNA作用、进行DNA重组的数学模型。更重要的是，他还证明正则语言中的一类——严格局部可测语言，与拼接语言的子类——持续拼接语言等价。

During studying different levels potential yield of main cropping modes, bring forward the conception of "equivalence potential yield", and this conception made potential yield of different crops comparable and transpositional. So we can analyze the main factors influencing mostly different levels potential yield of monoculture and main cropping modes for different regions.

在对种植模式生产潜力的研究过程中提出了等价生产潜力的概念，以解决不同作物间生产力的横向比较与换算问题，同时注意到单一作物与种植模式间的生产潜力影响因素，并量化分析了这些主要的影响。

Connectedness and δ—connected component are denned. Some properties and equivalent conditions about δ—connected axe given. It is respectively discussed that δ—connected L—topological spaces are abroader than connected L—topological spaces.

定义了L-拓扑空间的δ-连通性和δ-连通分支的概念，讨论了它们的一些性质，给出δ-连通的一些等价刻画，证明了δ-连通L-拓扑空间是比连通L-拓扑空间更广泛的一类空间。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失