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In order to overcome the technological difficulties encountered in the course of insulation fault diagnosis on the base of dissolved gases analysis, several kinds of mathematic models and actualized methods are brought forward to improve the reliability and veracity of fault diagnosis of transformers. The research works are shown mainly as followings:1 A modified fuzzy multi-criteria method is brought forward for insulation fault diagnosis of transformer. Furthermore, a new method for insulation fault diagnosis is proposed on the base of fuzzy multi-criteria together with rule reasoning. With fuzzy diagnosis in the method, fault reasons are filtrated and then the reasons in low probability are prohibited, Moreover, the left reasons are testified by using rule reasoning and then final concludes are drawn in much less misjudge probability and better results.2 On the base of geometry characteristics of C- partition to sample set of DGA data of transformer, a method is put forward to compute effective radius of neighbor field of a sample, number of clusters and values of initial centers. Moreover, the fuzzy C- means cluster model with adaptive weight is brought forward in the first time and then the fault classifier is designed for insulation fault diagnosis of transformer.3 According to the weakness of the degree of gray of gray incidence, a new formula to compute DGI is put forward and then incidence order criterion is ascertained. Moreover, a new DGI model for fault diagnosis is proposed according to the further analysis to relationship between fault reason and content of oil dissolved gases of transformer.

为解决在应用油中溶解气体分析方法（Dissolved Gases Analysis，简称DGA）诊断变压器内部绝缘故障时所遇到的主要技术难题，论文提出了用于提高变压器故障诊断准确性和可靠性的数学模型及实现方法，主要研究工作如下：1）提出了一种改进的变压器绝缘故障诊断模糊综合评判方法；进一步提出了将模糊综合诊断与规则推理相结合进行绝缘故障诊断的方法，该方法采用模糊推理对故障原因进行"过滤"，滤掉可能性极小的原因，然后进一步利用规则推理验证剩下的可能原因，得出最终结论，大大减少了误判比率，获得了较好的效果。2）根据以变压器DGA数据为特征量的样本空间的c-划分几何特性出发，提出了一种求取样本有效邻域半径和聚类数及聚类中心初值的方法，在此基础上，首次提出了一种自适应加权的变压器绝缘故障诊断的模糊c-均值聚类模型，并设计出故障分类器。3）针对常用灰色关联度的不足，提出了一新的灰色关联度计算公式及确定关联序的准则；并在此基础上，通过深入分析变压器发生绝缘故障时的原因与油中溶解特征气体含量的关系，建立了一种新的故障诊断灰色关联模型；通过实例分析证明，该方法能有效地诊断出变压器绝缘故障及故障部位，大大提高了诊断的准确性。

In Chapter 3, we discuss the other orthogonalities in in Banach space, and give some properties of them. The emphase of the chapter is to study the relations of Birkhoff orthogonality, Isosceles orthogonality and Pythagorean orthogonality, and it is proved that if one of these induces another, then the space is an inner product space.

第三章研究其它几种正交性问题，讨论Birkhoff正交性、Isosceles正交性与Pythagorean正交性之间的关系，证明了：如果这三种正交性的任一种都蕴含另一种，那么此空间就是内积空间。

Isolates from watermelon-growing areas were classified into 3 races like race 0, race 1 and race 2 which were 8 (17.4), 30 (65.2), and 8 (17.4%), respectively. Pathogenecity of race 0 isolates are weakest which only make Sugar Baby susceptible; isolates of race 1 are intermediately pathogenetic, they make Sugar Baby and Charleston susceptible Gray but Calhoun Gray resistant; isolates belonging to race 2 possess the strongest pathogenecity, which make 3 hosts susceptible. Isolates of race 0 mainly distribute over the central and southern Hebei province, whereas race 2 cover the middle and north of Hebei, isolates of race 1 exist in the whole watermelon-growing areas in Hebei province.

根据鉴别寄主对供试菌系的抗感反应，将46个西瓜枯萎病菌系划分为0号、1号和2号3个不同的生理小种，分别包括8，30和8个菌系，占供试菌系的17.4%、65.2%和17.4%；0号生理小种菌系致病性最弱，仅使品种Sugar Baby感病，以冀中和冀南居多；1号生理小种菌系致病力中等，使鉴别寄主Sugar Baby和Charleston Gray感病，而使Calhoun Gray抗病，分布在整个河北省西瓜种植区；2号生理小种的菌系致病力最强，使3个鉴别寄主均能感病，主要分布在冀中和冀北。

Indices~ mP 0 and 1 were fitted, respectively, with the heat of formation,ionic hydration energy, lattice energy ,internuclear distance bond lengthof 20 kinds of alkali halides; with the lattice energy of 20 kinds of alkali-earth metal halides,with the ionic hydration heat of 51 kinds of metals, and with the ionic standard heat of formation of 80 kinds of i.

用mP的0和1阶指数分别与20种碱金属卤化物的生成焓ΔfH m、离子水化能ΔhG m、晶格能U1、气态碱金属卤化物核间距R0，20种碱土金属卤化物的晶格能U2，51种金属离子水合焓ΔhH m关联，拟合的回归方程的相关系数为m和80种离子标准生成焓ΔfH 0.9753(0.9834)、0.9761(0.9816)、0.9964(0.9986)、0.9967(0.9967)、0.9789(0.9890)、0.9901和0.9805，满足优级或良级标准。

Based on the isoperimetric graph partitioning method, we propose several practical segmentation algorithms. The first is the iterative two-way cut method which can segment an image into pieces with particular characteristics each other by iteration. The second is simultaneous K-way cut method which divides the image into K parts synchronously. The last is an interactive method separating objects of interest from the background by the user's input specifying the object of interest manually.

基于等周分割方法，我们提出了几种实用的分割算法：第一种是迭代2分方法，它通过迭代的方法将图像分割成各具特征的小区域；第二种是同时直接K分法，同时将图像分割成K个部分；最后一种方法是交互分割法，它依赖人工输入来指定所要分割的感兴趣目标，将图像目标从背景中分离出来。

I.sanguinea and I. typhifolia have thin seed capsules and compact endosperms. The seed testa of I, lactea is thick and keratose.

这三个种均为湿生植物：溪荪、北陵种皮较薄，但胚乳较为致密，为中生种类：马蔺种皮厚，胚乳硬实，紧紧包被种胚，具有旱生植物的特征。

By this reaction, an aldose is converted into another aldose and the corresponding ketose, and a ketose is converted into the corresponding two aldoses.

单糖的异构化涉及羰基和相邻近的羟基，通过这个反应，一种醛糖转化为另一种醛糖，和相对应的酮糖，一种酮糖转化为相对应的两种醛糖。

Amphibians recorded were 8 species in 5 families, and reptiles were 13 species in 8 families. Among these, Guenther's frog, Chinese cobra, and Taiwan banded krait are in the wildlife conservation species list of Taiwan.

其中陆栖哺乳类共5科11种，两生类5科8种，爬虫类8科13种，保育类野生动物有贡德氏赤蛙、眼镜蛇、雨伞节(Bungarus multicinctus multicinctus)等3种。

It is a tool, a means to learn the "content" of the material one is reading. In other words, a foreign langue, just like one's mother tongue, is a system of symbols for communication.

一它是一种工具－一种认知其他「实体内容」的一种工具或手段，也可以说，它是本国语文以外的另一种专供传播用的「符号」。

Leaper said that studies that used this measure of talkativeness tended to find less difference between men and women than studies that looked at how much time people spent talking.

里波说，有两种调查，第一种就是采取上述健谈衡量标准的调查，着眼点在于每天究竟使用多少词汇，而第二种调查的着眼点则在于每天究竟用多少时间说话。在探讨男女之间差异的时候，以这两种调查相比，就会有这样的倾向，即前者调查出的差异，比后者调查出的差异要少。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。