数的几何

Without using Lie derivative and Lie bracket operation of differential geometry , we only use the algebra method to give a sufficient condition of single input exact feedback linearizable bilinear systems.

摘 要 研究了单输入的双线性系统的精确线性化及其鲁棒控制器设计问题，避免了用微分几何的李导数、李括号的复杂运算，只用纯代数的方法给出了一般单输入双线性系统精确线性化的充分条件。

The product rule and chain rule, the notion of higher derivatives, Taylor series, and analytical were introduced by Isaac Newton in an idiosyncratic notation which he used to solve problems of mathematical physics .

该产品的规则和链的规则，概念，更高的衍生物，泰勒级数，并分析介绍了牛顿的特殊符号，他用来解决问题的数学物理。在他的出版物，牛顿改写他的想法，以适应数学习语的时间，取代的计算几何无穷小的等价论点被认为是无可指责的。

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。

On the basis of HPLC analytical results, a reaction mechanism between chlorine dioxide and phenol had been proposed. The rate control step in the process of reaction was studied by using ab initio method. Opmital geometry of every species in reaction was caculated by the available gratient optimum software. The result of harmonic vibrational frequencies indicated that phenolate radical was a stable intermediale product.

根据对ClO〓氧化苯酚后的高压液相色谱图，提出了ClO〓与苯酚氧化反应的机理，并对反应机理中的速度控制步骤进行量子化学理论剖析，利用梯度优化软件计算了参加反应物种的平衡几何构型，振动频率分析的结果表明：酚氧自由基是稳定的反应中间体，利用ab initio计算软件计算了参加反应物种的总能量，酚盐负离子中的氧原子电荷密度，布居数和前线轨道。

The module of the brick and the presence of it's tectonic has provided good interpretation of the pure geometry form of the concrete of parliament house.

事实上，这些砖建筑和中心的混凝土国会形成了一种良好的印证的关系，砖的模数和建构关系所生成的形式很好的说明了国会主体建筑混凝土建筑的抽象几何形式。

Based on this information and the method of fuzzy identification, fuzzy belonging-functions and equations are derived for the low porosity and low permeability reservoirs of Silurian in the block.

根据毛管压力曲线和相对渗透率的分形几何公式计算孔隙的分维数；以储层测井信息所反应的储层地质特性为基础，利用模糊识别方法，建立了该区块志留系低孔渗储层测井信息的模糊隶属函数和隶属方程；所得隶属度的大小可以用来判断储层的所属类型。

The participants are interviewed one-to-one and the result shows that when students are conjecturing geometry, different ways of initial observational behaviors for picture cards appear, and that the behavior of collecting data is related to the whole amount and the correct rate of conjectures. Most of the students adopt the method of only observing one piece of diagram during the initial period of observation and are able to attain more correct and bigger amount of conjectures.

结果显示学生在进行几何臆测，对於图卡的初期观察行为会呈现不同的方式，而且该资料收集行为与学生能产生的全部臆测命题数和臆测命题正确率相关，多数的学生在初期观察时，采用仅观察一张图例的方式，而且可以获得更多且更正确的臆测命题。

Under the precondition of assuming the stock price did not following the famous geometric Brown law, and agents have no exact knowledge of the probability distribution for the uncertain economic shock and return rate perturbation, chapter five presents the uncertain dynamic models of portfolio choice and option hedging respectively. In this chapter, we define the H〓 norm of transfer function from disturbance input to control output as financial risk measurement, and investigate the risk-attenuating robust H〓 portfolio investment and option hedging strategies.

第五章在金融证券价格并非服从几何布朗运动，收益率波动和外部噪声扰动的统计特性未知的情况下，分别建立了金融经济领域证券组合投资及期权套期保值问题的动态模型，引入从扰动输入到评价输出传递函数的H〓范数作为金融风险的度量指标，运用鲁棒H〓控制技术，研究了抑制金融风险的动态证券投资和期权套期保值决策问题。

We once believed that such things as the growth patterns of tree branches, and the networks of tree roots, the contours of mountain chains, and the directional meanderings of rivers and streams were random, because that was the simplest of explanations.

……我们曾经认为树枝的生长模式、树根的分布网络、山脊的外形轮廓，以及河流的蜿蜒曲折都是随意产生的，因为这是最简单的解释。但随着分形几何（分形几何学fractal geometry，空间具有不一定是整数的维，而存在一个分数维数。

In order to disclosure the reason why the electrocatalysis activeness and selectivity droped after being used several hundred hours continuously, the x-ray diffraction, scanning electron microscopy and energy dispersive spectroscope have been used to characterize the surface condition variations of Monel metal. The results indicated: Monel metal belongs to the Cu-Ni alloy around the electrolysis experiment.And after being used for 600hr, the surface layer element composition and geometry distribution of the alloy changed, namely in the alloy the Cu element /which superficial free enthalpy was smaller,"concentrated" to the alloy surface,and formed one kind of marble structure microcrystallite.Thus the electrode surface becamed rough a

为了揭示蒙乃尔合金阴极在连续使用数百个小时后电催化活性剂选择性下降的原因，采用X射线衍射仪、电子扫描电镜和电子能谱分析仪对电解实验所用的蒙乃尔阴极材料在电解实验前后的表面状态进行了表征，结果表明：所使用的蒙乃尔合金阴极材料在电解实验前后均属于Cu-Ni合金，使用600hr后，由于表面层元素组成和几何排布发生了变化，即合金中表面自由焓较小的Cu元素向合金表面&富集&，形成一种大理石结构的微晶，表面粗糙、不均一，这是造成其对硝基苯电还原的催化活性及选择性随着使用时间延长而逐渐下降的主要原因，同时也为此类电极的修饰改进提供了方向。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。