几何基础

Firstly, illustrate the fundamentals (differential-integral optimizing theory) of the category of algorithms briefly in the sight of differential and integral calculus. Then two examples of the category of algorithms are listed.

首先从函数逼近的角度论述了数值积分与全局最优化的关系，随后从微积分的基本原理和定积分的定义出发对该类算法的几何意义和数学基础作了简要论述；在此基础上给出了该类算法的几个具体实现。

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。

Firstly, This paper processes geometry filtration based on character of orbit's apogee and perigee after orbit model is analyzed and based. Secondly Space Debris is separated into two kinds, coplanar and not coplanar according as location interrelation of target and debris. In Dynamic filtration's processing, considering prediction time limit and orbit perturbation, secular effects which have increaser effect is considered so that some need catching danger time point is appeased, some law about time when target and debris pass intersectant line each other is inferred, when debris and object are in different plane and some similar law also is inferred otherwise. The time list is arithmetical progression. These laws can improve calculation efficiency remarkably; Lastly orbit predict is a course approaching least distance. Danger time point in the last step become beginning time point from which debris and object's position and velocity are calculated by SXP4 Model which is an analytic model.By result, determine that relative movement trend is closer or apart, farther calculate the interval apart from time when predictive least relative distance occurs. Least relative distance and time when least distance occurs is calculated finally. It is a fast approach course adopting varied interval.

本文在分析、建立轨道摄动计算模型的基础上，首先采用基于轨道远、近地点特征对大量编目在册的空间碎片进行初步几何静态筛选，然后根据碎片与目标轨道面的相对位置特点把碎片分为异面与准共面两种情况以进行动态筛选，在筛选过程中考虑到预报时限长度和轨道摄动影响，引入了轨道摄动中具有积累效应的长期项以满足危险时间点的捕捉要求，利用了长期项摄动变化线性的特点导出了碎片与目标异面情况下各自过交线的时间序列成准等差数列的规律性和准共面情况下类似的规律性，从而显著地提高了前期轨道筛选的计算效率；最后对剩余危险碎片和目标飞行器利用SXP4轨道预报模型在前期轨道筛选的基础上以各个危险探测时间点为预报的时间起点，并根据预报计算结果，分析目标和碎片在该时间点的运动趋势是相互远离还是相互接近，推出预计最小相对距离发生时刻相对此刻的时间长度，得到其随时间变化的局部最小相对距离以及危险距离发生的时刻和相对速度，这是一个采用变时间步长、快速逼近最小相对距离的过程。

This article first explains the content and the theoretical basis of the Geometers Sketchpad and the integration of geometry teaching, and then analyzed the feasibility and the advantages of the Geometers Sketchpad integrating with teaching, and then put forward what principles and measures should be noted in the integration of teaching, and finally gave some specific cases.

本文首先针对几何画板与平面几何整合教学的内涵和理论基础进行分析，接着分析了几何画板整合教学的可行性及其优势，然后针对整合教学提出应注意的原则及措施，最后对整合教学给出了具体案例。

This paper analyses the different influence on the fundamental matrix by the different matched points in images and theweighted factor is introduced to express the distance between the matched point and the epipolar line which has the obvious geometry meaning.

分析了图像匹配点对基础矩阵的不同影响，引入具有明显几何意义的匹配点到对极线的距离作为匹配点的加权因子，将匹配点集合看作随机变量并将加权因子作为匹配点的概率分布。在此基础上对原始图像数据进行归一化处理，利用8点算法得到基础矩阵。

The distribution, host and geometric shape feature of vein-bearing fault structural belts, auriferous quartz and gold orebodies in gold orefield, ore-control regularity of Xiao qinling gold deposit are briefly discussed.

本文简要叙述了小秦岭金矿田内含脉断裂带、含金石英脉和金矿体的分布和赋存特征及其几何形态特征，探讨了形成机理，提出用统计分析、趋势分析和自相似性分析为一体的累集式几何解析原理进行深部预测找矿；同时在仔细观察、分析的基础上，总结了小秦岭金矿控矿规律。

To obtain more uniform temperature distribution and relative lowest temperature over cross section of the rotor, on the basis of test data of a given example of a 150MW turbo generator with air coolant, numerical solution of two dimensional modelling equations of air turbulent flow and heat transfer in and between cooling duct and rotor were carried by the Finite Volume Method at condition of varying configuration parameters of sub slot, the number of winding's cooling ducts and center distance of them, and the diameter of slot wedge.

为了能够得到转子截面较均匀并且最高温度值较低的优化温度分布，文中在150MW空冷汽轮发电机转子实验研究基础上，改变副槽的几何形状、径向通风沟的条数及间距、槽楔出风口直径等几何量，采用有限体积法求解转子本体及通风道内空气的传热及紊流流动等二维离散方程组。

Based on the theoretical work between strengthening effect and grain diameter index, the ratio of geometric area is analyzed.

作者在前人得出的加固效果与粒径指数关系的理论工作基础上，分析了根据粒径指数和一定的加固后影响范围的几何面积的比值，则可以确定承载力改善值，以及每米单位长度 L 的沉管干振碎石桩所需的填充料的体积关系，同时，如果我们已知土的粒径指数值和给出加固效果值，则可以得到每米碎石桩的体积与加固后影响范围的几何面积的比值。

The number of support, vectors is decreased by 28%. Then, the structure of the Riemannian geometry is introduced in the input space, and using the Riemannian geometric modifies the kernel function of the classifier and gets less improved support vectors at the second training.

在第一次训练后产生的支持向量的基础上，将黎曼几何结构引入到输入空间，利用黎曼几何结构将分类器中的核函数进行修改，在第二次训练中再次减少了支持向量数目。

Based upon studying its relationships with other subjects, this paper points out three origins of the idea of Riemann for geometry : mathematics, physics and philosophy.

在分析黎曼的几何思想和其他学科关系基础上，指出了其几何思想的三个来源：数学、物理和哲学。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。