圆几何

ABSTRACT Based on theoretical analysis of axial compression of ring-shape specimen between two flat dies by an upper-bound technique,it is possible to carry out the measurement of both the friction coefficient of lubricant and the basic flow stress of the ring material under particular temperature and strain rate.

摘 要 根据圆环压缩的连续速度场上限定理的理论分析，通过圆环试样压缩前后的几何尺寸的变化，能测量润滑剂的摩擦因数和圆环材料的流变应力。

The works in the project just done can be summarized as five respects.(1) A device was designed to fabricate the asymmetrical resonant cavities by a pendant drop. A series ARCs with variable parameters provides a valuable experimental method for investigating the characteristics of ARCs.(2) The relationship between the number of active modes and the shape parameters in an ARC was investigated. The experimental lasing threshold was compared with theoretical result, the good agreement between two shown that it was the decrease of the number of active modes in an ARC that decreased lasing threshold.(3) Dye lasing gain was used to enhance the signals of stimulated Raman scattering of the weak gain Raman modes in a circular cavity made by a pendant drop, the instantaneous SRS spectra of weak gain Raman modes in ethanol was obtained by this new method.(4) The SRS signals of minority compound in a binary chemical complex was obtained by using dye lasing gain method. The detection concentration of minority compound was reduced to an order compared with normal SRS method.(5) A cylindrical circular cavity was formed by a liquid jet, which was used to reduce the pump intensity required for laser induced plasma spectroscopy. The limit of detection of trace element in aqueous sample was greatly decreased by this new method.

我们设计并成功制作了使悬垂液滴连续变形的装置，用此装置可以方便地改变非圆对称谐振腔的几何参数，为ARCs的研究提供了一种有效的实验方法；研究了ARCs中活性模式数和变形参数间的变化规律，激光阈值的数值计算结果和激光辐射的实验结果作了比较，二者吻合的曲线说明ARCs中活性模式数量的减少是受激辐射放大阈值降低的原因；在由单元化合物构成的微型圆对称谐振腔中，首次尝试用"激光增益"增强弱增益拉曼模式的受激拉曼散射信号，获得了乙醇分子中弱增益拉曼模式的瞬态SRS光谱；在由二元混合物构成的微型圆对称谐振腔中，用染料的激光增益增强了少量化合物的SRS信号，把少量化合物的SRS信号探测浓度降低了近一个数量级，在SRS应用于瞬态过程的组份分析方面做了卓有成效的探索；用石英毛细管形成的稳定液拄构成拄形谐振腔，降低了激光诱导等离子体光谱需要的激励能量，有效地降低了水相样品的痕量元素分析极限，为LIPS应用于微量元素的化学分析开拓了一条新的技术路线。

Thus, evaluation of the minimum zone circle could be solved effectively.Three methods of assessment of roundness error were proposed in this dissertation. Based on the criteria of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle and convex hull, a unified approach was proposed to evaluate roundness error of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle. Evaluation of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle was fulfilled with rotation based the contact pattern. The minimum circumscribed circle and maximum inscribed circle were evaluated with curvature and the curvature circle.

本文提出了三种圆度误差评定的方法：根据最小区域圆、最小外接圆、最大内接圆在极坐标系下的判别准则，利用计算几何中的凸壳理论，提出了一种统一的评定方法，实现了对最小区域圆、最小外接圆、最大内接圆的误差评定；基于接触斑点的检验原理，利用旋转法，实现了最小区域圆、最小外接圆和最大内接圆的误差评定；利用曲率和曲率圆，实现了对最小外接圆和最大内接圆的误差评定。

The basic principle is based on spherical astronomy and elementary geometry of the trajectory mapping method based on the observation of a celestial body zenith distance, then the ship is located in order to sing the next point as the center of this satellite zenith distance of the ship's position as the radius of the circle, observing the same two objects, or objects at different times of the two observations, we can get two ship's position round, then the ship must have been a point of intersection of two ship's position on the circle.

其基本原理是建立在球面天文学和初等几何中的轨迹作图法基础上的，观测一个天体的天顶距，则航船就位于以星下点为圆心，此星天顶距为半径的船位圆上，观测两个天体或者不同时间同一天体的两个观测值，就可以得到两个船位圆，则航船一定在两个船位圆的一个交点上。

Using the relations between harmonic conjugation elements,we can determine the relations between polar point and polar line more widely.

度量几何中圆的切割线之间所确定的数量关系，推广到射影几何里一般二次曲线中，利用调和共轭元素之间的关系，更广泛地确定了极与极线的相互关系，着重介绍了二次曲线的度量性质与射影性质的内在联系。

Most geometric inequalities concerning convex bodies have the property that the occurence of the equality sign characterizes geometrically significant objects, like balls , ellipsoids .

中文摘要：在几何中，大多几何不等式都有这样一个性质：当取一些特殊的凸体时，比如球，圆，椭球等，等号成立。

For example, after spinning the geometric shape circle on its axis to any degree, the geometry of the shape remains unchanged. Therefore, the geometric shape circle is symmetrical relative to the revolvement on its axis.

例如，平面几何图形圆，绕轴心作某一角度旋转，圆的几何图形保持不变，所以，圆的几何形状具有对轴心的旋转对称。

By roundness image processing,the characteristic information of round parts can be got.Thus we can precisely and swifty test the roundness error and correlative geometry dimension and shape error of the parts.Through the comparison to the standard objects or design demands,we can estimate whether the part is qualified

对采集到的零件图片进行图像处理，得到零件的圆度特征信息，从而精确快速的检测出零件圆度误差和相关几何尺寸和形位公差，通过与标准件或设计要求的比较，判断出被测零件的圆度是否合格。

This thesis makes use of complex numbers to study geometry. It mainly considers the following questions: using complex numbers to express collected points and curves on the level;geometric applications of complex numbers on collinear,concurrent,round,Mobius Mappings of Complex numbers problems,etc..Meanwhile,this thesis recommends some methods for thinking on mathematics.

本文利用复数来研究几何，主要考虑如下的问题：平面上的点集的复数表示；平面曲线的复数表示；复数在共线、共点、共圆、复数的麦比乌斯变换等几何问题上的应用，在说明这些应用的同时介绍一些数学上常用的思考方法。

After extraction of the arc region from regions, the seed for an arc is obtained. By traversals for the graph, the seed arc grows by constrains for the same circle.

圆弧及圆的识别先从邻接图顶点中抽取圆弧域，作为种子圆弧，然后从此出发遍历图，按照同圆来建立路径，进行整弧和整圆增长，最终获得圆弧和圆的几何表达。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。