圆几何

Accordingly, in education, the teacher should pay attention to directive student to learn to use geometrical figure, handle the consciousness of physical problem with auxiliary circle especially, increase the capacity that uses geometrical knowledge to solve physical problem thereby.

因此，在教学中，教师应注重指导学生学会利用几何图形，尤其是用辅助圆处理物理新问题的意识，从而提高运用几何知识解决物理新问题的能力。

In this paper, a complex mapping function is devised to transform the contour surface of an arc crack to a unit circle on the auxiliary plane.

本文之研究方法乃是首先设计一复变函数，将原有弧形裂纹之几何形状映像至辅助平面成为一单位圆，然后再以此映像函数代入相关之边界方程式中。

In this paper, a complex mapping function is devised to transform the contour surface of an arc crack to a unit circle on the auxiliary plane. By substituting the mapping function into it governing boundary equation, the complex stress functions can be obtained as

本文之研究方法乃是首先设计一复变函数，将原有弧形裂纹之几何形状映像至辅助平面成为一单位圆，然后再以此映像函数代入相关之边界方程式中。

This researchcombines the latest achievements of computer technology withmeasurement technology, in order to develop a special on-line measuringmachine, which has functions such as processing and transform of highprecision signals; digital processing and calculation; logic judgment andfault diagnosis and automatic operation, so that the geometric parametersof the four engine borings can be measured simultaneously at one station.Therefore, with efficient detection, group assembly of borings andcylinders can be realized.

该测量机的功能是实现在线同时测量内燃机四个缸孔直径、圆度、圆柱度、位置度等几何参数，并通过计算机控制自动采集测量信息、自动处理高精度信号和数据处理，且具有逻辑判断与故障诊断、自动化操作等能力，从而提高检测量效率，真正实现缸孔、缸套的成组装配。

We also show that the one-to-one defensive competition problem is a generalization of the Tukey median problem and the smallest enclosing circle problem which are two famous problems in computational geometry.

同时我们也讨论了竞争性区位设施之防御问题与其他计算几何领域内的著名题目例如，Tukey 中间值及最小圆盘集合之间的关系。

Such as measurement of refractive index distribution is one of the most important test, and thus can be measured optical fiber preform of a series of geometric parameters such as core / package ratio, concentricity, roundness and so on.

比如折射率分布测量就是其中一项最重要的测试，并由此可测得光纤预制棒的一系列几何参数，如芯/包比、同心度、不圆度等。

Mathematics: Understands and applies basic and advanced properties of the concepts of geometry; Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems; Understands the basic concepts of right triangle trigonometry (e.g., basic trigonometric ratios such as sine, cosine, and tangent); Uses trigonometric ratio methods to solve mathematical and real-world problems (e.g., determination of the angle of depression between two markers on a contour map with different elevations); Uses properties of and relationships among figures to solve mathematical and real-world problems e.g., uses the property that the sum of the angles in a quadrilateral is equal to 360 degrees to square up the frame for a building; uses understanding of arc, chord, tangents, and properties of circles to determine the radius given a circular edge of a circle without the center

数学：理解和应用几何概念的初级和高级特性；用毕德哥拉斯定理、逆定理以及特殊直角三角形性质解决数学的和现实世界的问题；理解基本的直角三角形三角比；运用三角比方法解决数学的或现实的问题。（等高线图上的两个标记之间的俯角确定）运用形体之间的关系及其属性解决数学的或现实的问题（利用四边形内角和等于360度来为建筑物框架取正，运用弧，弦，切线和圆的性质确定缺少中心的一段圆弧的圆心

In this paper we define the concept of Projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. We prved that if M be a complete projective Blaschke n-sphere and its universal covering manifold is isometric to a complete (n+1) dimensional parabolic, elliptic or hyperbolic affine hypersphere, then M is a quotient space of E^n, S^n or D^n by a isometric subgroup of its corresponding spaces.

在这篇文章中我们定义了射影Blaschke流形的概念，将等仿射微分几何的理论推广到了射影Blaschke流形，并证明：如果n维完备射影Blaschke 超球面 M 的通用覆盖流形分别是完备的抛物型、椭圆型或双曲型仿射球，则M分别是n维欧氏空间、n维超球面或n维单位圆盘关于各自空间的一个等距离散子群的商，从而对完备射影Blaschke 超球面进行了分类。

The effect of tribology factors on bearing vibration is studied experimentally. AR model and WPT are used to processing the normal arid abnormal signals. The results are as follows:1. The vibration of ball bearings is caused by the tribology action of contact pairs of ball and ring races and has the essential of tribo-dynamics. Any factors affecting the tribology characteristics of contact pairs will affect vibration and noise of bearings consequently.2. Vibration characteristics of bearing keep almostly unchanged with the increasing of axial load expecting the increasing of nature frequencies. When radial load increasing with axial load unchanged, nature frequencies keep unchanged but some new vibration peaks appears in the spectrum.3. Vibration amplitudes are damped and nature frequency are enhanced with sufficient lubrication. Vibration and noise of bearings increase obviously and roar can happen and the contact surfaces scratch slightly under insufficient and unclean lubrication state. Bearing will be disabled in a few minutes without any lubrication.4. Bearing vibration is unstable under low speed. With the speed increasing, the vibration become stable and natural frequencies increase slightly but the amplitudes increase apparently.5. Bearing vibration can be excited only by some harmonics ofwaviness without lubrication and by all harmonics with lubrication based on the theoretical analysis.6. The nature frequencies of ball bearings decrease with the increasing sizes. When international clearance increasing, nature frequencies decrease in radial and increase in axial and angular and the amplitudes increase in radial and decrease in axial and angular. When the number of balls increasing, nature frequencies increase and amplitudes decrease. When the pitch diameter increasing, axial nature frequency increase and others nearly keep no change. When outer race groove curvature radius increasing, nature frequencies increase in radial and decrease in axial and angular and amplitudes keep no change in radial and increase in axial and angular. When inner race groove curvature radius increasing, nature frequencies decrease and amplitudes increase.7. The distortion in amplitude and frequency components of bearing vibration signals picked up by the present probe measurement method is founded and right conclusions cannot be achieved by the signals. When accelerometer is rigidly screwed with steel stud onto a flat outer surface of a ball bearing, vibration signal can be got without distortion and the reliability of research on bearing vibration is assured.8. AR model is suitable for large samples of bearing vibration signals, square root of length of samples can be used as the upper limitation of order determination and the FPE order selection criterion is effective. Many advantages of AR spectrum are founded over the classical based on FFT.9. Time-Frequency analysis is necessary for abnormal noise of ball bearings. WPT overcomes the principle shortcomings of STFT and proved to be a best tool to process the abnormal signals.

理论分析和试验研究表明： 1球轴承振动是钢球—滚道接触副中的各种摩擦学作用引起的，具有摩擦动力学的本质，任何对接触副的摩擦学特性有影响的因素都将对球轴承的振动和噪声特性产生影响； 2中心轴向载荷作用下，载荷增大使球轴承的固有振动频率升高，载荷越大同样的载荷增幅引起的频率升幅减小，足够大的中心轴向载荷作用下载荷的变化对球轴承振动的频率特性不会产生明显的影响； 3轴向和径向联合载荷作用下，径向载荷不大时球轴承振动的固有频率基本不变，但是可能引起变刚度激励的非线性振动，出现新的频峰，过大的径向载荷将使部分钢球脱离接触，使球轴承的振动和噪声呈现不稳定状态； 4润滑对球轴承的振动和噪声特性有重要的影响，良好的润滑对振动有明显的抑制作用，润滑不充分时，振动和噪声的水平会有明显增高，一定条件下还会激发接触副中的谐振，发出啸声，造成接触表面的伤害，无润滑干接触时，短时的运转就会损伤接触副表面，使振动和噪声迅速增大，并随时可能引发严重的磨损和卡滞失效；接触副润滑良好时，油膜的"刚化效应"使球轴承振动的固有频率有所提高，润滑剂中含有弥散性污浊时，振动的幅度总体升高，但弥散性污浊不会改变球轴承振动的频率特性；浙江大学博士学位论文：球轴承振动的研究 5低速时，球轴承振动的基本特征呈现不稳定状态，随着转速的提高，球轴承振动的频率特性趋于稳定，固有频率频峰升高； 6理论分析表明，干接触时钢球和滚道表面波纹度的某些谐波分量能激励球轴承的振动，振动的幅值与谐波幅值成正比，实际球轴承中钢球的分布不可能完全均匀，波纹度的激励作用会随时发生；润滑接触的分析表明，波纹度的任意谐波分量均能激励球轴承的振动； 7球轴承的几何和结构参数分析表明，球轴承尺寸越大，径向、轴向和角振动的固有频率越低；钢球中心圆直径增大，球轴承的径向和轴向振动的固有频率基本不变，角振动的固有频率有所上升，振动的幅频特性基本不变；径向游隙加大使球轴承的径向振动固有频率降低，轴向和角振动的固有频率有所升高，径向振动幅频特性的幅值升高，而轴向和角向降低；钢球的数量增多使球轴承振动的固有频率上升，幅频特性的幅值下降，径向振动的幅值下降最为明显；外圈沟曲率半径系数增大使球轴承径向振动的固有频率升高，轴向和角振动的固有频率降低，径向幅频特性基本不变，轴向和角向幅频特性幅值升高；内圈沟曲率半径系数增大使径向、轴向和角振动固有频率均下降，振动幅频特性的幅值均有升高； 8试验对比表明，传感器采用探针式安装时，由于探针接触副接触特性的影响，钡(量得到的球轴承振动信号有失真，采用专门设计和制作的试验球轴承，以固定式安装加速度计，首次测量得到了球轴承振动的真实信号，通过对振动信号的分析，验证了球轴承振动的理论模型； 9)基于时间序列分析的AR模型适用于大样本球轴承振动信号的分析，以样本长度的均方根值作定阶上界，FPE做判阶准则，给出的AR谱光滑，频率分辨率高，是球轴承振动分析的简便而可靠的手段； 10以时频域分析的小波包变换分析球轴承异音信号能够比较好地定位和聚焦异音发生的时间，时间间隔，频率范围，同样是球轴承振动分析的可靠的手段，可用作球轴承故障诊断技术。

Firstly, a quantitative relation about finite deformation and geometrical parameters which exhibit variation of laser spectral image was introduced. And then, particular emphasis was put on some important computer processing steps related to the analysis of spectral image, such as digitizing, segmentation, feature extraction and analytical algorithms. Lastly, some examples about an experiment of a ring subject to large diametral compression were given.

文中首先给出了有限应变和平均整旋角与反映频谱图像变化的几何参数之间的定量关系，然后着重介绍了与频谱图像分析有关的数字化、分割、特征提取和分析算法等重要的图像处理过程，最后给出圆环受径向荷载大变形实验的分析实例。

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。