椭圆几何

Based on the laminate theory, a laminate weakened by damage is treated as an anisotropic thin plate. Using the complex potential method in the plane theory of elasticity of an anisotropic body, the series solution of finite anisotropic thin plate containing an elliptical inclusion is proposed with the help of Faber series. A hybrid element with an elliptical inclusion for anisotropic materials is obtained by using the hybrid variable principle, and the element efficiency is verified by numerical examples. The state of the damage is modeled by an elliptical soft inclusion, and using the point stress criterion based on characteristic curve and Yamada-Sun etc. criteria, the prediction of the strength of a composite laminate with damage is set up. The effects of various parameters on the stress distribution and the residual strength of a composite laminate weakened by damage are detailedly studied.

首先基于经典层板理论，将复合材料层板的弹性问题化归为均匀各向异性板来求解；采用各向异性体平面弹性理论中的复势方法，以Faber级数为工具，给出了有限大含椭圆核各向异性板弹性问题的级数解形式；利用杂交变分原理，成功导出含椭圆核各向异性板杂交应力有限元，并用算例验证了该单元的可行性和有效性；采用含刚度折减椭圆形弹性核的冲击损伤模型，引入基于特征曲线和Yamada-Sun破坏准则的点应力判据，建立了含损伤复合材料层板剩余强度的分析方法；通过数值计算详细讨论了各种几何参数对损伤层板应力分布、剩余强度的影响，得到了一系列对工程应用具有实用价值的结论。

The relation between the spectrographic aperture ratio and elliptical eccentricity, spectral angle is also analyzed according to the elliptical geometry, it will decrease when the x-ray wavelength increases.

根据椭圆的几何关系，研究了光谱相对孔径与椭圆的离心率和谱线探测角之间的关系，它随X射线波长增大而减小。

It begins with a historical introductory chapter, and then devotes three chapters to surveying real projective geometry, and three to elliptic geometry.

它从历史绪论，然后用了三个篇章测量实际射影几何和3至椭圆几何。

The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry.

这本书是结构，以便读者可以选择部分文本阅读，还带了一个完整的画面，有些地区的微分几何开始入门级和曲线的部分，在欧氏空间变得更有挑战性，终于到达了高级的主题，形成了最大的一部分书：变换团体、几何的微分方程、几何结构、等价问题的几何形状，G-structures椭圆算子和接触几何。

And then, a window-type novel x-ray crystal spectrometer was put forward based on the elliptically curved crystal analyzer. It was coupled to an x-ray CCD camera, and a set of system had been designed and constructed. The spectrograph is useful in the experiments of x-ray diagnostics, for example in x-ray lasers, inertial confinement fusion, laser-matter interaction, and so on.

本论文从X射线晶体衍射和椭圆自聚焦几何光学原理出发，剖析追究了椭圆型弯曲X射线晶体谱仪在实际应用中产生问题的根源，率先从技术上提出解决目前椭圆型弯曲X射线晶体谱仪存在问题的思路，论证了其相应实施方案的可行性。

In the fourth chapter, I analyze and contrast many architectural cases in history and modern times which ellipse were applied to, and explore the ellipse"s development in historic sense. The fifth chapter investigates the dynamic relationship between geometry and architecture based on ellipse"s geometric character, and analyzes ellipse architecture"s characters in symbolism, dualism, diversity and unity these four facets. In the sixthchapter, taking ellipse architecture as examples, I try to explore the relationship between the more general geometry"s purity and architecture"s complexity, and build the foundation for future exploration of geometry"s purity.

第四章从历史和现代两个方面展开了大量对椭圆形式在建筑中应用的个案和实例的研究与对比，探讨了椭圆形式在历史上意义的变迁；第五章以椭圆的几何特性为立足点，研究了椭圆几何--建筑之间的动态关系，从标志性，二元对立，多样和统一四个方面分析了椭圆建筑的特点；第六章以椭圆建筑为例，尝试探讨了更一般的几何的纯粹性与建筑的复杂性的关系，对几何纯粹性意义的挖掘为进一步的研究提供基础；第七章采用了类型对比的研究方法，分析了安藤忠雄和库哈斯两位设计哲学截然不同的建筑师对椭圆形式的使用；另外，以位置关系为线索，将椭圆和其他的几何形式结合起来，总结了一般情况下几何的纯粹性对建筑复杂性的作用。

It featured the vocabulary of the circle, oval, rectangle and hexagon, and design characters including plants as space as well as the order formed through the juxtaposition and copy of the pure geometry.

圆形、椭圆、方形和六边形成为丹麦几何景观的特征词汇，同时也生成了用植物塑造和组合空间、运用简单几何形的并置与重复来创造秩序的几何景观的设计特征。

Image analysis validly assesses the disciform geometry of herpetic stromal keratitis and confirms that increased severity is associated with uveitis and reduced vision.

图像分析有效地评估了单纯疱疹性基质性角膜炎的椭圆几何图，并证实增加的严重性与葡萄膜炎及视力下降有关。

A new mathematical model is put forward numerically to simulate the wheel ovalization.. In the numerical simulation, the dynamic model of a half railway vehicle coupled with a tangent track is employed. Using the new numerical method investigates vehicle-track coupling system dynamic responses including lateral and vertical displacement of wheelsets and the vehicle, lateral and vertical vibration acceleration of the track at different phase angle of the two side wheels of the same wheelset, which are compared with that of the traditional model. The numerical results show that the discipline and frequency of dynamic responses are accordant, amplitude and phase of lateral dynamic responses are different. It is concluded the traditional track geometric irregularity excitation model does not simulate the effect of periodic wheels ovalization on vehicle-track coupling system dynamic behavior truly, the new model is more accurate and reasonable.

本文研究了车轮二阶周期性非圆化—椭圆化，建立了一个新的模拟车轮椭圆化的数学模型，结合车辆－轨道空间耦合动力学模型，计算了同一轮对左右车轮不同相位和车轮椭圆度下轮对和车体的横、垂向位移，钢轨横、垂向振动加速度，并与传统模型计算结果作了对比，分析表明两种模型的动力响应变化规律和频率一致，但横向动力响应幅值和相位均存在不同程度不可忽略的差异，因此传统的轨道几何不平顺激励模型不能真实模拟车轮的周期性椭圆化对车辆－轨道耦合动态行为的影响，而本文模型更能反映实际椭圆车轮与钢轨接触情形，计算方法准确而合理。

Based on moving least squares surface, the differential properties of each sample point on PSO are first evaluated. In terms of covariance analysis, the elliptical splat of sample point is then determined on its tangent plane. Finally, the splats are rendered from far to near by using elliptical weighted average filtering. According to the differential properties, moreover, the suggestive contours of PSG are attained so that non-photorealistic rendering of PSG is realized.

首先根据构造的移动最小二乘曲面计算采样点的表面几何属性，然后根据协方差分析确定点元在其切平面上的椭圆表示，最后采用椭圆加权平均滤波从远到近单遍绘制各点元，此外，根据表面几何属性确定点模型的轮廓线，实现了点模型的非真实感绘制。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。