几何的

Based on the theory of gearing and differential geometry, a series of geometric relationships between conjugate tooth surfaces are analyzed, basic relationships of normal curvature as well as geodesic torsion between conjugate tooth surfaces are derived mathematically for the most general form of gearing.

基于微分几何和齿轮啮合理论，分析了共轭啮合齿面间的一系列几何关系，从而揭示了两个作空间共轭啮合运动的齿面之间的法曲率、短程挠率的内在几何联系。作为上述理论的具体应用，研究了准双曲面齿轮传动两齿面之间在给定参考点处的法曲率、短程挠率的关系

The relationship of the optimal geometric distribution of the constellation and the positioning error is given.

在分析定位误差的基础上，研究了星座最佳几何配置，以及几何位置相对较好、星的个数较少的4颗卫星的定位问题，并给出了星座的最佳几何分布与定位误差的关系仿真。

It is embodied in the three research programs of modern physics:(1) According to the program of geometrization of physics, the essence of the Curved Space in gravitational field needs to be explicated by Riemannian geometry, differential geometry, tensor analysis;(2)According to the program of quantum field theory, the generation and annihilation operator can represen...

它分别体现在现代物理学的三大研究纲领中：(1)根据物理学的几何化纲领，引力场弯曲空间的奥秘需要通过黎曼几何、微分几何与张量分析来解读；(2)根据量子场论纲领，场理论的"产生和湮灭"算符，能方便而精确地表征和重构相关的微观作用机制；"场的本体论"和"生成辩证法"同时得到体现。

The method of simulation deformation about hanging wall with the fault-related folding model by the premises of fault geometrical parameter is go by the name of structure forward.

构造反演是指利用地层变形形态反推使之变形的断层的几何参数；构造正演是在已知断层几何形态的情况下根据断层相关褶皱模型模拟相应的上盘地层变形过程，两者是一对相互可逆的几何推算过程，是构造建模的重要组成部分。

First of all, the paper gave a briefing on the development of white LED and the problems need to addressed of RGB LED mixed white lighting; Then established colors distributed computing model of the RGB LED white lighting module; Final designed a number of different geometric structure of the RGB LED light source module, by changing angles (interior angle or the angle Centre) of the geometry and the LED colors with different priorities, programmed by using of Matlab software, simulated the color distribution correspond to such light source models.

首先，本文简要介绍了白光LED的发展现状及RGB LED混合白光需要解决的问题；其次建立了RGB LED的颜色分布计算模型；最后设计了几种不同几何结构排列的RGB LED光源模块，通过改变几何结构中角度、不同颜色LED的排列次序，利用Matlab软件编程，模拟以及仿真得到这些光源模型相应的光源颜色分布，并评价其颜色均匀性，进而得到最佳几何排列结构的RGB LED光源模块。

Based on Fermat's theorem, the law of reflection and refraction is obtained, and the geometrical ray tracing method of reflected light is introduced. In response to geometric optics rainbow theory and Airy rainbow theory, the relationship formula of the N-order rainbow angle with the refraction index and the Airy peak value position formula are derived, and the physics causation of the first order rainbow are discussed and analyzed in detail. The distribution properties of the first and second order Airy structures of spherical particles are calculated.

利用费马原理推导了反射和折射定律，以反射射线的跟踪为例介绍了几何光学射线跟踪方法的推导过程；根据几何光学彩虹理论和Airy理论，推导了N阶几何光学彩虹角与入射角和折射率的关系及Airy峰的位置表达式，详细阐述了一阶彩虹形成的物理原因，计算了球形粒子的一、二阶Airy分布。

Because of the condition of 〓 for two neighbour parametricspline surfaces is too strong,here,instead of it,some simple and practicableconditions of 〓 resulted from the general theorem obtained by Prof.LiuDing Yuan in Chapter 1 were proved,and three 〓 triangular splinesurfaces schemes wre presented:one is piecewise cubic spline surface patcheshaving local 〓 and whole 〓 continuity based on the refined HCTtriangulation,another is the same degree spline surface patches but based onthe refined Powell-Sabin triangulation,the third is piecewise quartic splinesurface patches having local 〓 and whole 〓 continuity based on therefined P-S triangulation.

由于对参数曲面，一阶导数连续的要求较强，我们采用第一章从刘鼎元定理导出的简单实用的几何连续条件，讨论了基于HCT加细三角剖分和P-S加细三角剖分上的两种局部达一阶导数连续而整体有一阶几何连续的分片三次样条曲面构造算法，一种局部达二阶导数连续整体有一阶几何连续的分片四次样条曲面构造方法。

If the pertubation factors in judgments are stochastic,it was proved in this paper that the matrix of GMJ will converge in probability at a consistent positive reciprocal matrix whose vector of priorities is just the geometric mean of the vectors of p...

如果判断矩阵的干扰因子是随机的，文章证明了几何平均综合矩阵将依概率收敛于一个一致性的正互反矩阵，其排序向量刚好是各判断矩阵的几何平均综合排序向量。无疑这对于在群组决策时几何平均综合判断矩阵法的使用是重要的。

We use a size changeable adjacent field to describe the topological structure of 3D unorganized points in our algorithm. It can offer essential dynamic information for tessellation and points normal.

算法采用可以控制大小的邻域作为空间散乱数据点的拓扑关系的几何描述，为网格划分和点的法向量的几何描述提供了必要的动态几何信息。

The special geometric restrictions like parallelism andperpendicularity implicated in vanishing elements are deeply studied. In single-view case,the theory is presented to interpret relationship between two planar lines by applying 3Dinvariants of vanishing points. In two-view case, the method on extraction vanishing pointof an arbitrary spatial line is described, and moreover, the theory is presented to interpretrelationship between two elements in 3D space, such as two lines, two planes, line andplane, and so on.

4详细论述了消失元素(消失点、消失直线、消失平面等)所体现的垂直、平行等特殊几何约束关系；对单视图，提出了一种利用消失点列的3D不变量解释平面直线关系的方法；对双视图，提出了利用自共轭三角形和对极几何约束，提取任意直线的消失点的算法，并在此基础了提出了一种利用消失元素的3D不变量解释直线间、直线与平面间、平面间等多种空间几何关系的方法。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。