查询词典 mean curvature

Some geometric data of ellipse in hyperbolic space are considered,such as set inclusion,arc length,geodesic curvature,curvature,area and total curvature .

在双曲空间中，考察椭圆的包含关系，对弧长元素、测地曲率、曲率、面积及全曲率等几何量做出细致考察。

After analyzing the curvature of the forming surface and the relativ emotion between the forming surface and the curved tooth surface during envelope tooth cutting,the authors work out the equations for calculating the induced normal curvature and geodesic deflection,the principal curvature and direction of the tooth surface of this kind of circular-arc gear .

通过对产形面曲率和包络切齿时产形面与齿曲面相对运动关系的分析，推导出双向圆弧齿轮齿面的诱导法曲率、诱导短程挠率和齿面的主曲率、主方向等计算公式。

The method includes identifying (101) a surface in the image, and for each point in the image, calculating (102) a first curvature measure, forming (103) a set of rings of points about each point, each ring being of equal geodesic distance from a center point for the ring, calculating (104), for each ring, a standard deviation of the first curvature measure, and selecting (105) those rings with a minimum standard deviation for the first curvature measure.

该方法包括在所述图像中识别(101)表面；为该表面中的每个点计算(102)第一曲率量；为该表面中的每个点形成(103)围绕每个点的一组点环，每个环具有到该环的中心点的相等的测地距；为每个环计算(104)第一曲率量的标准偏差；以及选择(105)那些具有第一曲率量的最小标准偏差的环。

Given a hyperbolic plane H2(-1)=,whose sectional curvature k is function K is the Gaussian curvature of the conformal metric g = e2ug ,then K satisfies the conformal Gauss curvature equation .

设H~2(-1)=是具常截面曲率k==1的双曲平面，其中B={∈R~2：x~2+y~2＜1}是单位圆盘，g=4(dx~2+dy~2)/(1-x~2-y~2)~2是所谓的Poincaré度量。考虑H~2(-1)上的共形形变度量？

If the infimum of sectional curvature R_c in M~n satisfies: then M~n must be totally geodesic in M~,T_c is the supremum of Ricci curvature and t_c is the infimum of Ricci curvature in M~

如果M~n的截面曲率下确界R_c满足：则M~n一定是全测地的其中T_c，t_c分别是M~(n+p上Ricci曲率上确界和下确界。

From this viewpoint, we fulfilled to control the step-size with the curvature of integral curve. The step-size is smaller in calculating these points that the value of the curvature is bigger and the step-size is bigger in calculating these points that the value of the curvature is smaller, which is rather reasonable choice and is also a creative point in this paper.

从这个想法出发，在文中实现了以积分曲线的曲率控制步长大小的作法，在曲率大的点步长小，而在曲率小的点步长大，这是非常合理的选择，也是本文的一个创新点。

The line of curvature is relation to many basic conception with curve and surface, by which normal curvature and principal curvature are easier.

曲率线将曲线与曲面中的许多基本概念有机地联系起来，使得法曲率和主曲率的求解简单化。

A method for identifying the damage, using the influence line curvature of deflection differential values at a point before and after the damage is proposed, that is, when the moving load is in the area without the damage, the influence line curvature is zero, however when the moving load is in the area with the damage, the influence line curvature evidently increases and has the relationship with the positions of the damage points and the rigidity of the beam before and after the damage.

提出利用损伤前、后某一点的挠度差值影响线曲率来识别损伤的方法，即当移动荷载位于无损区域时，挠度差值影响线曲率为0，当移动荷载位于有损区域时，挠度差值影响线曲率明显增大，且与损伤点的位置、损伤前后的刚度有关。

In this paper an analysis has been made to some regions of magnetosphere, including the Nightside, Cusp and Duskside. By applying the Curvature Radius Method to the magnetic field data measured by four satellites of Cluster, the geometrical structure of Magnetic Field Lines, including the curvature radius, directions of curvature and normal of the osculating planes of the Magnetic Field Lines have been investigated.

本文采用曲率半径分析方法，结合Cluster立体探测的相关知识和背景，利用Cluster立体探测的优势，通过对Cluster 2001年的立体探测数据的研究，分析了磁层各区域的磁力线结构，包括背阳面、Cusp区以及昏侧，得出各区域中磁力线的曲率半径大小，曲率矢量以及磁力线密切面的法线矢量的方向。

The model for calculating the stability of the resonator containing a laser rod with curvature ends was developed,which was based on the transfer matrix theory of Gauss beam. The results from the numerical simulations on some typical resonators indicate that the laser rod with curvature ends can expand the stable region of plano-plano,plano-concave and plano-convex cavity notability;despite the laser rod with curvature ends can improve the stability of above mentioned cavities,it costs the effective mode volume.

计算结果表明，对于几类典型的谐振腔如平平腔、平凹腔，球面端面激光棒可以显著的扩展强热聚焦作用下的稳定工作范围；球面端面激光棒在提高约束稳定性和热稳定性的同时，通常是以牺牲有效模式体积为代价的。

I think people in this lifetime in a rebirth.

我觉得人在这一生里其实也在轮回。

He had to tie her hands together.

他不得不把她的双手绑在一起。