曲率

Through the new research methods, this thesis has made the following contributions in this field: 1. For the first time the curvature radii and relative angles of a planar continuous curve at discrete points are chosen as local parameters to represent the curve, which reflect clearly the local geometrical characteristics of the curve and are easy to be dealt with.

借助于新的研究方法，本文在这一领域作出如下贡献：（1）首次提出用曲线上离散点处曲率半径和相对转角作为局部参数表示平面连续曲线，直观地反映曲线各个局部的几何特征，且便于曲线的修改和变换，并通过机构运动分析，快速求出机构轨迹的这两个局部参数。

Cosmic space-energy and cosmic gravitation pair is such coincidence, the spatial measurement of stable relative time-space cosmic energy is the 1/3 spatial measurement of cosmic time-space, the spatial curvature of stable relative time-space cosmic energy is the 2/3 spatial measurement of cosmic time-space.

宇宙空间能与宇宙引力的匹配是那样的吻合，宇宙能量的稳定相对时空的宇称为宇宙时空宇称的1/3，空间的曲率为宇宙时空宇称的2/3。

The main contents and achievements are summarized as following: 1. The principle of tension leveling of metal strip is described systematically using relative tension and relative curvature on the basis of plane hypothesis including the stress distribution on the section, the condition to undergo plastic longitudinal elongation, the calculation of longitudinal elongation, the change of tension along the strip etc.. 2. The tension leveling process of metal strip on a multi-roll arrangement is investigated detailed by nonlinear finite element method and many rules to guide the strain, deformation, stress and bending moment are discovered and illustrated.

本文的主要内容和成果如下： 1、以平面假设为前提，采用解析分析方法，建立了以相对张力和相对弯曲曲率为基本参数的平面应变金属带材拉伸弯曲变形基本原理较为系统的描述，描述涉及到应力分布与两个基本参数的关系、带材塑性延伸的边界条件、带材延伸率的计算、带材张力变化的计算等。

The stable structure of mass base__ the particle of photon most afterwards reach the verge of relative macrocosm, combine the relative space-energy of self, again come to do the quantum of stable spatial measurement radiate reach the relative vacuum of spatial curvature is 1/3 index of change level, return in the dark energy of cosmic energy, by the stable speed of (9/4)×107 m /s come to do random shift, later on again at random relatively gather.

基础质量的稳定结构--光微粒子最终到达相对的宏观世界的边沿，携带自己的相对空间能，再次成为稳定宇称量子辐射到更平直的空间的曲率指数为1/3的相对真空中去，回到宇宙能量的暗能量行列，以(9/4)×107m/s 的稳定速度成随机地移动，以后再随机地相对聚结。

Its principle is that the turning points of the curve are decided by the sign and the magnitude of τ, the relative curvature of y=f, and T=yxn/(1+y'x2)3/2, where x=lg△K, y=lg.

其原理是：根据y=f的相对曲率τ=y_x~n/1+y_x~(′2~(3/2)的正负和大小来判定曲线的转折点，这里x=1g，y=Ig。

In this paper,we mainly discuss the first eigenvalue on a compact Riemannia manifold with positive Ricci curvature.

主要讨论具有正Ricci曲率的紧Riemann流形上的第一特征值，给出一种下界估计。

The paper discusses the structure of the soul in a complete noncompact Riemannian manifold M with nonnegative curvature,and proves that if the soul of the manifold is unique,then the soul actually degenerates to a pole.

讨论了具非负曲率的完备非紧黎曼流形上的核心的结构，证明了如果核心是惟一的，那么核心将退化为极点。

The n-dimensional umbilical submanifolds in a Riemannian manifold of quasi constant curvature are discussed.

摘要讨论拟常曲率黎曼流形中的全脐子流形，得到关于这类子流形的两个定理。

Endowed with a Riemannian metric derived from the gray scale information of a given image, the image space became a Riemannian manifold. On this Riemannian manifold, we evolved a curve by the mean curvature flow using the level set methods.

在图像空间上直接赋予一种由图像灰度信息导出的黎曼度量，使之成为黎曼流形，然后在此黎曼流形上利用水平集方法对曲线以平均曲率流进行演化。

The temperature stress of annular super-long structure is different from that of the regular rectangle structure. For the annular super-long structure, the temperature stress value is mainly related with the curvature of the structure, besides the influence of constraint rigidness.

环形超长结构在温度场作用下的受力情况有异于常规矩形结构，温度应力的分布除受约束刚度的影响外，更大程度上与结构曲率有关。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。