曲率

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。

If the change of step-size is controlled by the value of curvature of integral curve, the result can avoid such an error accumulation.

定步长的缺点在于不管是积分曲线的各个点的曲率如何都取一样的步长，这样肯定会在曲率大的一些点带来比较严重的误差，这种误差将在每一步的计算中积累。

The weakness of fixed step-size is that step-size is not variable regardless the curvature of each point of the integral curve change or not, which will affirmatively bring serious error in these points that the value of curvature is bigger. And, this kind of error will accumulate in calculating process.

定步长的缺点在于不管是积分曲线的各个点的曲率如何都取一样的步长，这样肯定会在曲率大的一些点带来比较严重的误差，这种误差将在每一步的计算中积累。

The whole process of moment-curvature relationship for RC beam was analyzed with the relative depth of compressive zone of the beam about 0.15 using the strip integral method and computer programme. The relationships between moment and strain of concrete, strain of steel, depth of compressive zone were got.

采用条带积分法，应用计算机编程，对相对受压区高度为0.15左右的钢筋混凝土梁的弯矩－曲率关系进行全过程分析，得出弯矩－曲率关系曲线，并给出弯矩与混凝土应变、钢筋应变及梁的相对受压区高度的对应关系。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

Finally, we would point out excellent method for gaussian and mean curvature estimation.

最终得出结论，指出现有方法中对高斯曲率和平均曲率的计算效果最优的方法。

This paper concerns submanifolds with constant mean curvature in Euclideanspaces or unit spheres.

本文考虑欧氏空间或单位球面中平均曲率为常数的子流形，主要考虑极小的，即平均曲率为零的子流形。

In this thesis, we study stable and complete submanifolds with constant mean curvature and some L~p-norm curvature in Euclidean spaces and hyperbolic spaces.

在本文中，我们较系统的研究了欧氏空间和双曲空间中具有常平均曲率和某一有限L~p范数曲率的稳定完备子流形。

Aimed at the feature of footprint range image, the paper has defined the concept of the form index and proposed the segmentation method based on the mean curvature and Gaussian curvature.

本文针对足迹深度图像的特点，定义了形状索引的概念，提出了一种基于高斯曲率和平均曲率的分割方法。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。