查询词典 mean curvature

Then, the first and second fundamental forms, Gaussian curvature and mean curvature of the surfaces are directly calculated according to the principles of differential geometry.

首先，根据微分几何中的基本知识，得到了该种度量形式下的平移曲面的第一、第二基本形式以及高斯曲率和平均曲率；然后，主要利用高斯曲率和平均曲率之间的线性关系和平方关系，得到了这类平移曲面的分类定理。

Using the mathematical tool"DifferenceGeometry",it is possible to define the discrete geometric metrics such as discretefirst fundamental form,discrete second fundamental form,discrete unit mainnormal vector,discrete Gauss curvature,discrete mean curvature and discreteLaplacian.

首先，运用"差分几何"这一工具，可以构造离散第一、第二基本形式，离散单位主法向，离散高斯曲率，离散中曲率等离散几何量和离散Laplace算子。

Theorem 4 There is no compact totally real 2-harmonic submanifold with non-zero parallel mean curvature and positive sectional curvature in a locally symmetric Bochner -Kaehler manifold.

定理4局部对称Bochner-Kaehler流形中不存在具有非零平行平均曲率向量且截面曲率大于零的紧致全实2-调和子流形。

In the present paper,a sharp inequality is obtained between the Ricci curvature and the squared mean curvature of semi-invariant submanifold s in cosymplectic space forms,and some conditions are reached to make the equality hold.

对余辛流形的半不变子流形进行研究，利用曲率的分量表示之间的简单的代数关系，得到了这类子流形的R icc i曲率与平均曲率平方之间的一个不等式，并讨论了等式成立的充分必要条件

The concept of the weighted logarithmic power mean is introduced; its relation with two-parameter mean is given; the inequality for weighted logarithmic power mean is derived; the magnitude relation among upper bounds of geometric mean and arithmetic mean of geometrically convex functions are made certain.

建立了几何凸函数的对称拟算术平均不等式，对文献[1]提出的不等式进行了推广统一；引进加权对数幂平均的概念，建立起其与双参数平均之间的关系，得到加权对数平均不等式，从而确定了几何凸函数的几何平均、算术平均的上界的大小关系；最后，提出了几何凸函数的对称拟算术平均不等式的推广问题。

The first part is introduction in which some excellent results are given. For example, LeachandSholander mean of two variables E and its monotonicity, Some results of paper and [4] are also given. In Chapter l,mean function and mean family of n variables in one dimension are given. On the base of mean function of n variables of paper [1], weproof that is mean function and discuss its monotonicity andcontinuity.

第一部分是引言，主要介绍了一些已有的结果，如：一般的两个变元的Leach and Sholander均值B以及它的单调性，又介绍了文[1][4]中一些已有的结果，第一章主要介绍了一维n元平均函数和平均族，在已有的文[1]中给出的参差域K上的n元平均函数概念的基础上，证明一般形式的是平均函数，讨论了它的单调性和连续性，其中还将已有的二元Stolarsky平均推广到了n元平均。

The LMD algorithm uses extrema to define the local mean and envelope, then to smooth the mean and envelope. To decrease errors in the smoothing process by using moving averaging, a new local mean and envelope definition method (the spline-based LMD) is proposed. The upper envelope and the lower envelope are obtained by connecting the local maxima and the local minima using a cubic spline line. The local mean is defined as a mean of the upper envelope and the lower envelope. A nonlinear simulation signal and a practical vibration signal are decomposed by the LMD and the spline-based LMD.

LMD算法用极值点来定义局部均值函数和局域包络函数，然后用滑动平均来平滑均值和包络函数，针对用滑动平均平滑均值和包络函数误差较大的缺点，提出了采用三次样条对上、下极值点分别插值求得上下包络线，然后由上下包络线的平均获得局部平均函数，由上下包络线相减的绝对值获得局部包络的方法。

With the evaluation, each group measuring value is considered as a single subsystem, and the minmax-difference, mean difference and the mean square value of each group are calculated. Then, the ratio of the mean difference to the measurement mean value is defined as the system-relatively error of subsystem and the ratio of the minmax difference to the measurement mean value is defined as the accidence-relatively error of the subsystem.

以每组为一个子系统，分别计算出每组的极差、平均差和标准差，然后定义平均差和测量平均值的比值为子系统的系统相对误差，定义极差和测量平均值的比值为子系统的偶然相对误差。

From the results of different coefficient and similar coefficient,Schima superbashowed high total mean different coefficient and low total mean similar coefficient;Castanopsis chinensis showed high total mean different coefficient and media totalmean similar coefficient;Cryptocarya chinensis showed low total mean differentcoefficient and high total mean similar coefficient.

从相异系数和相似系数的计算看，荷木总平均相异系数最大，总平均相似系数最小；锥栗总平均相异系数大，总平均相似系数居中；厚壳桂总平均相异系数最小，总平均相似系数最大。

This study included 204 patients with AIS（36 males,168 females）,selected from December 2006 to April 2008,with mean age 15.0 years old,mean Cobb angle 50.1°,mean Risser sign 3.4,mean main curve span 6.8 vertebrae and mean apical rotation 2.0°.Preoperative radiographs included a standing posteroanterior film and supine maximal voluntary side bending films of the spine.

选取2006年12月～2008年4月在我院脊柱外科手术治疗的204例AIS患者，男性36例，女性168例，平均年龄15.0岁；平均Cobb角50.1°；平均Risser征3.4度；主弯跨度平均6.8个椎体；主弯顶椎旋转度平均2.0度。

Dixie itself is a nickname for the American South.

Dixie 本身是美国南部的别称。

I think John Terry epitomises that and a big reaction is what we will be looking for.

而我认为特里就是这样一个典型，他正是我们期望看到的那个领秀。