查询词典 integral curvature

On the other hand, Let M~n be an z-dimensional complete noncompactoriented submanifold with finite total curvature in an-dimensional simplyconnected space form F~ of constant curvature c. In this thesis, we provethat if M satisfies one of the following: n≥3, c=0 and integral from n=M H~n＜∞;n≥5, c=-1 and H＜1-2/n~(1/2); n≥3, c=1 and H is bounded, where Hdenotes the mean curvature of M. then the dimension of the space of L~2 harmonic1-forms on M is finite.

本文还证明：若具常曲率c的完备单连通空间型F~中具有有限全曲率的n维完备非紧可定向子流形M满足下面条件之一：n≥3，c=0且integral from n=M H~n＜∞；n≥5，c=-1且H＜1-2/n~(1/2；n≥3，c=1且H有界的，则M上L~2调和1-形式空间的维数是有限的，这里H为M的平均曲率。

Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain 3×3 symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature.

通过计算3×3对称矩阵的特征值和特征向量可以得出主曲率和主方向，而该对称矩阵是由积分公式定义并且与曲率张量的矩阵表达密切相关。

The earliest such theorem is the Gauss-Bonnet theorem, which gives the Euler characteristic in terms of the integral of the Gaussian curvature.

这方面最早的结果是 Gauss-Bonnet定理，它表明曲面的Euler示性数能用Gauss曲率的积分表示。

This paper will base on the bilayer-coupling model phase diagram, under bilayer-coupling model, through building a few initial shapes which are close to the target shapes, with the constraint condition of the area A, the volume V, and the average curvature integral M and using reduced quantity, finally some budding and the multi-budding vesicles will be obtained through Surface Evolver software gradually subdividing and long time evolution.

本文从双层模型的相图出发，在双层模型下，通过建立一些与目标形状相近似的初始形状，在面积A，体积V和平均曲率的积分M的约束条件和使用约化量的情况下，经Surface Evolver软件的逐次细分并长时间演化，得到了一些budding和multi-budding型的生物膜泡形状。

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

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。

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。

B- spline Expression of Integral Curvature Line on NURBS Surface.

李宏坤，王国瑾，刘利刚， NURBS 曲面上积分曲率线的 B 样条表示，计算机辅助设计与图形学学报，2006， 18(3)：

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。

A magnetic source and condenser for protecting a pipe, ionizing any fluid flowing therein, and ionizing any dissolved and suspended solids in such fluid, comprising:a magnetic source including a magnet having a pair of opposed planar major faces and a planar minor face extending between said major faces and perpendicular to said major faces,said magnet being charged so that one of said major faces is a south pole and the other of said major faces is a north pole,a magnetic condenser a pair of pole pieces, each of said pole pieces having a pair of opposed planar major faces, one of which is an inner major face and the other of which is an outer major face, the area of said inner major faces being equal to that of the major faces of said magnet, the area of said outer major face being larger than each of said major faces of said magnet,said pole pieces being positioned on opposite sides of said magnet such that said pole pieces sandwich said magnet, said inner major face of each pole piece is contiguous with and completely covers an entire major face of said magnet, and said outer major face of each pole piece faces away from said magnet,each pole piece having an integral foot extending perpendicularly to said inner major face of each pole piece such that said pole pieces have two respective integral feet which extend toward each other and are substantially coplanar, each foot having a distal and a proximal surface with respect to said magnet, each foot having an end which is spaced from the end of the opposite foot,said distal surface of each foot having a predetermined concave curvature which will conformingly mate with an outside surface of a pipe having a predetermined convex curvature,said proximal surface of each foot being contiguous with said minor face of said magnet

我要求： 1。一台磁性来源和冷凝器为保护管子，电离任何流体流动在其中，和电离任何被溶化的和暂停的固体在这样的流体里，包括：一个磁性来源包括磁铁有一对被反对的平面主要面孔和一张平面较小面孔延伸在前述主要面孔和垂线之间对前述主要面孔，前述磁铁被充电以便前述主要面孔的当中一个是南极并且其他前述主要面孔是北极，一台磁性冷凝器每对杆片断，每个前述杆片断有一对被反对的平面主要面孔，其中之一比每个是是一张外面主要面孔的一张内在主要面孔和其他，前述内在主要面孔区域是相等的与那前述磁铁，前述外面主要面孔区域的主要面孔大的前述磁铁的前述主要面孔，前述杆片断被安置在前述磁铁的反面这样，前述杆片断三明治认为磁铁，各个杆片断的前述内在主要面孔是接触的与和完全地包括前述磁铁的一张整个主要面孔，和各个杆片断面孔的前述外面主要面孔从前述磁铁，各个杆片断有一只缺一不可的脚垂直地延伸对各个杆片断的前述内在主要面孔这样，前述杆片断有延伸往彼此和极大地coplanar 的二各自缺一不可的英尺，各只脚有末端和接近表面谈到前述磁铁，各只脚有被间隔从相反脚的末端的末端，各只脚前述末端表面有与管子一个外表面conformingly 将联接有被预先决定的凸面曲度的被预先决定的凹面曲度，各只脚前述接近表面是接触的与前述磁铁的前述较小面孔

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。