双曲率

Helfrich firstly proposed the spontaneous curvature model based on the similarities of the lipid membrane and the nematic phase liquid crystal,thus proved the existence of the biconcave shape.

Helfrich根据向列相液晶与类脂膜的相似性，于1973年最先提出了膜的自发曲率弹性理论，并由此证明了膜的双凹盘形的存在；同时，考虑到膜泡双层间的面积差对膜泡能量的影响，1989年S。

Next, what have double input and variable of 2 dimension appearance in the light of a kind is nonlinear system, used opposite curvature concept and curve to design controller of contract of appearance of 2 dimension plane by basic theorem, the curve of contrail of appearance be accusinged that controller of contract of this kind of appearance can assure a system and referenced contrail curve have identical figure.

梗概： 针对一般控制系统，利用微分几何中的曲线理论提出了外形变量、被控外形轨迹曲线和外形合同控制等概念。然后，针对一类具有双输入及二维外形变量的非线性系统，利用相对曲率概念和曲线论基本定理设计了二维平面外形合同控制器，这种外形合同控制器能够保证系统的被控外形轨迹曲线和参考轨迹曲线具有完全相同的外形。

Structure form adopts converse triangle beam double-hole connection welded by general electric trolley wall plate and steel plate, connection shaft, triangle beam bottom is connected with girder by nut and thrust bearing, triangle beam could rotate 360 degrees horizontally, thus realize whole set electric trolley horizontal rotation, largely reduce curve track curvature radius of electric hoist traveling mechanism.

描述： 结构形式采取通用电动小车墙板与一个钢板和连接轴组焊的倒三角形吊梁双孔连接，三角吊梁下面通过螺母及推力轴承与一个横梁连接，三角吊梁相对横梁可在水平方向做360度旋转，从而实现电动小车的整体水平方向转动，大大减小了电动葫芦运行机构弧形轨道曲率半径。

We give another definition of flux.which is an extention of that for minimal surfaces in Euclidean space. After that we discuss its quality and application.

这里我们同样研究双曲空间中中曲率为1的曲面的Flux，我们给出其的另一种定义方式，这个定义是欧氏情况的推广，并研究其性质及应用。

He also proved Harnack estimates for positive bisectional holomorphic curvature and is the major worker in the Ricci-Kahler flow today.

他还证明了正双截曲率流形的Harnack估计，他是当今Ricci－凯勒流理论的国际权威。

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？

In this paper,we deal with the flux of CMC-1 surfaces in hyperbolic space.

本文讨论双曲空间中常中曲率曲面的Flux。

So it is different from the case for composite laminated shell with anti-symmetrical lay-up.

这与反对称铺层复合材料层合壳的双稳态曲率方向相同的情况不同。

In the last part of this dissertation, we discuss how to model an image is discussed and how to segment an image by EDEK.Zero-Cross principle is a classical concept in signal processing. We generalize the concept to be zero normal curvature after the geometry frame built. Furthermore, we present the explanation to choose the dual parameters in SPMVIF. And we research why the Laplacian gradient superior to edge gradient.

梯度方向二阶导数过零原理是信号处理中的经典结论，在运用微分几何的知识建立SPMVIF的几何框架的同时，将这个结论推广到零-法曲率的形式；另外我们对SPMVIF的双参数选取规则进行了讨论并给出它们的几何意义，并且对SPMVIF中法向矢量选取时拉普拉斯梯度优于边缘图像梯度的结论给予统计信息熵的解释。

A planar geometric spline, biarc spline, is generalized to a 3D geometric spline whose curvature and torsion are all constant.

给出基于非线性规划解的双圆柱螺线样条局部构造法，把平面几何样条——双圆弧样条推广到常曲率和常挠率的空间几何样条。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新