几何的

In this thesis,we mainly study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. We study the topology of these manifolds via comparisonal geometry methods.In chapter 1 ,we will make a general description on the recent researches in our field.

在本文中，我们主要研究了Ricci曲率有下界完备非紧的Riemann流形的拓扑问题，在比较几何的基础上研究了有特定曲率条件的Riemann流形的拓扑，得到了有关其拓扑结构的一些结果。

Without using Lie derivative and Lie bracket operation of differential geometry , we only use the algebra method to give a sufficient condition of single input exact feedback linearizable bilinear systems.

摘 要 研究了单输入的双线性系统的精确线性化及其鲁棒控制器设计问题，避免了用微分几何的李导数、李括号的复杂运算，只用纯代数的方法给出了一般单输入双线性系统精确线性化的充分条件。

The major purpose of this article was to illustrate the innovating instruction of the topic-"triangle" for the third graders. From the experience of the classrooms, it is considered that the curriculum is only to instill into children some geometric nouns, such as the sides, the apexes and the angles. A closed graph with three angles is usually to be named as a triangle without thinking about children's understanding of the real meaning.

本文的主要目的乃是针对教学者本身以往在教国小三年级学童的「三角形」这个单元时，自觉只是在灌输孩子一些几何的名词，例如：这个就是边、顶点和角；有三个角的封闭图形就是三角形，并没有去考虑到孩子是否真正的理解这些语词的涵意。

In this paper,the methods of distance geometry are used to explore the angles of a simplex ,and the second cosine law of a simplex in another form is obtained.

运用距离几何的研究方法，研究了和单形相关的角，给出了单形第二余弦定理的另一种形式，以此为基础得出了BartO¨s体积公式一种简洁的证法；探讨了单形的几个体积公式之间的联系，并推广了单形的一个体积公式。

In this paper we define the concept of Projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. We prved that if M be a complete projective Blaschke n-sphere and its universal covering manifold is isometric to a complete (n+1) dimensional parabolic, elliptic or hyperbolic affine hypersphere, then M is a quotient space of E^n, S^n or D^n by a isometric subgroup of its corresponding spaces.

在这篇文章中我们定义了射影Blaschke流形的概念，将等仿射微分几何的理论推广到了射影Blaschke流形，并证明：如果n维完备射影Blaschke 超球面 M 的通用覆盖流形分别是完备的抛物型、椭圆型或双曲型仿射球，则M分别是n维欧氏空间、n维超球面或n维单位圆盘关于各自空间的一个等距离散子群的商，从而对完备射影Blaschke 超球面进行了分类。

This paper proves the existence of utility function by using Riemannian geometry methods, which build a bridge between Riemannian geometry and economics.

运用黎曼几何的方法证明了效用函数的存在性，引进了广义的边际效用趋势概念，该定义揭示了以效用函数为度量与一般的欧氏度量的偏离，并证明了这个定义是内蕴的。

Figments of Reality - The Evolution of the Curious Mind by Ian Stewart (340 pages) Mathematics and geometry professor Stewart, who writes the "mathematical recreations" column in Scientific American, and biologist Cohen are witty, erudite, clever, at times funny, and generally clearheaded in this rationalist's view of the universe and human evolution.

凭空现实演变的好奇心的Stewart伊恩(340页)教授的数学和几何的Stewart作家&数学娱乐性&栏科学美国人科恩是生物学家、机智、博学、聪明、有时逗趣这和一般清醒理智看待宇宙和人类进化。

What we needed was (1) geometry based subdivision,(2) reasonable number of quadrilaterals, and (3) very low computational cost.

我们需要的是：（1）基与几何的再分，（2）合理的四边形数量，（3）非常低的计算成本。

Notice that (1) the subdivision is geometry based, i.e. high curvature areas receive more quadrilaterals, and (2) low curvature areas contain more quadrilaterals than necessary due to the crack-preventing nature of the process.

注意（1）这个细分是基与几何的，就是，大曲率的区域有更多的四边形，因为这个过程有防止出错的特性。

Epipolar geometry constraint is calculated by nonlinear error propagation at initial time to accelerate the speed of stereo matching; global and local methods are integrated to extract foreground objects precisely; and only pixels on objects' contour are reprojected into 3D space to fasten the depth calculation process.

使用视觉计算实现视频增强现实遮挡处理，用非线性误差扩散模型提高了对极几何的求解精度；将全局和局部高斯核相结合，提高并加快了物体前景轮廓线的提取精度和速度；仅用轮廓线上的点进行立体匹配的方法加快了真实物体深度反求的速度。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。