顶点的

Let G be a finite group, and S a subset of G not containing theidentity element 1. The Cayley digraph Cay on G with respect to S is definedas a directed graph with vertex set G and edge set {|g∈G, s∈S}. IfS~(-1)=S, then Cay is undirected and in this case, we view two directededges and as an undirected edge {u, v}. Obviously, the right regularrepresentation R of G, the acting group of G by right multiplication, is asubgroup of the full automorphism group AutCay(G, S of Cay.

给定有限群G，设S是G的不含单位元1的子集，群G关于子集S的Cayley有向图Cay是一个以G顶点集合，而以｛|g∈G，s∈S｝为边集合的有向图，特别地，若S~(-1)=S，则X=Cay是无向的，此时我们把一条无向边｛u，v｝等同于两条有向边和，易见，群G的右正则表示R，即G在G上的右乘作用，为图Cay的全自同构群AutCay

This thesis contributes to geometry compression in the following aspects: Proposes a method of progressive spherical mesh parameterization based on local parameterization by directly projecting the deleted vertices to its neighborhood. Based on spherical mesh paramterization, an adaptive subdivision remeshing method by progressivly redistributing of sampling points is proposed, by this means, the main geometry information of the original mesh can be captured with only a small amount of samples, it can also be used in mesh simplification. By regarding attributes binded on mesh vertices as geometry signals and transferring them onto a uint sphere by means of spherical mesh parameterization, meshes with different attributes are compressed with spherical wavelet successfully with high compression rate. As a kind of lossy geometry compression technique, two mesh simplification algorthimes are also presented in this thesis.

归纳起来，本文的主要贡献有：提出了以直接投影局部参数化方法为基础的网格累进球面参数化方法；在网格球面参数化方法的基础之上，提出了一种基于累进优化布点方案的网格细分采样方法，该方法可以用很少的采样点就可以捕获到网格的主要特征，因此我们也将其用于后面的网格简化工作当中；通过将网格顶点上定义的各种属性看成几何信号，并以网格球面参数化为手段将几何信号迁移到单位球面上，从而成功地实现了用球面小波对各种几何信号的压缩；作为一种有损压缩方法，本文还提出了基于统一距离的网格简化算法和基于重采样的网格简化算法。

Given a ring and a set of communication requests. Each request is represented by a pair of nodes, and associated with a profit. To satisfy a request in the undirected ring, we need to determine a path between the two nodes of the request in the ring. To satisfy a request in the directed ring, we need to determine a directed path from the source to the destination of the request in the directed ring. The goal of the call admission control problem is to determine and satisfy a maximum profit subset of the requests such that for every edge of the ring, the number of satisfied requests that are routed through the edge does not exceed the capacity of the edge.

要在无向环中实现一个呼叫，需在环中指定该请求所对应的两个顶点之间的一条路，要在有向环中实现一个呼叫，需在环中指定该请求的源节点到目的节点的一条路，环网络呼叫接纳控制问题的目标是确定最大利润的呼叫子集，在环中实现该子集中的每一个呼叫，使得经过每一边的呼叫的数目不超过该边的容量，对于无向和有向环网络呼叫接纳控制问题，我们均首次给出了多项式时间近似方案。

Nor did they render unsound the negotiated purchases of fine businesses at sensible prices. Imagine the cost to us, then, if we had let a fear of unknowns cause us to defer or alter the deployment of capital. Indeed, we have usually made our best purchases when apprehensions about some macro event were at a peak. Fear is the foe of the faddist, but the friend of the fundamentalist.

葛拉罕的投资哲学造成丝毫的损伤，也从没有让以合理的价格买进优良的企业看起来有任何的不妥，想象一下，若是我们因为这些莫名的恐惧而延迟或改变我们运用资金的态度，将会使我们付出多少的代价，事实上，我们通常都是利用某些历史事件发生，悲观气氛到达顶点时，找到最好的进场机会，恐惧虽然是盲从者的敌人，但却是基本面信徒的好朋友。

Yves Saint Laurent, Marc Bohan, Gianfranco Ferre and John Galliano at Dior died after being taken over, the extraordinary ability to design Dior momentum to the top, and they uphold the spirit of the design are the same - Dior's exquisite tailoring. 2001 French designer Hedi Slimane took over the renamed after DIOR HOMME, he stressed that the design of the perfect line, the ultra-small size of clothing through the lean young male models showing a bit of a morbid sense of beauty, sweeping the world .

Yves Saint Laurent、Marc Bohan、Gianfranco Ferre以及John Galliano在Dior过世后陆续接手，非凡的设计功力将Dior的声势推向顶点，而他们秉持的设计精神都是一样的——Dior的精致剪裁。2001年法国籍设计师Hedi Slimane接手改名后的DIOR HOMME，他的设计强调完美的线条，超小尺码的服装透过精瘦的年轻男模特儿呈现出一种带点病态的美感，风靡了全球。

Compared with the global harmonic mapping method, this approach has the following advantages.(1) The efficiency of the algorithm is greatly improved. The computational cost involved no longer increases exponentially with the number of vertices of the meshes to be fused.(2) The algorithm is robust as the ambiguity in graph structure combination is alleviated.(3) The detail of the cut mesh is fully kept.(4) The topology restriction of the original algorithm is eliminated.

与原有的基于全局调和映射的融合方法相比，新方法的算法效率大幅度提升，求解时间不再随融合模型顶点数的增加而呈指数增长；减少了二维网格拓扑合并中奇异情况出现的概率，提高了算法的稳定性；被剪切网格的细节得到完整保留；消除了原算法对融合区域拓扑的限制。

A complement of Leger's picture place is now offered by the summits of the freestanding walls, and by the top of the rather curious gazebo--all of which lie on the same surface.

莱热的图面在建筑上的对应现在由阁楼及顶层休息室的屋面、顶层自由墙体的顶部和位于同一表面的上的相当奇特的眺望台的顶点所确定（图11，图14）。

Next, of fashionable network media there are two the largest interests in forming: The brand of planar and fashionable media that the first force is a tradition digitlizes value of transition, patulous brand and consequence to realize media, builds network vogue media, representative website includes Trends- style net of Chinese of international of Mi Na of osmund net of Xin of annals of woman of China of net of net, Vogue China, Yoka, ELLE, OnlyLady-, Ixinwei-, Mina-, Rayli- luck beautiful female net, these websites rely on the advantage such as the brand of the planar media with powerful oneself, content, channel, held the acme on character.

其次，时尚网络媒体的构成中有两股最大的势力：第一股势力是传统的平面时尚媒体品牌为实现媒体数字化转型、扩展品牌价值与影响力，所建立的网络时尚媒体，代表性的网站包括Trends-时尚网、Vogue中国、Yoka网、ELLE中国、OnlyLady-女人志、Ixinwei-昕薇网、Mina-米娜国际中文网、Rayli-瑞丽女性网等，这些网站依托自身强大的平面媒体的品牌、内容、渠道等优势，占据了品质上的顶点。

In the rhombohedron, each top site is occupied by a pair of ligand-unsupported Ag atoms which are surrounded by six phenol groups in an ethane-like structure. The phenol groups at another ends of the ligands bridge the rhombohedrons into novel non-interpenetrating three-dimensional network.

在每个棱柱体内，每个顶点由无桥连配体支持的、周围的六个酚羟基以一种不寻常的、类似于乙烷分子结构的扭曲方式排列的一对 Ag 原子占据，配体另一端酚羟基将棱面体连接成新颖的非穿插的具有棱形通道(沿 a 和 b 轴方向)的三维网络结构。

The meshwork results are obtained from the later pictures. They clearly show the structure of four-dimension reseau and some meshwork results of shell data. The reason why the whole results are not achieved is that there are too many circumstances in which five or more dots share the same orb. In this case, the principle Delaunay is not in point any more, then the process of establishing meshwork will be intermitted.

后面的四幅图是后来所作的工作，得到了一个正方体四顶点以及其中心点的建网结果，从这里能清楚地看到四面体网格的结构，还有对贝壳数据点云的部分建网结果，之所以没有完成整个贝壳数据的建网是因为数据中存在较多的五点或五点以上共球的情况，这种情况下Delaunay准则不再适用，建网会中断，所以只完成了一个部分。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。