Yang index of the deleted product

For any a -dimensional polyhedron is constructed such that the Yang index of its deleted product equals . This answers a question of Izydorek and Jaworowski (1995). For any a -dimensional closed manifold with involution is constructed such that , but can be mapped into a -dimensional polyhedron without antipodal coincidence.

     

图的联结数与分数n-边(点)可消去图

讨论了图的联结数bind(G)与分数n-边(点)可消去图之间的关系,给出了一个图是分数n-边(点)可消去图的若干充分条件.     

Families of pairs of graphs with a large number of common cards

The vertex‐deleted subgraph G?v, obtained from the graph G by deleting the vertex v and all edges incident to v, is called a card of G. The deck of G is the multiset of its unlabelled vertex‐deleted subgraphs. The number of common cards of G and H (or between G and H) is the cardinality of the multiset intersection of the decks of G and H. In this article, we present infinite families of pairs of graphs of order n ≥ 4 that have at least \begin{eqnarray*}2\lfloor\frac{1}{3}(n-1)\rfloor\end{eqnarray*} common cards; we conjecture that these, along with a small number of other families constructed from them, are the only pairs of graphs having this many common cards, for sufficiently large n. This leads us to propose a new stronger version of the Reconstruction Conjecture. In addition, we present an infinite family of pairs of graphs with the same degree sequence that have \begin{eqnarray*}\frac{2}{3}(n+5-2\sqrt{3n+6})\end{eqnarray*} common cards, for appropriate values of n, from which we can construct pairs having slightly fewer common cards for all other values of n≥10. We also present infinite families of pairs of forests and pairs of trees with \begin{eqnarray*}2\lfloor\frac{1}{3}(n-4)\rfloor\end{eqnarray*} and \begin{eqnarray*}2\lfloor\frac{1}{3}(n-5)\rfloor\end{eqnarray*} common cards, respectively. We then present new families that have the maximum number of common cards when one graph is connected and the other disconnected. Finally, we present a family with a large number of common cards, where one graph is a tree and the other unicyclic, and discuss how many cards are required to determine whether a graph is a tree. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 146–163, 2010     

关于(g,f)-2-消去图

一个图G称为一个(g,f)-2-消去图,如果G的任何两条边不属于它的一个(g,f)-因子.本文给出了当g＜f时一个图是(g,f)-2-消去图的一个充要条件.     

一个关于图是[a,b;n]-均匀的度条件

设t,a,b和n为整数且1≤a＜b,t≥3以及n≥1.如果G的导出子图不含有K1,t,则该图G称为K1,t-无爪图.如果对于图G中含有n条边的任意匹配M,都在G中有[a,b]-因子F包含M以及在G中有另一个[a,b]-因子F'不包含M,则图G称为[a,b;n]-均匀图.给出了K1,t-无星图G是[a,b;n]-均匀图的度条件.进一步,指出本文中的结果在某种意义上说是最佳的.     

On the Haefliger-Hirsch-Wu invariants for embeddings and immersions

We prove beyond the metastable dimension the PL cases of the classical theorems due to Haefliger, Harris, Hirsch and Weber on the deleted product criteria for embeddings and immersions. The isotopy and regular homotopy versions of the above theorems are also improved. We show by examples that they cannot be improved further. These results have many interesting corollaries, e.g.? 1) Any closed homologically 2-connected smooth 7-manifold smoothly embeds in .? 2) If and then the set of PL embeddings up to PL isotopy is in 1-1 correspondence with?. Received: July 6, 2000     

Chapter 5 Duality,classification and slacks in DEA

This paper presents seven theorems which expand understanding of the theoretical structure of the Charnes-Cooper-Rhodes (CCR) model of Data Envelopment Analysis, especially with respect to slacks and the underlying structure of facets and faces. These theorems also serve as a basis for new algorithms which will provide optimal primal and dual solutions that satisfy the strong complementary slackness conditions (SCSC) for many (if not most) non-radially efficient DMUs; an improved procedure for identifying the setE of extreme efficient DMUs; and may, for many DEA domains, also settle in a single pass the existence or non-existence of input or output slacks in each of their DMUs. This paper also introduces the concept of a positivegoal vector G, which is applied to characterize the set of all possible maximal optimal slack vectors. The appendix C presents an example which illustrates the need for a new concept,face regular, which focuses on the role of convexity in the intersections of radial efficient facets with the efficient frontier FR. The same example also illustrates flaws in the popular sum of the slacks methodology.R.M. Thrall is Professor of Administration and Noah Harding Professor of Mathematical Sciences, Emeritus, Rice University.     

Structural analysis of the recombinant therapeutic product rFVIII and its PEGylated variants using 2-D DIGE

2-D DIGE is a method that circumvents the gel-to-gel variability inherent in conventional 2-DE and is particularly useful for studying proteome changes in diverse applications such as developmental biology and tissue proteomics. We developed a 2-D DIGE protocol for recombinant factor VIII (rFVIII), a therapeutic protein used for the treatment of hemophilia A. The factor VIII heterodimer is composed of heterogeneous, heavily glycosylated heavy and light chains that are held together by a divalent cation. 2-DE of rFVIII led to a separation of the various fragments whose identity could be determined by Western blot. A comparison of two rFVIII batches by 2-D DIGE revealed their identical composition, whereas an rFVIII variant lacking its central B domain was congruent with the smallest heavy and light chain fragments of rFVIII only. A simpler pattern was obtained upon removal of the terminal sialic acids of rFVIII's glycans, due to a better focusing in the first dimension. 2-D DIGE was also well suited to structurally evaluate various PEGylated rFVIII conjugates. 2-D DIGE thus proved an excellent and straightforward method for structural analysis of rFVIII. Our data suggest that the method could serve as a tool for quality control of very complex pharmaceutically active ingredients.     

图的（g，f）－因子和因子分解

设Ｇ是一个图，ｇ，ｆ是定义在图Ｇ的顶点集上的两个整数值函数且图Ｇ的一个（ｇ，ｆ）－因子是Ｇ的一个支撑子图Ｆ使对任意的ｘ∈Ｖ（Ｆ）有本文给出了一个图（ｇ，ｆ）－可因子化的若干充分条件和一个图是（ｇ，ｆ）－消去图的充分必要条件，并研究了这些条件的应用。     

${\mathbb C}^n$中两球相交域的奇异积分

本文研究了双球相交域边界上的带有圆形挖去邻域的奇异积分,得到了带有全纯核的奇异积分的主值和Plemelj公式.