Characterizing directed path graphs by forbidden asteroids

An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker and Boland. Their result says that a chordal graph is an interval graph if and only if it does not contain an asteroidal triple. In this paper, we prove an analogous theorem for directed path graphs which are the intersection graphs of directed paths in a directed tree. For this purpose, we introduce the notion of a special connection. Two non‐adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex‐disjoint chordless paths satisfying certain conditions. A special asteroidal triple is an asteroidal triple such that each pair is linked by a special connection. We prove that a chordal graph is a directed path graph if and only if it does not contain a special asteroidal triple. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:103‐112, 2011     

泛剩余交

本文建立了泛剩余交理论，并揭示了它与剩余交和一般剩余交的关系，得到：在交换局部环Ｒ的扩张Ｓ＝Ｒ（Ｘ）＝Ｒ［Ｘ］_{mＲ［Ｘ］}中，存在ＩＳ的一个ｓ－剩余交ＵＲＩ（ｓ；Ｉ），使得对Ｉ在Ｒ中的任意ｓ－剩余交Ｊ，ＵＲＩ（ｓ；Ｉ）是Ｊ的本质形变，且是Ｉ的一般ｓ－剩余交ＲＩ（ｓ；Ｉ）局部化ＲＩ（ｓ；Ｉ）_{mＲ［Ｘ］}．并给出了一些应用，为研究剩余交和一般剩余交提供了工具．     

Ampleness of intersections of translates of theta divisors in an abelian fourfold

We prove the ampleness of the cotangent bundle of the intersection of two general translates of a theta divosor of the Jacobian of a general curve of genus . From this, we deduce the same result in a general, principally polarized abelian variety of dimension .

     

一类(a+1,3)型的距离正则图

设Γ是直径为d且型为(α 1,3)的距离正则图,其中α≥2.用l(c,a,b)表示交叉阵列l(Γ)中列(c,a,b)~t的个数,记r=r(Γ)=l(c_1,a_1,b_1),s=s(Γ)=l(c_(r 1),a(r 1),b_(r 1)).那末,若c_(r 1)=3且a_(r 1)=3a,则d=r s 1,c_d=4且Γ为正则拟2d边形.     

Boundedly connected sets and the distance to the intersection of two sets

We prove that if (X,d) is a metric space, C is a closed subset of X and x∈X, then the distance of x to R∩S agrees with the maximum of the distances of x to R and S, for every closed subsets R,S⊂C such that C=R∪S, if and only if C is x-boundedly connected.     

Combined Modelling of Triply Paired Electronic States of HO2+ ion with 3 Symmetry using Coupled Eigen Model

The multi state triply paired coupled adiabatic electronic states of , symmetries for the title ion have been modelled using the triply paired coupled eigen valued functions with the principal aim of getting a set of well optimized triply paired coupled functions, capable of explaining all the microscopic topograhical features present in the chosen coupled electronic states. The high quality size truncated dynamically correlated points at the limit of complete basis set (CBS) were utilized for this purpose. The proposed model function are presented in an “easy to understand” linear form with respect to the pre-defined variables which are directly dependent on the diabatic potentials and coupling strengths found in the diabatic matrix. Its most important feature (an essential criterion to be selected for modelling the triply degenerate seam pathway) is the ability to predict the existence of an uniquely defined triply degenerate iso-energetic geometry among the chosen coupled states in addition to the prediction of the existence of many doubly degenerate iso-energetic geometries in those states and hence can be adaptable to any general molecular system where such triply or doubly degenerate geometries are believed to occur. The title ion is one among them where many doubly iso-energetic geometries were located but not the triply degenerate one as it is a three atomic system unlike the polyatomic case where the triply degenerate geometry will most likely to be found. To do this work, one requires the knowledge of four asymptotic diatomic curves upon atom+diatom dissociation whose correct correlated spectroscopic states are O₂⁺ , O₂ , O₂⁺ , OH⁺ . The quality and the characteristics of analytical surface of the ion is discussed well in detail.