4p阶3度点传递图

一个图称为点传递图,如果它的全自同构群在它的顶点集合上作用传递.证明了一个4p(p为素数)阶连通3度点传递图或者是Cayley图,或者同构于下列之一;广义Petersen图P(10,2),正十二面体,Coxeter图,或广义Petersen图P(2p,k),这里k2≡-1(mod 2p).     

4p阶三度点传递图

一个图称为点传递图或对称图如果它的自同构群分别在点集或点集有序对上传递.设P为素数,给出了4p阶连通三度点传递图分类(徐明曜等在[Chin.Ann.Math.,2004,25B(4):545-554]中分类了4p阶连通三度对称图).确定了4p阶互不同构的连通三度点传递图的个数f(4p);当P=2,3,5,7时,f(4p)分别为2,4,8,6;当P≥11且4|(p-1)时,f(4p)=5+p-3/2,当P≥11且4|(p-1)时,f(4p)=3+p-3/2.     

p~2阶弧传递循环图的正规性条件

群G关于S的有向Cayley图X=Cay(G,S)称为pk阶有向循环图,若G是pk阶循环群.利用有限群论和图论的较深刻的结果,对p2阶弧传递(有向)循环图的正规性条件进行了讨论,证明了任一p2阶弧传递(有向)循环图是正规的当且仅当(|Aut(G,S)|,p)=1.     

4p~2阶4度半传递图

如果图X的全自同构群Aut(X)作用在其顶点集V(X)和边集E(X)上都是传递的,但作用在弧集Arc(X)上非传递,则称X是半传递图.研究了4p~2(p3且p≡-1(mod4))阶4度半传递图,确定了4p~2阶4度半传递图的连通性及其自同构群的阶.     

PSL(2,p)上的弧传递3度Cayley图

设T=PSL(2,p),其中p为不小于5的素数.给出了T上的连通的弧传递3度Cayley图的分类,并且决定了T的所有满足条件o(α)=2和o(t)=3的生成元对(α,t).     

点传递自补图

图Γ称为点传递自补图,如果Γ的图自同构群AutΓ在顶点集合VΓ作用是传递的,且Γ的补图(Γ)与图Γ是同构的.本文主要研究了通过Cayley同构来构造点自补Cayley图,并证明了内循环群上的这类图必然是循环自补图.     

极小Cayley图的限制性边连通度

一个连通图X的边集的一个子集C称为一个限制性边割,如果它是一个边割,且X／C不含孤立点。X的限制性边连通度λ′（X）定义为所有限制性边割的最小基数。本文完全决定了极小Cayley图的限制性边连通度。     

全正规弧传递和1/2-弧传递Cayley图

给出了全正规弧传递和1/2-弧传递Cayley图的构造,并构造了一些群类上分类结果.     

2p2阶3度Cayley图

Cayley图Cay(G,S)称之为正规的,如果G的右正则表示是Cay(G,S)全自同构群的正规子群。本文决定了2p~2(p为素数)阶群上3度连通Cayley图的正规性,作为该结果的一个应用,对每一个1(?)s(?)5,对2p~2阶3度s-正则Cayley图作了分类。     

几乎自补Cayley图及其在CI-群上的应用

设X为点传递图,F是与图X具有相同顶点集合的1因子图,若X∪F的补图X∪F≌X称X是几乎自补点传递图.通过Cayley同构方法构造了一族几乎自补点传递图.并将此方法应用一类CI-群上,得到了在此类群上的几乎自补的Cayley图的构造.     

Combinatorial principles between RRT 2 2 and RT 2 2

We study the strength of some combinatorial principles weaker than Ramsey theorem for pairs over RCA0. First, we prove that Rainbow Ramsey theorem for pairs does not imply Thin Set theorem for pairs. Furthermore, we get some other related results on reverse mathematics using the same method. For instance, Rainbow Ramsey theorem for pairs is strictly weaker than ErdSs- Moser theorem under RCA0.     

Infra-red spectral studies of CHF2-CHCl2 and CBrCl2-CBrCl2

The infra-red spectra of two polyhalogenated ethanes, 1, 1-difluoro-2, 2-dichloro ethane and 1, 2-dibromo-1, 1, 2, 2-tetrachloro ethane were obtained in the region of 2·5–38 microns. The spectra of CHF₂-CHCl₂ were obtained in gas, liquid and solid states and also in solvents of widely varying dielectric constants. These spectral studies showed that the molecule exists in the form of two rotational isomers. The fundamental modes of the two isomers were identified on the basis of intensity changes from gas to liquid to solid and in solvents of different dielectric constants. The observed infra-red absorption bands have been assigned in terms of the fundamental absorption bands. Spectra of CBrCl₂-CBrCl₂ were obtained in the solid and vapour phase and in various solvents. These spectra showed that CBrCl₂-CBrCl₂ exists only in the trans form. The infra-red spectra, combined with Raman data available from literature was used for complete assignment of the observed absorption bands.     

P2Q2Iso2D=2D Isoparametric FEM in Matlab

A short Matlab implementation realizes a flexible isoparametric finite element method up to quadratic order for the approximation of elliptic problems in two-dimensional domains with curved boundaries. Triangles and quadrilaterals equipped with varying quadrature rules allow for mesh refinement. Numerical examples for the Laplace equation with mixed boundary conditions indicate the flexibility of isoparametric finite elements.     

Descent on 2-Fibrations and Strongly 2-Regular 2-Categories

We consider pseudo-descent in the context of 2-fibrations. A 2-category of descent data is associated to a 3-truncated simplicial object in the base 2-category. A morphism q in the base induces (via comma-objects and pullbacks) an internal category whose truncated simplicial nerve induces in turn the 2-category of descent data for q. When the 2-fibration admits direct images, we provide the analogous of the Beck–Bénabou–Roubaud theorem, identifying the 2-category of descent data with that of pseudo-algebras for the pseudo-monad q ^*Σ _q . We introduce a notion of strong 2-regularity for a 2-category R, so that its basic 2-fibration of internal fibrations c od:F ib(R)→R admits direct images. In this context, we show that essentially-surjective-on-objects morphisms, defined by a certain lax colimit, are of effective descent by means of a Beck-style pseudo-monadicity theorem.     

Non-symmetric 2-designs modulo 2

Necessary conditions are obtained for the existence of a 2 – (v, k, ) design, for which the block intersection sizess ₁,s ₂, ...,s _n satisfys ₁ s ₂ ... s _n s (mod 2 ^e ), wheree is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.Research done at AT&T Bell Laboratories.     

环$F_2 uF_2 u^2F_2$上的循环码及自对偶码

We give the structures of a cyclic code over ring
R = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},
where u^3 = 0, of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.     

Comparison of relative risk,attributable risk and logistic response procedures for 2×2×2 andc 2×2×2 contingency tables

Summary A numerical evaluation was made on three different χ² statistics in order to compare mutagenic risk frequencies between two experimental groups in a 2×2×2 contingency table andc 2×2×2 contingency tables. The three methods involve 1) a relative risk approach, 2) an attributable risk approach and 3) a logistic response approach. A relatively large difference was observed among χ² statistics in the three approaches using actual data under the hypothesis that there is no difference between the two groups under scrutiny. With regard to approximate power, it appears that approaches 2) and 3) give fairly stable results. Approach 1) has greater power if there is a small difference in the control groups. It was confirmed that the approximate power of approach 1) is extremely large when the difference in the relative risk frequencies between the two groups under contrast is constant and each relative risk frequency is small. This paper was presented at the 48th annual meeting of Japan Statistical Association in Tokyo, Japan, 1980.