关于凸体的一个不等式的简单证明

<正> 本文涉及Grunbaum一个已被解决的问题. 设K是R~n中的紧致凸体,P是K的一个内点.过P任作K的一条弦C(p),并以C′(p)记平行于C(p)的任意一条弦.|C(p)|和|C′(p)|分别表C(p)与C′(p)的长.令     

On the inverse problem relative to dynamics of the ω function

Let P be the set of prime numbers and P (n) denote the largest prime factor of integer n > 1. Write C3 = {p1p2p3 : pi ∈ P (i = 1, 2, 3), pi = pj (i = j)}, B3 = {p1p2p3 : pi ∈ P (i = 1, 2, 3), p1 = p2 or p1 = p3 or p2 = p3, but not p1 = p2 = p3}. For n = p1p2p3 ∈ C3 ∪ B3, we define the w function by ω(n) = P (p1 + p2)P (p1 + p3)P (p2 + p3). If there is m ∈ S - C3 ∪ B3 such that ω(m) = n, then we call m S-parent of n. We shall prove that there are infinitely many elements of C3 which have enough C3-parents an...     

An asymptotic property of the number of spanning trees of double fixed step loop networks

Let T(C(p,1,q))be tbe number of spanning trees of circulant graph C(p,1,q). In this note we show that T(C(p 1,1,q))/T(C(p,1,q))→2,p→ ∞.     

与ω函数的动力学相关的逆问题

用P记素数的集合,P（n）表示整数n（〉1）的最大素因子．记C3={p1p2p3：Pi∈P（i=1,2,3）,pi≠pj（i≠j）}, B3={p1p2p3：pi∈P（i=1,2,3）,p1=p2或p1=p3或p2=p3,但非p1=p2=p3}． 对于礼=p1p2p3∈C3UB3,定义训函数为 w（n）=P（p1＋p2）P（p1＋p3）P（p2＋p3）．如果有m∈S∪→C3∪B3,使得w（m）=n,则称m为n的S-亲源． 本文证明：在C3中有无穷多个元,它们有足够多的C3-亲源;在B3中有无穷多个元,它们也有足够多的C3-亲源．本文还证明,在B3中有无穷多个元,它们有足够多的B3-亲源．     

关于多项式的一条猜想

设C是常数,p(z)与q(z)为多项式,若p(a)=C也使q(a)=C,则记为p9或qp.[1]提出如下猜想: 设p,q为次数大于1的多项式,若p=0q=0 且 p′=1q′=1,则p=q,其中p′为p的导数。     

关于广义Dedekind群

如果群G的任意循环子群H满足|HG:H|≤p,其中p是素数,那么称G是C*(p)-群.若群G是有限C*(p)-p-群,则当p＞3时,该群的幂零类至多为2;若p=3,该群的幂零类至多为3,而且当cl(G)=3时,exp(G)=9;同时,若G与任意有限C*(p)-p群G × K直积是C*(p)-P-群G×K,则G是初等阿贝尔p-群.最后还对局部幂零的C*(p)-群进行了探讨.     

环R{D,C}的一些性质

研究环R{D,C}的一些性质,证明了:1)环R{D,C}是弱拟morphic环当且仅当D是弱拟morphic环且对任意的x∈C,存在y∈C使得Cx=l_C(y).Dx=l_D(y);2)环R{D,C}是EIFP环当且仅当D和C都是EIFP环;3)环S=R{D,C}是左p.p.-环的充分必要条件是环D和C都是左p.p.-环.     

Graphs on which a group of order pq acts edge-transitively

Let Γ be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p ≥ q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut(Γ) contains a subgroup G of order pq that acts edge-transitively on Γ, then Γ is one of the following graphs: (1) pK 1,1 ; (2) pqK 1,1 ; (3) pK q,1 ; (4) qK p,1 (p q); (5) pC q (q 2); (6) qC p (p q); (7) C p (p q = 2); (8) C pq ; (9) (Z p , C) where C = {±rμ | μ∈ Z q } with q 2, q|(p-1) and r ≡ 1 ≡ r q (mod p); (10) K p,1 (p q); (11) a double Cayley graph B(G, C) with C = {1-r μ | μ∈ Z q } and r ≡ 1 ≡ r q (mod p); (12) K pq,1 ; or (13) K p,q .     

THE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORUSTHE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORU

1. IntroductionGiven a locally compact abelian group G and a multiplier p on G, one can associate tothem the twisted group C*-algebra C*(G, p), which is the universal object for unitary prepresentations of G. C* (Zm, p) is said to be a noncommutative torns of rank m and denotedby A.. The multiplier p determines a subgroup S. of G, called its symmetry group, andthe multiplier p is called totally skew if the symmetry group S. is trivial. And A. is calledcompletely irrational if p is totally…     

球面Jackson多项式逼近的正逆定理

研究了球而Jackson多项式Jv,sf的逼近阶,建立立该多项式逼近的强型正向与逆向不等式.利用球面光滑模较好地刻画了Jackson多项式的逼近性能,证明了存在与v和f无关的常数C1和C2,使得对于定义在球面上任意p-幂勒贝格可积或连续函数f成立C1ω(f,1/v)p≤‖Jv,sf-f‖p≤C2ω(f,1/v)p,其中ω(f,t)p是f的光滑模.     

图的割宽最大值问题

§ 1　IntroductionThe cutwidth minimization problem for graphs arises from the circuitlayout of VLSIdesigns[1 ] .Chung pointed outthatthe cutwidth often corresponds to the area of the layoutin array layout in VLSI design[2 ] .In the layout models,the cutwidth problem deals withthe number of edges passing over a vertex when all vertices are arranged in a path.For agraph G with vertex set V(G) and edge set E(G) ,a labeling of G is a one-to-one mapping ffrom V(G) to the integers.The cutwid…     

4p阶二面体群的弱3-CI性

决定了4p(p是奇素数)阶二面体群的连通3度Cayley图的完全分类,并证明4p阶二面体群不是弱3-CI群,从而否定了C.H.Li关于"所有有限群都是弱3-CI群"的猜想     

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).     

Asymptotic enumeration theorems for the numbers of spanning trees and Eulerian trails in circulant digraphs and graphs

The asymptotic properties of the numbers of spanning trees and Eulerian trails in circulant digraphs and graphs are studied. Let be a directed circulant graph. Let and be the numbers of spanning trees and of Eulerian trails, respectively. Then

小度数循环图的计数

循环图已被用于平行计算，网络等方面．循环图研究的一个基本问题是对互不同构的循环图进行计数．对于给定的一个正整数ｎ，用Ｃ（ｎ，ｋ）表示互不同构的具有几个顶点，度数为ｋ的连通循环图的个数．文中给出了度数为 ４和５的循环图的一般结构，并对ｎ＝ｐａｑｂ（ｐ，ｑ皆为素数，ａ，ｂ＞０），给出了Ｃ（ｎ，４）的计算公式．     

线图泛圈性的一个充分条件

本文证明了如果Ｇ是２连通线图,Ｇ不是圈,ｎ＝｜Ｖ（Ｇ）｜≥９且Ｇ的每个同构于Ａ的导出子图都满足（ａ１,ａ２）,则Ｇ是泛圈图     

几类多圈图的拉普拉斯谱刻画

设图G是一个简单连通图. 如果任何一个与图G同拉普拉斯谱的图都与图G同构,则称图G是由其拉普拉斯谱确定的. 定义了双圈图\theta_{n}(p_1,p_2,\cdots,p_t) 和m 圈图H_n(m\cdot C_3;p_1,p_2,\cdots,p_t). 证明了双圈图\theta_{n}(p)和\theta_{n}(p,q),三圈图H_n(3\cdot C_3;p)和H_n(3\cdot C_3;p,q)分别是由它们的拉普拉斯谱确定的.     

A Local Analysis of Imprimitive Symmetric Graphs

Let Г be a G-symmetric graph admitting a nontrivial G-invariant partition . Let Г be the quotient graph of Г with respect to . For each block B ∊ , the setwise stabiliser G_B of B in G induces natural actions on B and on the neighbourhood Г (B) of B in Г . Let G_(B) and G_[B] be respectively the kernels of these actions. In this paper we study certain “local actions" induced by G_(B) and G_[B], such as the action of G_[B] on B and the action of G_(B) on Г (B), and their influence on the structure of Г. Supported by a Discovery Project Grant (DP0558677) from the Australian Research Council and a Melbourne Early Career Researcher Grant from The University of Melbourne.     

Classifying cubic symmetric graphs of order 10p or 10p~2

A graph is called s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular cyclic or elementary abelian coverings of the Petersen graph for each s ≥ 1 are classified when the fibre-preserving automorphism groups act arc-transitively. As an application of these results, all s-regular cubic graphs of order 10p or 10p2 are also classified for each s ≥ 1 and each prime p, of which the proof depends on the classification of finite simple groups.