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1.
这是一道看似寻常的最值问题:四面体ABCD中,AD、BD、CD三棱两两垂直,且AD=1,BD+CD=4.求图1S△ABC的最大值与最小值.从解题常规看,入手并不难.如图1所示,在平面ABC内,作AE⊥BC,垂足为E,联DE.则DE⊥BC.设BD=x,易知 DE=BD·CDBC=x·(4-x)x2+(4-x)2=4x-x22x2-8x+16 AE=AD2+DE2=x4-8x3+18x2-8x+162x2-8x+16而 S△ABC=12AE·BC =12x4-8x3+18x2-8x+16(1)面对这…  相似文献   

2.
令G为一具有n个节点的平面近三角剖分图,C为G的一个少圈二重覆盖(SCDC).本文首先给出了G的一些生成元,由此可以得到G的一个SCDC.若G为一外平面近三角剖分图,得到 |C|≤n-2的一充分必要条件;若 G至少有一个内点,得到|C|≤n-2的一充分条件.  相似文献   

3.
圆周角     
一、启发提问1.什么是圆周角?它与圆心角的定义有何关系?2.圆周角定理中的圆周角和圆心角有什么特殊限制?3.圆周角定理的证明过程告诉了我们什么数学思想方法?二、读书指导1.填空(1)圆周角定义的两个特征是,.(2)所对的圆周角等于它所对的圆心角的.2.选择下列图形中7-21,∠BAC是圆周角的是( )三、议练活动1.已知:如图7-22,⊙O中,∠ABC=50°,则∠AOC=度.图7-22      图7-23  2.如图7-23,AB、AC分别与⊙O交于B、E和C、D,BD是⊙O的直径,∠BOC…  相似文献   

4.
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  相似文献   

5.
关于Abel群上Cayley图的Hamilton圈分解   总被引:3,自引:0,他引:3  
王殿军  王建中 《数学进展》1994,23(6):551-554
设G(F,T∩T^-1)是有限Abel群F上的Cayley图,T∩T^-1只含2阶元,此文证明了当T是F的极小生成元集时,若d(G)=2k,则G是k个边不相交的Hamilton圈的并,若d(G)=2k+1,则G是k个边不相交的Hamilton圈与一个1-因子的并。  相似文献   

6.
一、选择题(每小题4分,共28分)1.已知:如图D-1,BC切⊙O于B,∠AOB=110°,则∠ABC=( )(A)110° (B)55° (C)70° (D)35°图D-2图D-1  2.如图D-2,⊙O是Rt△ABC的内切圆,切点为D、E、F,∠C=90°,AC=6,BC=8,则AF+BE=( )(A)8 (B)6 (C)10 (D)123.两圆的直径分别为10和6,圆心距为4,则两圆的位置关系是( )(A)外离 (B)外切 (C)相交 (D)内切4.如图D-3,弦AB、CD相交于P,PA=…  相似文献   

7.
读完《异面直线距离的公式求法》[1]一文,感觉可类比求出异面直线所成的角.如图图11,α⊥β,ABα,CDβ,∠ABC=θ1,∠DCA=θ2.于是在平面β内过A作AE∥DC,则∠EAC=θ2.异面直线AB,DC所成的角是∠BAE.又α⊥β,∴∠B...  相似文献   

8.
正规Cayley图     
综述了自1990年以来12-传递图研究的一些新成果,正规Cayley图的相关结论。  相似文献   

9.
一、启发提问图7-461.如图7-46,圆心到直线l的距离就是半径OA,由上节知识可知直线l与⊙O,这里的直线l有两个限制条件,它们是,.2.圆的切线垂直于经过切点的.3.切线性质定理的两个推论的题设和结论分别是什么?4.切线的性质定理及其两个推论的题设和结论有什么关系?二、例题示范例1 已知:如图7-47,点C是⊙O的AB的中点,CD∥AB.求证:CD是⊙O的切线.分析 要证CD是⊙O的切线,根据判定定理只需要连结OC,证明OC⊥CD即可;用垂径定理由已知条件可知OC⊥AB,而AB∥CD,因此…  相似文献   

10.
1966年第2期《数学通报》上刊有一篇题为《有一组对边相等和一组对角相等的四边形是平行四边形吗?》(以下简称为《四边形》)的文章,作为数学教师当然知道这是个错误命题,但是文章始终未给出反例的作法.图1其实这个问题并不难解决,下面我们从这个命题的条件分析起.如图1,四边形ABCD中∠A=∠C=α,AD=BC=a,AB=b,DC=c,BD=e,由余弦定理得  e2=a2+c2-2accosα,  e2=a2+b2-2abcosα.∴ a2+c2-2accosα =a2+b2-2abcosα,b2-c…  相似文献   

11.
设Γ=K_(s[t])是一个完全多部图,其中st是一个偶数,则存在一个二面体群R=D_(2n)(n=st/2),使得R能构造出一个同构于K_(s[t])的Cayley图.讨论了当s、t满足什么条件时,完全多部图Γ有同构于Cay(R,S)的齐次分解.  相似文献   

12.
半二面体群的小度数Cayley图   总被引:1,自引:0,他引:1  
群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut X中正规.研究了4m阶半二面体群G=〈a,b a2m=b2=1,ab=am-1〉的3度和4度Cayley图的正规性,其中m=2r且r>2,并得到了几类非正规的Cayley图.  相似文献   

13.
二面体群D_(2n)的4度正规Cayley图   总被引:4,自引:0,他引:4  
王长群  周志勇 《数学学报》2006,49(3):669-678
设G是有限群,S是G的不包含单位元1的非空子集.定义群G关于S的 Cayley(有向)图X=Cay(G,S)如下:V(x)=G,E(X)={(g,sg)|g∈G,s∈S}. Cayley图X=Cay(G,S)称为正规的如果R(G)在它的全自同构群中正规.图X称为1-正则的如果它的全自同构群在它的弧集上正则作用.本文对二面体群D2n以Z22 为点稳定子的4度正规Cayley图进行了分类.  相似文献   

14.
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schr?dinger-type differential operator). Using tools such as scattering approach and eigenvalue interlacing inequalities we derive several formulas relating the number of the zeros of the n-th eigenfunction to the spectrum of the graph and of some of its subgraphs. In a special case of the so-called dihedral graph we prove an explicit formula that only uses the lengths of the edges, entirely bypassing the information about the graph??s eigenvalues. The results are explained from the point of view of the dynamics of zeros of the solutions to the scattering problem.  相似文献   

15.
We consider k‐factorizations of the complete graph that are 1‐rotational under an assigned group G, namely that admit G as an automorphism group acting sharply transitively on all but one vertex. After proving that the k‐factors of such a factorization are pairwise isomorphic, we focus our attention to the special case of k = 2, a case in which we prove that the involutions of G necessarily form a unique conjugacy class. We completely characterize, in particular, the 2‐factorizations that are 1‐rotational under a dihedral group. Finally, we get infinite new classes of previously unknown solutions to the Oberwolfach problem via some direct and recursive constructions. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 87–100, 2008  相似文献   

16.
In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.  相似文献   

17.
Acta Mathematica Sinica, English Series - We show that, up to isomorphism, there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n ≥ 4....  相似文献   

18.
《Discrete Mathematics》2023,346(6):113362
The study of perfect state transfer on graphs has attracted a great deal of attention during the past ten years because of its applications to quantum information processing and quantum computation. Perfect state transfer is understood to be a rare phenomenon. This paper establishes necessary and sufficient conditions for a bi-Cayley graph having a perfect state transfer over any given finite abelian group. As corollaries, many known and new results are obtained on Cayley graphs having perfect state transfer over abelian groups, (generalized) dihedral groups, semi-dihedral groups and generalized quaternion groups. Especially, we give an example of a connected non-normal Cayley graph over a dihedral group having perfect state transfer between two distinct vertices, which was thought impossible.  相似文献   

19.
The Paul Erd?s and András Gyárfás conjecture states that every graph of minimum degree at least 3 contains a simple cycle whose length is a power of two. In this paper, we prove that the conjecture holds for Cayley graphs on generalized quaternion groups, dihedral groups, semidihedral groups and groups of order \(p^3\).  相似文献   

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