两类圈的广义Mycielski图的邻强边色数

设G是简单图,V(Mn(G))={v01,v02,…,v0p;v11,v12,…,v1p;…;vn1,vn2,…,vnp};E(Mn(G))=E(G)∪{vijv(i 1)k|v0jv0k∈E(G),1≤i,j≤p,i=0,1,…,n-1},则Mn(G)称为G的广义Mycielski图,其中,V(G)={v0i|i=1,2,…,p}.本文得到了Mn(Cm)的邻强边色数,其中,Cm是m阶圈,且m≡0(mod 5)或m≡0(mod 6).     

关于图的L(2,1)-标号问题

图的L(2，1)—标号问题来自频率分配问题并且是NP—完全性问题。得到：(Ⅰ)G是p个顶点的简单图，对正整数k≥3，当p≥2k^2和△≥p／k时，有L(G)≤△^2。(Ⅱ)△(G)表示图G的最大度，则L(G)≥△(G) 1。(Ⅲ)若V(G)可划分为独立集V1，V2，…，Vk，且V(G)=U^ki=1Vi及Vi∩Vj=Ф，i≠j，则L(G)≤p k-2。     

关于Ulam猜想的部分结果和Czh+1∪nK2的对角Ramsey数

证明了n=7时的重构猜想,给出p(p≥7)阶图G的p个主子图G1,G2,…,Gp.其中G1,G2,…,G6中的点v1,v2,…,v7未标定,点v8,v9,…,vp标定;G7,…,Gp中的点全不标号,则G可由G1,G2,…,Gp在同构意义下惟一重构.还证明了Czh 1∪nK2的对角R am sey数为R(Czh 1∪nK2)=m ax{3(h n) 1,4h 1}.式中h,n∈Z且h≥2,n≥1.     

素数原根的两个猜想

应用计算机编程,对素数原根进行了研究,通过对100亿以下素数进行了验证,得出了两个猜想：（1）若P和q=4p＋1都是素数,则q的最小原根为2;（2）若p和q=2p＋1都是素数,当p=1（mod 4）时,2是q的最小原根,而当P=3（mod4）时,2不是q的最小原根。在验证这两个猜想的过程中,还发现对于P和2^kp＋1都为素数时,2不是2^k p＋1的最小原根（k〉2）。     

全纯函数与其导数分担的正规定则

设,为区域D内的一个全纯函数族,k(≥2)是一正整数,p是小于k的正整数,K为一正数.若对于任意的f∈F,f与fCM分担zp,且当f(z)=zp,z∈D时,有|f(k)(z)|≤K,则F在D上是正规的.     

与任意图(m,r)-正交的(g,f)-因子分解

设G是一个图,用y(G)和E(G)表示它的顶点集和边集,并设g(x)和f(x)是定义在V(G)上的两个整数值函数,且对C每个x∈V(G),有5/2r-1≤g(x)≤f(x),则图G的一个支撑子图,称为G的一个(g,f)-因子,如果对每个x∈V(G),有g(x)≤d,(x)≤f(x)．图G的(g,f)-因子分解是指E(G)能划分成边不交的(g,f)-因子,设F=|F1,F2,…,Fm|和H分别是图G的因子分解和子图,若对所有1≤i≤m有|E(H)∩E(Fi)|=r,则称,和H(m,r)-正交．本文证明：若G是一个(mg m-1,mf-m 1)-图,H是G中任一有mr条边的子图,则G有一个(g,f)-因子分解与H(m,r)-正交。     

若干合成图的星全染色

简单图G和H的合成图是指具有顶点集V（G）×V（H）的简单图G[H],它的顶点（u,v）和另一个顶点（u,v＇）相邻当且仅当或者uu＇∈E（G）,或者“u=u’且vv’∈E（H）．文中研究了n＋1阶简单图G与m阶简单图H的合成图的星全染色,其中G为Wn。,扇Fm或星Sn．得到以下结果：（1）若△（H）=2且n≥4,m≥5,则G[H]的星全色数为（2n＋1）m;（2）若x（H）=△（H）=m-1且n,m≥4,则G[H]的星全色数为2（n＋1）m-1．     

三色拉姆塞数R_3（C_8）研究

用r种颜色对图G的所有边着色,记着第i色的边构成的子图为Gi,如果存在一种着色方法使得每一个Gi（1≤i≤r）都不包含图H,则称图G对于H可以r着色.拉姆塞数Rr（H）是使得完全图Kn对于H不可以r着色的最小正整数n.令Cm表示长度为m的圈,Dzido等证明了R3（C2k）≥4k.本文对k=4的情形进行研究,利用计算机,通过大量的计算证明了R3（C8）=16.     

关于Cm·Sn和CmΔSn的全染色

设m≥3,n≥2V(Cm.Sn)={ui|i=1,2,…,m}∪{vij|i=1,2,…,m;j=1,2,…,n},E(Cm.Sn)={u1u2,u2u3,…,u(m-1)um,umu1}∪{uivij|i=1,2,…,m;j=1,2,…,n}则称Cm.Sn为m个Sn(星)的心联图.V(CmΔSn)={ui|i=1,2,…,m}∪{vij|i=1,2,…,m;j=1,2,…,n},E(CmΔSn)={v11v21,v21v31,…,v(m-1)1vm1,vm1v11}∪{uivij|i=1,2,…,m;j=1,2,…,n}则称CmΔSn为m个Sn(星)的沿联图.本文给出Cm·Sn和CmΔSn全染色以及全色数.     

关于Cm·Sn和Cm△Sn的全染色

设m≥3,n≥2V(Cm·Sn)={ui|i=1,2,…,m}∪{vij|i=1,2,…,m;j=1,2,…,n},E(Cm·Sn)={u1u2,u2u3,…,u(m-1)um,umu1}∪{uivij|i=1,2,…,m;j=1,2,…,n} 则称Cm·Sn为m个Sn(星)的心联图.V(CmΔSn)={ui|i=1,2,…,m}∪{vij|i=1,2,…,m;j=1,2,…,n},E(CmΔSn)={v11v21,v21v31,…,v(m-1)1vm1,vm1v11}∪{uivij|i=1,2,…,m;j=1,2,…,n} 则称CmΔSn为m个Sn(星)的沿联图.本文给出Cm·Sn和CmΔSn全染色以及全色数.     

Existence of Almost Resolvable Directed 7-Cycle Systems

Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDkCS （v） had been completely solved. This paper shows that there exists an ARD7CS（v） if and only if v≡1 （rood 7） and v≥8.     

Splitting Balanced Incomplete Block Designs with Block Size 2×k

This paper investigated the existence of splitting balanced incomplete block designs with blck size 2 ×k.The necessary conditions for such a design are λ(v-1)≡0(mod k),and λv(v-1 )≡0 (mod 2k 2). It will show that the above necessary conditions are also sufficient for k = 3 with the definite exception(v,λ)= (10,1) and with several possible exceptions.     

图的符号k-控制

设G（V,E）为一个图,k为任意的正整数且k不超过｜G｜,若有一个函数f：V｜1,－1｜满足：V中至少有k个点满足f[v]≥1,则称f为图G的一个符号k-控制函数,图G的符号k-控制数定义为γks^-11（G）=min{f（V）｜f为图G的一个符号k-控制}．给出了图的符号k-控制数的下界的一个改进的结论,并确定了轮图的符号k-控制数、     

ROLE OF ANTISENSE AND DECOY OLIGONUCLEOTIDE OF NF-κB IN VESSEL STENOSIS AND NEOINTIMA FORMATION IN BALLOON-INJURED RAT ARTERY

Objective To examine antisense and decoy oligonucleotides of nuclear factor kappa B in vivo effects on intima proliferation and balloon-injured monocytes chemotactic protein-1 ( MCP-1 ) and extracellular signal regulated kinase-2 ( ERK2 ) expression in the carotid artery of rats. Methods Sprague-Dawley rats underwent balloon-dilation injury of the left carotid artery. Rats are divided into 7 groups ( n = 18 ) and each group includes 6 time points (6 h, 1, 3, 5, 7, 14 d) ( n =3). Uninjured right carotid artery of the same rat was used as controls. Results In model group, sense group and scramble group, vessel intima area , media area and intima/media ratio increased after 5 d and reached the maximum after 7 d. The effect of antisense plus decoy group on intimal hyperplasia was more obvious than that of antisense group and decoy group alone. MCP-1 mRNA expression was increased expression continuously at 3, 5 and 7 d and decreased at 14 d. Compared with model group, sense group and scramble group, antisense group, decoy group and antisense plus decoy group had lowered MCP-1 mRNA expression in each time point ( P ＜ 0. 05 ). NF-κB p65 was dispersed positive stain 6 h after injury and increased after 1 d and peaked at 7 d, but the protein expression was weak at 14 d. ERK2 protein synthesis increased at 1 d and reached the peak at 7 d, while protein expression after 14 d was similar to that at 7 d. Treatment of antisense group,decoy group and antisense plus decoy group inhibited protein synthesis more significantly than those of model group,sense group and scramble group ( P ＜ 0. 05 ). Conclusion NF-κB modulates genes expression and protein synthesis of MCP-1 and ERK2. Celluar proliferation in vessel wall was dynamically changed after balloon angioplasty injury. Antisense and decoy oligonucleotide of NF-κB by local lipofectamine transfer inhibit NF-κB activating gene modulation and neointimal hyperplasia.     

两类图的算术标号

对于一个（p，g）图G，如果存在一个v（G）到非负整数集N0的一个映射以称为顶点标号）满足：（1）f（u）≠f（v），其中u≠v，且u，v∈V，（c）；（2）{f（u）＋f（v）｜uv∈E（G））={k，k＋d，…，k＋（g-1）d），称图G为（k，d）-算术图。证明了图Fm．4是（d，2d）-算术图和图Fm．6是（d，3d）-算术图。     

Network Decomposition and Maximum Independent Set Part Ⅱ：Application Research

According to the researches on theoretic basis in part I of the paper，the spanning tree algorithms solving the maximum independent set both in even network and in odd network have been developed in this part，part Ⅱ of the paper．The algorithms trans form first the general network into the pair sets network，and then decompose the pair sets network into a series of pair subsets by use of the characteristic of maximum flow passing through the pair sets network．As for the even network，the algorithm requires only one time of trans formation and decomposition，the maximum independent set can be gained without any iteration processes，and the time complexity of the algorithm is within the bound of O(｜V｜^3)．However，as for the odd network，the algorithm consists of two stages．In the first stage，the general odd network is transformed and decomposed into the pseudo-negative envelope graphs and generalized reverse pseudo-negative envelope graphs alternately distributed at first；then the algorithm turns to the second stage，searching for the negative envelope graphs within the pseudo-negative envelope graphs only．Each time as a negative envelope graphhas been found．renew the pair sets network by iteration at once．and then tum back to the first stage．So both stages form a circulation process up to the optimum．Two available methods，the adjusting search and the picking-off search are specially developed to deal with the problems resulted from the odd network．Both of them link up with each other harmoniously and are embedded together in the algorithm．Analysis and study indicate that the time complexity of this algorithm is within the bound of O(｜V｜^5)．     

Construction of Pure Mendelsohn Triple Systems

This paper determined the existence of λ-fold pure Mendelsohn triple system of order υ satisfying λυ(υ-1)≡0 (mod 3) and υ≥4λ 5, or υ=2λ 2, and in the case of λ=4,5,6, which completely settled their existence.