零和Ramsey数R(C_3,Z_3)的下界——(3)

Bialostocki和Dierker给出了古典Ramaey定理下列有趣的推广:设G是一个有m条边的图,整数k≥2,且k|m,Z_k表示k阶循环群。定义R(G,Z_k)表示一个极小整数t,使得对K_t的边的任意Z_k—染色(即一个泛函C:E(K_t)→Z_k),K_t中都存在一个同构于G的子图具有下列性质 sum from e∈E(G) C(e)≡0(mod k)。本文证明R(C_3,Z_3)≥11。     

巧证定理:a~3 b~3 c~3≥3abc(a,b,c∈R~ )

介绍一种定理证明的较简单的方法：∵ａ，ｂ，ｃ∈Ｒ＋∴（ａ３＋ｂ３）＋（ｃ３＋ａｂｃ）≥２ａ３ｂ３＋２ａｂｃ４≥２·２ａ３ｂ３·ａｂｃ４＝４ａｂｃ∴ａ３＋ｂ３＋ｃ３≥３ａｂｃ并且仅当ａ３＝ｂ３，ｃ３＝ａｂｃ，且ａ３ｂ３＝ａｂｃ４ａ＝ｂ＝ｃ时，上式才取等...     

The spectrum of (gv, g, 3, λ)-DF in Z_(gv)

In this paper, the necessary and sufficient conditions for the existence of a (gv, g, 3, λ)- difference family in Zgv are established. As a consequence, the existence spectrum of a cyclic (3, λ)-GDD of type gv without short orbits is determined.     

rep(A_3,I,A)中的Gorenstein投射模

设A是域k上的有限维代数,(Q,I)是带关系的箭图,令Λ=AkkQ/I.Λ的模范畴Λ-Mod及有限生成模范畴Λ-mod分别与(Q,I)在A上的表示范畴Rep(Q,I,A)及有限维表示范畴rep(Q,I,A)等价.给出了范畴rep(A_3,I,A)中Gorenstein投射模的具体构造,其中(A_3,I)=3α→2β→1,I=βα.在此基础上,给出了代数A是自入射代数的一个充分必要条件.     

C(m,3)的交叉数

众所周知,任何一类非平凡图交叉数的精确值的确定都是非常困难的．作者证明了对任意k(?)2,h∈{0,1,2},循环图C(3k h,3)的交叉数为k h,但C(6,3),C(7,3)的交叉数都是1．C(5,3)的交叉数也是1．     

典型群PSU(3,q~2)与2-(v,k,1)设计

讨论自同构群是酉群 PSU(3 ,q2 ) (q=2 l)的区 -本原的 2 -(v,k,1 )设计 .首先证明了它必是点 -本原的 ,然后确定了这种类型的设计 ,即它只能为 2 -(q3+1 ,q+1 ,1 )设计     

U(3,Z_p),U(4,Z_p)及U(5,Z_p)的共轭类

通过计算相关矩阵的秩,求出了U(3,Z_p),U(4,Z_p)及U(5,Z_p)的共轭类.     

上同调运算与群π(K,L;SY_(N-3,y))

<正> 文[1]利用上同伦边缘引入上同调运算,如 s_p~2,Φ_0等,并指出,在精确到群扩张的范围内,这些运算可以决定群 π~(N-3)(K,L),甚至还可决定群 π~(N-r)(K,L)的结构.由[4],所有自(K,L)到(Y_n,y)的连续映射的同伦类构成阿倍尔群π(K,L;Y_n,y),     

SL(3,p~n)的Cartan不变量

K表示特征数p>0的代数闭域。G是K上单连通半单代数群。Γ_n=G(FP~n)是P~n个元素的有限域上型G的有限Chevalley群,它在K上的群代数是KΓ_n.Λ_n表示不同构的不可约KΓ_n-模M_(λ,n)的指标集,也是不同构的主不可分解KΓ_n-模R_(λ,n)的指标集,它可以看作G的权格X中“限制”优势权的集合X_(p~n)。因此|Λ_n|=p~(R·rankG.Γ_n的Cartan不变量C_(λ,μ(λ,μ∈Λ_n)等于M_(μ,n)作为R_(λ,n)的合成因子出现的重数,形成|Λ_n|阶对称矩阵。     

SG(N,3)上的调和分析

该文研究R^N中分形上的的调和分析问题,得到了SG（N,3）上的调和函数及Dirichlet问题与Neumann问题解的存在唯一性定理,并给出了解的具体形式和SG（N,3）上的Gauss-Green公式。     

L(m,3)的对称链分解

对称链是一种特殊的偏序,用它已经得到了许多非常漂亮的结果.如果一个偏序集可以分解成不相交的对称链之并,则称此偏序集具有对称链分解.但目前已证明具有这种分解的偏序集并不多.L(m,n)＝{(x₁,x₂,…,x_n)|x_i均为整数且0≤x₁≤x₂≤…≤x_m≤n},序关系≤定义为:X=(x₁,x₂,…,x_m<     

The sizes of optimal (n,4,λ,3) optical orthogonal codes

Let $\Phi (n,k,{\lambda }_a,{\lambda }_c)$ denote the largest possible size among all $(n,k,{\lambda }_a,{\lambda }_c)$-OOCs. An $(n,k,{\lambda }_a,{\lambda }_c)$-OOC with $\Phi (n,k,{\lambda }_a,{\lambda }_c)$ codewords is said to be optimal. In this paper, the exact value of $\Phi (n,4,\lambda ,3)$ is determined. Equivalently, the size of an optimal $(n,4,\lambda ,3)$ optical orthogonal code is calculated.     

2-(v,k,1)设计和PSL(3,q)(q是奇数)

§ 1　 IntroductionA2 -(v,k,1 ) design D=(S,B) consists ofa finite set Sof v points and a collection Bof some subsets of S,called blocks,such that any two points lie on exactly one blockand each block contains exactly k points.A flag of Dis a pair(α,B) such thatα∈S,B∈Bandα∈B,the set of all flags is denoted by F.We assume that2≤k≤v.An automorphism of Dis a permutation of the points which leaves the set Binvari-ant,all the automorphisms form a group Aut D.Let G be a subgroup of A…     

Stiefel流形 O_(n,3)的KO-群

<正> §1.引言设 O_(n,3)为向量空间 K~n 中的所有三维正交标架所组成的 Stiefel 流形.当 K 为实数(复数、四元数)时,分别记为 V_(n,3)(W_(n,3)、X_(n,3)).本文分别计算它们的 KO-群.对于 O_(n,3),按照[8,第四章]指出的方法给以胞腔剖分.     

Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n)

We show that points in specific degree-2 hypersurfaces in the Grassmannian $Gr(3,n)$ correspond to generic arrangements of n hyperplanes in ${\mathbb{C}}^3$ with associated discriminantal arrangement having intersections of multiplicity three in codimension two.     

Noether’s problem for GL(2, 3)

We prove that Noether’s problem has an affirmative answer for the group GL(2, 3), over every field K. In particular, the group admits a generic polynomial over . As a consequence, so does the group . Research was partially supported by MCYT grant BFM2003-01898.     

无向超环面网C(3,3…,3)的(n,2n)控制数

The(d,k)-dominating number is a new measure to characterize reliability of resourcesharing in fault tolerant networks.This paper obtains that the(n,2n)-dominating number of the n-dimensional undirected toroidal mesh C(3,3,…,3)is equal to 3(n≥3).     

Enumeration of 2-(9, 3, λ) Designs and Their Resolutions

We consider 2-(9, 3, ) designs, which are known to exist for all 1, andenumerate such designs for = 5 and their resolutions for 3 5, the smallestopen cases. The number of nonisomorphic such structures obtained is 5 862 121 434, 426, 149 041, and 203 047732, respectively. The designs are obtained by an orderly algorithm, and the resolutions by two approaches:either by starting from the enumerated designs and applying a clique-finding algorithm on two levels or by anorderly algorithm.