最优(v,{3,4},1,Q)-光正交码的构造

在光纤码分多址(OCDMA)系统中,变重量光正交码被广泛使用,以满足多种服务质量的需求.利用分圆类和斜starter给出了直接构造方法,借助有关循环差阵的递归构造方法,从而构造了两类循环填充设计.通过建立循环填充设计与变重量光正交码之间的联系,证明了当Q∈{{2/3,1/3},{3/4,1/4}}时,最优(v,{3,4},1,Q)-光正交码存在的无穷类.     

The Existence of （v, 4, 1） Disjoint Difference Families with v a Prime Power

A （v, k, λ） difference family （（v, k, λ）-DF in short） over an abelian group G of order v, is a collection F=（Bi｜i ∈ I} of k-subsets of G, called base blocks, such that any nonzero element of G can be represented in precisely A ways as a difference of two elements lying in some base blocks in F. A （v, k, λ）-DDF is a difference family with disjoint blocks. In this paper, by using Weil＇s theorem on character sum estimates, it is proved that there exists a （p^n, 4, 1）-DDF, where p = 1 （rood 12） is a prime number and n ≥1.     

一种OLS/OOC二维光正交码的构造与性能分析

利用不同的序列作为波长跳频序列和时间扩频序列可以构造出不同的二维光正交码在众多文献中已有所报道.在经过正交拉丁方(OLS)与跳频序列的相关性研究之后.做了以下主要工作:首先,将正交拉丁方(OLS)序列作为波长跳频序列,结合一维时间扩频序列(OOC),构造了一种OLS/OOC二维光正交码.然后,本文对构造的OLS/OOC进行了多种性能仿真和分析.相对于PC/OOC、OCFHC/OOC等二维光正交码而言,OLS/OOC的波长数并不局限于素数,更能充分利用MWOCDMA系统中的有效波长数.仿真和分析表明:码字具有很好的相关性能,码字容量直逼理论极限,为一种渐近最优二维光正交码.     

码重为3和7的最优光正交码的具体构造

对光正交码(OOC)构造的关注源于它在光码分多址网络中有许多应用.截至目前,对于码重为W∈{{3,4},{3,5},{3,6},{4,5},{4,6]}的变重量光正交码的构造已经取得许多结果.然而,对于码重为W={3,7}的变重量光正交码的具体构造非常的少.给出一系列新的最优变重量光正交码(33p,{3,7},1,{4/5,1/5})-OOC的具体构造,对于任何素数p≡3(mod 4)且p≥7.     

Flag-transitive point-primitive 2-（v,k,4） symmetric designs and two dimensional classical groups

Let D be a 2-(v, k, 4) symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ⊴ G ≤ Aut(X) where X ≅ PSL ₂(q). Then D is a 2-(15, 8, 4) symmetric design with X = PSL ₂(9) and X _x = PGL ₂(3) where x is a point of D.     

典型群PSU（3，q2）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。     

图C_（4n＋2）×P_（4k＋3）的优美性

图Ｃ＿（４ｎ＋２）×Ｐ＿（４ｋ＋３）的优美性杨燕昌，王广选（北京工业大学应用数学系，北京１０００２２）（北京密云县医院计算机室，北京　１０１５００）关键词乘积图，标号，优美图．分类号ＡＭＳ（１９９１）０５Ｌ７８／ＣＣＬＯ１５７．５关于一般乘积图Ｃ＿ｌ...     

ON THE EMDEN-FOWLER EQUATION u″（t）u（t） = c1＋c2u′（t）^2 WITH c1≥0, c2≥0

In this article, we study the following initial value problem for the nonlinear equation
{u″u（t）=c1＋c2u′（t）^2, c1≥0, c2≥0,
u（0）=u0, u′（0）=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions.     

SUZUKI GROUPS Sz（q） AND 2-（v,k, 1） BLOCK DESIGNS

It is proved that if D be a 2-(v,k,1) design with G≤Aut D block primitive then G does not have a Suzuki group Sz(q) as the socle.     

最优(m,n,4,1)光正交签名码的进一步结果

为支持高速多址网络中二维图像的传输,Kitayama首次提出码分多址并行图像传输系统的概念.作为码分多址并行图像传输系统的首选光地址码,光正交签名码(OOSPC)是一族具有良好相关性的Hamming重量为k的m×n(0,1)-矩阵.用Θ(m,n,k,λ)表示所有参数为(m,n,k,λ)的OOSPC中码字容量可能的最大值,则称码字容量为Θ(m,n,k,λ)的(m,n,k,λ)-OOSPC是最优的.本文将针对满足下列条件之一的正整数m和n:(1)mn≡8,16(mod 24),gcd(m,n,2)=2,且mn≡16(mod 32)和gcd(m,n,4)=2不同时成立,其中m和n的所有奇素因子均模6余1;(2)mn≡0(mod 24)且gcd(m,n,6)=2,证明Θ(m,n,4,1)=|mn-1/12|,即构造码字容量为|mn-1/12|的最优(m,n,4,1)-OOSPC.     

二分（0，mf—m＋1）-图的正交（0，f）-因子分解

设G=（X,Y,E（G））是一个二分图,分别用V（G）=X∪Y和E（G）表示G的顶点集和边集．设f是定义在V（G）上的整数值函数且对任意x∈V（G）有f（x）≥k．设H1,H2,…,Hk是G的k个顶点不相交的子图,且｜E（Hi）｜=m,1≤i≤k．本文证明了每个二分（0,mf—m＋1）．图G有一个（0,f）-因子分解正交于Hi（i=1,2,…,k）     

^2F4（q2）与2-（v，k，3）对称设计

本文要证明不存在一个非平凡2-（v,k,3）对称设计,它的旗传递自同构群的基柱是^2F4（q2）     

关于二元样条空间S3r^4（△＊）的维数

设△＊是任何三角剖分△的ＨＣＴ细分的三角剖分。本文建立了定义于△＊上的二元样条函数空间Ｓ３ｒ＾ｒ（△＊）的维数公式，我们的证明方法同时给出了Ｓ３ｒ＾４（△＊）的一组显示的基函数，并阐明基函数具有某种意义的局部最小支集。     

Existence of a-fold Perfect （v, {5, 8}, 1）-Mendelsohn Designs

Let v be a positive integer and let K be a set of positive integers. A （v, K, 1）-Mendelsohn design, which we denote briefly by （v, K, 1）-MD, is a pair （X, B） where X is a v-set （of points） and B is a collection of cyclically ordered subsets of X （called blocks） with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t =1, 2,..., r, every ordered pair of points of X are t-apart in exactly one block of B, then the （v, K, 1）-MD is called an r-fold perfect design and denoted briefly by an r-fold perfect （v, K, 1）-MD. If K = {k） and r = k - 1, then an r-fold perfect （v, （k）, 1）-MD is essentially the more familiar （v, k, 1）-perfect Mendelsohn design, which is briefly denoted by （v, k, 1）-PMD. In this paper, we investigate the existence of 4-fold perfect （v, （5, 8}, 1）-Mendelsohn designs.     

LIE SYMMETRY ANALYSIS AND PAINLEVE ANALYSIS OF THE NEW （2＋1）-DIMENSIONAL KdV EQUATION

Lie point symmetries associated with the new （2＋1）-dimensional KdV equation ut ＋ 3uxuy ＋ uxxy = 0 are investigated. Some similarity reductions are derived by solving the corresponding characteristic equations. Painlevé analysis for this equation is also presented and the soliton solution is obtained directly from the Bǎcklund transformation.     

The L（3,2, 1）-labeling on Bipartite Graphs

An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.     

广义函数δ（x_1,…,x_（2m））和δ（x_1,…,x_（2m-1））I（x_（2m））的乘积（英文）

AB 用非标准分析和广义函数的调和表示,给出广义函数δ（x_1,…,x_（2m））和δ（x_1,…,x_（2m-1））Ⅰ（x_（2m））的乘积.