非交换Hadamard差集存在的一个必要条件

本文把文[1]的想法推广到非交换的情形,得到非交换Hadamard差集存在的一个必要条件.作为它的推论,一是解决了文[2]遗留下的一个未决情形,简化了其相应结果的证明;二是在自共轭条件满足时,对著名的交换Hadamard差集的Turyn指数界条件作出了改进.最后,提出了一个4p4阶群中交换Hadamard差集不存在的一个猜想.     

关于Arasu和Ma的一个引理的注记

通过改进Ａｒａｓｕ和Ｍａ的一个引理,在没有自共轭条件的情形下得到了一个关于西罗子群的指数界的差集存在的必要条件,作为它的一个应用,首次得到了不依赖于自共轭条件的指数界,从而对ＭｃＦａｒｌａｎｄ族与Ｓｐｅｎｃｅ族差集证明了Ｌａｎｄｅｒ猜想。     

非奇异M-矩阵的Hadamard积的最小特征值的估计

针对非奇异M-矩阵A与其逆矩阵的Hadamard积的最小特征值τ(AoA~(-1))的估计问题,利用逆矩阵元素的范围,给出了τ(AoA~(-1)1)上下界的收敛的估计序列.理论证明和数值算例表明所得估计能达到真值且比某些现有结果精确.     

正定矩阵的Hadamard乘积的一个矩阵不等式的精细

周知的正定矩阵A和B的Hadamard乘积矩阵不等式 :(A B) -1 ≤A-1 B-1 被精细为(A B) -1 ≤diag((A-1 (α) -1 B(α) ) -1 ,(A(α′) B-1 (α′) -1 ) -1 ) ,≤diag(A-1 (α) B(α) -1 ,A(α′) -1 B-1 (α′) )≤A-1 B-1 ,这里A(α)是A的主子矩阵且α′是α的补序列 ;同时给出了这些不等式的等式成立的充分必要条件     

几乎差集偶的分圆构造

本文研究了几乎差集偶的构造问题.利用分圆方法构造几乎差集偶,获得几乎差集偶的若干性质和一些几乎差集偶的类.     

非负性最小方差集的选择理论与实现

本文首先给出了最小方差集的运算模型，在此基础上指出了非负解的重要意义，并给出了非负解的枚举算法，最后给出了一个实例     

Ⅱ型循环拟差集的一些不存在性定理

本文研究(v,k,λ)-Ⅱ型循环拟差集存在的必要条件,特别对 v≡1(mod 4)的情形,给出了一些不存在性定理。最后指出:满足 v≡1(mod 4),v<100的整数v,除了 v=45,69,73,81,93外,其余参数的(v,k,λ)-Ⅱ型循环拟差集的存在性问题均获得完满解决。     

一个新的与Hadamard不等式相关的映射

对于一个最近发表的凸函数的Hadamard不等式的推广形式的不等式,本文引进了—个与这个不等式相关的的映射,从而给出了该不等式连续的加细.同时提及了它的某些应用.     

广义差集与几乎完美序列

提出了广义差集的概念,并且给出了广义差集的一些初等性质.从应用的角度讲,广义差集就是使得其±1特征序列的自相关函数是(最多)三值的一种组合结构.因此,广义差集不仅仅是在概念(理论)上的推广,它还具有深层次的应用背景.事实上,给出了一些广义差集,它不是可分差集,也不是相对差集.同时也给出了一类广义差集存在的一些必要条件,使得这些广义差集对应的±1特征序列成为几乎完美序列.并举例说明本文中的方法是有效的.     

关于Whiteman差集

设p,q是不同的奇素数.本文证明了如果W(p,q)是Whiteman差集,则必有     

SOME NEW FAMILIES OF SDSS AND HADAMARD MATRICES

ＳＯＭＥＮＥＷＦＡＭＩＬＩＥＳＯＦＳＤＳＳＡＮＤＨＡＤＡＭＡＲＤＭＡＴＲＩＣＥＳ￥ＸｉａＭｉｎｇｙｕａｎ（夏明远）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｕａｚｈｏｎｇＮｏｒｍａｌＵｎｉｕ．，Ｗｕｈａｎ４３００７０，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ...     

Indivisible plexes in latin squares

In this paper, we present two constructions of divisible difference sets based on skew Hadamard difference sets. A special class of Hadamard difference sets, which can be derived from a skew Hadamard difference set and a Paley type regular partial difference set respectively in two groups of orders v ₁ and v ₂ with |v ₁ − v ₂| = 2, is contained in these constructions. Some result on inequivalence of skew Hadamard difference sets is also given in the paper. As a consequence of Delsarte’s theorem, the dual set of skew Hadamard difference set is also a skew Hadamard difference set in an abelian group. We show that there are seven pairwisely inequivalent skew Hadamard difference sets in the elementary abelian group of order 3⁵ or 3⁷, and also at least four pairwisely inequivalent skew Hadamard difference sets in the elementary abelian group of order 3⁹. Furthermore, the skew Hadamard difference sets deduced by Ree-Tits slice symplectic spreads are the dual sets of each other when q ≤ 3¹¹.      

类切饼集上测度的局部维数存在的充要条件

本文研究了类切饼集上有限Borel正则测度的局部维数性质.利用中值定理和有界畸变原理,获得了一类类切饼集上测度的局部维数存在的一个充要条件,所获结果包含了已有结果.     

NECESSARY AND SUFFICIENT CONDITION FOR OSCILLATION OF A CLASS OF HIGHERORDER NEUTRAL EQUATIONS

ＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＯＳＣＩＬＬＡＴＩＯＮＯＦＡＣＬＡＳＳＯＦＨＩＧＨＥＲＯＲＤＥＲＮＥＵＴＲＡＬＥＱＵＡＴＩＯＮＳＬｉｎＹｉｚｈｏｎｇ（林宜中）（ＦｕｊｉａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，福建师范...     

SOME ESTIMATIONS FOR DETERMINANT OF THE HADAMARD PRODUCT OF H-MATRICES

In this paper,some new results on the estimations of bounds for determinant ofHadamard Product of two H-matrices are given.Several recent results are improved andgeneralized.     

THE OPPENHEIM-TYPE INEQUALITIES FOR THE HADAMARD PRODUCT OF M-MATRIX AND POSITIVE DEFINITE MATRIX

For the lower bound about the determinant of Hadamard product of A and B, where A is a n x n real positive definite matrix and B is a n x n M-matrix, Jianzhou Liu [SIAM J. Matrix Anal. Appl., 18(2)(1997).. 305-311] obtained the estimated inequality as follows     

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF HYPERBOLIC AND ELLIPTIC TYPE PARTIAL DIFFERENCE EQUATIONS

1 IntroductionQualitative theory for discrete dynamics systems with 1-D, that is, forordinary delay difference equation which is parallel to the qualitative theoryof ordinary delay differential equations has been investigated by a number ofauthors in recent years. Some of the results obtained have been collected inthe book by Gy6ri and Ladas [1, Chapter 7]. While nonlinear discrete dynamics systems with 2-D, that is, delay partial difference equations are equallyimportant in terms of physica…     

Hadamard and Conference Matrices

We discuss new constructions of Hadamard and conference matrices using relative difference sets. We present the first example of a relative -difference set where n – 1 is not a prime power.