On the maximum size of Erdős-Ko-Rado sets in H(2d+1, q^2)

Erd?s-Ko-Rado sets in finite classical polar spaces are sets of generators that intersect pairwise non-trivially. We improve the known upper bound for Erd?s-Ko-Rado sets in \(H(2d+1, q^2)\) for \(d>2\) and \(d\) even from approximately \(q^{d^2+d}\) to \(q^{d^2+1}.\)      

On (4p~2q~(2b),2p~2q~(2b)-pq~b,p~2q~(2b)-pq~b) Menon Difference Sets

Ｏｎ（４ｐ２ｑ２ｂ，２ｐ２ｑ２ｂ－ｐｑｂ，ｐ２ｑ２ｂ－ｐｑｂ）ＭｅｎｏｎＤｉｆｅｒｅｎｃｅＳｅｔｓＷａｎＺｈａｏｚｅ（万兆泽）（ＣｏｌｅｇｅｏｆＭａｔｈｅｍａｔｉｃＳｃｉｅｎｃｅ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１００８７１）Ａｂｓ...     

所有形如a2=b+c的勾股数组(a,b,c)

本刊文[1](第17页)给出了勾股数组(3,4,5),(5,12,13)满足的规律:32=4 5,52=12 13.能否求出所有形如a2=b c的勾股数组(a,b,c)呢?这是一个有趣的问题.     

当$4q^{5}-5q^{4}-2q+1\leq d \leq 4q^{5}-5q^{4}-q$时$[g_{q}(6,d),6,d]_{q}$码的不存在性

证明了对于q≥17,当4q~5-5q~4-2q+1≤d≤4q~5-5q~4-q时,不存在达到Griesmer界的[n,k,d]_q码.此结果推广了Cheon等人在2005年和2008年的非存在性定理.     

Trajectories of the zeros of hypergeometric polynomials F(−n, b; 2b; z) for b < − 1/2

In a previous paper [2] we studied the zeros of hypergeometric polynomials F(−n, b; 2b; z), where b is a real parameter. Making connections with ultraspherical polynomials, we showed that for b > − 1/2 all zeros of F(−n, b; 2b; z) lie on the circle |z − 1| = 1, while for b < 1 − n all zeros are real and greater than 1. Our purpose now is to describe the trajectories of the zeros as b descends below the critical value − 1/2 to 1 − n. The results have counterparts for ultraspherical polynomials and may be said to “explain” the classical formulas of Hilbert and Klein for the number of zeros of Jacobi polynomials in various intervals of the real axis. These applications and others are discussed in a further paper [3].     

Group theoretic characterizations of Buekenhout–Metz unitals in $\mathop{\mathrm{PG}}(2,q^{2})$

Let G be the group of projectivities stabilizing a unital \(\mathcal{U}\) in \(\mathop{\mathrm{PG}}(2,q^{2})\) and let A,B be two distinct points of \(\mathcal{U}\). In this paper we prove that, if G has an elation group of order q with center A and a group of projectivities stabilizing both A and B of order a divisor of q?1 greater than \(2(\sqrt{q}-1)\), then \(\mathcal{U}\) is an ovoidal Buekenhout–Metz unital. From this result two group theoretic characterizations of orthogonal Buekenhout–Metz unitals are given.     

不等式（a~2／b）≧2a.b的应用

不等式（ａ~２／ｂ）≧２ａ.ｂ的应用陈晓春（四川三峡学院数学系６３４０００）由基本不等式变形可得不等式其中ａ∈Ｒ，ｂ∈Ｒ＋，等号当且仪当ａ＝ｂ时成立．不等式（＊）是简单的．但用它来求解某些具有一定难度的题目，却十分简捷、新颖．本文的目的即是通过例题说明...     

比较a/b与(a 2b)/(a b)的大小

设a,b∈R~ 且a>b,讨论并比较a/b与a 2b/a b的大小。原题中含有两个变元a、b,为使问题化繁为简,引进新的变元t,且令t=a/b,显然有t>l,则(a 2b)/(a b)=(t 2)/(t 1)>1,这样,要讨论的两个分式的大小比较就转化为讨论t与(t 2)/(t 1)的大小比较了。 1°设t=t 2/t 1,则有t~2 t=t 2t~2=2,由