来宾市旅游资源特色及开发构想

来宾市旅游资源丰富，特色鲜明，品位高，但存在旅游资源开发落后，利用程度低等问题。对来宾市旅游资源状况评价，分析其旅游资源开发价值和开发现状，提出旅游资源开发的构想。     

计算非线性问题的分歧解

对一类二阶非线性微分方程的正解进行了进一步的研究,考虑正解为退化的奇异解时,利用非线性泛函分析知识和分歧理论方法,首次推导论证了一个积分公式E(α),并得出它的具体数值符号可以判断解曲线在相平面(λ,u)中的转向情况.     

Algebraic methods in plane geometry

In this article we examine the role of mappings in elementary geometry. After making some comments about the Erlangen programme initiated by Felix Klein in 1872, wherein he proposed a way of studying geometries based on the underlying transformation groups, we see how theorems like Von Aubel’s theorem and Napoleon’s theorem can be proved in an elegant manner using similarity mappings, and how some construction problems may be solved using isometries. At the end we present a recent proof by Alain Connes of “Morley’s Miracle”, based on affine transformations. Shailesh Shirali heads a Community Mathematics Center at Rishi Valley School (KFI). He has a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis on problem solving and the historical aspects of the subject.     

The prime ordeal

Prime numbers have fascinated mankind through the ages. In fact, one may think that we know all about them. However, this is not so! One does not know the answers to many basic questions on primes. We shall concentrate here mainly on questions and discoveries whose statements are elementary and accessible. Right at the end, we mention a result whose statement is simple but whose proof uses rather sophisticated mathematics. Even here, we do not try to be exhaustive. The subject is too vast for that to be possible. After a long stint (1981–1999) at TIFR, Bombay, B Sury moved to ISI, Bangalore.     

替换定理的两个证明

替换定理是高等代数 (线性代数 )中向量空间理论的一个十分重要的定理 ,文章给出了两个新证明。     

一类三次系统极限环的唯一性

研究一类非的平面三次系统,给出了极限环的不存在性,存在性与唯一性,得到了更深入的结论.     

拓扑空间中的KKM型定理及其应用

在具有性质（H）的拓扑空间中引入了广义RKKM映射的概念．给出了一些非空交定理和不动点定理,证明了一个极大极小不等式,并进行了推广．     

数学期望在高等数学教学中的应用

本文讨论了数学期望在高等数学教学过程中几个方面的应用,为学习高等数学提供了概率背景.首先,给出了积分第一中值定理以及推广的积分第一中值定理的概率解释.接着,证明了平面薄板的重心坐标实际上可以看作二维随机变量的数学期望.最后,用数学期望重新给出了凸、凹函数的定义以及詹森(Jensen)不等式.     

浅谈蝴蝶定理的再推广及其应用

本文以高等几何的相关理论为背景,充分利用射影几何的交比,从二次曲线定弦BC上的任意一点、二次曲线内或外的任意一定点A、正方形、变态的二次曲线等四个方面对蝴蝶定理进行了再推广,并给出推广后命题的一些简单应用。     

非线性椭圆特征值问题多解的存在性

利用三个临界点定理讨论了散度形式的非线性椭圆特征值问题的多个弱解的存在性,这种方法也适用于其他一些非线性椭圆方程.