Social exclusion and inequality in higher education in China: A capability perspective

Following calls for further research in education inequality beyond input and output measures, especially with a qualitative approach, and building on the implications of capability deprivation on equality (0375 and 0380), we extend the findings of 0305, 0310, 0315 and 0320 capability approach to higher education (HE). This article employs social exclusion theory as the analytical framework to examine educational inequalities in China posed by the HE admission system in Post-Mao era. This paper is driven by certain key motivations and makes a significant contribution to the extant literature. Firstly, the paper seeks to outline a usable definition of social exclusion in the context of HE enrolment. Following this, 0305, 0310, 0315 and 0320 capability approach is adopted for the first time as a theoretical construct to examine the situation facing HE in China. Sen's approach facilitates an appraisal of the process of exclusion in HE enrolment. The importance of the capability approach is that it allows one to recognize different needs and choices confronting different social groups by distinguishing between different types of social exclusion in this area. Finally, this information is used to evaluate responses which are available to the existing issues within the current Chinese HE enrolment mechanism i.e. that the mechanism is fundamentally flawed and risks reducing, rather than enhancing, capability by excluding certain groups of students from fair competition in terms of access.     

柯西不等式证法探讨

利用配方法、构造二次三项式、二元二次型的正定性、拉格朗日恒等式、行列式性质、数学归纳法以及算术平均-几何平均不等式等7种方法给出了柯西不等式的7种证法.     

关于平均值不等式的若干证明

本文总结了平均值不等式的三种证法,一是数学归纳法,第二是函数法,最后是特殊不等式法。总之,平均值不等式的证明方法很多。     

参数对不等式解法产生的影响

主要剖析了参数在解不等式过程中产生的影响,结合现行高中教材,从统一的函数背景、统一的解法策略加以分析、归纳,阐明了参数不等式解法产生的影响。     

关于Hardy-Hilbert不等式的多参数推广

对Hardy-Hilbert不等式进行了研究,并将其进一步改进如下：若p〉1,1/p＋1/q=1,0〈A,B≤1,an,bn≥0,使0〈∑∞n=0apn〈∞,0〈∑∞n=0bqn〈∞,则∑∞m=0∑∞n=0ambn/Am＋Bn＋1〈{∑∞n=0（π/Bsin（π/p）-（3p-B）（ p-1）/6p（2An＋）11/p）anp}1/p{∑∞n=0（π/Asin（π/p）-（3q-A）（q-1）/6q（2Bn＋1）1/q）bnq}1/q.所得结果改进和推广了最近文献的一些相应结果.     

一类加权p-Laplace算子基本解和Hardy-Sobolev型不等式

从另一个角度研究欧氏空间Rn上的Hardy-Sobolev不等式.通过考察一类加权p-Laplace算子基本解,得到Hardy型不等式.利用积分关系法建立Hardy-Sobolev型不等式.所得结果丰富和拓展了Rn中的已有结论.     

论数学解题的自然性

以自然结构为理论依据,分析、研究及推广了历史名题Ｃａｕｃｈｙ－Ｓｃｈｗａｒｚ不等式,并简述了数学解题的自然审美观和研究问题及发现问题的思维方法．     

一个混合类的Hilbert型不等式

引进一对共轭指数（p,q）,给出了一个带最佳常数因子的混合类Hilbert型不等式及其等价式．     

不等式自动发现和判定程序agl2010的若干改进及应用

对不等式自动发现和判定程序agl2010进行了若干改进,扩充了程序功能,提高了运算效率;讨论了自动发现不等式过程中的若干技巧和策略;以实例的方式介绍了agl2010程序的应用.     

微分形式的 Aλr3 (λ1,λ2 ;Ω)-加权的Poincaré型不等式

利用H(o)lder不等式得到了微分形式的局部 Ar (λ1,λ2 ;Ω)-加权Poincaré型不等式,所得结果能被广泛应用于某些重要方程解的高阶可积性理论.