CH2N+HONO反应的动力学研究

用直接从头算动态学方法对CH2N＋HONO→CH2NH＋NO2反应进行了研究.用BH＆HLYP/6-31＋G（d,p）方法对所有稳定结构和过渡态的几何结构进行了优化,并用内禀反应坐标方法计算了最小能量路径（MEP）.在QCISD（T）/6-311＋G（2df,2pd）理论水平上对所有结构的能量进行了进一步校正.用变分过渡态理论（CVT）在考虑小曲率隧道（SCT）校正的水平上计算了200～2500K温度范围内标题反应的热速率常数,计算结果表明,上述温度范围内热速率常数有正的温度效应,计算结果与文献数据能够很好地吻合.     

高等代数观点下中学数学问题的新认识两例

利用<高等代数>观点,给出中学数学两问题的新思考:抛物线相似与Cauchy不等式应用.     

一个新的积分不等式及其应用

从离散型W．H．Young不等式出发，以归纳类比和分类讨论思想为基础，得到了一个新的积分不等式，并运用构造性方法给出了一种十分简洁的证明，又进一步讨论了新的积分不等式与P．Schweitzer反向积分不等式的关系，同时指出了由新的积分不等式能够得到Hoelder积分不等式、Minkowski积分不等式及Buniakowski—Schwarz积分不等式等，凸显其内在规律性和应用的广泛性。     

一元二次不等式的新解法

传统的一元二次不等式解法步骤多，用时长，已不能适应现代教学需要．采用新的解题方法，可以达到快速、准确，起到事半功倍的效果。     

When marketisation and privatisation clash with socialist ideals: Educational inequality in Urban China

In the last two decades, China's education has experienced significant transformations and restructuring on account of privatization and marketization. Unlike the Mao era when the state assumed the major responsibilities in financing and providing education, individuals and families have now to bear increasing financial burdens in paying for education. The marketization and privatization of education has undoubtedly intensified educational inequalities and widened regional disparities between the economically developed areas in the eastern coast and the less economically developed areas in the middle and north-western parts of the country. The growing inequalities in education and the increasing financial burdens presented by education have been a source of social discontentment, which have in turn prompted the central government to revisit its approaches to educational development. This article sets out to examine, how in this wider policy context, China's education has been transformed following the adoption of more pro-competition and market-oriented reform measures. This article is based on intensive secondary data analysis, fieldwork observations, and findings from a household survey conducted in eight different Chinese cities about people's perceived education hardship. The article concludes by considering how the Chinese government has attempted to address the problems of educational inequalities that have intensified on account of two decades of education marketization.     

几个不等式的推广及其成立等式的条件

推广了Cauchy不等式,Holder不等式和Minkowski不等式,给出了推广不等式成立等式的充要条件,并应用平均值不等式证明了所得结果.     

一个与Fermat问题相关的最佳线性不等式

运用三角形的Fermat问题的结论与两个条件不等式,利用导数,证明了涉及平面上任一点到三角形三顶点距离之和的一个最佳线性不等式,提出了一个相关的问题.     

一类广义集值拟向量变分不等式解的存在性

研究了Banach空间中一类G-可导映射的广义拟向量变分不等式问题,运用KKM定理证明这类问题解的存在性,并在适当的条件下证明了此类问题与Konnov I V和Yao J C等人提出的广义向量变分不等式问题是等价的。     

三角不等式原理对聚类算法的改进

聚类分析是数据挖掘中的一个重要研究领域,面对大规模的、高维的数据,如何建立有效的聚类算法是目前一个研究热点。现已有多种直接和快速的聚类算法,但是当处理海量数据时,时间效率仍然有待提高。本文应用三角不等式原理,分别对TTSAS算法和k-means算法提出改进,避免其中冗余的距离计算,提高原算法效率。     

示性函数在概率论中的应用

讨论了示性函数的若干性质,并利用示性函数简洁地证明了切比雪夫不等式和其它几个重要的概率公式.