Important Inequality

Extension of one important inequality

一个重要不等式的推广

It is well known that the Hilbert inequality is an important inequality in applications .

众所周知，Hilbert不等式是一个有重要应用的不等式。

The weighted arithmetic-geometric mean inequality is a very important inequality in mathematics .

加权算术&几何平均值不等式是数学中的一个重要不等式。

This paper shows an inserted-value form of the weighted average inequality , Thus producting another important inequality .

给出了加权平均不等式的一个插值形式，并由此得出了另一个重要的不等式。

An important inequality is used to establish some criteria for the oscillation of forced difference equation and it is generalized to higher order .

借助一个重要的不等式研究一类带有强迫项的时滞差分方程的振动性，并推广至高阶的情形。

The existence of the quadratic variation of local square integrable strong martingales is proved . The important inequality of Burkholder Davis Gundy is obtained .

证明了基于停线的局部平方可积强鞅的二次变差的存在性，得到了重要的Burkholder-Davis-Gundy不等式。

In this paper , we use Sylvester inequality , properties of linear space , properties of rank of matrix and decomposition of matrix , then give a modification for an important inequality which is related to rank of matrix .

根据Sylvester不等式、矩阵秩的性质、线性子空间的性质及矩阵的满秩分解，给出了一个重要不等式的一个改进形式。

One of the most important questions in inequality proof was discussed , i.e. , using the valid inequality to prove an inequality .

论述了不等式证明中的重要问题之一，利用已成立的不等式证明不等式的问题。

As I told him , although I have concerns about some of his secondary points and policy prescriptions , I agree with his most important conclusions : inequality is a growing problem and that governments should play a role in reducing it .

就像我和他说的那样，虽然我对他的一些次要观点和政策评估表示担忧，我依然同意他最重要的那个结论：不平等问题还在扩大，而且政府必须出面解决它。

On the expenditure side , health care is one of the most important sources of inequality . Because rural income is strongly related to human capital , the uneven access to health care will translate into a larger income gap in the long run .

在支出方面，医疗和教育费用是支出不平等的重要解释因素，由于农户收入和人力资本高度相关，长期来看，医疗和教育支出的不平等将会导致更大的收入差距。

Gender discrimination is an important aspect of social inequality in the United States .

性别歧视是美国社会不平等的一个重要方面。

These results of experiment 1 and 2 suggested that the central executive system play a important role in solving inequality problems ;

综合实验结果表明：中央执行系统在不等式求解中起重要作用；

In virtually all rich countries other than America such benefits ( rather than progressive tax systems ) became the most important instruments for reducing inequality .

实际上，在所有富国中，除了美国，这样的福利（而不是累进税体系）成为了减少不平等性最重要的手段。

Economical condition is one of the important factors that create inequality of educational opportunities , so subsidizing poor student is a powerful measure to promote equality of educational opportunities .

经济因素是造成教育机会不均等的重要因素，因此，为贫困学生提供资助就成为促进教育机会均等的重要措施。

The decomposition results reveals that education inequality is the most important contributor to urban-rural inequality in China , and it accounts for34.69 % of China 's urban-rural inequality !

分解结果表明，教育水平差异是中国城乡收入差距最重要的影响因素，其贡献程度达到34.69%！

Chapter 3 discusses the fundamentals inequalities in the rearrangement invariant martingale space , such as the corresponding important Doob 's maximal inequality , Burkholder-Gundy-Davis inequality and Rosenthal 's inequality .

第三章讨论重排不变鞅空间中的基本不等式，包括Doob极大不等式、Burkholder-Gundy-Davis不等式和Rosenthal不等式。

The convex functions have a lot of superior properties . The definition and the convexity of it are established on the base of inequality . The fact makes convex functions be important tools to prove inequality . So we can establish and improve lots of inequalities .

凸函数有许多很好的性质，它的凸性和其本身的定义是建立在不等式基础上的，这一事实使得凸函数成为了证明不等式的重要工具，由此建立和改进了大量的不等式。