一次成功的探究性教学

借奥赛班讲解＂用均值不等式证明不等式＂的课堂内容,开发学生的发散思维,提高学生独立思考能力。     

浅析函数的单调性在不等式证明中的应用

在高等数学的学习过程当中，不等式的证明是一个比较常见的问题，在各种考试当中经常出现。它也是高等数学学习的一个难点，大多数学生在遇到不等式证明问题时都不知到如何下手，苦于没有思路，这主要是因为不等式的证明没有固定的模式，也没有具体的定理明确指出用来证明不等式，而许多不等式证明问题又都存在一题多法，证明方法灵活多变，有一定的技巧性。虽然这样，但不等式的证明也是有一些基本方法的，下面就针对不等式的证明，总结了几种常用的方法。现举例说明如何利用函数的单调性来证明不等式。     

柯西不等式的几种证明方法

如果某一知识跟很多学科或者一个学科的很多分支有着密切联系,那么这个知识肯定是很重要的,而二次型、欧式空间内积、詹森不等式都是高等数学中代数、实函、微积分的基本内容。本文运用二次型理论、欧式空间中内积性质和詹森(Jensen)不等式三种方法证明柯西不等式,并简要说明柯西不等式与高等数学之间的联系。     

利用导数证明不等式方法研究

本文总结了利用微分理论证明不等式的十多种方法:导数定义法、单调性法、极值与最大最小值法等,本文将主要探讨导数在不等式证明中的应用。     

柯西不等式及其变式的应用

柯西不等式是一个非常重要的不等式，它以对称和谐的结构和广泛的应用引起了学者的讨论，井出现了许多的变式，现从柯西不等式的定义入手，对柯西不等式的几种证明方法进行了阐述，并逐步说明了在求最值、解方程、确定参数的取值范围、不等式的证明、推导空间点到直线的距离等，推导三角不等式，解决一些比较难求的最值问题及一些比较难证的数学题等方面的应用。     

论约束条件下Schwarz不等式的改进

把Schwarz不等式的积分形式化为二重积分形式,借助均值不等式给出了Schwarz不等式的又一种证明方法。接着讨论了Schwarz不等式在证明Minkonshi等不等式中的应用,从而得出约束条件下对该不等式的改进。     

凸函数及其相关的一些重要不等式

讨论了凸函数的有关内容。凸函数与连续函数、可微函数、可积函数之间有着紧密的联系，具有很强烈的几何背景。直观上看它的图像是向下鼓鼓的，进一步由数学表达式表示出其图像的特征，从而引出凸函数的定义及严格凸函数的定义。讨论了凸函数的一些性质。定义和性质给出后，又讨论了几种判断函数凸性的方法。在有了严格凸函数的定义及相应的判断函数严格凸的方法后，我们又得到一些严格的不等式。把凸函数定义中的不等式推广为更一般的情况得到了重要的詹森不等式及其改进形式。利用詹森（Jensen）不等式又得到了一些著名的不等式。     

积分不等式的证明

通过若干实例较系统地介绍了积分不等式的证明方法和技巧,以便使积分不等式的证明更为简捷。     

国际贸易的"相对价格不等式"与"广义比较优势"

本文在哈伯勒运用比较成本解释比较优势原理的基础上,提出国际贸易的"相对价格不等式".经过要素禀赋理论、产品生命周期理论和规模优势理论对该不等式的检验,本文得出该不等式在经典的国际贸易理论中是成立的结论.在此基础上,本文提出"广义比较优势"概念,并指出其不仅有重要的理论研究意义,而且在当今全球金融危机冲击和影响下,有着重要的理论现实意义.     

一类不等式的加强

针对一类不等式,给出相关讨论,揭示其内在联系,并提出待研究的问题。     

Spatial inequality and household poverty in Ghana

The study analyses district-level consumption inequality in Ghana, explores the relative contribution of within- and between-district inequalities to national inequality and examines the relationship between household poverty and inequality. The last three rounds of the Ghana Living Standard Survey are used. We observe that the contribution of within-district inequality to national inequality is higher than inequality between districts. Also, district-level consumption inequality shows a significant effect on household poverty, but with varying signs. We surmise that the variation in signs is as a result of the state of economic activity and factors that affect both poverty and inequality.     

Understanding Income Inequality in China: A Multi-Angle Perspective

Economic reforms have brought about spectacular growth and vast improvements of people’s living standards in China since 1978. In the meantime, unbalanced regional growth and income inequality have become two important concerns of future development. Most available studies on income distribution have either focused on the rural population or on the urban citizens. This paper stresses the importance of adopting a multi-angle approach to fully understand income inequality in China. We first use some top-down information to form a general picture of inequality for the whole country, and then use some bottom-up household survey data to explain in detail the development of inequality over time regarding rural/urban inequality, rural inequality, urban inequality and inter-regional inequality, the relative importance of different income sources to overall inequality. This revised version was published online in July 2006 with corrections to the Cover Date.     

Human capital inequality and income inequality: testing for causality

This study investigates the causal relationship between human capital inequality and income inequality in case of Pakistan. The annual time series data ranging from 1973 to 2009 is used for econometric analysis. Johanson co-integration and Granger Causality tests are used to confirm the existence of long run relationship and the causal relationship between human capital inequality and income inequality. The results indicate that there is positive relationship between the two types of inequalities in the long run. The estimates of causality test indicate that income inequality causes the human capital inequality but human capital inequality does not cause income inequality. Policy initiatives to reduce income inequality may empower people economically to avail skill building opportunities and accumulate their human capital through access to educational services.     

Unbalanced regional growth and regional income inequality in the latter stages of development

This paper empirically examines the pattern of regional income inequality displayed in advanced stages of economic development, building from the convergent phase of the inverted-U hypothesis, originally developed by Kuznets for personal income inequality, but adapted by Williamson for regional income inequality. It is hypothesized that once the inverted-U pattern is completed, regional income inequality increases, rather than remaining stable. Four analyses of intrastate per capital income inequality among countries are undertaken to test the hypothesis that regional inequality increases. Results indicate strong support for the hypothesis that regional income inequality increases in the latter stages of development.     

Can innovation improve income inequality? Evidence from panel data

Income inequality is a source of social instability and armed conflict, which in turn are detrimental to economic development. This study examines the role of innovation in income inequality in twenty-three developed countries, using a panel mean group estimator that takes cross-sectional dependence into consideration. Three income inequality indicators are used: the Standardized World Income Inequality Database (SWIID), the University of Texas Inequality Project (UTIP), and the Estimated Household Income Inequality (EHII). The innovation indicators are patent applications and patents granted. The empirical results based on the common correlated effect mean group (CCEMG) reveal that innovation widens income inequality. We also investigate whether the innovation–income inequality nexus is subject to a country’s level of globalization and financial development. The findings suggest that the interaction terms between innovation with these two variables have positive effects on income inequality, whereas innovation failed to reduce income inequality. Globalization and financial development are found to drive income inequality. The empirical results are robust to different income inequality and innovation measures as well as estimation techniques.     

The resource curse and income inequality in Iran

This paper has investigated the relationship between oil revenues and inequality in Iran from 1969 to 2012. For this purpose, a threshold regression model has been used for capturing the non-linearity impact of the share of oil revenues in GDP on inequality. Two indicators have been applied for inequality: “Gini coefficient” and “the share of the richest decile of household expenditures which were relative to the poorest decile”. Estimation results of both inequality models suggested that there is a non-linear relationship as a u-shape between “oil revenues/GDP” and inequality in two regimes of oil revenues including high and low oil revenues regimes. The threshold level of oil revenues divided by GDP was about 10% for both inequality models. Before this threshold value, in low oil revenues regime, an increase of oil revenues would decrease income inequality, but after the threshold level and staying in high oil revenues regime, a rise in oil revenues would increase income inequality in Iran.     

A SURVEY OF TRADE AND WAGE INEQUALITY: ANOMALIES,RESOLUTIONS AND NEW TRENDS

This paper surveys recent studies on trade and wage inequality. We first introduce some trade‐based explanations for increased wage inequality. There are, however, a number of criticisms of this line of thought based on the ‘trade‐wage inequality anomaly’, the ‘price‐wage anomaly’, and the small volume of trade. Mainly due to these criticisms, trade‐based explanations for rising wage inequality have been limited in the economic literature. Rather, the primary explanations for wage inequality have been based on skill‐biased technological change. Some trade models, however, have weakened the above criticisms, and more economists now argue that the effect of trade, though relatively small compared to that of technological change, is more significant than generally believed. Finally, we attempt to link new trends in inequality, such as job polarization and within‐group inequality, to the trade and wage inequality literature.     

中国城乡居民住房不平等分析

随着中国城镇住房分配体制的转型,居民的居住条件在很大程度上依赖于家庭的收入水平,因此不断扩大的收入差距也在无形中影响着住房的不平等状况。基于2002年和2013年的城镇和农村的住户调查数据,本文从住房面积和房产价值两个角度分析中国农村和城镇居民住房不平等的总体状况。研究发现,在住房市场化体制建立和发展的过程中,虽然从财产所有权上的住房均等化有所提升,家庭居住面积有了很大的改善,但人均居住面积分布的不均等程度却进一步扩大。房产价值的不平等分析表明,虽然这一时期居民的住房财富高速增长,但城乡内部和城乡之间的房产差距都急剧扩大。基于回归分解的方法考察住房财富不平等的影响因素后发现,区域差异、收入差异和人力资本是造成居民房产价值分布差距不断扩大的重要因素。     

Corruption control,shadow economy and income inequality: Evidence from Asia

Developing countries often suffer from high corruption, high income inequality and poor institutional arrangements that give rise to large shadow economies. Earlier evidence shows that shadow economies moderate the negative effects of corruption on income inequality in highly unequal South American countries. For Asia, we show that the persistence of shadow economies raises inequality even if corruption control is strong. Supported by static and dynamic panel data analyses of 21 countries in Asia between 1995 and 2015, we show that in order to combat rising inequality, corruption control must be complemented by the ability to translate secondary and tertiary school enrolment into industrial and, more importantly, service sector jobs. Countries with low corruption but high inequality can reduce inequality by committing to higher public consumption expenditures. Further, combining greater trade openness with low corruption lowers inequality, except for countries in South Asia.     

Permanent and transitory wages of British men, 1975–2001: year,age and cohort effects

We examine the mean and variance–covariance structure of log-wages over calendar time and the life cycle of British men, hereby controlling for birth cohort effects. We attribute the strong increase in mean log-wage during the 1980s and 1990s to a rise in mean log-wage with the year of birth. This rise is diminishing with the year of birth, which implies lower wage inequality between cohorts with the year of birth. Wage inequality has increased during the 1980s and early 1990s and remained fairly stable in the second half of the 1990s. The year effects, however, show increasing wage inequality up to 2001, mainly due to a strong rise in transitory wage inequality. Transitory wages are strongly correlated over time and an increase in transitory wage inequality therefore has highly persistent inequality consequences. The stable wage inequality in the second half of the 1990s is attributed to lower within-cohort wage inequality for the younger cohorts. The age effects show that permanent wage inequality increases with age, in particular up to age 30 and over age 50. Copyright © 2007 John Wiley & Sons, Ltd.