论证一类不等式问题 展示数学发现的方法

通过对一个不等式的加强和完善,探求出推广这一类问题的途径,解决了一类不等式问题。     

幂方根不等式的推广及应用

给出并证明了幂方根不等式的推广及其推论 ,利用此推广简证了几个重要不等式 ,利用其推论完善了一类初等代数问题     

自反Banach空间一类完全广义集值强非线性混合似变分不等式问题

研究了一类完全广义集值强非线性混合似变分不等式在自反Banach空间下的问题，借助一个极大极小不等式，证明了这类完全广义集值强非线性混合似变分不等式的解的存在唯一性定理。     

关于具有给定极点的有理函数导数的不等式

给出了一类具有给定极点的有理函数的导数在Lp 尺度下的Varma型和Turán型不等式,从而推广了有关文献中关于多项式的著名不等式.     

时滞细胞神经网络的代数抗饱和补偿设计

针对时滞细胞神经网络,提出了一种基于代数判据的抗饱和补偿设计。运用M矩阵理论、迪尼导数、系统参数设计了无饱和输入限制系统镇定的代数判据。在此基础上,利用不等式放缩原理、分区讨论与大中取大综合方法和Lyapunov理论,得出了二次矩阵不等式形式的抗饱和控制设计方案,进而将之转化为线性矩阵不等式。同时,给出了吸引域及其最大化方法。仿真验证了该设计方案的可行性和有效性。     

鲁棒H∞次优控制问题

证明了鲁棒H∞次优控制问题可以归结为两个代数黎卡提不等式的解.利用不等式形式上的特点,还研究H∞/H2混合次优控制问题,并给出了应用实例以说明本结果的有效性.     

具有leakage时滞的随机马尔科夫跳变神经网络的稳定性

研究一类具有leakage时滞的随机马尔科夫跳变神经网络的稳定性,通过构造一个新的Lyapunov-Kra—sovskii泛函,并应用It6公式、随机不等式技术,得到了基于线性矩阵不等式（LMI）的均方意义下的全局稳定性判定条件．     

利用詹森不等式推广几个数学问题

詹森（Jensen）不等式是解决不等式问题的一个重要方法，也是发现数学问题的重要手段。运用詹森不等式的关键是通过观察所给代数式的函数特征，构造一个凹或凸的函数，以利解题。     

基于状态观测器的四旋翼飞行器鲁棒控制

针对一类具有不确定性的系统,当系统状态难以测量时,通过构造状态观测器,设计了基于状态观测器的鲁棒控制。通过选取李雅普诺夫函数,推导出满足鲁棒控制器存在的充分性条件,再通过Schur补性质将矩阵不等式转化为等价的线性矩阵不等式。利用MATLAB中的LMI工具箱求解线性矩阵不等式,得状态观测器增益和状态反馈控制器增益。最后,将结论应用于四旋翼飞行器中,证明了所提方法的有效性。     

非线性时滞系统模糊控制的一种新方法

针对一类状态变量具有时滞的非线性系统，研究了其模糊控制器的设计问题。采用线性矩阵不等式（LMI）的方法，设计了与状态变量导数有关的模糊控制器，得到了系统存在模糊控制器的充分条件，并利用线性矩阵不等式的解给出具体的形式，最后通过仿真说明了控制器的有效性。     

Defence Spending and Income Inequality in Taiwan

The rising trend in income inequality has recently attracted a renewed interest in the determinants of this growing trend across many countries. This article adds to the debate by investigating the impact of defence expenditure as a possible determinant of inequality in Taiwan, a country once was considered to be a poster child of an equitable growth, but now income inequality has become one of the Taiwan’s growing challenges. Applying the bounds test approach to cointegration and four long-run estimators for the period from 1976–2011, we found a long-run relationship between the various measures of inequality and defence expenditure where defence expenditure exerts a positive and a statistically significant impact on the worse income inequality in Taiwan. Further application of the lag-augmented causality test procedure also reveals a unidirectional causality running from defence expenditure to income inequality with defence expenditure causing income inequality to rise.     

Does Income Inequality Derive the Separatist Terrorism in Turkey?

Separatist terrorism has been a severe problem for Turkey since the mid-1980s. The conventional wisdom contends that economic deprivation in southeastern Turkey is the fundamental reason for the long-running battle against the Kurdish rebels. Considering that there is limited empirical literature on the roots of terrorism in Turkey, yielding conflicting results about the claim that the main cause of terrorism is deprived economic conditions, this study aims to answer whether there is a causal relationship between income inequality and separatist terrorism in Turkey. To this end, the Global Terrorism Data Base for the period of 1973–2006, two Theil indices of pay inequality as proxy for income inequality, and the vector autoregression and Autoregressive Moving Average (ARMA) methods are utilized. The results support the early findings that income inequality, a particular focus in this paper and an essential indicator of economic deprivation, is not a main cause of escalation of separatist terrorism in Turkey.     

离散系统的绝对稳定性

给出了离散系统绝对稳定性问题的充分条件:约束条件下的矩阵不等式的正定解;基于这一思路可以构造控制器来镇定一类非线性系统;最后还给出了设计实例以说明结果的有效性。     

离散型随机BAM神经网络时滞分布依赖全局指数稳定性

研究一类具有随机时滞与随机干扰的离散型BAM神经网络的全局指数稳定性,所建模型同时考虑离散时滞变化区间与分布概率对稳定性的影响．通过构造新的Lyapunov泛函并结合线性矩阵不等式（LMI）方法,得到了均方意义下依赖于时滞分布的全局指数稳定性条件．     

超凸度量空间中KKM理论的一些应用

在超凸度量空间利用广义度量KKM映象原理的特性得到一类新的广义极大极小不等式,并进一步借助这类极大极小不等式,在更广泛的条件下,获得鞍点问题的一个新的存在性结果。     

Military Expenditures,Income Inequality,Welfare and Political Regimes: A Dynamic Panel Data Analysis

The goal of this paper is to investigate the relationship between type of welfare regimes and military expenditures. There is a sizeable empirical literature on the development of the welfare state and on the typology of the welfare regimes. There appear to be, however, no empirical studies that examine welfare regimes with special attention to military spending. This study aims at providing a comprehensive analysis on the topic by considering several different welfare regime typologies. To do so, we use dynamic panel data analysis for 37 countries for the period of 1988–2003 by considering a wide range of control variables such as inequality measures, number of terrorist events, and size of the armed forces. We also replicate the same analyses for the political regimes. Our findings, in line with the literature, show that there is a positive relationship between income inequality and share of military expenditures in the central government budget, and that the number of terrorist events is a significant factor that affects both the level of military expenditure and inequality. Also, the paper reveals a significant negative relationship between social democratic welfare regimes and military expenditures.     

Does defence expenditure have a spillover effect on income inequality? A cross-regional analysis in China

China’s defence expenditure has been growing rapidly along with GDP growth during the past two decades. Meanwhile, the income gap has continued to increase. There are conflicting views regarding whether the defence expenditure is capable of reducing income inequality. Therefore, this paper investigates the existence of any spillover effect of defence expenditure on income inequality, with a special focus on the regional differences among 31 provinces and 7 military regions in China. We extend panel cointegration and the impulse response function by using panel data during the period of 1997–2012. The empirical results show that the defence expenditure has an impact on income inequality, and the effect varies over different regions in China. The defence expenditure has a spillover effect on income inequality in the full sample panel and the southeastern panel. An increase in the defence expenditure does not crowd out social welfare spending due to the high level of economic development and government expenditure. On the contrary, in the northern panel, the effect is opposite because of the unbalanced economic development levels within the panel. Beijing as the capital of China, benefits more from the expansion of defence expenditure thus widening the income gap. In addition, the impulse response analyses further confirm a stronger effect of the defence expenditure on income inequality in the northern and the southeastern panels over a short period.     

The impact of military spending and income inequality on economic growth in Turkey

An extensive literature on the effect of military expenditures on economic growth yields conflicting results. However, a crucial issue that has not been investigated in this context is the possible effect of inequality. The impact of military expenditures on economic growth in Turkey has also received substantial attention. Yet, the majority of these studies are not constructed based on a structural model, but rather examine the causality between the variables in question. Considering these two shortcomings in the literature and the lack of consistent results, this study attempts to provide further evidence for the relationship between military expenditures and economic growth for the case of Turkey by considering income inequality within an augmented Solow growth model. Our findings for the 1963–2008 period show that while income inequality has a positive impact on economic growth, military expenditures have no significant effect.