On Isolations for the Brunn-Minkowski Inequality of Quermassintegrals and Dual Quermassintegrals

Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals,respectively.

THE ORLICZ BRUNN-MINKOWSKI INEQUALITY FOR DUAL HARMONIC QUERMASSINTEGRALS

Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.

Attitudes toward income inequality:perspectives from farmers living in a poverty-stricken rural area of China

The attitude of the least advantaged people to income inequality is important in regard to social stability,which is also a major concern of the government and researchers in China.This paper aimed to investigate the perceptions and attitudes of the least advantaged people toward income inequality in China.An empirical analysis was conducted on farmers' attitudes to income inequality based on a questionnaire survey of 308 farmers in four villages in Yingshan,Hubei Province.Our results show that the respondents consider the income inequality as severe,and ability,hard work,and individual choices are the major determinant factors of income.It is shown that farmers in less developed areas are more likely to accept income inequality,and they ascribe this to their own failure rather than to social injustice.However,it is not the case that people living in poverty-stricken areas are satisfied with antipoverty policies;and these policies are expected to be further improved to increase the income of the poor.

Income Inequality in Mountain Areas: The Case of Agroforestry Farming Systems in Uluguru Mountains, Tanzania

Land degradation due to use of unsustainable agricultural practices has affected many communities in rural mountain areas rendering them to be more vulnerable to income poverty and inequality. In this case, agroforestry systems promise to offer great solutions as they can be developed in unfavourable conditions where other production systems would either rapidly degrade the land or otherwise would not be possible. However, little is known whether agroforestry can address issues of income inequality in mountain areas. Hence, we conducted a study to investigate the nature and determinants of income inequality in Uluguru Mountains, Tanzania. Specifically, we used the cross-sectional research design and we calculated the income percentile shares, Gini coefficients and the coefficient of variation (CV), to pinpoint the nature of income inequality in the study area. The determinants of income inequality were analysed using the step by step multiple linear model. The results of analysis suggested prevalence of income inequality. Crop production was the main source of income in the agroforestry systems of the study area. Earnings from crops and timber were decreasing income-inequality amongst smallholder farmers. Our disaggregated analysis showed that off-farm income was also decreasing income-inequality for farmers with farmlands located close to homestead, for female-headed households, for farmers who did not access extension services, and those who were members of community-based financial institutions. Estimated incomes increased with household assets, size of farmland, and age of household head. However, the same decreased with household size. We found gender disparity to be one of the key issues that need attention in formulating future policies to reduce inequality. We recommend promotion of livelihood diversification as well as the designing and implementation of tailor-made training and farm financing mechanism to help the less resource-endowed farmers in mountain areas to raise their economic portfolios and social status and combat income poverty and inequality.

What Efforts has the Chinese Government Made to Reduce Educa­tional Inequality in Poor Areas?

Since the founding of the People’s Republic of China in 1949,China’s per capita education level has risen from less than two years to 9.91 years.However,as the province with the lowest per capita education level in China,Tibet has only reached the level of 6.75 years per capita.This illustrates the worrying educational inequality that still exists between China’s poorer and more developed regions.This educational inequality can also be expressed by the Gini coefficient of education.In order to eliminate this educational inequality,the Chinese government has made great efforts.The Chinese government has expanded the demand for education through the right incentive system and the nine-year compulsory education law.On the other hand,the Chinese government directly or indirectly grants subsidies to education suppliers and demanders to achieve the purpose of increasing education output.Based on the positive externality of education itself,the Chinese government attaches great importance to the cultivation of human resources for offspring,and hopes to transform China’s quantity-based demographic dividend into quality-based demographic dividend,and finally realize sustained economic growth.We believe that some education-related policies promulgated by China have indeed reduced educational inequality in poor areas to some extent,but there is still potential for progress in further addressing educational inequality in poor areas by the Chinese government.

Brunn-Minkowski inequalities for star duals of intersection bodies and two additions

In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.

The Brunn-Minkowski Inequalities for Centroid Body

In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the original.

Generalizations of a Matrix Inequality

In this paper, some new generalizations of the matrix form of the Brunn-Minkowski inequality are presented.

再分配视域下河北省人口老龄化与城乡收入不平等的关系分析

再分配作为调节收入分配的重要工具,在实现共同富裕目标中发挥着重要作用。河北省作为人口大省,日益加重的人口老龄化对经济社会发展、城乡收入等产生了重要影响。研究发现:一方面,河北省人口老龄化拉大了城乡收入差距,加剧了城乡收入不平等,尤其是在二线城市和大规模城市中,人口老龄化引致的城乡收入不平等效应更加明显;另一方面,经济增长作为“做大蛋糕”和“分好蛋糕”的原动力,能够有效“对冲”人口老龄化对城乡收入分配不公的负面影响,而人口老龄化倒逼技术进步又在一定程度上加剧了城乡收入不平等。因此,河北省不仅要做大“财富蛋糕”,更要使全体社会成员共享“经济蛋糕”,以此加速推进共同富裕进程。

互联网使用、生计资本与村庄内部收入不平等——以太行山革命老区为例

村庄内部收入不平等是居民收入不平等的重要方面,是影响共同富裕和农民幸福感的重要因素。本文基于太行山革命老区32个村庄519个农户的实地调查数据,运用内生转换模型考察互联网使用对村庄内部农户收入不平等的影响,并利用KHB中介效应模型分析互联网发挥作用的机制。研究发现:(1)互联网使用有助于缓解村庄内部收入不平等;(2)互联网使用缓解村庄内部农户收入不平等的作用在非贫困村中比在脱贫村中更大,反映了互联网使用需要与基础设施、产业条件等因素配套才能有效缓解村庄内部收入不平等;(3)互联网使用主要通过缩小低收入农户和高收入农户在金融资本上的差距缓解农户收入不平等,社会资本、物质资本和人力资本也发挥显著的中介作用。

平面上几个对偶Brunn-Minkowski不等式

对于平面中具有二阶光滑边界的凸体,给出了一个与之对偶的星体,称之为曲率星体.并且用积分几何与凸几何的方法,得到了该星体的一些性质及其相关的几何不等式.

基于收入分配视角的粤港澳大湾区一体化发展效率研究——来自政策指数量化的检验

区域一体化通过改变区域内要素的流动方向和强度,实现资源配置优化和经济效率提升。为了探究粤港澳大湾区一体化发展对于地区居民相对收入差距以及城市内部的城乡收入差距的调节作用,并深入挖掘粤港澳大湾区各城市间的合作潜力,本文从弱化行政壁垒、增强经济合作、交通互联互通、劳动力流动以及科技创新技术共享五个维度构建政策措施指数,使用基于Farrell框架的DEA方法对粤港澳大湾区的一体化发展效率进行测算,评价由区域一体化带来的社会福利效应。研究结果发现,粤港澳大湾区一体化发展缩小地区居民相对收入差距的效果显著,但是,由于经济开放等具有城市倾向的活动存在,一体化发展缩小城乡收入差距的效率有待提升。几乎所有具有合作潜力的城市都可以获得潜在收益,其中,一体化效率、技术效率、协同效率和规模效率都存在不同程度的提升空间。另外,经济欠发达城市的合作潜力更突出。进一步,城市间多方合作是提高一体化发展效率的主要推动方式,而且专业化合作与多样化合作均对区域收入协调具有正向影响,但专业化合作的影响更显著。由于各城市本身发展存在差异,区域一体化缩小居民收入差距的效果也存在地区异质性。在粤港澳大湾区一体化发展中,各类一体化活动的合作潜力存在差异,其中,经济一体化与科技创新一体化对于缩小地区居民收入差距具有显著作用,可以作为区域一体化发展的主要途径。

SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES

The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.

Resilient Fixed-Order Distributed Dynamic Output Feedback Load Frequency Control Design for Interconnected Multi-Area Power Systems

The paper proposes a novel H∞ load frequency control(LFC) design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback(DOF) tracking-regulator control scheme. To this end, we consider a nonlinear interconnected model for multiarea power systems which also include uncertainties and timevarying communication delays. The design procedure is formulated using semi-definite programming and linear matrix inequality(LMI) method. The solution of the proposed LMIs returns necessary parameters for the tracking controllers such that the impact of model uncertainty and load disturbances are minimized. The proposed controllers are capable of receiving all or part of subsystems information, whereas the outputs of each controller are local. These controllers are designed such that the resilient stability of the overall closed-loop system is guaranteed. Simulation results are provided to verify the effectiveness of the proposed scheme. Simulation results quantify that the distributed(and decentralized) controlled system behaves well in presence of large parameter perturbations and random disturbances on the power system.

Volume Difference Inequalities for the Polars of Mixed Complex Projection Bodies

In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski type inequality and Aleksandrov-Fenchel inequality for the polars of mixed complex projection bodies.

Isotropic dual p-surface area measure

It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the （n-1）-dimensional volume of the intersection of a dual p-surface isotropic convex body in terms of its affine invariant dual p-surface quantity is given. Furthermore, the dual p-isopermetric inequality is obtained.

Weighted Integral Means of Mixed Areas and Lengths Under Holomorphic Mappings

This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f ,r） and the mixed length （2πr）-βL（ f ,r） （0≤β≤1 and 0〈r〈1） of f （rD） and？f （rD） under a holomorphic map f from the unit disk D into the finite complex plane C.

Brunn-Minkowski面积不等式的两种证法

给出Brunn-Minkowski面积不等式的两种特殊证明方法.首先描述面积、周长及混合面积的傅里叶级数表示法,再介绍一个内积空间及一个有关实数不等式的引理,把傅里叶级数表达式带入实数不等式中并利用内积算法得到结论;再把Minkowski和的定义推广到一般情形,把面积、周长表示为t的函数,利用函数的凹凸性证明了Brunn-Minkowski面积不等式.

基于优化泛函的多时滞广域电力系统稳定性分析

针对大规模互联电力系统中时滞现象对系统稳定运行造成的不可忽略的影响,研究多个时滞影响下广域电力系统的稳定性问题。首先,建立多时滞电力系统模型。其次,构造一种新的包含多时滞积分项相互耦合的增广型Lyapunov-Krasovskii(L-K)泛函,并采用一种新方法,将构造的泛函作为整体判断其正定性,放松了对泛函矩阵正定性的限制。然后,利用基于辅助函数的积分不等式对泛函导数进行估计,得到了具有较小保守性的多时滞电力系统稳定性判据。最后,通过对典型二阶时滞系统、单机无穷大系统以及WSCC 3机9节点系统进行仿真分析,验证了所提方法的优越性。

城市人口集聚对劳动者就业满意度的影响研究

近年来,我国人口迁移流动向都市圈、城市群集聚的趋势更为明显。在我国城镇化加速发展的背景下,将集聚理论纳入成本—收益分析框架,结合中国劳动力动态调查微观数据与城市宏观数据,研究城市人口集聚对劳动者就业满意度的影响。研究发现:第一,城市人口集聚通过个人收入、职业匹配与公共服务等集聚收益对劳动者就业满意度产生正向影响;通过工作压力、城市房价与交通拥堵等集聚成本对劳动者就业满意度产生负向影响。综合来看,目前我国城市人口集聚仍能提升劳动者就业满意度。第二,城市人口集聚对城市户籍劳动者、高教育水平劳动者与体制内劳动者的就业满意度提升更大;相比人口高度集聚城市,人口中度集聚城市的规模扩张更可能提升劳动者就业满意度。第三,基于集聚经济理论“空间发展钟形曲线”,都市圈空间不平等表现为经济一体化的集聚阶段或分散阶段。相比经济一体化分散阶段的都市圈,处于集聚阶段的都市圈,城市人口规模扩张更可能提升劳动者就业满意度。