ON CRITICAL CASES OF SOBOLEV'S INEQUALITIES FOR HEISENBERG GROUPS

We prove some Trudinger-type inequalities and Brezis-Gallouet-Wainger inequality on the Heisenberg group, extending to this context the Euclidean results by T. Ozawa.

Mapping and measuring urban-rural inequalities in accessibility to social infrastructures

Equal access to social infrastructures is a fundamental prerequisite for sustainable development,but has long been a great challenge worldwide.Previous studies have primarily focused on the accessibility to social infras-tructures in urban areas across various scales,with less attention to rural areas,where inequality can be more severe.Particularly,few have investigated the disparities of accessibility to social infrastructures between urban and rural areas.Here,using the Changsha-Zhuzhou-Xiangtan urban agglomeration,China,as an example,we investigated the inequality of accessibility in both urban and rural areas,and further compared the urban-rural difference.Accessibility was measured by travel time of residents to infrastructures.We selected four types of social infrastructures including supermarkets,bus stops,primary schools,and health care,which were funda-mentally important to both urban and rural residents.We found large disparities in accessibility between urban and rural areas,ranging from 20 min to 2 h.Rural residents had to spend one to two more hours to bus stops than urban residents,and 20 min more to the other three types of infrastructures.Furthermore,accessibility to multiple infrastructures showed greater urban-rural differences.Rural residents in more than half of the towns had no access to any infrastructure within 15 min,while more than 60%of the urban residents could access to all infrastructures within 15 min.Our results revealed quantitative accessibility gap between urban and rural areas and underscored the necessity of social infrastructures planning to address such disparities.

Does digitalization mitigate regional inequalities?Evidence from China

Regional inequality significantly influences sustainable development and human well-being.In China,there exists pronounced regional disparities in economic and digital advancements;however,scant research delves into the interplay between them.By analyzing the economic development and digitalization gaps at regional and city levels in China,extending the original Cobb-Douglas production function,this study aims to evaluate the impact of digitalization on China's regional inequality using seemingly unrelated regression.The results indicate a greater emphasis on digital inequality compared to economic disparity,with variable coefficients of 0.59 for GDP per capita and 0.92 for the digitalization index over the past four years.However,GDP per capita demonstrates higher spatial concentration than digitalization.Notably,both disparities have shown a gradual reduction in recent years.The southeastern region of the Hu Huanyong Line exhibits superior levels and rates of economic and digital advancement in contrast to the northwestern region.While digitalization propels economic growth,it yields a nuanced impact on achieving balanced regional development,encompassing both positive and negative facets.Our study highlights that the marginal utility of advancing digitalization is more pronounced in less developed regions,but only if the government invests in the digital infrastructure and education in these areas.This study's methodology can be utilized for subsequent research,and our findings hold the potential to the government's regional investment and policy-making.

Is it possible to run after positive affective experiences instead of health benefits without tackling social inequalities?

We recently read the opinion piece titled“Why people should run after positive affective experiences instead of health benefits”,which was carried out by Maltagliati et al.^(1)and published in the Journal of Sport and Health Science.The article started an important discussion about a physical activity(PA)promotion approach that encourages the use of affective experience to PA activity.Although we agree with the authors’point of view and believe that its message can generate an important insight for PA promotion,the authors presented a scenario where behavior change seems to be exclusively dependent on the individual.Recognizing the existence of other barriers to an active lifestyle(e.g.,social inequalities)could enhance the authors’suggested approach because many people live in conditions that reduce their opportunities to engage in affective experiences related to PA;furthermore,affective experiences can vary depending on individual context.

Understanding the educational inequalities in suicide attempts and their mediators:a Mendelian randomisation study

Background Educational inequalities in suicide have become increasingly prominent over the past decade.Elucidating modifiable risk factors that serve as intermediaries in the impact of low educational attainment on suicide has the potential to reduce health disparities.Aims To examine the risk factors that mediate the relationship between educational attainment and suicide attempts and quantify their contributions to the mediation effect.Methods We conducted a two-sample Mendelian randomisation(MR)analysis to estimate the causal effect of educational attainment on suicide attempts,utilising genome-wide association study summary statistics from the Integrative Psychiatric Research(iPSYCH;6024 cases and 44240 controls)and FinnGen(8978 cases and 368299 controls).We systematically evaluated 42 putative mediators within the causal pathway connecting reduced educational attainment to suicide attempts and employed two-step and multivariable MR to quantify the proportion of the mediated effect.Results In the combined analysis of iPSYCH and FinnGen,each standard deviation(SD)decrease in genetically predicted educational attainment(equating to 3.4 years of education)was associated with a 105%higher risk of suicide attempts(odds ratio(OR):2.05;95%confidence interval(Cl):1.81 to 2.31).0f the 42 risk factors analysed,the two-step MR identified five factors that mediated the association between educational attainment and suicide attempts.The respective proportions of mediation were 47%(95%Cl:29%to 66%)for smoking behaviour,36%(95%Cl:0%to 84%)for chronic pain,49%(95%Cl:36%to 61%)for depression,35%(95%Cl:12%to 59%)for anxiety and 26%(95%Cl:18%to 34%)for insomnia.Multivariable MR implicated these five mediators collectively,accounting for 68%(95%Cl:40%to 96%)of the total effect.Conclusions This study identified smoking,chronic pain and mental disorders as primary intervention targets for attenuating suicide risk attributable to lower educational levels in the European population.

Ostrowski’s Type Inequalities for Generalized(h,m)−Preinvex Functions with Its Applications

A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

Global prevalence and gender inequalities in at least 60 min of self-reported moderate-to-vigorous physical activity 1 or more days per week:An analysis with 707,616 adolescents

Background:Guidelines recommend that adolescents should accumulate an average of 60 min per day of moderate-to-vigorous physical activity(MVPA).However,using only this cut-off could hide important information.For instance,from a population-level point of view,increasing physical activity for those with no or low physical activity could provide more health benefits than increasing physical activity for those with intermediate levels.Also,including a more sensitive cut-point of≥1 days per week could be an additional strategy for identifying those with low access/opportunities for physical activity practice.Thus,the current study aims to estimate the prevalence of≥60 min of MVPA≥1 days per week among adolescents globally,and to describe any relevant gender inequalities.Methods:We used representative datasets from 146 countries/territories collected between 2003 and 2019.MVPA was self-reported.Participants were grouped into younger(≤14 years old)and older(>14 years old)adolescents.Crude Poisson regression models were used to identify the relative differences in≥60 min of MVPA≥1 days per week between boys and girls,and random-effects meta-analysis models were used to identify the pooled estimates.Analyses were stratified by country and region.Results:Approximately 80%of both younger and older adolescents reported≥60 min of MVPA≥1 days per week.This prevalence was≥94%in Europe and Central Asia and North America,while the estimates for the other regions were<77%.The prevalence of≥60 min of MVPA≥1 days per week was higher among boys than girls,with the largest differences occurring among the oldest adolescents(Prevalence ratio_(≤14y)=1.04(95%confidence interval(95%CI)):1.03-1.04)vs.Prevalence ratio_(>14y)=1.09(95%CI:1.08-1.10)).Conclusion:Approximately 8 out of 10 adolescents reported accumulating≥60 min of MVPA≥1 days per week,with notable differences between regions.Gender differences were observed in several countries,especially among the oldest adolescents.Priorities for physical activity promotion among adolescents should include increasing access/opportunities for physical activity among those who do not achieve≥60 min of MVPA≥1 days per week and reducing gender inequalities.

A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES

In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.

NEW DOOB'S MAXIMAL INEQUALITIES FOR MARTINGALES

Let 1≤q≤∞,b be a slowly varying function and letΦ:[0,∞)■[0,∞)be an increasing convex function withΦ(0)=0 and■Φ(r)=∞.In this paper,we present a new class of Doob’s maximal inequality on Orlicz-Lorentz-Karamata spaces LΦ,q,b.The results are new,even for the Lorentz-Karamata spaces withΦ(t)=tp,the Orlicz-Lorentz spaces with b≡1,and weak Orlicz-Karamata spaces with q=∞in the framework of LΦ,q,b-Moreover,we obtain some even stronger qualitative results that can remove the△2-condition of Liu,Hou and Wang(Sci China Math,2010,53(4):905-916).

Generalization of Inequalities in Metric Spaces with Applications

In this paper, which serves as a continuation of earlier work, we generalize the idea of inequalities in metric spaces and use them to demonstrate that the incomplete metric space can be used to obtain a Banach space.

What in Fact Proves the Violation of the Bell-Type Inequalities?

A. Peres constructed an example of particles entangled in the state of spin singlet. He claimed to have obtained the CHSH inequality and concluded that the violation of this inequality shows that in a measurement in which some variables are tested, other variables, not tested, have no defined value. In the present paper is proved that the correct conclusion of the violation of the CHSH inequality is different. It is proved that the classical calculus of probabilities of test results, obeying the Kolmogorov axioms, is unfit for the quantum formalism, dominated by probability amplitudes.

A Note on Sharp Affine Poincaré-Sobolev Inequalities and Exact in Minimization of Zhang’s Energy on Bounded Variation and Exactness

As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING

In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented.

Regularization Methods to Approximate Solutions of Variational Inequalities

In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y0, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.

1985—2019年新疆维吾尔族7~18岁中小学生身高生长趋势及不平衡性分析

目的:了解新疆7~18岁维吾尔族中小学生身高的发育情况、变化趋势及城乡不平衡性。方法:选取1985、2000、2010年和2019年4次全国学生体质与健康调研中的新疆7~18岁维吾尔族中小学生共18112例,分为城男、乡男、城女、乡女4个群体,计算各阶段身高的增幅、每10年增速、发育高峰年龄及变异系数,对差异进行单因素方差分析。结果:1985—2019年,新疆维吾尔族7~18岁中小学生身高总体呈增加趋势,城男、乡男、城女、乡女平均身高分别增长了7.59、5.27、6.00、2.88 cm(P均<0.001)。各年龄组增幅不一,男生和城市学生增幅较大。城市学生2010—2019年身高增速最快(城男4.65 cm/10年、城女4.97 cm/10年),乡村学生1985—2000年身高增速最快(乡男4.04 cm/10年、乡女3.22 cm/10年),2000—2010年各组身高均呈负增长。维吾尔族7~18岁中小学生除城女身高突增高峰年龄提前外,城男、乡男和乡女突增高峰年龄较平稳,近年有下降趋势;维吾尔族城市18岁男女平均身高差从1985的11.39 cm增大到2019年的14.20 cm,乡村地区从1985年的11.44 cm增大到2019年的13.26 cm,乡村学生增长潜力较大。身高不平衡使用身高变异系数(coefficient of variation of height,CV-h)来衡量,结果表明,34年间乡村学生CV-h有减小趋势,城市学生CV-h则增大,2010年开始城市学生CV-h大于乡村学生,各年份男生CV-h均大于女生。结论:维吾尔族7~18岁中小学生身高呈持续增长趋势,总体增速减缓,特别是乡村男女,但城市增速增高;维吾尔族学生存在明显的城乡身高不平衡现象,城市内部不平衡性扩大,乡村减小。应更多地关注这些地区差异,并制定政策和战略,以减少身高不平衡性。

中国家庭联合收入财富不平等测度研究

使用年金法构建同时包含收入和财富的一维指标,即联合收入财富,基于该指标全面测度中国经济不平等程度并进行分解。结果发现:与收入不平等相比,联合收入财富基尼系数提高了13.36个百分点,其中房屋是影响家庭经济不平等的最重要财富形式;联合收入财富不平等程度在各年龄分组、城乡和地区之间存在较大的异质性;联合收入财富不平等主要由收入和财富年金值的边际分布本身所导致,而两大边际分布之间的关系对总体不平等的影响相对较小。

房价对城镇居民消费不平等的影响研究

基于中国家庭追踪调查库(CFPS)2010—2018年数据,采用面板计量模型和中介效应模型,研究房价对城镇居民消费不平等的影响效应及作用机制。结果表明:房价会正向影响城镇居民消费不平等,运用工具变量法进行内生性检验以及其他稳健性检验后,以上结论稳健。机制检验结果表明,房价会通过家庭人均消费支出影响城镇居民消费不平等,房价对居住支出和教育文化娱乐支出的影响程度较大,进一步说明房价上升会通过影响消费结构加剧城镇居民消费不平等。异质性检验结果表明,相对于城镇中低收入、中低金融资产家庭而言,房价变动对城镇高收入、高金融资产家庭居民消费的影响更明显。为此,应稳定房价、合理引导住房支出和调整居民消费结构,以促进消费公平,缩小消费不平等。

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。

新型基础设施影响劳动工资和工资差距的内在机制

本文从新型基础设施的产品偏向性出发,在一般均衡框架下探讨了新型基础设施影响劳动工资和工资差距的内在机制。研究发现,新型基础设施直接带来的效率提升可以促进各类劳动工资增长,但间接导致的要素重新配置可能产生不同的结果,总效应取决于资本与各类劳动之间的替代性以及技能型中间品与非技能型中间品之间的替代性。结合中国的实际情况,技能型产品偏向型的新型基础设施可能导致工资差距扩大,但可以带来劳动工资的“普惠性”增长。