We will show in this paper that if A is very close to 1, thenI（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dVcan be attained, where M is a compact-manifold ...We will show in this paper that if A is very close to 1, thenI（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dVcan be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled ＂On an inequality by Trudinger and Moser and related elliptic equations＂ （Comm. Pure. Appl. Math., 55, 135-152, 2002）.展开更多
Let F:R^(n)-→[0,+∞)be a convex function of class C^(2)(R^(n)/{0})which is even and positively homogeneous of degree 1,and its polar F0 represents a Finsler metric on R^(n).The anisotropic Sobolev norm in W^(1,n)(R^(...Let F:R^(n)-→[0,+∞)be a convex function of class C^(2)(R^(n)/{0})which is even and positively homogeneous of degree 1,and its polar F0 represents a Finsler metric on R^(n).The anisotropic Sobolev norm in W^(1,n)(R^(n))is defined by||u||F=(∫_(R_(n)(F^(n)(↓△u)+|u|^(n)dx)^(1/n)In this paper,the following sharp anisotropic Moser-Trudinger inequality involving L^(n)norm u∈W^(1,n)^(SUP)(R^(n),||u||F≤1∫_(R^(n))Ф(λ_(n)|u|n/n-1(1+a||u||^(n)_(n)1/n-1)dx<+∞in the entire space R^(n)for any 0<a<1 is estabished,whereФ(t)=e^(t)-∑^(n-2)_(j=0)tj/j!,λ_(n)=n^(n/n-1)k_(n)1/n-1 and kn is the volume of the unit Wulf ball in Rn.It is also shown that the above supremum is infinity for all α≥1.Moreover,we prove the supremum is attained,that is,there exists a maximizer for the above supremum whenα>O is sufficiently small.展开更多
Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite a...Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite and can be attained.This partially generalizes a well-known work of Chang and Yang(1988)who have obtained the inequality whenβ=0.展开更多
In this paper,we investigate a singular Moser-Trudinger inequality involving L^(n) norm in the entire Euclidean space.The blow-up procedures are used for the maximizing sequence.Then we obtain the existence of extrema...In this paper,we investigate a singular Moser-Trudinger inequality involving L^(n) norm in the entire Euclidean space.The blow-up procedures are used for the maximizing sequence.Then we obtain the existence of extremal functions for this singular geometric inequality in whole space.In general,W^(1,n)(R^(n))→L^(q)(R^(n))is a continuous embedding but not compact.But in our case we can prove that W^(1,n)(R^(n))→L^(n)(R^(n))is a compact embedding.Combining the compact embedding W^(1,n)(R^(n))→Lq(R^(n),|x|^(−s)dx)for all q≥n and 0<s<n in[18],we establish the theorems for any 0≤α<1.展开更多
Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponen...Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponent.In this paper,we mainly study two things,one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2.The other is to study the generalized Moser-Trudinger inequality with a singular Weight.展开更多
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of c...An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.展开更多
In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic...In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.展开更多
In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies ...In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies the Orlicz Busemann-Petty centroid inequality of Lutwak,Yang and Zhang[23].展开更多
Environmental inequality is a prevalent issue in developing countries undergoing urban expansion.Urban expansion induces the formation and evolution of environmental inequality by creating environmental and structural...Environmental inequality is a prevalent issue in developing countries undergoing urban expansion.Urban expansion induces the formation and evolution of environmental inequality by creating environmental and structural conditions that lead to the spatial relocation of environmental hazards and the socio-spatial segregation of different groups in developing countries.This study investigated the spatial patterns and temporal trends of environmental inequality under urban expansion in Guangzhou,a megacity in China.It considered how environmental disparities and socio-demographic attributes interact in terms of industrial pollution exposure using additive semiparametric quantile regression,combined with spatial visualisation,on the basis of the economic and population census data from 1990 to 2020.This study revealed that urban expansion sparked the spatial displacement of environmental risks and the social-spatial differentiation,exposing the peripheral regions and disadvantaged groups to higher environmental risks.A reciprocal transformation occurred between central and peripheral regions,as well as a process of redistributing environmental risks across social space.In the context of urban expansion in developing countries,the causes of environmental inequality shifted from individual socio-economic differences to structural factors,such as industrial layout and social division of labour in cities,leading to the spatial displacement and concealment of environmental inequality.This study provides insights and guidance for policymakers to address the issue of environmental inequality in the context of urban expansion.展开更多
In this paper,using the blow-up analysis,we prove a singular Hardy-Morser-Trudinger inequality,and find its extremal functions.Our results extend those of Wang and Ye(2012),Yang and Zhu(2016),Csato and Roy(2015)and Ya...In this paper,using the blow-up analysis,we prove a singular Hardy-Morser-Trudinger inequality,and find its extremal functions.Our results extend those of Wang and Ye(2012),Yang and Zhu(2016),Csato and Roy(2015)and Yang and Zhu(2017).展开更多
In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudin...In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudinger functional. Since the prob-lems involve more complicated norm and multiple singular points, not only we can＇tuse the symmetrization to deal with a one-dimensional inequality, but also the pro-cesses of the blow-up analysis become more delicate. In particular, the new inequalityis more general than that of [1, 2].展开更多
Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s co...Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.展开更多
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
Poverty and income inequality are problems faced by many countries including China.Since the implementation of Targeted Poverty Alleviation(TPA),absolute poverty has been eradicated,meanwhile,Chinese rural residents&#...Poverty and income inequality are problems faced by many countries including China.Since the implementation of Targeted Poverty Alleviation(TPA),absolute poverty has been eradicated,meanwhile,Chinese rural residents' income and inequality have experienced unprecedented new dynamics,but still,very few studies have focused on them.Hence,we attempt to examine the new trends in Chinese farmers' income inequality and to understand its causes during this period.We observe that China's urban-rural income ratio has been shrinking and the urban-rural inequality has been decreasing from 2014 to 2021.The reduction in the Theil index indicates a decrease in the regional inequality of farmers' income as well,and the decline in inter-regional inequality among eight economic zones contributes about 80% to increased equality.These new trends are caused by the fact that,with the TPA,the incomes of rural residents especially that in destitute areas,grew faster than that of urban residents and farmers in prosperous areas.The higher share of non-agricultural industry and agricultural mechanization level have significant positive impact on regional equality of farmers' income,while urban-rural dual structure has significant negative inhibitory effects.The lowest farmers' income and the highest inequality in the Northwest,and the slowest growth in the Northeast deserve more attention in rural Revitalization.From these findings,we propose four policy implications that would be applied to improve Chinese farmers' income equality,govern relative poverty,and achieve common prosperity in the post-poverty era.展开更多
Built-up land has increased rapidly in recent decades,thus aggravating the competition for land between multiple uses.The increase in urban land can be decomposed into changes in population and changes in built-up lan...Built-up land has increased rapidly in recent decades,thus aggravating the competition for land between multiple uses.The increase in urban land can be decomposed into changes in population and changes in built-up land per person.Yet,it is unclear how this decomposition differs by country and how this decomposition changes over time.Moreover,we don’t know whether these changes affect the inequality in built-up land per capita.Here,we analyze the global distribution of built-up land per capita in the year 2020,as well as the changes therein between 1985 and 2020.We find that built-up land per capita in 2020 differs by an order of magnitude between countries,ranging from 15 m^(2) per person in Ethiopia to 734 m^(2) per person in Australia.Moreover,we find a wide range of different change trajectories,including both increases and decreases in built-up land per capita and in total population.As the total area of urban land increased in all countries,decreases in urban land consumption reflect a situation where the population increases faster than the total amount of urban land.We also find a large inequality in urban land consumption across countries,as indicated by a Gini index of 0.47 in 1985,decreasing only slightly to 0.45 in 2020.These findings suggest the need for a regionally differentiated approach to reduce urban land take,focusing first on mitigating further increases in those countries that already have a high urban land consumption.展开更多
Objective:We examine how inequality in women's health has changed in India and its major states between 2015 and 2021.We also attempt to identify the sources of any change in this inequality using a decomposition ...Objective:We examine how inequality in women's health has changed in India and its major states between 2015 and 2021.We also attempt to identify the sources of any change in this inequality using a decomposition analysis.In order to suggest suitable policies for reducing this inequality,we attempt to identify the factors that are strongly associated with it.Methods:We construct an index of women's health from five indicators using the principal component analysis.Based on this index we measure inequality in women's health using the coefficient of variation and the Theil index.To identify the sources of change in this inequality,we apply Theil decomposition technique.Results:We find that inequality in women's health has increased significantly in India between 2015 and 2021.During this period,this inequality has increased significantly in six states,while it has decreased significantly in five states.The decomposition analysis suggests that the increase in this inequality between 2015 and 2021 has been driven by an increase in interstate inequality.We also find a strong positive association between inequality in women's health and inequality in public health amenities and social development.Conclusion:We suggest that for reducing inequality in women's health in developing countries like India,policies should focus on eliminating disparities in income,female education and provision of public health amenities.展开更多
Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in th...Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.展开更多
Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hie...Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hierarchical, use the distance function to measure the dissimilarities among actors. These distance functions need to fulfill various properties, including the triangle inequality (TI). However, in some cases, the triangle inequality might be violated, impacting the quality of the resulting clusters. With experiments, this paper explains how TI violates while performing traditional clustering techniques: k-medoids, hierarchical, DENGRAPH, and spectral clustering on social networks and how the violation of TI affects the quality of the resulting clusters.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
文摘We will show in this paper that if A is very close to 1, thenI（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dVcan be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled ＂On an inequality by Trudinger and Moser and related elliptic equations＂ （Comm. Pure. Appl. Math., 55, 135-152, 2002）.
基金Supported by Natural Science Foundation of China(Grant Nos.11526212,11721101,11971026)Natural Science Foundation of Anhui Province(Grant No.1608085QA12)+1 种基金Natural Science Foundation of Education Committee of Anhui Province(Grant Nos.KJ2016A506,KJ2017A454)Excellent Young Talents Foundation of Anhui Province(Grant No.GXYQ2020049)。
文摘Let F:R^(n)-→[0,+∞)be a convex function of class C^(2)(R^(n)/{0})which is even and positively homogeneous of degree 1,and its polar F0 represents a Finsler metric on R^(n).The anisotropic Sobolev norm in W^(1,n)(R^(n))is defined by||u||F=(∫_(R_(n)(F^(n)(↓△u)+|u|^(n)dx)^(1/n)In this paper,the following sharp anisotropic Moser-Trudinger inequality involving L^(n)norm u∈W^(1,n)^(SUP)(R^(n),||u||F≤1∫_(R^(n))Ф(λ_(n)|u|n/n-1(1+a||u||^(n)_(n)1/n-1)dx<+∞in the entire space R^(n)for any 0<a<1 is estabished,whereФ(t)=e^(t)-∑^(n-2)_(j=0)tj/j!,λ_(n)=n^(n/n-1)k_(n)1/n-1 and kn is the volume of the unit Wulf ball in Rn.It is also shown that the above supremum is infinity for all α≥1.Moreover,we prove the supremum is attained,that is,there exists a maximizer for the above supremum whenα>O is sufficiently small.
基金supported by National Natural Science Foundation of China(Grant Nos.11721101 and 11401575)。
文摘Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite and can be attained.This partially generalizes a well-known work of Chang and Yang(1988)who have obtained the inequality whenβ=0.
文摘In this paper,we investigate a singular Moser-Trudinger inequality involving L^(n) norm in the entire Euclidean space.The blow-up procedures are used for the maximizing sequence.Then we obtain the existence of extremal functions for this singular geometric inequality in whole space.In general,W^(1,n)(R^(n))→L^(q)(R^(n))is a continuous embedding but not compact.But in our case we can prove that W^(1,n)(R^(n))→L^(n)(R^(n))is a compact embedding.Combining the compact embedding W^(1,n)(R^(n))→Lq(R^(n),|x|^(−s)dx)for all q≥n and 0<s<n in[18],we establish the theorems for any 0≤α<1.
文摘Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponent.In this paper,we mainly study two things,one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2.The other is to study the generalized Moser-Trudinger inequality with a singular Weight.
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金supported by the NSFC(12171378)supported by the Characteristic innovation projects of universities in Guangdong province(2023K-TSCX381)+3 种基金supported by the Young Top-Talent program of Chongqing(CQYC2021059145)the Major Special Project of NSFC(12141101)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937).
文摘An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.
文摘In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.
基金Supported in part by NSFC(12071378,12461009),20XLB012,KJQN202100527,CSTB2022NSCQ-MSX0259 and KJQN202300557.
文摘In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies the Orlicz Busemann-Petty centroid inequality of Lutwak,Yang and Zhang[23].
基金Under the auspices of the National Natural Science Foundation of China(No.42271181,41871111)。
文摘Environmental inequality is a prevalent issue in developing countries undergoing urban expansion.Urban expansion induces the formation and evolution of environmental inequality by creating environmental and structural conditions that lead to the spatial relocation of environmental hazards and the socio-spatial segregation of different groups in developing countries.This study investigated the spatial patterns and temporal trends of environmental inequality under urban expansion in Guangzhou,a megacity in China.It considered how environmental disparities and socio-demographic attributes interact in terms of industrial pollution exposure using additive semiparametric quantile regression,combined with spatial visualisation,on the basis of the economic and population census data from 1990 to 2020.This study revealed that urban expansion sparked the spatial displacement of environmental risks and the social-spatial differentiation,exposing the peripheral regions and disadvantaged groups to higher environmental risks.A reciprocal transformation occurred between central and peripheral regions,as well as a process of redistributing environmental risks across social space.In the context of urban expansion in developing countries,the causes of environmental inequality shifted from individual socio-economic differences to structural factors,such as industrial layout and social division of labour in cities,leading to the spatial displacement and concealment of environmental inequality.This study provides insights and guidance for policymakers to address the issue of environmental inequality in the context of urban expansion.
文摘In this paper,using the blow-up analysis,we prove a singular Hardy-Morser-Trudinger inequality,and find its extremal functions.Our results extend those of Wang and Ye(2012),Yang and Zhu(2016),Csato and Roy(2015)and Yang and Zhu(2017).
文摘In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudinger functional. Since the prob-lems involve more complicated norm and multiple singular points, not only we can＇tuse the symmetrization to deal with a one-dimensional inequality, but also the pro-cesses of the blow-up analysis become more delicate. In particular, the new inequalityis more general than that of [1, 2].
文摘Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
基金supported by the GanSu Provincial Science and Technology Program(No.22ZD6FA005)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA23060704).
文摘Poverty and income inequality are problems faced by many countries including China.Since the implementation of Targeted Poverty Alleviation(TPA),absolute poverty has been eradicated,meanwhile,Chinese rural residents' income and inequality have experienced unprecedented new dynamics,but still,very few studies have focused on them.Hence,we attempt to examine the new trends in Chinese farmers' income inequality and to understand its causes during this period.We observe that China's urban-rural income ratio has been shrinking and the urban-rural inequality has been decreasing from 2014 to 2021.The reduction in the Theil index indicates a decrease in the regional inequality of farmers' income as well,and the decline in inter-regional inequality among eight economic zones contributes about 80% to increased equality.These new trends are caused by the fact that,with the TPA,the incomes of rural residents especially that in destitute areas,grew faster than that of urban residents and farmers in prosperous areas.The higher share of non-agricultural industry and agricultural mechanization level have significant positive impact on regional equality of farmers' income,while urban-rural dual structure has significant negative inhibitory effects.The lowest farmers' income and the highest inequality in the Northwest,and the slowest growth in the Northeast deserve more attention in rural Revitalization.From these findings,we propose four policy implications that would be applied to improve Chinese farmers' income equality,govern relative poverty,and achieve common prosperity in the post-poverty era.
基金supported by the Netherlands Organization for Scientific Research NWO in the form of a VIDI grant(Grant No.VI.Vidi.198.008).
文摘Built-up land has increased rapidly in recent decades,thus aggravating the competition for land between multiple uses.The increase in urban land can be decomposed into changes in population and changes in built-up land per person.Yet,it is unclear how this decomposition differs by country and how this decomposition changes over time.Moreover,we don’t know whether these changes affect the inequality in built-up land per capita.Here,we analyze the global distribution of built-up land per capita in the year 2020,as well as the changes therein between 1985 and 2020.We find that built-up land per capita in 2020 differs by an order of magnitude between countries,ranging from 15 m^(2) per person in Ethiopia to 734 m^(2) per person in Australia.Moreover,we find a wide range of different change trajectories,including both increases and decreases in built-up land per capita and in total population.As the total area of urban land increased in all countries,decreases in urban land consumption reflect a situation where the population increases faster than the total amount of urban land.We also find a large inequality in urban land consumption across countries,as indicated by a Gini index of 0.47 in 1985,decreasing only slightly to 0.45 in 2020.These findings suggest the need for a regionally differentiated approach to reduce urban land take,focusing first on mitigating further increases in those countries that already have a high urban land consumption.
文摘Objective:We examine how inequality in women's health has changed in India and its major states between 2015 and 2021.We also attempt to identify the sources of any change in this inequality using a decomposition analysis.In order to suggest suitable policies for reducing this inequality,we attempt to identify the factors that are strongly associated with it.Methods:We construct an index of women's health from five indicators using the principal component analysis.Based on this index we measure inequality in women's health using the coefficient of variation and the Theil index.To identify the sources of change in this inequality,we apply Theil decomposition technique.Results:We find that inequality in women's health has increased significantly in India between 2015 and 2021.During this period,this inequality has increased significantly in six states,while it has decreased significantly in five states.The decomposition analysis suggests that the increase in this inequality between 2015 and 2021 has been driven by an increase in interstate inequality.We also find a strong positive association between inequality in women's health and inequality in public health amenities and social development.Conclusion:We suggest that for reducing inequality in women's health in developing countries like India,policies should focus on eliminating disparities in income,female education and provision of public health amenities.
文摘Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.
文摘Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hierarchical, use the distance function to measure the dissimilarities among actors. These distance functions need to fulfill various properties, including the triangle inequality (TI). However, in some cases, the triangle inequality might be violated, impacting the quality of the resulting clusters. With experiments, this paper explains how TI violates while performing traditional clustering techniques: k-medoids, hierarchical, DENGRAPH, and spectral clustering on social networks and how the violation of TI affects the quality of the resulting clusters.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
