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
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
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
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
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
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
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
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
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
The inequality sup n≥1｜n∑k=1 sinkx/k｜≤3√π,plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and ...The inequality sup n≥1｜n∑k=1 sinkx/k｜≤3√π,plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and improves their results by introducing a new class of sequences called γ-piecewise bounded variation sequence （γ-PBVS）.展开更多
In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some suf...Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.展开更多
Using the targets such as absolute dispersion, ratio of high - low Income, coefficient of variation and Ginl coefficient, we analyze the China’s per capita income inequality from 1952 to 1995. We find the trends in t...Using the targets such as absolute dispersion, ratio of high - low Income, coefficient of variation and Ginl coefficient, we analyze the China’s per capita income inequality from 1952 to 1995. We find the trends in the China’s per capita Income differences, i.e., from 1952 to 1978 the differences increase; from 1978 to the early of 1990’ s decrease; and from the early of 1990’ s to 1995 a little increase. But in the light of absolute levels, the differences Increase from year to year. And we preliminarily analyze the cause of the regional per capita income inequality.展开更多
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.
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.
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.
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 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.
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.
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Supported by the National Science Foundation of China(60970151,70973110)the Natural Science Foundation of Zhejiang Province(Y7080068)the Professor Foundation of Zhejiang Gongshang University(07-13)
文摘The inequality sup n≥1｜n∑k=1 sinkx/k｜≤3√π,plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and improves their results by introducing a new class of sequences called γ-piecewise bounded variation sequence （γ-PBVS）.
文摘In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
文摘Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.
文摘Using the targets such as absolute dispersion, ratio of high - low Income, coefficient of variation and Ginl coefficient, we analyze the China’s per capita income inequality from 1952 to 1995. We find the trends in the China’s per capita Income differences, i.e., from 1952 to 1978 the differences increase; from 1978 to the early of 1990’ s decrease; and from the early of 1990’ s to 1995 a little increase. But in the light of absolute levels, the differences Increase from year to year. And we preliminarily analyze the cause of the regional per capita income inequality.
