In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmoni...In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmonic Prékopa-Leindler inequality is used.We prove that these new inequalities are more efficient in estimating the variance and entropy for some functions with exponential terms.展开更多
Ambient fine particulate matter(PM_(2.5))pollution causes the largest environmental health risk globally,yet ex-posure levels and the resulting health risks vary across countries with different income levels.Global we...Ambient fine particulate matter(PM_(2.5))pollution causes the largest environmental health risk globally,yet ex-posure levels and the resulting health risks vary across countries with different income levels.Global wealth inequality has intensified in recent years,yet the relationship between wealth inequality and health risks related to PM_(2.5) pollution remains poorly understood.In this study,we evaluated the global mortality and health cost at-tributable to PM_(2.5) exposure from 2017 to 2021,and analyzed the relationship between wealth inequality,PM_(2.5) pollution,and the associated health risks across regions with varying economic levels.We found a consistent decline in mortalities and health costs attributable to PM_(2.5) exposure from 2017 to 2020,followed by a rebound after 2020,driven primarily by the resurgence of PM_(2.5) concentrations and a deceleration in the reduction of baseline mortality rates.We also found that the average PM_(2.5) concentration and associated risks decrease as domestic wealth inequality decreases and national income level increases.However,regions with extremely high levels of wealth inequality consistently show lower national average PM_(2.5) concentrations and health risks.These findings highlight the need to consider healthcare security during emergencies,as well as policy fairness across economic regions,in the formulation of global PM_(2.5) pollution control measures to promote sustainable,more equitable economic growth and coordinated air pollution management.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
This study examines the impact of artificial intelligence(AI)on carbon inequality(CI)in 67 countries from 1995 to 2019.The results suggest that(i)AI significantly amplifies CI both between and within countries due to ...This study examines the impact of artificial intelligence(AI)on carbon inequality(CI)in 67 countries from 1995 to 2019.The results suggest that(i)AI significantly amplifies CI both between and within countries due to its energy requirements and uneven deployment;(ii)trade openness and global value chain(GVC)positioning mitigate AI’s effect on inter-country CI,while robust governance—marked by larger government size and institutional transparency—curtails intra-country disparities;(iii)specific thresholds(trade openness>4.74,GVC position>−1.07,government size>2.90,transparency>−0.22)shift the impact of AI from exacerbating to reducing CI.The adverse effects of AI can be reversed through enhanced trade,GVC integration,and strong governance.Key policy implications:Policymakers must prioritize exceeding these thresholds to leverage AI for sustainable and equitable outcomes.This requires(a)promoting trade liberalization to spread the benefits of AI globally,reducing inter-country CI;(b)strengthening GVC participation to offset the carbon-intensive use of AI;(c)building government capacity and transparency to ensure fair adoption of AI domestically;and(d)embedding these strategies in climate policies to align AI with the long-term goals of environmental justice and the SDGs,particularly climate action(SDG 13)and reducing inequalities(SDG 10).展开更多
The purpose of this paper is to study some famous inequalities in Euclidean space.We are able to reveal an elegant relation between the famous Selberg inequality and Bessel inequality in Euclidean space.
The Hardy integral inequality is one of the most important inequalities in analysis. The present paper establishes some new Copson-Pachpatte （C-P） type inequalities, which are the generalizations of the Hardy integr...The Hardy integral inequality is one of the most important inequalities in analysis. The present paper establishes some new Copson-Pachpatte （C-P） type inequalities, which are the generalizations of the Hardy integral inequalities on binary functions.展开更多
In this paper, we find some new inequalities by Redheffer inequality, Jordan inequality and Jensen inequality. As application, we generalize one result which was given in [1].
In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which gi...In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.展开更多
Energy poverty in developing countries is a critical issue characterized by the lack of access to modern energy services,such as electricity and clean cooking facilities,as marked in SDG 7.This study explores the corr...Energy poverty in developing countries is a critical issue characterized by the lack of access to modern energy services,such as electricity and clean cooking facilities,as marked in SDG 7.This study explores the correlations between energy poverty,energy intensity,resource abundance,and income inequality,as these factors have been theorized to play important roles in influencing energy poverty in developing countries.By observing that the dataset is heterogeneous across the countries and over the time frame,we use the Method of Moments Quantile Regression(MMQR)to analyze our developing countries’data from 2000 to 2019.Our findings indicate that energy intensity is a significant factor influencing energy poverty,suggesting that higher energy consumption relative to the sample countries can exacerbate this issue.Additionally,we observe that income inequality within the sample countries is a critical determinant of energy poverty levels,highlighting the dynamics between economic disparity and access to energy resources.Interestingly,our study reveals that resource abundance acts as a blessing rather than a curse in terms of energy poverty,implying that countries rich in natural resources may have better opportunities to combat energy deprivation.Finally,we emphasize the vital role of financial markets in addressing energy poverty on a global scale,suggesting that robust financial systems can facilitate investments and innovations aimed at improving energy access for vulnerable populations.The results from the robustness analysis support the empirical results obtained from the main estimation.The empirical findings of the present study advance important comprehensions for policymakers to adopt energy policies that address the complex challenges of energy poverty and promote inclusive energy access.展开更多
Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significan...Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.展开更多
This study explores the housing distribution effect of the Housing Provident Fund(HPF)system on households.Utilizing data from the China Household Finance Survey conducted in 2013,2015,2017,and 2019,this study empiric...This study explores the housing distribution effect of the Housing Provident Fund(HPF)system on households.Utilizing data from the China Household Finance Survey conducted in 2013,2015,2017,and 2019,this study empirically investigates this effect from two dimensions:the impact of HPF payments on household income and housing loan behavior,and the impact on the Gini coefficient of housing assets within the group.The results indicate that the HPF payment does not significantly impact household income levels.Instead,it increases their likelihood of obtaining housing loans,particularly for middle-income households.Additionally,for any group of families,the HPF payment decreased the housing Gini coefficient among households by approximately 0.11 units.This study may be the first to provide the most direct empirical evidence on the extent of HPF’s impact on housing inequality within a group.It also questions the inference in the literature that“HPF will aggravate housing inequality within the group.”Based on this study’s findings,we expect that housing inequality will continue to be alleviated with continued HPF implementation.In particular,this effect will be more significant if the credit support for lowincome families to purchase houses through the HPF can be further enhanced.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
The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces....The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.展开更多
An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solutio...An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.展开更多
In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat eq...In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.展开更多
Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for...Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.展开更多
Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient c...Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.展开更多
We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan d...We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.展开更多
A parametrization of density matrices of ddimensions in terms of the raising J+and lowering J−angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann paramete...A parametrization of density matrices of ddimensions in terms of the raising J+and lowering J−angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta j1and j2is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the X-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel’son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell’s inequality.展开更多
基金Supported in part by the NSFC(12071378,12461009)the Natural Science Basic Research Program of Shaanxi(2023-JC-YB-036)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSQ033).
文摘In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmonic Prékopa-Leindler inequality is used.We prove that these new inequalities are more efficient in estimating the variance and entropy for some functions with exponential terms.
基金supported by the National Natural Science Foundation of China(Nos.42305089 and 42175106)the Self-supporting Program of Guangzhou Laboratory(No.SRPG22-007)+1 种基金the Youth Science and Technology Fund Project of Gansu(No.22JR5RA512)the Fundamental Research Funds for the Central Universities(No.lzujbky-2022-pd05).
文摘Ambient fine particulate matter(PM_(2.5))pollution causes the largest environmental health risk globally,yet ex-posure levels and the resulting health risks vary across countries with different income levels.Global wealth inequality has intensified in recent years,yet the relationship between wealth inequality and health risks related to PM_(2.5) pollution remains poorly understood.In this study,we evaluated the global mortality and health cost at-tributable to PM_(2.5) exposure from 2017 to 2021,and analyzed the relationship between wealth inequality,PM_(2.5) pollution,and the associated health risks across regions with varying economic levels.We found a consistent decline in mortalities and health costs attributable to PM_(2.5) exposure from 2017 to 2020,followed by a rebound after 2020,driven primarily by the resurgence of PM_(2.5) concentrations and a deceleration in the reduction of baseline mortality rates.We also found that the average PM_(2.5) concentration and associated risks decrease as domestic wealth inequality decreases and national income level increases.However,regions with extremely high levels of wealth inequality consistently show lower national average PM_(2.5) concentrations and health risks.These findings highlight the need to consider healthcare security during emergencies,as well as policy fairness across economic regions,in the formulation of global PM_(2.5) pollution control measures to promote sustainable,more equitable economic growth and coordinated air pollution management.
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.
基金supported by National Natural Science Foundation of China(Grant No.72104246).
文摘This study examines the impact of artificial intelligence(AI)on carbon inequality(CI)in 67 countries from 1995 to 2019.The results suggest that(i)AI significantly amplifies CI both between and within countries due to its energy requirements and uneven deployment;(ii)trade openness and global value chain(GVC)positioning mitigate AI’s effect on inter-country CI,while robust governance—marked by larger government size and institutional transparency—curtails intra-country disparities;(iii)specific thresholds(trade openness>4.74,GVC position>−1.07,government size>2.90,transparency>−0.22)shift the impact of AI from exacerbating to reducing CI.The adverse effects of AI can be reversed through enhanced trade,GVC integration,and strong governance.Key policy implications:Policymakers must prioritize exceeding these thresholds to leverage AI for sustainable and equitable outcomes.This requires(a)promoting trade liberalization to spread the benefits of AI globally,reducing inter-country CI;(b)strengthening GVC participation to offset the carbon-intensive use of AI;(c)building government capacity and transparency to ensure fair adoption of AI domestically;and(d)embedding these strategies in climate policies to align AI with the long-term goals of environmental justice and the SDGs,particularly climate action(SDG 13)and reducing inequalities(SDG 10).
基金Supported by Shandong Provincial Natural Science Foundation(ZR2024MA053).
文摘The purpose of this paper is to study some famous inequalities in Euclidean space.We are able to reveal an elegant relation between the famous Selberg inequality and Bessel inequality in Euclidean space.
基金Project supported by the National Basic Research Program of China(No.2011CB302402)theNational Natural Science Foundation of China(No.11171053)
文摘The Hardy integral inequality is one of the most important inequalities in analysis. The present paper establishes some new Copson-Pachpatte （C-P） type inequalities, which are the generalizations of the Hardy integral inequalities on binary functions.
文摘In this paper, we find some new inequalities by Redheffer inequality, Jordan inequality and Jensen inequality. As application, we generalize one result which was given in [1].
文摘In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.
文摘Energy poverty in developing countries is a critical issue characterized by the lack of access to modern energy services,such as electricity and clean cooking facilities,as marked in SDG 7.This study explores the correlations between energy poverty,energy intensity,resource abundance,and income inequality,as these factors have been theorized to play important roles in influencing energy poverty in developing countries.By observing that the dataset is heterogeneous across the countries and over the time frame,we use the Method of Moments Quantile Regression(MMQR)to analyze our developing countries’data from 2000 to 2019.Our findings indicate that energy intensity is a significant factor influencing energy poverty,suggesting that higher energy consumption relative to the sample countries can exacerbate this issue.Additionally,we observe that income inequality within the sample countries is a critical determinant of energy poverty levels,highlighting the dynamics between economic disparity and access to energy resources.Interestingly,our study reveals that resource abundance acts as a blessing rather than a curse in terms of energy poverty,implying that countries rich in natural resources may have better opportunities to combat energy deprivation.Finally,we emphasize the vital role of financial markets in addressing energy poverty on a global scale,suggesting that robust financial systems can facilitate investments and innovations aimed at improving energy access for vulnerable populations.The results from the robustness analysis support the empirical results obtained from the main estimation.The empirical findings of the present study advance important comprehensions for policymakers to adopt energy policies that address the complex challenges of energy poverty and promote inclusive energy access.
基金supported by the National Science Fund for Distinguished Young Scholars(42225107)the National Natural Science Foundation of China(42001326,42371414,42171409,and 42271419)+1 种基金the Natural Science Foundation of Guangdong Province of China(2022A1515012207)the Basic and Applied Basic Research Project of Guangzhou Science and Technology Planning(202201011539)。
文摘Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.
基金funded by the Humanities and Social Sciences Research Project of the Ministry of Education of China(Project No.23XJC790007).
文摘This study explores the housing distribution effect of the Housing Provident Fund(HPF)system on households.Utilizing data from the China Household Finance Survey conducted in 2013,2015,2017,and 2019,this study empirically investigates this effect from two dimensions:the impact of HPF payments on household income and housing loan behavior,and the impact on the Gini coefficient of housing assets within the group.The results indicate that the HPF payment does not significantly impact household income levels.Instead,it increases their likelihood of obtaining housing loans,particularly for middle-income households.Additionally,for any group of families,the HPF payment decreased the housing Gini coefficient among households by approximately 0.11 units.This study may be the first to provide the most direct empirical evidence on the extent of HPF’s impact on housing inequality within a group.It also questions the inference in the literature that“HPF will aggravate housing inequality within the group.”Based on this study’s findings,we expect that housing inequality will continue to be alleviated with continued HPF implementation.In particular,this effect will be more significant if the credit support for lowincome families to purchase houses through the HPF can be further enhanced.
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 NSFC(No.12171062)the Natural Science Foundation of Chongqing(No.CSTB2022NSCQ-JQX0004)+1 种基金the Chongqing Talent Support Program(No.cstc2024ycjh-bgzxm0121)Science and Technology Project of Chongqing Education Committee(No.KJZD-M202300503)。
文摘The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.
基金Supported by Scientific Research Fund of Hunan Provincial Education Departmen(t23A0361)。
文摘An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.
基金Partially supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province(Nos.KYCX22-2211,KYCX22-2205)。
文摘In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.
文摘Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.
基金supported by the project Disuguaglianze analitiche e geometriche,funded by the Gruppo per Analisi Matematica la Probabilitàe le loro Applicazioni.
文摘Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.
文摘We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.
文摘A parametrization of density matrices of ddimensions in terms of the raising J+and lowering J−angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta j1and j2is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the X-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel’son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell’s inequality.
