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
Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a genera...Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.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
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
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
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
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
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
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
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.
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
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
Since 2000,China's investment in Africa has grown rapidly,following a steady upward trajectory.However,this influx of Chinese capital has sparked both economic and political controversies.By integrating multi-sour...Since 2000,China's investment in Africa has grown rapidly,following a steady upward trajectory.However,this influx of Chinese capital has sparked both economic and political controversies.By integrating multi-source data—from micro-level individual projects to national statistics—this study examines the impact of Chinese investment on African economic development between 2000 and 2022.The results reveal a significant positive correlation between Chinese investment and economic growth across different scales,with investment-intensive regions achieving stronger economic outcomes.The DID analysis indicates that the Belt and Road Initiative has contributed positively to Africa's economic development.Both static and dynamic panel models confirm that Chinese investment significantly stimulates growth,exhibiting notable lag effects.Furthermore,β-convergence models demonstrate that Chinese investment fosters economic convergence among African countries.Regarding regional inequality,the findings suggest that Chinese investment helps to narrow disparities across Africa,promoting a more balanced economic landscape.Overall,this research underscores the constructive role of China's investment in fostering economic growth and reducing inequality within the African context.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
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 study,we propose a novel method for establishing Milne’s rule-type inequalities within the context of quantum calculus applied to differentiable convex functions.Initially,we obtain a quantum integral identit...In this study,we propose a novel method for establishing Milne’s rule-type inequalities within the context of quantum calculus applied to differentiable convex functions.Initially,we obtain a quantum integral identity,which serves as the foundation for deriving several new Milne’s rule inequalities tailored for quantum differentiable convex functions.These inequalities are particularly relevant in Open-Newton’s Cotes formulas,facilitating the determination of bounds for Milne’s rule in both classical and q-calculus domains.Additionally,we conduct computational analysis on these inequalities for convex functions and present mathematical examples and graphical representation to demonstrate the validity of our newly established results within the realm of q-calculus.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
In this paper, we investigate the effect of exceptional points(EPs) on the violation of Leggett–Garg inequality(LGI) and no-signaling-in-time(NSIT) conditions and compare the different effects between the Hamiltonian...In this paper, we investigate the effect of exceptional points(EPs) on the violation of Leggett–Garg inequality(LGI) and no-signaling-in-time(NSIT) conditions and compare the different effects between the Hamiltonian EP(HEP) and Liouvillian EP(LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits.Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases,the NSIT conditions can be violated in a wider parameter regime than the LGI.展开更多
Purpose–This paper investigates how high-speed rail(HSR)influences socioeconomic inequality by providing the first systematic bibliometric review of research trends,methodological approaches and thematic structures.I...Purpose–This paper investigates how high-speed rail(HSR)influences socioeconomic inequality by providing the first systematic bibliometric review of research trends,methodological approaches and thematic structures.It examines whether HSR fosters balanced regional development or reinforces spatial disparities.Design/methodology/approach–Using the Bibliometrix R package,237 records were retrieved from the Web of Science(1985–2024).Citation indicators,keyword co-occurrence and collaboration networks were combined with natural language processing(NLP)to classify studies by territorial scale,methodology,economic variables and inequality outcomes.Findings–The paper offers the first structured overview of how the literature conceptualizes the link between HSR and inequality.It highlights persistent gaps–scarcity of city-level analyses,limited socioeconomic indicators and reliance on Chinese case studies–providing a foundation for more comparative and interdisciplinary research.Originality/value–This paper contributes by offering a structured overview of how the literature has conceptualized and measured the relationship between HSR and inequality.By identifying persistent research gaps–such as the scarcity of city-level analyses,limited use of socioeconomic indicators,and overreliance on Chinese case studies–it provides a foundation for more comparative and interdisciplinary approaches.The study informs policymakers and researchers on how to design future infrastructure projects that balance efficiency with equity.展开更多
In this paper,we explicitly establish Poincaréinequality for 1≤p<∞ over simple geometric domains,such as segment,rectangle,triangle or tetrahedron.We obtain sharper bounds of the constant in Poincaré in...In this paper,we explicitly establish Poincaréinequality for 1≤p<∞ over simple geometric domains,such as segment,rectangle,triangle or tetrahedron.We obtain sharper bounds of the constant in Poincaré inequality and,in particular,the explicit relation between the constant and the geometric characters of the domain.展开更多
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 the Postgraduate Scientic Research Innovation Project of Chongqing Normal University(YKC24010)Chunna Zeng's research was supported by the Major Special Project of the National Natural Science Foundation of China(12141101)+2 种基金the Young Top-Talent program of Chongqing(CQYC2021059145)the Technology Research Foundation of Chongqing Educational committee(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937)。
文摘Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.
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.
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.
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 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 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).
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.
基金National Natural Science Foundation of China,No.42101424,No.42001115。
文摘Since 2000,China's investment in Africa has grown rapidly,following a steady upward trajectory.However,this influx of Chinese capital has sparked both economic and political controversies.By integrating multi-source data—from micro-level individual projects to national statistics—this study examines the impact of Chinese investment on African economic development between 2000 and 2022.The results reveal a significant positive correlation between Chinese investment and economic growth across different scales,with investment-intensive regions achieving stronger economic outcomes.The DID analysis indicates that the Belt and Road Initiative has contributed positively to Africa's economic development.Both static and dynamic panel models confirm that Chinese investment significantly stimulates growth,exhibiting notable lag effects.Furthermore,β-convergence models demonstrate that Chinese investment fosters economic convergence among African countries.Regarding regional inequality,the findings suggest that Chinese investment helps to narrow disparities across Africa,promoting a more balanced economic landscape.Overall,this research underscores the constructive role of China's investment in fostering economic growth and reducing inequality within the African context.
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.
文摘In this study,we propose a novel method for establishing Milne’s rule-type inequalities within the context of quantum calculus applied to differentiable convex functions.Initially,we obtain a quantum integral identity,which serves as the foundation for deriving several new Milne’s rule inequalities tailored for quantum differentiable convex functions.These inequalities are particularly relevant in Open-Newton’s Cotes formulas,facilitating the determination of bounds for Milne’s rule in both classical and q-calculus domains.Additionally,we conduct computational analysis on these inequalities for convex functions and present mathematical examples and graphical representation to demonstrate the validity of our newly established results within the realm of q-calculus.
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financially supported by the National Natural Science Foundation of China (Grants Nos. 11775019 and 11875086)。
文摘In this paper, we investigate the effect of exceptional points(EPs) on the violation of Leggett–Garg inequality(LGI) and no-signaling-in-time(NSIT) conditions and compare the different effects between the Hamiltonian EP(HEP) and Liouvillian EP(LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits.Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases,the NSIT conditions can be violated in a wider parameter regime than the LGI.
文摘Purpose–This paper investigates how high-speed rail(HSR)influences socioeconomic inequality by providing the first systematic bibliometric review of research trends,methodological approaches and thematic structures.It examines whether HSR fosters balanced regional development or reinforces spatial disparities.Design/methodology/approach–Using the Bibliometrix R package,237 records were retrieved from the Web of Science(1985–2024).Citation indicators,keyword co-occurrence and collaboration networks were combined with natural language processing(NLP)to classify studies by territorial scale,methodology,economic variables and inequality outcomes.Findings–The paper offers the first structured overview of how the literature conceptualizes the link between HSR and inequality.It highlights persistent gaps–scarcity of city-level analyses,limited socioeconomic indicators and reliance on Chinese case studies–providing a foundation for more comparative and interdisciplinary research.Originality/value–This paper contributes by offering a structured overview of how the literature has conceptualized and measured the relationship between HSR and inequality.By identifying persistent research gaps–such as the scarcity of city-level analyses,limited use of socioeconomic indicators,and overreliance on Chinese case studies–it provides a foundation for more comparative and interdisciplinary approaches.The study informs policymakers and researchers on how to design future infrastructure projects that balance efficiency with equity.
基金Supported by National Natural Science Foundation of China(Grant Nos.12001170 and 11601124)Innovative Funds Plan of Henan University of Technology(Grant No.2021ZKCJ11).
文摘In this paper,we explicitly establish Poincaréinequality for 1≤p<∞ over simple geometric domains,such as segment,rectangle,triangle or tetrahedron.We obtain sharper bounds of the constant in Poincaré inequality and,in particular,the explicit relation between the constant and the geometric characters of the domain.
