In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of c...An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.展开更多
In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic...In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.展开更多
In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies ...In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies the Orlicz Busemann-Petty centroid inequality of Lutwak,Yang and Zhang[23].展开更多
Inspired by the idea of stochastic quantization proposed by Parisi and Wu,we reconstruct the transition probability function that has a central role in the renormalization group using a stochastic differential equatio...Inspired by the idea of stochastic quantization proposed by Parisi and Wu,we reconstruct the transition probability function that has a central role in the renormalization group using a stochastic differential equation.From a probabilistic perspective,the renormalization procedure can be characterized by a discretetime Markov chain.Therefore,we focus on this stochastic dynamic,and establish the local Poincaré inequality by calculating the Bakry-Émery curvature for two point functions.Finally,we choose an appropriate coupling relationship between parameters K and T to obtain the Poincaré inequality of two point functions for the limiting system.Our method extends the classic Bakry-Émery criterion,and the results provide a new perspective to characterize the renormalization procedure.展开更多
Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s co...Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.展开更多
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
Poverty and income inequality are problems faced by many countries including China.Since the implementation of Targeted Poverty Alleviation(TPA),absolute poverty has been eradicated,meanwhile,Chinese rural residents&#...Poverty and income inequality are problems faced by many countries including China.Since the implementation of Targeted Poverty Alleviation(TPA),absolute poverty has been eradicated,meanwhile,Chinese rural residents' income and inequality have experienced unprecedented new dynamics,but still,very few studies have focused on them.Hence,we attempt to examine the new trends in Chinese farmers' income inequality and to understand its causes during this period.We observe that China's urban-rural income ratio has been shrinking and the urban-rural inequality has been decreasing from 2014 to 2021.The reduction in the Theil index indicates a decrease in the regional inequality of farmers' income as well,and the decline in inter-regional inequality among eight economic zones contributes about 80% to increased equality.These new trends are caused by the fact that,with the TPA,the incomes of rural residents especially that in destitute areas,grew faster than that of urban residents and farmers in prosperous areas.The higher share of non-agricultural industry and agricultural mechanization level have significant positive impact on regional equality of farmers' income,while urban-rural dual structure has significant negative inhibitory effects.The lowest farmers' income and the highest inequality in the Northwest,and the slowest growth in the Northeast deserve more attention in rural Revitalization.From these findings,we propose four policy implications that would be applied to improve Chinese farmers' income equality,govern relative poverty,and achieve common prosperity in the post-poverty era.展开更多
Built-up land has increased rapidly in recent decades,thus aggravating the competition for land between multiple uses.The increase in urban land can be decomposed into changes in population and changes in built-up lan...Built-up land has increased rapidly in recent decades,thus aggravating the competition for land between multiple uses.The increase in urban land can be decomposed into changes in population and changes in built-up land per person.Yet,it is unclear how this decomposition differs by country and how this decomposition changes over time.Moreover,we don’t know whether these changes affect the inequality in built-up land per capita.Here,we analyze the global distribution of built-up land per capita in the year 2020,as well as the changes therein between 1985 and 2020.We find that built-up land per capita in 2020 differs by an order of magnitude between countries,ranging from 15 m^(2) per person in Ethiopia to 734 m^(2) per person in Australia.Moreover,we find a wide range of different change trajectories,including both increases and decreases in built-up land per capita and in total population.As the total area of urban land increased in all countries,decreases in urban land consumption reflect a situation where the population increases faster than the total amount of urban land.We also find a large inequality in urban land consumption across countries,as indicated by a Gini index of 0.47 in 1985,decreasing only slightly to 0.45 in 2020.These findings suggest the need for a regionally differentiated approach to reduce urban land take,focusing first on mitigating further increases in those countries that already have a high urban land consumption.展开更多
Objective:We examine how inequality in women's health has changed in India and its major states between 2015 and 2021.We also attempt to identify the sources of any change in this inequality using a decomposition ...Objective:We examine how inequality in women's health has changed in India and its major states between 2015 and 2021.We also attempt to identify the sources of any change in this inequality using a decomposition analysis.In order to suggest suitable policies for reducing this inequality,we attempt to identify the factors that are strongly associated with it.Methods:We construct an index of women's health from five indicators using the principal component analysis.Based on this index we measure inequality in women's health using the coefficient of variation and the Theil index.To identify the sources of change in this inequality,we apply Theil decomposition technique.Results:We find that inequality in women's health has increased significantly in India between 2015 and 2021.During this period,this inequality has increased significantly in six states,while it has decreased significantly in five states.The decomposition analysis suggests that the increase in this inequality between 2015 and 2021 has been driven by an increase in interstate inequality.We also find a strong positive association between inequality in women's health and inequality in public health amenities and social development.Conclusion:We suggest that for reducing inequality in women's health in developing countries like India,policies should focus on eliminating disparities in income,female education and provision of public health amenities.展开更多
Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in th...Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.展开更多
Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hie...Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hierarchical, use the distance function to measure the dissimilarities among actors. These distance functions need to fulfill various properties, including the triangle inequality (TI). However, in some cases, the triangle inequality might be violated, impacting the quality of the resulting clusters. With experiments, this paper explains how TI violates while performing traditional clustering techniques: k-medoids, hierarchical, DENGRAPH, and spectral clustering on social networks and how the violation of TI affects the quality of the resulting clusters.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
This study assesses the role of mobile money innovations on income inequality and gender inclusion in 42 sub-Saharan African countries from 1980 to 2019 using interactive quantile regressions.It finds that,first,incom...This study assesses the role of mobile money innovations on income inequality and gender inclusion in 42 sub-Saharan African countries from 1980 to 2019 using interactive quantile regressions.It finds that,first,income inequality unconditionally reduces the involvement of women in business and politics.Second,mobile money innovations interact with income inequality to have a positive impact on women in business and politics.Third,the net effects of mobile money innovations on gender inclusion through income inequality are consistently negative.Fourth,as the positive conditional or interactive effects and negative net effects are consistent across the conditional distribution of gender inclusion,thresholds at which mobile money innovations can completely dampen the negative effect of income inequality on gender inclusion are provided.Therefore,policymakers should work toward improving conditions for mobile money innovations.They should also be aware that reducing both income inequality and enhancing mobile money innovations simultaneously leads to more inclusive outcomes in terms of gender inclusion.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
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
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
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 examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).A...In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.展开更多
Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金supported by the NSFC(12171378)supported by the Characteristic innovation projects of universities in Guangdong province(2023K-TSCX381)+3 种基金supported by the Young Top-Talent program of Chongqing(CQYC2021059145)the Major Special Project of NSFC(12141101)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937).
文摘An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.
文摘In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.
基金Supported in part by NSFC(12071378,12461009),20XLB012,KJQN202100527,CSTB2022NSCQ-MSX0259 and KJQN202300557.
文摘In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies the Orlicz Busemann-Petty centroid inequality of Lutwak,Yang and Zhang[23].
基金supported by the National Natural Science Foundation of China(No.12288201).
文摘Inspired by the idea of stochastic quantization proposed by Parisi and Wu,we reconstruct the transition probability function that has a central role in the renormalization group using a stochastic differential equation.From a probabilistic perspective,the renormalization procedure can be characterized by a discretetime Markov chain.Therefore,we focus on this stochastic dynamic,and establish the local Poincaré inequality by calculating the Bakry-Émery curvature for two point functions.Finally,we choose an appropriate coupling relationship between parameters K and T to obtain the Poincaré inequality of two point functions for the limiting system.Our method extends the classic Bakry-Émery criterion,and the results provide a new perspective to characterize the renormalization procedure.
文摘Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
基金supported by the GanSu Provincial Science and Technology Program(No.22ZD6FA005)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA23060704).
文摘Poverty and income inequality are problems faced by many countries including China.Since the implementation of Targeted Poverty Alleviation(TPA),absolute poverty has been eradicated,meanwhile,Chinese rural residents' income and inequality have experienced unprecedented new dynamics,but still,very few studies have focused on them.Hence,we attempt to examine the new trends in Chinese farmers' income inequality and to understand its causes during this period.We observe that China's urban-rural income ratio has been shrinking and the urban-rural inequality has been decreasing from 2014 to 2021.The reduction in the Theil index indicates a decrease in the regional inequality of farmers' income as well,and the decline in inter-regional inequality among eight economic zones contributes about 80% to increased equality.These new trends are caused by the fact that,with the TPA,the incomes of rural residents especially that in destitute areas,grew faster than that of urban residents and farmers in prosperous areas.The higher share of non-agricultural industry and agricultural mechanization level have significant positive impact on regional equality of farmers' income,while urban-rural dual structure has significant negative inhibitory effects.The lowest farmers' income and the highest inequality in the Northwest,and the slowest growth in the Northeast deserve more attention in rural Revitalization.From these findings,we propose four policy implications that would be applied to improve Chinese farmers' income equality,govern relative poverty,and achieve common prosperity in the post-poverty era.
基金supported by the Netherlands Organization for Scientific Research NWO in the form of a VIDI grant(Grant No.VI.Vidi.198.008).
文摘Built-up land has increased rapidly in recent decades,thus aggravating the competition for land between multiple uses.The increase in urban land can be decomposed into changes in population and changes in built-up land per person.Yet,it is unclear how this decomposition differs by country and how this decomposition changes over time.Moreover,we don’t know whether these changes affect the inequality in built-up land per capita.Here,we analyze the global distribution of built-up land per capita in the year 2020,as well as the changes therein between 1985 and 2020.We find that built-up land per capita in 2020 differs by an order of magnitude between countries,ranging from 15 m^(2) per person in Ethiopia to 734 m^(2) per person in Australia.Moreover,we find a wide range of different change trajectories,including both increases and decreases in built-up land per capita and in total population.As the total area of urban land increased in all countries,decreases in urban land consumption reflect a situation where the population increases faster than the total amount of urban land.We also find a large inequality in urban land consumption across countries,as indicated by a Gini index of 0.47 in 1985,decreasing only slightly to 0.45 in 2020.These findings suggest the need for a regionally differentiated approach to reduce urban land take,focusing first on mitigating further increases in those countries that already have a high urban land consumption.
文摘Objective:We examine how inequality in women's health has changed in India and its major states between 2015 and 2021.We also attempt to identify the sources of any change in this inequality using a decomposition analysis.In order to suggest suitable policies for reducing this inequality,we attempt to identify the factors that are strongly associated with it.Methods:We construct an index of women's health from five indicators using the principal component analysis.Based on this index we measure inequality in women's health using the coefficient of variation and the Theil index.To identify the sources of change in this inequality,we apply Theil decomposition technique.Results:We find that inequality in women's health has increased significantly in India between 2015 and 2021.During this period,this inequality has increased significantly in six states,while it has decreased significantly in five states.The decomposition analysis suggests that the increase in this inequality between 2015 and 2021 has been driven by an increase in interstate inequality.We also find a strong positive association between inequality in women's health and inequality in public health amenities and social development.Conclusion:We suggest that for reducing inequality in women's health in developing countries like India,policies should focus on eliminating disparities in income,female education and provision of public health amenities.
文摘Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.
文摘Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hierarchical, use the distance function to measure the dissimilarities among actors. These distance functions need to fulfill various properties, including the triangle inequality (TI). However, in some cases, the triangle inequality might be violated, impacting the quality of the resulting clusters. With experiments, this paper explains how TI violates while performing traditional clustering techniques: k-medoids, hierarchical, DENGRAPH, and spectral clustering on social networks and how the violation of TI affects the quality of the resulting clusters.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘This study assesses the role of mobile money innovations on income inequality and gender inclusion in 42 sub-Saharan African countries from 1980 to 2019 using interactive quantile regressions.It finds that,first,income inequality unconditionally reduces the involvement of women in business and politics.Second,mobile money innovations interact with income inequality to have a positive impact on women in business and politics.Third,the net effects of mobile money innovations on gender inclusion through income inequality are consistently negative.Fourth,as the positive conditional or interactive effects and negative net effects are consistent across the conditional distribution of gender inclusion,thresholds at which mobile money innovations can completely dampen the negative effect of income inequality on gender inclusion are provided.Therefore,policymakers should work toward improving conditions for mobile money innovations.They should also be aware that reducing both income inequality and enhancing mobile money innovations simultaneously leads to more inclusive outcomes in terms of gender inclusion.
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 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 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.
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.
基金supported by the National Natural Science Foundation of China(12371327)the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0107).
文摘In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.
文摘Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
