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AN IMPROVED HARDY'S INEQUALITY
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作者 Assal MILOUD Rahmouni ATEF 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1382-1386,共5页
In this paper we shall extend Hardy's inequality associated with Fourier trans- form to the strip n(2-p) ≤σ〈 n+p(N+ 1) where N = [n(1/p- 1)], the greatest integer not exceeding n(1/p - 1).
关键词 Hardy's space Hardy's inequality
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A MATHEMATICAL PROOF OF A PROBABILISTIC MODEL OF HARDY'S INEQUALITY
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作者 Prateek K 《Analysis in Theory and Applications》 2012年第1期95-100,共6页
In this paper using an argument from [1] , we prove one of the probabilistic version of Hardy's inequality.
关键词 random variables uniform partition Hardy's inequality
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Fermions: Spin, Hidden Variables, Violation of Bell’s Inequality and Quantum Entanglement
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作者 Doron Kwiat 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第4期1613-1627,共15页
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
关键词 FERMIONS SPIN Hidden Variables Bell’s inequality Violation Spin Entanglement
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THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE
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作者 东瑜昕 林和子 陆琳根 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期189-194,共6页
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
关键词 asymptotically nonnegative sectional curvature logarithmic Sobolev inequality ABP method
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Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems
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作者 Yao Li Hongwei Liu Jiamin Lv 《Journal of Harbin Institute of Technology(New Series)》 CAS 2024年第2期38-49,共12页
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
关键词 variational inequality inertial method non-monotonic step size rule Lipschitz continuity pseudomonotone mapping
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A Study of Triangle Inequality Violations in Social Network Clustering
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作者 Sanjit Kumar Saha Tapashi Gosswami 《Journal of Computer and Communications》 2024年第1期67-76,共10页
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
关键词 CLUSTERING Triangle inequality Violations Traditional Clustering Graph Clustering
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AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS
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作者 Safoura Rezaei ADERYANI Azam AHADI +1 位作者 Reza SAADATI Hari M.SRIVASTAVA 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期311-338,共28页
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
关键词 permuting tri-homomorphism in Banach algebra permuting tri-derivation on C*-algebra fixed point theorem Ulam-Hyers-Rassias stability aggregate special functions tri-additiveψ-functional inequality
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Atomic decompositions and Hardy's inequality on weak Hardy-Morrey spaces 被引量:2
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作者 HO Kwok-Pun 《Science China Mathematics》 SCIE CSCD 2017年第3期449-468,共20页
We introduce the weak Hardy-Morrey spaces in this paper.We also obtain the atomic decompositions of the weak Hardy-Morrey spaces.By using these decompositions,we establish the Hardy inequalities on the weak Hardy-Morr... We introduce the weak Hardy-Morrey spaces in this paper.We also obtain the atomic decompositions of the weak Hardy-Morrey spaces.By using these decompositions,we establish the Hardy inequalities on the weak Hardy-Morrey spaces. 展开更多
关键词 Hardy spaces Morrey spaces weak Lebesgue spaces atomic decompositions Hardy's inequality
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The relation between Hardy's non-locality and violation of Bell inequality
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作者 向阳 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第6期7-11,共5页
We give an analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy's... We give an analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy's non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy's non- locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the CabeUo's argument of Hardy's non-locality (a generalization of Hardy's argument) and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy's non-locality under the constraint of information causality with the aid of the above derived relation between Hardy's non-locality and Bell operator. 展开更多
关键词 Hardy's non-locality Bell inequality information causality
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THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES 被引量:1
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作者 徐庆华 方炜康 +1 位作者 冯伟珩 刘太顺 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2075-2088,共14页
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo... Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space. 展开更多
关键词 Fekete and Szego inequality successive coefficients difference bound close-to-starlike mappings complex Banach space
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Verification of the Landau Equation and Hardy’s Inequality
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作者 Salih Yousuf Mohamed Salih 《Applied Mathematics》 2023年第3期208-229,共22页
We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interactio... We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities. 展开更多
关键词 Hardy’s inequality Sobolev Inequalities the Landau Equation L-Estimate
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NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY
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作者 杨云龙 江楠 张德燕 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2333-2346,共14页
Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this pa... Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality. 展开更多
关键词 cone-volume measure dilation position log-Brunn-Minkowski's inequality log-Minkowski's inequality relative positive center
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The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality
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作者 Louis Sica 《Journal of Modern Physics》 CAS 2023年第6期802-817,共16页
It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising... It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising fact is not immediately obvious from Bell’s inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra. 展开更多
关键词 Bell inequality Bell Theorem Wigner inequality Entanglement LOCALITY REALISM
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Some Refinement of Holder’s and Its Reverse Inequality
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作者 Musa O. Tijani Adefisayo Ojo Oludotun Akinsola 《Advances in Pure Mathematics》 2023年第9期597-609,共13页
Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality... Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented. 展开更多
关键词 Young’s inequality Kittaneh-Manasrah’s inequality Integrable Function Holder’s Cauchy-Schwarz inequality
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TRANSPORTATION COST-INFORMATION INEQUALITY FOR A STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL-COLORED NOISE
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作者 李瑞因 王新宇 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2519-2532,共14页
In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1... In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1),and is correlated for the spatial variable.The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof. 展开更多
关键词 stochastic heat equation transportation cost-information inequality fractionalcolored noise
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Inertial Subgradient Extragradient Algorithm for Solving Variational Inequality Problems with Pseudomonotonicity
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作者 Yuwan Ding Hongwei Liu Xiaojun Ma 《Journal of Harbin Institute of Technology(New Series)》 CAS 2023年第5期65-75,共11页
In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes. More... In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes. Moreover, weak convergence and R-linear convergence analyses of the algorithm are constructed under appropriate assumptions. Finally, the efficiency of the proposed algorithm is demonstrated through numerical implementations. 展开更多
关键词 variational inequality extragradient method PSEUDOMONOTONICITY Lipschitz continuity weak and linear convergence
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Structural Gender Inequality and Mental Health among Chinese Men and Women
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作者 Lei Yang Zhipeng Sun 《International Journal of Mental Health Promotion》 2023年第1期31-43,共13页
Little is known about the association between structural gender inequality and health in patriarchal China.This study employed a sample from the Chinese Women’s Social Status,consisting of 26,139 participants aged 18... Little is known about the association between structural gender inequality and health in patriarchal China.This study employed a sample from the Chinese Women’s Social Status,consisting of 26,139 participants aged 18 and 70 years(13,494 women and 12,645 men).Structural gender inequality was assessed at the macro-,meso-,and micro-levels.Mental health was measured by the summed scores of eight questions on depressive symptoms.Multilevel linear regression was applied for analysis.Results showed that total sex ratio at birth was associated with poorer mental health among women and men but sex ratio at birth of the second-born child predicted better mental health.Gender inequality at meso-level resulted in poorer mental health and gender inequality at micro-level was associated with poorer mental health both for men and women.Eliminating structural gender inequality promotes populations’mental health in China. 展开更多
关键词 Structural gender inequality PATRIARCHY mental health men and women social determinants
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1985—2019年新疆维吾尔族7~18岁中小学生身高生长趋势及不平衡性分析 被引量:1
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作者 王洋 阿力木江·依米提·塔尔肯 《南京医科大学学报(自然科学版)》 北大核心 2024年第1期80-88,共9页
目的:了解新疆7~18岁维吾尔族中小学生身高的发育情况、变化趋势及城乡不平衡性。方法:选取1985、2000、2010年和2019年4次全国学生体质与健康调研中的新疆7~18岁维吾尔族中小学生共18112例,分为城男、乡男、城女、乡女4个群体,计算各... 目的:了解新疆7~18岁维吾尔族中小学生身高的发育情况、变化趋势及城乡不平衡性。方法:选取1985、2000、2010年和2019年4次全国学生体质与健康调研中的新疆7~18岁维吾尔族中小学生共18112例,分为城男、乡男、城女、乡女4个群体,计算各阶段身高的增幅、每10年增速、发育高峰年龄及变异系数,对差异进行单因素方差分析。结果:1985—2019年,新疆维吾尔族7~18岁中小学生身高总体呈增加趋势,城男、乡男、城女、乡女平均身高分别增长了7.59、5.27、6.00、2.88 cm(P均<0.001)。各年龄组增幅不一,男生和城市学生增幅较大。城市学生2010—2019年身高增速最快(城男4.65 cm/10年、城女4.97 cm/10年),乡村学生1985—2000年身高增速最快(乡男4.04 cm/10年、乡女3.22 cm/10年),2000—2010年各组身高均呈负增长。维吾尔族7~18岁中小学生除城女身高突增高峰年龄提前外,城男、乡男和乡女突增高峰年龄较平稳,近年有下降趋势;维吾尔族城市18岁男女平均身高差从1985的11.39 cm增大到2019年的14.20 cm,乡村地区从1985年的11.44 cm增大到2019年的13.26 cm,乡村学生增长潜力较大。身高不平衡使用身高变异系数(coefficient of variation of height,CV-h)来衡量,结果表明,34年间乡村学生CV-h有减小趋势,城市学生CV-h则增大,2010年开始城市学生CV-h大于乡村学生,各年份男生CV-h均大于女生。结论:维吾尔族7~18岁中小学生身高呈持续增长趋势,总体增速减缓,特别是乡村男女,但城市增速增高;维吾尔族学生存在明显的城乡身高不平衡现象,城市内部不平衡性扩大,乡村减小。应更多地关注这些地区差异,并制定政策和战略,以减少身高不平衡性。 展开更多
关键词 身高 维吾尔族 学生 长期趋势 不平衡性
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中国家庭联合收入财富不平等测度研究 被引量:1
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作者 刘穷志 任静 郭汝婷 《经济与管理评论》 CSSCI 北大核心 2024年第4期31-43,共13页
使用年金法构建同时包含收入和财富的一维指标,即联合收入财富,基于该指标全面测度中国经济不平等程度并进行分解。结果发现:与收入不平等相比,联合收入财富基尼系数提高了13.36个百分点,其中房屋是影响家庭经济不平等的最重要财富形式... 使用年金法构建同时包含收入和财富的一维指标,即联合收入财富,基于该指标全面测度中国经济不平等程度并进行分解。结果发现:与收入不平等相比,联合收入财富基尼系数提高了13.36个百分点,其中房屋是影响家庭经济不平等的最重要财富形式;联合收入财富不平等程度在各年龄分组、城乡和地区之间存在较大的异质性;联合收入财富不平等主要由收入和财富年金值的边际分布本身所导致,而两大边际分布之间的关系对总体不平等的影响相对较小。 展开更多
关键词 联合收入财富不平等 年金法 Rothe分解
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房价对城镇居民消费不平等的影响研究 被引量:3
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作者 鞠方 罗嘉昊 +1 位作者 周建军 蒋涵玉 《经济经纬》 CSSCI 北大核心 2024年第2期77-87,共11页
基于中国家庭追踪调查库(CFPS)2010—2018年数据,采用面板计量模型和中介效应模型,研究房价对城镇居民消费不平等的影响效应及作用机制。结果表明:房价会正向影响城镇居民消费不平等,运用工具变量法进行内生性检验以及其他稳健性检验后... 基于中国家庭追踪调查库(CFPS)2010—2018年数据,采用面板计量模型和中介效应模型,研究房价对城镇居民消费不平等的影响效应及作用机制。结果表明:房价会正向影响城镇居民消费不平等,运用工具变量法进行内生性检验以及其他稳健性检验后,以上结论稳健。机制检验结果表明,房价会通过家庭人均消费支出影响城镇居民消费不平等,房价对居住支出和教育文化娱乐支出的影响程度较大,进一步说明房价上升会通过影响消费结构加剧城镇居民消费不平等。异质性检验结果表明,相对于城镇中低收入、中低金融资产家庭而言,房价变动对城镇高收入、高金融资产家庭居民消费的影响更明显。为此,应稳定房价、合理引导住房支出和调整居民消费结构,以促进消费公平,缩小消费不平等。 展开更多
关键词 房价变动 消费不平等 财富效应 消费结构
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