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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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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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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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Several Hermite-Hadamard Type Inequalities for Harmonically Convex Functions in the Second Sense with Applications 被引量:1
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作者 Wang Wen Yang Shi-guo Liu Xue-ying 《Communications in Mathematical Research》 CSCD 2016年第2期105-110,共6页
In this paper, we first introduce the concept "harmonically convex functions" in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Final... In this paper, we first introduce the concept "harmonically convex functions" in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown. 展开更多
关键词 hermite-hadamard's inequality harmonically convex function mean inequality
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New Majorized Results on Hilbert's Integral Inequality
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作者 谢鸿政 吕中学 辛玉梅 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第4期69-75,共7页
In this paper, some new majorized results on Hilbert’s integral inequality are showed.
关键词 Hilbert’s integral inequality
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SOME INEQUALITIES OF HERMITE-HADAMARD TYPE FOR s-CONVEX FUNCTIONS 被引量:9
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作者 Mohammad W. Alomari Maslina Darus Ugur S. Kirmaci 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1643-1652,共10页
In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.
关键词 convex function s-convex function Hadamard’s inequality
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Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex 被引量:4
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作者 Ling Chun Feng Qi 《Applied Mathematics》 2012年第11期1680-1685,共6页
In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
关键词 INTEGRAL inequality hermite-hadamards INTEGRAL inequality s-Convex Function Derivative Mean
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Hermite-Hadamard Type Fractional Integral Inequalities for Preinvex Functions 被引量:1
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作者 lian tie-yan tang wei +1 位作者 zhou rui ji you-qing 《Communications in Mathematical Research》 CSCD 2018年第4期351-362,共12页
In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function... In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function. 展开更多
关键词 hermite-hadamard's integral inequality Riemann-Liouville fractional integral Holder's integral inequality
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On an Extension and a Refinement of Van der Corput's Inequality 被引量:10
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作者 YANG Bi-cheng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期94-98,共5页
By introducing a parameter α, we give an extension of Van der Corput's inequality. Also a new strengthened version of it is considered.
关键词 Van der Corput's inequality weight coefficient Euler-Maclaurin's formula
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THE HADAMARD INEQUALITY FOR CONVEX FUNCTION VIA FRACTIONAL INTEGRALS 被引量:4
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作者 M.E.ZDEMR S.S.DRAGOMIR C.YILDIZ 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1293-1299,共7页
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
关键词 Hadamard's inequality convex functions power-mean inequality Riemann-Liouville fractional integration
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A Hilbert-Type Inequality with Some Parameters and the Integral in Whole Plane 被引量:11
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作者 Zitian Xie Zheng Zeng 《Advances in Pure Mathematics》 2011年第3期84-89,共6页
In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as ... In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis. 展开更多
关键词 Hilbert-Type INTEGRAL inequality WEIGHT Function Holder’s inequality
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GENERALIZED ROSENTHAL'S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES 被引量:5
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作者 于林 《Acta Mathematica Scientia》 SCIE CSCD 2009年第2期305-312,共8页
A generalized Rosenthal's inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexi... A generalized Rosenthal's inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given. 展开更多
关键词 Rosenthal's inequality Ф-inequality MARTINGALEs p-uniform smoothness q-uniform convexity
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Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>P</i>-Convex 被引量:1
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作者 Boyan Xi Shuhong Wang Feng Qi 《Applied Mathematics》 2012年第12期1898-1902,共5页
In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are P-convex.
关键词 INTEGRAL inequality hermite-hadamards INTEGRAL inequality P-Convex Function Derivative
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Bohr's Inequality on the Unit Ball B^n 被引量:2
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作者 王建飞 刘太顺 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第2期159-165,共7页
Bohr's type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball B^n to B^n, f(0)=p, then we have sum from k=0 to∞|Dφ_P(P)[D^kf(0)(z^k)]|/k!||Dφ_P(P)||<1 for|z|<max{1/2+|... Bohr's type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball B^n to B^n, f(0)=p, then we have sum from k=0 to∞|Dφ_P(P)[D^kf(0)(z^k)]|/k!||Dφ_P(P)||<1 for|z|<max{1/2+|P|,(1-|p|)/2^(1/2)andφ_P∈Aut(B^n) such thatφ_(p)=0. As corollaries of the above estimate, we obtain some sharp Bohr's type modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical result of Bohr. 展开更多
关键词 Bohr's inequality holomorphic mapping homogeneous expansions
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Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality 被引量:1
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作者 Zuoshunhua Shi Wu Di Dunyan Yan 《Analysis in Theory and Applications》 2014年第2期193-204,共12页
Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be poin... Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be pointed out that we con- sider whole ranges of p and q, i.e., 0 〈 p ≤∞ and 0 〈 q ≤∞. 展开更多
关键词 Holder's inequality Young's inequality Hardy-Littlewood-sobolev inequality Lorentz space.
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On Reverses of the Blaschke-Santalo Inequality for Convex Bodies 被引量:2
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作者 WANG Wei-dong ZHOU Yan-ping 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第4期605-611,共7页
Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of t... Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty's conjecture for projection bodies, respectively. 展开更多
关键词 convex body Blaschke-santal5 inequality REVERsE Petty's conjecture
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On an Extension of Hibert's Inequality and Applications 被引量:1
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作者 YANG Bi-cheng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期96-102,共7页
This paper gives a new generalization of Hilbert's inequality with a best constant factor involving the β function. An applications, we consider the equivalent form and some particular results.
关键词 Hilbert's inequality weight coefficient β function Holder's inequality
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Refinements to Hadamard’s Inequality for Log-Convex Functions 被引量:1
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作者 Waadallah T. Sulaiman 《Applied Mathematics》 2011年第7期899-903,共5页
In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.
关键词 Log-Convex FUNCTIONs Hadamard’s inequality INTEGRAL inequality
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DOOB'S INEQUALITY, BURKHOLDER-GUNDY INEQUALITY AND MARTINGALE TRANSFORMS ON MARTINGALE MORREY SPACES 被引量:1
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作者 Kwok-Pun HO 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期93-109,共17页
We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey sp... We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces. 展开更多
关键词 Morrey spaces Banach function space block spaces Doob's inequality Burkholder-Gundy inequality martingale transform Davis decomposition MARTINGALE
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Inequalities relating to L_p-version of Petty's conjectured projection inequality 被引量:1
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作者 王卫东 冷岗松 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第2期269-276,共8页
Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequalit... Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality are given, respectively. 展开更多
关键词 Lp-version Petty projection inequality Petty's conjectured projectioninequality Lp-projection body REVERsE
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