Fermions: Spin, Hidden Variables, Violation of Bell’s Inequality and Quantum Entanglement

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.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

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.

Inequality of rural residents'income in China since the targeted poverty alleviation strategy:New trends,causes,and policy implications

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.

Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

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.

A Study of Triangle Inequality Violations in Social Network Clustering

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.

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

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.

THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

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.

Verification of the Landau Equation and Hardy’s Inequality

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.

NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY

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.

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

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.

Some Refinement of Holder’s and Its Reverse 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.

TRANSPORTATION COST-INFORMATION INEQUALITY FOR A STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL-COLORED NOISE

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.

Inertial Subgradient Extragradient Algorithm for Solving Variational Inequality Problems with Pseudomonotonicity

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.

Structural Gender Inequality and Mental Health among Chinese Men and Women

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.

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

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。

中国家庭联合收入财富不平等测度研究

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。

房价对城镇居民消费不平等的影响研究

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。

再分配视域下河北省人口老龄化与城乡收入不平等的关系分析

再分配作为调节收入分配的重要工具,在实现共同富裕目标中发挥着重要作用。河北省作为人口大省,日益加重的人口老龄化对经济社会发展、城乡收入等产生了重要影响。研究发现:一方面,河北省人口老龄化拉大了城乡收入差距,加剧了城乡收入不平等,尤其是在二线城市和大规模城市中,人口老龄化引致的城乡收入不平等效应更加明显;另一方面,经济增长作为“做大蛋糕”和“分好蛋糕”的原动力,能够有效“对冲”人口老龄化对城乡收入分配不公的负面影响,而人口老龄化倒逼技术进步又在一定程度上加剧了城乡收入不平等。因此,河北省不仅要做大“财富蛋糕”,更要使全体社会成员共享“经济蛋糕”,以此加速推进共同富裕进程。

新型基础设施影响劳动工资和工资差距的内在机制

本文从新型基础设施的产品偏向性出发,在一般均衡框架下探讨了新型基础设施影响劳动工资和工资差距的内在机制。研究发现,新型基础设施直接带来的效率提升可以促进各类劳动工资增长,但间接导致的要素重新配置可能产生不同的结果,总效应取决于资本与各类劳动之间的替代性以及技能型中间品与非技能型中间品之间的替代性。结合中国的实际情况,技能型产品偏向型的新型基础设施可能导致工资差距扩大,但可以带来劳动工资的“普惠性”增长。

多周期农产品废弃物供应链网络均衡模型构建

目的研究农产品废弃物可持续利用问题,既实现供应链整体利润最优,又减轻对环境的污染。方法在随机需求的背景下,考虑生产合作社对零售商的不同激励度,分析生产合作社、零售商、需求市场的最优状态,利用变分不等式建立相应的多周期供应链网络均衡模型。结果从多周期角度,实现了农产品废弃物供应链网络均衡利益最优化,可为合作社与零售商在较长时间达到一种均衡状态提供有效解决方案。结论既实现了多周期农产品废弃物的持续利用,又促进了循环经济的发展,同时还实现了供应链网络均衡、供应链整体利润最优和减轻环境污染等目标。