Deformed statistics Kullback-Leibler divergence minimization within a scaled Bregman framework

The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations defined by normal averages, within a measure-theoretic framework. Specifically, it is demonstrated that the dual generalized K-Ld is a scaled Bregman divergence. The Pythagorean theorem is derived from the minimum discrimination information principle using the dual generalized K-Ld as the measure of uncertainty, with constraints defined by normal averages. The minimization of the dual generalized K-Ld, with normal averages constraints, is shown to exhibit distinctly unique features.     

T-duality in Affine NA Toda Models

The construction of non-Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non-conformal two-dimensional integrable models naturally leads to the construction of a pair of actions, which share the same spectra and are related by canonical transformations.     

相移吸收二元性算法用于X射线混合衬度定量显微CT的可行性研究

本文采用相移吸收二元性(PAD)相位恢复算法来实现混合 衬度样品内部不同密度组分的定量成像, 采用数字模拟和实验研究验证该方法的可行性. 模拟结果表明, 对于三种不同材料其重构误差均小于1%, 且误差值随材料折射率的增大而减小. 利用上海光源X射线成像线站开展了实验研究, 结果表明用单距PAD相位恢复算法可获取样品的定量信息. 与模拟结果相比, 实验中的重构精度相对较低, 环状伪影可能是影响精度的主要原因. 模拟和实验研究过程中, 均只采用了一组单距投影数据. 可以认为, 相移吸收二元性算法可用于混合衬度样品的定量信息分析研究. 由于剂量相对较低, 应可适合于软组织和骨骼同时存在时生物医学样品的定量相衬CT研究.     

Generalized statistics variational perturbation approximation using q-deformed calculus

A principled framework to generalize variational perturbation approximations (VPAs) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting the perturbation expansion of the generalized free energy (GFE) with a variational procedure formulated using q-deformed calculus. A candidate q-deformed generalized VPA (GVPA) is derived with the aid of the Hellmann-Feynman theorem. The generalized Bogoliubov inequality for the approximate GFE are derived for the case of canonical probability densities that maximize the Tsallis entropy. Numerical examples demonstrating the application of the q-deformed GVPA are presented. The qualitative distinctions between the q-deformed GVPA model vis-á-vis prior GVPA models are highlighted.     

A New Quantum Analog of the Brauer Algebra

We introduce a new algebra depending on two nonzero complex parameters z and q such that its specialization at z=q ⁿ and q=1 coincides the Brauer algebra. We show that the action of the new algebra commutes with the representation of the twisted deformation of the enveloping algebra U(o _n) in the tensor power of the vector representation.     

Nucleon Spin Structure Functions in the Resonance Region and the Duality

We discuss the nucleon spin structure function gl and the difference between the proton and neutrontargets gp1 - gn1 , based on quark model calculation. Quark-hadron duality for the nucleon spin structure function is alsoanalyzed. Effects of the △(1232) and Roper P11(1440) resonances on the spin structure function and on the differencegn1 - gn1 are mentioned. The results of different models for the Roper resonance are also addressed.     

磁光材料Verdet常数贡献性的讨论

Verdet常数是表征材料磁光性能的重要参数,具有波长和温度依赖性.为了更好地分析入射光波长、温度等对Verdet常数的影响机理,从基础理论切入,分析了现有理论的优缺点.结合光的波粒二象性特性,提出了波动跃迁性贡献理论,即法拉第效应是光的波动性作用以及电偶极跃迁作用带来的贡献之和,波动性对偏转角的贡献为正,跃迁性贡献为负.在抗磁性材料中,波动性贡献大于跃迁性贡献,Verdet常数为正;顺磁性材料中,跃迁性贡献远大于波动性贡献,Verdet常数为负.进而分别以典型抗磁性材料重火石玻璃ZF1和顺磁性材料铽镓石榴石为例,并结合相关数据、参数、模型,对理论进行了验证.试验结果表明,在精确描述材料Verdet常数方面,波动跃迁性贡献理论具有一定的优越性.     

The duality between Morrey spaces and its pre-dual spaces characterized by heat kernel

Let L be an elliptic operator, we give arguments about the duality estimate between Morrey spaces and its pre-dual spaces characterized by the heat kernel associated to L that is given in [6],[8].     

在类比系统中研究引力和黑洞的性质

引力和量子力学的融合是理解时空起源和引力本质的重要问题,也是一个长期悬而未决的基础物理学根本问题。理论物理学家们对此提出了诸多理论猜想,也做出了许多预言。然而一些相关的预言涉及的效应极其微弱,因此难以通过实验观测加以证实。通过类比引力系统,人们可以将这些引力效应转化为实验室可测可控系统的一些效应。对这些类比系统的研究一方面可以帮助人们更深入地理解引力的性质本身,另一方面也可以为其他相关领域的研究提供启发和新的思路。文章将以几个具体的类比系统为例简要介绍类比引力研究的历史和最近的一些研究进展。