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Ying Xiong

Publications and source records attributed to Ying Xiong.

59 records · Page 4Linked to original sources
arXiv2013

Rigidity Theorem of Graph-directed Fractals

In this paper, we identify two fractals if and only if they are biLipschitz equivalent. Fix ratio $r,$ for dust-like graph-directed sets with ratio $r$ and integer characteristics, we show that they are rigid in the sense that they are uniquely determined by their Hausdorff dimensions. Using this rigidity theorem, we show that in some class of self-similar sets, two totally disconnected self-similar sets without complete overlaps are biLipschitz equivalent.

math.MG↗
arXiv2013

Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem

In this paper, we study the question of classifying self-similar sets under bi-Lipschitz mappings and obtain an important bi-Lipschitz invariant, which is an ideal of a ring related to IFS. Roughly speaking, different Lipschitz equivalence classes of self-similar sets correspond to different ideal classes of a related ring. This result reveals an interesting relationship between the Lipschitz classification problem in fractal geometry and the Gauss class number problem in algebraic number theory.

math.MG↗
arXiv2012

The New Finite Temperature Schrodinger Equation

Implant the thoughtway of thermostatistics in quantum mechanics, set up the new finite temperature Schrödinger equation, define the pure-state free energy, and revise the microscopic entropy introduced by Wu, et al.

physics.gen-ph↗
arXiv2000

Models for Accretion Disk Fluctuations through Self-Organized Criticality Including Relativistic Effects

The possibility that some of the observed X-ray and optical variability in active galactic nuclei and galactic black hole candidates is produced in accretion disks through the development of a self-organized critical state is reconsidered. New simulations, including more complete calculations of relativistic effects, do show that this model can produce light-curves and power-spectra for the variability which agree with the range observed in optical and X-ray studies of AGN and X-ray binaries. However, the universality of complete self-organized criticality is not quite achieved. This is mainly because the character of the variations depend quite substantially on the extent of the unstable disk region. If it extends close to the innermost stable orbit then a physical scale is introduced and the scale-free character of self-organized criticality is vitiated. Significant dependence of the power spectrum density slope on the type of diffusion within the disk and a weaker dependence on the amount of differential rotation are noted. When general relativistic effects are incorporated in the models, additional substantial differences are produced if the disk is viewed from directions far from the accretion disk axis.

astro-ph↗