We describe precise equivalences between theoretical descriptions of: (i) size-rank and first-digit laws for numerical data sets, (ii) intermittency at the transition to chaos in nonlinear maps, and (iii) cluster fluc...We describe precise equivalences between theoretical descriptions of: (i) size-rank and first-digit laws for numerical data sets, (ii) intermittency at the transition to chaos in nonlinear maps, and (iii) cluster fluctuations at criticality. The equivalences stem from a common statistical-mechanical structure that departs from the usual via a one-parameter deformation of the exponential and logarithmic functions. The generalized structure arises when configurational phase space is incompletely visited such that the accessible fraction has fractal properties. Thermodynamically, the common focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials. The theory is in quantitative agreement with real size-rank data and it naturally includes the bends or tails observed for small and large rank.展开更多
We propose a new statistical theory for classical and quantum small systems.It is a generalized scheme of the Boltzmann–Gibbs statistical theory by extending the Boltzmann–Gibbs statistical factor from infinite syst...We propose a new statistical theory for classical and quantum small systems.It is a generalized scheme of the Boltzmann–Gibbs statistical theory by extending the Boltzmann–Gibbs statistical factor from infinite systems to finite systems based on the microcanonical ensemble distribution function and keeping this factor in all thermodynamic processes.We reconstruct the statistical theory for finite systems by obtaining the expression of the average particle number and the thermodynamic quantities such as entropy and specific heat,in the finite systems.We also explore the discontinuous phase transitions in the interacting classical nanoscale gases without the thermodynamic limit.展开更多
We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statist...We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.展开更多
This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distribut...This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.展开更多
基金supported by DGAPA-UNAM and CONACyT (Mexican agencies)Ministerio de Educación de Espa a
文摘We describe precise equivalences between theoretical descriptions of: (i) size-rank and first-digit laws for numerical data sets, (ii) intermittency at the transition to chaos in nonlinear maps, and (iii) cluster fluctuations at criticality. The equivalences stem from a common statistical-mechanical structure that departs from the usual via a one-parameter deformation of the exponential and logarithmic functions. The generalized structure arises when configurational phase space is incompletely visited such that the accessible fraction has fractal properties. Thermodynamically, the common focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials. The theory is in quantitative agreement with real size-rank data and it naturally includes the bends or tails observed for small and large rank.
基金supported by the National Natural Science Foundation of China (11375045)the National Basic Research Programs of China (2012CB921604)
文摘We propose a new statistical theory for classical and quantum small systems.It is a generalized scheme of the Boltzmann–Gibbs statistical theory by extending the Boltzmann–Gibbs statistical factor from infinite systems to finite systems based on the microcanonical ensemble distribution function and keeping this factor in all thermodynamic processes.We reconstruct the statistical theory for finite systems by obtaining the expression of the average particle number and the thermodynamic quantities such as entropy and specific heat,in the finite systems.We also explore the discontinuous phase transitions in the interacting classical nanoscale gases without the thermodynamic limit.
基金the National Natural Science Foundation of China
文摘We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.
文摘This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.
