a new simple model is introduced for a liquid and an equation of state is derived based on this model and the statistical mechanical calculations. this equation of state works well for the non-polar and slightly polar liquids. the important conclusion that may be deduced from this equation of state is that if the reduced variables of state are chosen and defined appropriately, then, the princip...

The equilibrium properties of electrolyte solutions over wide ranges of concentration, temperature, and solvent dielectric constant are discussed on a corresponding-states basis. If low-melting salts are used, these properties can be studied up to the pure fused salt. We mainly focus on systems at low reduced temperature, where the depth of the interaction potential is large compared with the t...

Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter θ approaches infinity. The motivation for these results is to understand the differences in terms of large deviations between the two-parameter models and their one-parameter counterparts. New insight is obtained about the role of the second paramete...

Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter θ approaches infinity. The motivation for these results is to understand the differences in terms of large deviations between the twoparameter models and their one-parameter counterparts. New insight is obtained about the role of the second parameter...

The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, α and θ, corresponding to the stable component and Gamma component respectively. The moderate deviation principles are established for the two-parameter Poisson-Dirichlet distri...