A computationally efficient method is proposed to replace the piecewise linear number distribution in a hybrid bin scheme with a piecewise cubic polynomial. When the linear distribution is replaced by a cubic, the errors generated in solutions to the condensation/evaporation equation are reduced by a factor of two to three. Alternatively, using the cubic distribution function allows reducing th...

SUMMARY: Structural equation models are well-developed statistical tools for multivariate data with latent variables. Recently, much attention has been given to developing structural equation models that account for nonlinear relationships between the endogenous latent variables, the covariates, and the exogenous latent variables. [Guo et al. (2012)], developed a semiparametric structural equat...

This work deals with the focusing Nonlinear Schrödinger Equation in one dimension with pure-power nonlinearity near cubic. We consider the spectrum of the linearized operator about the soliton solution. When the nonlinearity is exactly cubic, the linearized operator has resonances at the edges of the essential spectrum. We establish the degenerate bifurcation of these resonances to eigenvalues ...

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 pri...