Parametric functions are currently used to represent droplet spectra in clouds and to develop bulk parameterizations of the microphysical processes and of their interactions with radiation. The most frequently used parametric functions are the Lognormal and the Generalized Gamma which have three and four independent parameters, respectively. In a bulk parameterization, two parameters are constr...

Abstract This paper is concerned with general spatially explicit versions of three stochastic models for the dynamics of money that have been introduced and studied numerically by statistical physicists: the uniform reshuffling model, the immediate exchange model and the model with saving propensity. All three models consist of systems of economical agents that consecutively engage in pairwise ...

Abstract For a parameter $\gamma \in (1,2)$, we study the fully nonlinear version of Alt–Phillips equation, $F(D^2u)=u^{\gamma -1}$, for $u\ge 0.$ We establish optimal regularity solution, as well $C^1$ regular part free boundary.