We find normal forms for parabolic Monge-Ampère equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation for such integrals; restricted to the analytic case, this equation is shown to have solutions. The other normal forms exhaust the different classes of parabolic Monge-Ampère equations with symmetry p...

A local likelihood estimator for a nonparametric nuisance function is proposed in the context of semiparametric skew-normal distributions. Constraints imposed on such functions result in a nonparametric estimator with a different target function for maximization from classical local likelihood estimators. The optimal asymptotic semiparametric efficiency bound on parameters of interest is achiev...

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution equation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. ...

We consider solutions of an elliptic partial differential equation in R with a stationary, random conductivity coefficient that is also periodic with period L. Boundary conditions on a square domain of width L are arranged so that the solution has a macroscopic unit gradient. We then consider the average flux that results from this imposed boundary condition. It is known that in the limit L → ∞...

The energy conditions of Einstein gravity (classical general relativity) are designed to extract as much information as possible from classical general relativity without enforcing a particular equation of state for the stress-energy. This systematic avoidance of the need to specify a particular equation of state is particularly useful in a cosmological setting — since the equation of state for...