On pseudomonotone elliptic operators with functional dependence on unbounded domains

We generalize F. E. Browder's results concerning pseudomonotone elliptic partial differential operators defined on unbounded domains. We show that under suitable assumptions, Browder's result holds true if the coefficient functions are functionals of the solution

Two-dimensional rectangle packing: on-line methods and results

The first algorithms for the on-line two-dimensional rectangle packing problem were introduced by Coppersmith and Raghavan. They showed that for a family of heuristics 13/4 is an upper bound for the asymptotic worst-case ratios. We have investigated the Next Fit and the First Fit variants of their method. We proved that the asymptotic worst-case ratio equals 13/4 for the Next Fit variant and that 49/16 is an upper bound of the asymptotic worst-case ratio for the First Fit variant.

An entropy production based method for determining the position diffusion's coefficient of a quantum Brownian motion

Quantum Brownian motion of a harmonic oscillator in the Markovian approximation is described by the respective Caldeira-Leggett master equation. This master equation can be brought into Lindblad form by adding a position diffusion term to it. The coefficient of this term is either customarily taken to be the lower bound dictated by the Dekker inequality or determined by more detailed derivations on the linearly damped quantum harmonic oscillator. In this paper, we explore the theoretical possibilities of determining the position diffusion term's coefficient by analyzing the entropy production of the master equation.Comment: 13 pages, 10 figure