In this article we consider variable coefficient time dependent wave equations in R×R. Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of C metrics which satisfy a weak asymptotic flatness condition at infinity.

This is a partially survey collection of material on gravity, entropy, and information with some new heuristic results related to the WDW equation.

This is a partially survey collection of material on gravity, entropy, and information with some new heuristic results related to the WDW equation.

A new semiempirical approach is presented for predicting air-to-water oxygen transfer rates in mixed tanks and gravity sewers, using methods adopted from mixing theory. First, a flocculation unit was used to impart selected mean velocity gradients (G) into a completely mixed tank, from which oxygen was first removed, and dissolved oxygen concentrations were measured with time. Regression analys...

Here, dark energy is obtained using dual roles of the Ricci scalar (as a physical field as well as geometry). Dark energy density, obtained in this model, mimics phantom and the derived Friedmann equation contains a term ρde/2λ with ρde being the dark energy density and λ, called as cosmic tension. It is like brane-gravity inspired Friedmann equation, which arises here without using the brane-g...

The Kawahara equation is a higher-order Korteweg-de Vries equation with an additional fifth order derivative term. It was derived by Hasimoto as a model of capillary-gravity waves in an infinitely long canal over a flat bottom in a long wave regime when the Bond number is nearly one third. In this paper, we give a mathematically rigorous justification of this modeling and show that the solution...

We do not know the symmetries underlying string theory. Furthermore, there must exist an inherently quantum, and spacetime independent, formulation of this theory. Independent of string theory, there should exist a description of quantum mechanics which does not refer to a classical spacetime manifold. We propose such a formulation of quantum mechanics, based on noncommutative geometry. This de...