Toric vector bundles: GAGA and Hodge theory

We prove a GAGA-style result for toric vector bundles with smooth base and give an algebraic construction of the Frölicher approximating vector bundle that has recently been introduced by Dan Popovici using analytic techniques. Both results make use of the Rees-bundle construction.

On Random Reynolds Roughness

Lubricant fluxes and lubrication forces have been calculated for statistical realizations of a piecewise planar slider running over a smooth base with an incompressible lubricant. The statistics of the response are not simply related to those of the roughness. The standard deviation of the force increases approximately as the fourth power of the roughness deviation for probable contact situations.