It is proved that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms. It is not required that manifolds are connected nor second countable nor paracompact. This solves a problem stated by A. Weinstein. Some related results are discussed as well.

This paper is devoted to a proof of regularity, near the initial state, for solutions to the Cauchy-Dirichlet and obstacle problem for a class of second order differential operators of Kolmogorov type. The approach used here is general enough to allow us to consider smooth obstacles as well as non-smooth obstacles. 2000 Mathematics Subject classification: 35R35, 35K70, 35R03, 35Q91

Many visualization systems use smoothly animated transitions to help the user interact with information structures. These transitions are intended to preserve perceptual constancy during viewpoint transformations, and to aid in the overall understanding of the dataset. However, animated transitions also have costs –they increase the transition time, and they can be complicated to implement – an...

A short proof of the fact that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms is given. It is not required that manifolds are second countable or paracompact. This solves a problem stated by A. Wienstein. Some related results are discussed as well.

This paper presents a new method to solve the interior and the exterior Neumann problems in simply connected regions with smooth boundaries. The method is based on two uniquely solvable Fredholm integral equations of the second kind with the generalized Neumann kernel. Numerical examples reveal that the present method offers an effective numerical method for the Neumann problems when the bounda...