The surface quasi-geostrophic (SQG) model describes the evolution of buoyancy at vertical boundaries in the limit of infinitesimal Rossby number. In this regime, the quasigeostrophic approximations are expected to hold. Numerical simulation of the SQG model often generate small-scale vortices which may have Rossby numbers that approach unity and may be outside the range of SQG. In this thesis w...

The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent vectors as derivations. Manifolds of mappings and diffeomorphisms are treated. Finally the differential structure on the inductive limits of the groups GL(n), S...

We determine the periodic cyclic homology of the Iwahori-Hecke algebras Hq, for q ∈ C∗ not a “proper root of unity.” (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a “weakly spectrum preserving” morphism of finite type algebras induces an isomorphism in periodic cyclic ...

We show that for certain translation invariant spaces 5, a necessary and sufficient condition for the eventual denseness of the corresponding scaled spaces Sh is that S contain a stable and locally supported partition of unity. These results have been motivated by recent work on approximation by multivariate piecewise polynomials on regular meshes.