Abstract. The absolutely continuous spectrum of one-dimensional Schrödinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the… (More)

We look at invariance of a.e. boundary condition spectral behavior under perturbations, W , of half-line, continuum or discrete Schrödinger operators. We extend the results of del Rio, Simon, Stolz… (More)

We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the… (More)

Disparities between the measured concentrations of ice-nucleating particles (INP) and in-cloud ice crystal number concentrations (ICNC) have led to the hypothesis that mechanisms other than primary… (More)

The paper is devoted to the study of slightly supercritical active scalars with nonlocal diffusion. We prove global regularity for the surface quasi-geostroph ic (SQG) and Burgers equations, when the… (More)

and some self-adjoint boundary condition at zero. The operator (1.1) describes a charged particle, such as an electron, in the electric field V (x). When V (x) is decaying quickly, one expects the… (More)

We consider surface quasi-geostrophic equation with dispersive forcing and critical dissipation. We prove global existence of smooth solutions given sufficiently smooth initial data. This is done… (More)

We use a nonlocal maximum principle to prove the global exis t nce of smooth solutions for a slightly supercritical surface quasi-geostrophic equati on. By this we mean that the velocity field u is… (More)

1. Pre-Introduction 2 2. Introduction and background 2 3. Three (sample) principal results 5 4. A criterion for ac spectrum 6 5. Expansions for generalized eigenfunctions 9 6. WKB approximation 10 7.… (More)