In this paper, we study the Cauchy problem of 2d Dirac equation with Hartree type nonlinearity c ( | ? ? ? ? ? ? , ? ? ) ? R ? { 0 } < 2 . Our aim is to show small data global well-posedness and scattering in H s for > 1 The difficulty stems from singularity low-frequency part ? ? ? potential. To overcome it adapt U p V space argument bilinear estimates [27] [25] arising null structure. We also...

Expressions for analyzing small-angle scattering data from semidilute solutions of polymers in a good solvent over a broad range of scattering vectors are examined. Three different scattering function expressions are derived from Monte Carlo simulations. The expressions are similar to those of polymer reference interaction site models, with a scattering-vector-dependent direct correlation funct...

A review of some of the author’s results in the area of inverse scattering is given. The following topics are discussed: 1) Property C and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3) Inverse scattering with ”incomplete“ data, 4) Inverse scattering for inhomogeneous Schrödinger equation, 5) Krein’s inverse scattering method, 6) Invertibility of...