Asymptotic Completeness for Compton Scattering

Scattering in a model of a massive quantum-mechanical particle, an ``electron'', interacting with massless, relativistic bosons, ``photons'', is studied. The interaction term in the Hamiltonian of our model describes emission and absorption of ``photons'' by the ``electron''; but ``electron-positron'' pair production is suppressed. An ultraviolet cutoff and an (arbitrarily small, but fixed) infrared cutoff are imposed on the interaction term. In a range of energies where the propagation speed of the dressed ``electron'' is strictly smaller than the speed of light, unitarity of the scattering matrix is proven, provided the coupling constant is small enough; (asymptotic completeness of Compton scattering). The proof combines a construction of dressed one--electron states with propagation estimates for the ``electron'' and the ``photons''.Comment: gap of previous version closed, large parts rewritten, more general results and more comprehensive exposition. 64 pages, 3 figure

Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure

Appropriateness of gastrointestinal endoscopy: risk of complications.

The balance between risks and benefits of gastrointestinal endoscopy for a given patient is essential in defining the appropriate use of endoscopic procedures. The current literature suggests that gastrointestinal endoscopy infrequently results in major procedure-related morbidity and mortality, while cardio-respiratory events occur commonly. However, true complication rates may be underestimated due to inconsistencies in the types of complications reported. No formal reporting requirements exist, and most of the published studies on complications come from centres with highly-skilled endoscopists

Airports: their planning, location, and control

Thesis (M.C.P.) Massachusetts Institute of Technology. Dept. of City Planning, 1947.Bibliography: leaves 108-112.by William R. B. Froehlich.M.C.P