On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications

We prove the Lewy-Stampacchia inequalities for the two obstacles problem in abstract form for T-monotone operators. As a consequence for a general class of quasi-linear elliptic operators of Ladyzhenskaya-Uraltseva type, including p(x)-Laplacian type operators, we derive new results of $C^{1,\alpha}$ regularity for the solution. We also apply those inequalities to obtain new results to the N-membranes problem and the regularity and monotonicity properties to obtain the existence of a solution to a quasi-variational problem in (generalized) Orlicz-Sobolev spaces

Marinari-Parisi and Supersymmetric Collective Field Theory

A field theoretic formulation of the Marinari-Parisi supersymmetric matrix model is established and shown to be equivalent to a recently proposed supersymmetrization of the bosonic collective string field theory. It also corresponds to a continuum description of super-Calogero models. The perturbation theory of the model is developed and, in this approach, an infinite sequence of vertices is generated. A class of potentials is identified for which the spectrum is that of a massless boson and Majorana fermion. For the harmonic oscillator case, the cubic vertices are obtained in an oscillator basis. For a rather general class of potentials it is argued that one cannot generate from Marinari-Parisi models a continuum limit similar to that of the d=1 bosonic string.Comment: 45 page

Modelling distribution functions and fragmentation functions

We present examples for the calculation of the distribution and fragmentation functions using the representation in terms of non-local matrix elements of quark field operators. As specific examples, we use a simple spectator model to estimate the leading twist quark distribution functions and the fragmentation functions for a quark into a nucleon or a pion.Comment: 5 pages RevTeX, talk presented at the First ELFE School on Confinement Physics, 22-28 July 1995, Cambridge, Englan

Bump-on-tail instability of twisted excitations in rotating cold atomic clouds

We develop a kinetic theory for twisted density waves (phonons), carrying a finite amount of orbital angular momentum, in large magneto optical traps, where the collective processes due to the exchange of scattered photons are considered. Explicit expressions for the dispersion relation and for the kinetic (Landau) damping are derived and contributions from the orbital angular momentum are discussed. We show that for rotating clouds, exhibiting ring-shaped structures, phonons carrying orbital angular momentum can cross the instability threshold and grow out of noise, while the usual plane wave solutions are kinetically damped.Comment: 5 pages, 5 figure

Impact of misalignments on the analysis of B decays

This note investigates the effects of a misaligned tracking system on the analysis of B decays. Misalignment effects of both the vertex locator and the inner and outer T-stations have been studied. $z$-scaling effects of the vertex locator are also considered. It is proven that misalignments of the order of the detector single-hit resolutions have little or negligible effects on the quality of the reconstruction and of the analysis of B decays. The studies were performed with a sample of $B^0_{(s)} \to h^+h^{'-}$ decays, but the impact of misalignments on the performance of the pattern recognition algorithms and on the primary vertex resolutions, assessed for the first time, are rather general and not restricted to $B^0_{(s)} \to h^+h^{'-}$ decays