Strong contraction of the representations of the three dimensional Lie algebras

For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof

America\u27s Problems, Present and Future

Never was this country faced with such grave danger. Yet we seem to be devoting more of our energies to fighting among our­selves than to fighting the enemy. The truly terrible danger that could overwhelm us is being largely overlooked

Present and Future National Objectives

Admiral Beary has asked me to talk to you on the subject of strategy. I certainly am not equipped to discuss strategy as it relates to specific weapons or to the role of the different services or even to the military importance of the atomic bomb. Since World War One, however, I have studied the inter-relationships of war and peace and some of my thoughts in this regard may in­terest you

Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.Comment: 21 pages, 13 figures, research articl

Single vortex fluctuations in a superconducting chip as generating dephasing and spin flips in cold atom traps

We study trapping of a cold atom by a single vortex line in an extreme type II superconducting chip, allowing for pinning and friction. We evaluate the atom's spin flip rate and its dephasing due to the vortex fluctuations in equilibrium and find that they decay rapidly when the distance to the vortex exceeds the magnetic penetration length. We find that there are special spin orientations, depending on the spin location relative to the vortex, at which spin dephasing is considerably reduced while perpendicular directions have a reduced spin flip rate. We also show that the vortex must be perpendicular to the surface for a general shape vortex.Comment: 6 pages, 4 figure