Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6-Li

We measure a zero crossing in the scattering length of a mixture of the two lowest hyperfine states of 6-Li. To locate the zero crossing, we monitor the decrease in temperature and atom number arising from evaporation in a CO2 laser trap as a function of magnetic field B. The temperature decrease and atom loss are minimized for B=528(4) G, consistent with no evaporation. We also present preliminary calculations using potentials that have been constrained by the measured zero crossing and locate a broad Feshbach resonance at approximately 860 G, in agreement with previous theoretical predictions. In addition, our theoretical model predicts a second and much narrower Feshbach resonance near 550 G.Comment: Five pages, four figure

The fundamental pro-groupoid of an affine 2-scheme

A natural question in the theory of Tannakian categories is: What if you don't remember \Forget? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable absolute Galois group of $R$ when it is a field. This gives a new definition for \'etale \pi_1(\spec(R)) in terms of the category of $R$-modules rather than the category of \'etale covers. More generally, we introduce a new notion of "commutative 2-ring" that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of $\pi_1$ for the corresponding "affine 2-schemes." These results help to simplify and clarify some of the peculiarities of the \'etale fundamental group. For example, \'etale fundamental groups are not "true" groups but only profinite groups, and one cannot hope to recover more: the "Tannakian" functor represented by the \'etale fundamental group of a scheme preserves finite products but not all products.Comment: 46 pages + bibliography. Diagrams drawn in Tik

High-Level Expression of Various Apolipoprotein (a) Isoforms by "Transferrinfection". The Role of Kringle IV Sequences in the Extracellular Association with Low-Density Lipoprotein

Characterization of the assembly of lipoprotein(a) [Lp(a)] is of fundamental importance to understanding the biosynthesis and metabolism of this atherogenic lipoprotein. Since no established cell lines exist that express Lp(a) or apolipoprotein(a) [apo(a)], a "transferrinfection" system for apo(a) was developed utilizing adenovirus receptor- and transferrin receptor-mediated DNA uptake into cells. Using this method, different apo(a) cDNA constructions of variable length, due to the presence of 3, 5, 7, 9, 15, or 18 internal kringle IV sequences, were expressed in cos-7 cells or CHO cells. All constructions contained kringle IV-36, which includes the only unpaired cysteine residue (Cys-4057) in apo(a). r-Apo(a) was synthesized as a precursor and secreted as mature apolipoprotein into the medium. When medium containing r-apo(a) with 9, 15, or 18 kringle IV repeats was mixed with normal human plasma LDL, stable complexes formed that had a bouyant density typical of Lp(a). Association was substantially decreased if Cys-4057 on r-apo(a) was replaced by Arg by site-directed mutagenesis or if Cys-4057 was chemically modified. Lack of association was also observed with r-apo(a) containing only 3, 5, or 7 kringle IV repeats without "unique kringle IV sequences", although Cys-4057 was present in all of these constructions. Synthesis and secretion of r-apo(a) was not dependent on its sialic acid content. r-Apo(a) was expressed even more efficiently in sialylation-defective CHO cells than in wild-type CHO cells. In transfected CHO cells defective in the addition of N-acetylglucosamine, apo(a) secretion was found to be decreased by 50%. Extracellular association with LDL was not affected by the carbohydrate moiety of r-apo(a), indicating a protein-protein interaction between r-apo(a) and apoB. These results show that, besides kringle IV-36, other kringle IV sequences are necessary for the extracellular association of r-apo(a) with LDL. Changes in the carbohydrate moiety of apo(a), however, do not affect complex formation

Domain perturbation for parabolic equations

Doctor of PhilosophyWe study the effect of domain perturbation on the behaviour of parabolic equations. The first aspect considered in this thesis is the behaviour of solutions under changes of the domain. We show how solutions of linear and semilinear parabolic equations behave as a sequence of domains $\Omega_n$ converges to an open set $\Omega$ in a certain sense. In particular, we are interested in singular domain perturbations so that a change of variables is not possible on these domains. For autonomous linear equations, it is known that convergence of solutions under domain perturbation is closely related to the corresponding elliptic equations via a standard semigroup theory. We show that there is also a relation between domain perturbation for non-autonomous linear parabolic equations and domain perturbation for elliptic equations. The key result for this is the equivalence of Mosco convergences between various closed and convex subsets of Banach spaces. An important consequence is that the same conditions for a sequence of domains imply convergence of solutions under domain perturbation for both parabolic and elliptic equations. By applying variational methods, we obtain the convergence of solutions of initial value problems under Dirichlet or Neumann boundary conditions. A similar technique can be applied to obtain the convergence of weak solutions of parabolic variational inequalities when the underlying convex set is perturbed. Using the linear theory, we then study domain perturbation for initial boundary value problems of semilinear type. We are also interested in the behaviour of bounded entire solutions of parabolic equations defined on the whole real line. We establish a convergence result for bounded entire solutions of linear parabolic equations under $L^2$ and $L^p$-norms. For the $L^p$-theory, we also prove H\"{o}lder regularity of bounded entire solutions with respect to time. In addition, the persistence of some classes of bounded entire solutions is given for semilinear equations using the Leray-Schauder degree theory. The second aspect is to study the dynamics of parabolic equations under domain perturbation. In this part, we consider parabolic equation as a dynamical system in an $L^2$ space and study the stability of invariant manifolds near a stationary solution. In particular, we prove the continuity (upper and lower semicontinuity) of both, the local stable invariant manifolds and the local unstable invariant manifolds under domain perturbation

Implementation of Early Intervention Protocol in Australia for 'High Risk' Injured Workers is Associated with Fewer Lost Work Days Over 2 Years Than Usual (Stepped) Care

The original version of this article unfortunately contained a spelling error in one of the co-authors's names. The family name of the co-author was incorrectly displayed as "James McCauley" instead of "James McAuley. The original article has been corrected

Bandgaps in the propagation and scattering of surface water waves over cylindrical steps

Here we investigate the propagation and scattering of surface water waves by arrays of bottom-mounted cylindrical steps. Both periodic and random arrangements of the steps are considered. The wave transmission through the arrays is computed using the multiple scattering method based upon a recently derived formulation. For the periodic case, the results are compared to the band structure calculation. We demonstrate that complete band gaps can be obtained in such a system. Furthermore, we show that the randomization of the location of the steps can significantly reduce the transmission of water waves. Comparison with other systems is also discussed.Comment: 4 pages, 3 figure