Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space

We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a uniform bound on the sup norm of solutions which can be given in terms of certain inverse powers of the radial and advanced/retarded time coordinate variables. As a model application, we show these estimates give a very simple proof small amplitude scattering for nonlinear scalar fields with higher than cubic interactions.Comment: 24 page

Targets for producing high purity I-123

Tellurium powder in improved targets is bombarded with a cyclotron beam to produce Xe-123. Flowing gas streams carry the Xe-123 through one cold trap which removes Xe-123 that subsequently decays to I-123. During this bombardment energy is deposited in the target material causing its temperature to rise. Some of the tellurium vaporizes and subsequently condenses on surfaces that are cooler than the vaporization temperature. Provision is made for the repeated bombardment of this condensed tellurium

The Blue Bond Proposal

Soaring debt levels and the crisis in Greece has sharpened the focus on fiscal sustainability among eurozone members. The European Union has to tackle high debt levels in vulnerable states which are compounded by a hike in risk premiums on government bonds leading to a debt trap, while designing ways to efficiently finance debt. Furthermore, European solidarity with weaker states should not undermine incentives for individual members to pursue fiscally sustainable policies. This Policy Brief proposes a Blue Bond to resolve these challenges. The authors, Bruegel Non-resident Fellow Jakob von Weizsäcker and Jacques Delpla from Conseil d'Analyse �conomique, Paris, explain the economics behind their proposal, its institutional underpinnings and the implication of it on various participating countries.

Revisiting Frank–Starling: regulatory light chain phosphorylation alters the rate of force redevelopment (ktr) in a length-dependent fashion

Force and power in cardiac muscle have a known dependence on phosphorylation of the myosin-associated regulatory light chain (RLC). We explore the effect of RLC phosphorylation on the ability of cardiac preparations to redevelop force (ktr ) in maximally activating [Ca2+ ]. Activation was achieved by rapidly increasing the temperature (temperature-jump of 0.5-20ºC) of permeabilized trabeculae over a physiological range of sarcomere lengths (1.85-1.94 μm). The trabeculae were subjected to shortening ramps over a range of velocities and the extent of RLC phosphorylation was varied. The latter was achieved using an RLC-exchange technique, which avoids changes in the phosphorylation level of other proteins. The results show that increasing RLC phosphorylation by 50% accelerates ktr by ∼50%, irrespective of the sarcomere length, whereas decreasing phosphorylation by 30% slows ktr by ∼50%, relative to the ktr obtained for in vivo phosphorylation. Clearly, phosphorylation affects the magnitude of ktr following step shortening or ramp shortening. Using a two-state model, we explore the effect of RLC phosphorylation on the kinetics of force development, which proposes that phosphorylation affects the kinetics of both attachment and detachment of cross-bridges. In summary, RLC phosphorylation affects the rate and extent of force redevelopment. These findings were obtained in maximally activated muscle at saturating [Ca2+ ] and are not explained by changes in the Ca2+ -sensitivity of acto-myosin interactions. The length-dependence of the rate of force redevelopment, together with the modulation by the state of RLC phosphorylation, suggests that these effects play a role in the Frank-Starling law of the heart.Published versio

The wave equation on the Schwarzschild metric II: Local decay for the spin 2 Regge Wheeler equation

Odd-type spin 2 perturbations of Einstein's equation can be reduced to the scalar Regge-Wheeler equation. We show that the weighted norms of solutions are in L^2 of time and space. This result uses commutator methods and applies uniformly to all relevant spherical harmonics.Comment: AMS-LaTeX, 8 pages with 1 figure. There is an errata to this paper at gr-qc/060807