The double duals and gauges of the Lanczos tensor

It is shown that: i) the Weyl tensor can be expressed in terms of the sum of a tensor and its double dual, where the tensor is constructed from the covariant derivatives of the Lanczos tensor, ii) a similar expression does not exist for the Riemann tensor in electromagnetic theory, iii) the electromagnetic field cannot be identified with the differential gauge freedom of the Lanczos tensor, iv) the symmetries of Einstein Maxwell theory and the Lanczos tensor do not prohibit the identification of the electromagnetic field with the algebraic gauge freedom of the Lanczos tensor, these symmetries require a differential equation relating the electromagnetic field tensor to the algebraic gauge vector and this is given.     

NMR Studies of Drugs. Applications of Achiral and Chiral Lanthanide Shift Reagents to a 5-Substituted-4-thiazolidinone

The 60 MHz ¹H NMR spectra of racemic 5-[[3,5-bis(1,1-dimethylethyl)-4-hydroxyphenyl]methyl]-4-thiazolidinone, 1, have been studied in CDCl₃ solution at 28° with the achiral lanthanide shift reagent (LSR), tris (6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedionato)europium (III), 2, and the chiral LSRs, tris[3-(heptafluoropropylhydroxymethylene)- (+)-camphoratojeuropium(III), 3, and tris[3-(trifluoromethylhydroxymethylene-(+) -camphorato]europium (III), 4, Significant enantiomeric shift differences were observed in the presence of added 3, for the aryl protons of 1 that should permit direct determination of enantiomeric excess. Relative magnitudes of lanthanide-induced shift for the different nuclei of 1 with the three LSRs are compared and discussed in terms of preferred LSR binding sites. A favored conformation of 1 with respect to rotation about the C(5)-CH₂ bond is suggested.     

Protoneutron star cooling with convection: the effect of the symmetry energy

We model neutrino emission from a newly born neutron star subsequent to a supernova explosion to study its sensitivity to the equation of state, neutrino opacities, and convective instabilities at high baryon density. We find the time period and spatial extent over which convection operates is sensitive to the behavior of the nuclear symmetry energy at and above nuclear density. When convection ends within the protoneutron star, there is a break in the predicted neutrino emission that may be clearly observable.     

Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light. This revised version was published online in November 2006 with corrections to the Cover Date.