Fermi-edge singularities in the mesoscopic x-ray edge problem

We study the x-ray edge problem for a chaotic quantum dot or nanoparticle displaying mesoscopic fluctuations. In the bulk, x-ray physics is known to produce Fermi-edge singularities-deviations from the naively expected photoabsorption cross section in the form of a peaked or rounded edge. For a coherent system with chaotic dynamics, we find substantial changes; in particular, a photoabsorption cross section showing a rounded edge in the bulk will change to a slightly peaked edge on average as the system size is reduced to a mesoscopic (coherent) scale.     

Toward oxygen binding curves of single respiratory proteins

Oxygen binding curves of single molecules promise to discriminate between different models describing cooperativity because load distributions are accessible. Individual tarantula hemocyanins could be detected by fluorescence correlation spectroscopy using intrinsic tryptophan fluorescence as sensor of bound oxygen. However, imaging of immobilized proteins was not possible due to fast photo-bleaching. It is shown that tetra-methyl-carboxy-rhodamine (TAMRA), commonly used as a fluorescence label in single-molecule spectroscopy, can also be applied to monitor bound oxygen. The dye's fluorescence is quenched due to F?rster energy transfer to the oxygenated active sites of hemocyanin.     

On the Gauss map of hypersurfaces with constant scalar curvature in spheres

In this work we consider connected, complete and orientable hypersurfaces of the sphere with constant nonnegative -mean curvature. We prove that under subsidiary conditions, if the Gauss image of is contained in a closed hemisphere, then is totally umbilic.

     

Fluorescence determination of steroidal dienones

Reaction of Δ^1,4-3-keto steroids with zinc and acid produces a characteristic fluorescence. Estrogenic, 3-keto and Δ⁴-3-keto steroids did not yield this fluorescence. Stabilization of the dienone fluorescence by extraction into butyl ether allowed quantitation of triamcinolone acetonide in liquid formulations in which this dienone was present at the 0.01% level. A mechanism for the reaction is proposed.     

An elementary proof of the prime number theorem with a remainder term

An elementary proof of the prime number theorem in the form $$\psi (x) - x = O(x exp\{ - (\log x)^{\tfrac{1}{7}} (log log x)^{ - 2} \} )$$ is given. The proof uses a generalization of Selberg's formula and a tauberian argument.     

High-resolution spectroscopy of the 16-μm bending fundamental of CF4

The 16-μm bending fundamentals (ν₄) of ¹²CF₄, ¹³CF₄, and ¹⁴CF₄ have been observed at Doppler-limited resolution using a tunable PbSnSe semiconductor diode laser. The tetrahedral splittings of the rotational manifolds have been observed in all three branches, and in particular the dense and partially overlapping transitions in the Q branches have been resolved and assigned. A least-squares fit of the Hamiltonian, including off-diagonal terms, yielded five scalar and three tensor spectroscopic constants for each of the three isotopes. From these constants the upper-state rotational constant B₄ and the Coriolis constant ζ₄ have been calculated, together with some of the other molecular constants. An absorption feature at about 0.18 cm^?1 to the red of the main Q branch of each isotopic species has been identified as the Q branch of (ν₂ + ν₄) ? ν₂, which is the transition that lases when CF₄ is pumped by a CO₂ laser at 9.4 μm (i.e., in ν₂ + ν₄).