Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k

Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.Comment: 19 pages, LaTe

Tripartite entanglement from interlinked χ(2)\chi^{(2)} parametric interactions

We examine the tripartite entanglement properties of an optical system using interlinked $\chi^{(2)}$ interactions, recently studied experimentally in terms of its phase-matching properties by Bondani et al [M. Bondani, A. Allevi, E. Gevinti, A. Agliati, and A. Andreoni, arXiv:quant-ph/0604002.]. We show that the system does produce output modes which are genuinely tripartite entangled and that detection of this entanglement depends crucially on the correlation functions which are measured, with a three-mode Einstein-Podolsky-Rosen inequality being the most sensitive.Comment: 15 pages, 5 figure

Scientific publications and presentations relating to planetary quarantine. Volume 5: The 1972 supplement

The sixth annual supplement to the bibliography on planetary quarantine contains 191 references, an author index and a permuted title index

Axistationary perfect fluids -- a tetrad approach

Stationary axisymmetric perfect fluid space-times are investigated using the curvature description of geometries. Attention is focused on space-times with a vanishing electric part of the Weyl tensor. It is shown that the only incompressible axistationary magnetic perfect fluid is the interior Schwarzschild solution. The existence of a rigidly rotating perfect fluid, generalizing the interior Schwarzschild metric is proven. Theorems are stated on Petrov types and electric/magnetic Weyl tensors.Comment: 12 page

Keplerian Motion of Broad-Line Region Gas as Evidence for Supermassive Black Holes in Active Galactic Nuclei

Emission-line variability data on NGC 5548 argue strongly for the existence of a mass of order 7 x 10^7 solar masses within the inner few light days of the nucleus in the Seyfert 1 galaxy NGC 5548. The time-delayed response of the emission lines to continuum variations is used to infer the size of the line-emitting region, and these determinations are combined with measurements of the Doppler widths of the variable line components to estimate a virial mass. The data for several different emission lines spanning an order of magnitude in distance from the central source show the expected V proportional to r^{-1/2} correlation and are consistent with a single value for the mass.Comment: 9 pages, 2 Figures. accepted by ApJ Letter