A New Lower Bound for the Distinct Distance Constant

The reciprocal sum of Zhang sequence is not equal to the Distinct Distance Constant. This note introduces a $B_2$-sequence with larger reciprocal sum, and provides a more precise estimation of the reciprocal sums of Mian-Chowla sequence and Zhang sequence.Comment: 4 pages, 3 ancillary table

Eigenvalue estimates for the Dirac-Schr\"odinger operators

We give new estimates for the eigenvalues of the hypersurface Dirac operator in terms of the intrinsic energy-momentum tensor, the mean curvature and the scalar curvature. We also discuss their limiting cases as well as the limiting cases of the estimates obtained by X. Zhang and O. Hijazi in [13] and [10]. We compare these limiting cases with those corresponding to the Friedrich and Hijazi inequalities. We conclude by comparing these results to intrinsic estimates for the Dirac-Schr\"odinger operator D_f = D - f/2.Comment: 22 pages, LaTeX, to appear in Journal of Geometry and Physic

New Models for X-Ray Synchrotron Radiation from the Remnant of Supernova 1006 AD

Galactic cosmic rays up to energies of around 10^15 eV are assumed to originate in supernova remnants (SNRs). The shock wave of a young SNR like SN 1006 AD can accelerate electrons to energies greater than 1 TeV, where they can produce synchrotron radiation in the X-ray band. A new model (SRESC) designed to model synchrotron X-rays from Type Ia supernovae can constrain values for the magnetic-field strength and electron scattering properties, with implications for the acceleration of the unseen ions which dominate the cosmic-ray energetics. New observations by ASCA, ROSAT, and RXTE have provided enormously improved data, which now extend to higher X-ray energies. These data allow much firmer constraints. We will describe model fits to these new data on SN 1006 AD, emphasizing the physical constraints that can be placed on SNRs and on the cosmic-ray acceleration process.Comment: 10 pages, 2 figures. to appear in "Cosmic Explosions", proceeding of the 10th Annual October Astrophysics Conference (ed. S.S. Holt and W. W. Zhang) LaTex aipproc.st