Radio Images of 3C 58: Expansion and Motion of its Wisp

New 1.4 GHz VLA observations of the pulsar-powered supernova remnant 3C 58 have resulted in the highest-quality radio images of this object to date. The images show filamentary structure over the body of the nebula. The present observations were combined with earlier ones from 1984 and 1991 to investigate the variability of the radio emission on a variety of time-scales. No significant changes are seen over a 110 day interval. In particular, the upper limit on the apparent projected velocity of the wisp is 0.05c. The expansion rate of the radio nebula was determined between 1984 and 2004, and is 0.014+/-0.003%/year, corresponding to a velocity of 630+/-70 km/s along the major axis. If 3C 58 is the remnant of SN 1181, it must have been strongly decelerated, which is unlikely given the absence of emission from the supernova shell. Alternatively, the low expansion speed and a number of other arguments suggest that 3C 58 may be several thousand years old and not be the remnant of SN 1181.Comment: 12 pages; accepted for publication in the Astrophysical Journa

The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

Analysis of aircraft spectrometer data with logarithmic residuals

Spectra from airborne systems must be analyzed in terms of their mineral-related absorption features. Methods for removing backgrounds and extracting these features one at a time from reflectance spectra are discussed. Methods for converting radiance spectra into a form similar to reflectance spectra so that the feature extraction procedures can be implemented on aircraft spectrometer data are also discussed

Lifting Grobner bases from the exterior algebra

In the article "Non-commutative Grobner bases for commutative algebras", Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and initial ideals of those ideals in the free associative algebra which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one notion of generic initial ideals in the free assoicative algebra, and show that gin's of ideals containing the commutator ideal, or the anti-commutator ideal, are finitely generated.Comment: 6 pages, LaTeX2