796 research outputs found
L2-invariants of nonuniform lattices in semisimple Lie groups
We compute L2-invariants of certain nonuniform lattices in semisimple Lie
groups by means of the Borel-Serre compactification of arithmetically defined
locally symmetric spaces. The main results give new estimates for
Novikov-Shubin numbers and vanishing L2-torsion for lattices in groups with
even deficiency. We discuss applications to Gromov's Zero-in-the-Spectrum
Conjecture as well as to a proportionality conjecture for the L2-torsion of
measure equivalent groups.Comment: 35 pages, 2 figure
Improved accuracies for satellite tracking
A charge coupled device (CCD) camera on an optical telescope which follows the stars can be used to provide high accuracy comparisons between the line of sight to a satellite, over a large range of satellite altitudes, and lines of sight to nearby stars. The CCD camera can be rotated so the motion of the satellite is down columns of the CCD chip, and charge can be moved from row to row of the chip at a rate which matches the motion of the optical image of the satellite across the chip. Measurement of satellite and star images, together with accurate timing of charge motion, provides accurate comparisons of lines of sight. Given lines of sight to stars near the satellite, the satellite line of sight may be determined. Initial experiments with this technique, using an 18 cm telescope, have produced TDRS-4 observations which have an rms error of 0.5 arc second, 100 m at synchronous altitude. Use of a mosaic of CCD chips, each having its own rate of charge motion, in the focal place of a telescope would allow point images of a geosynchronous satellite and of stars to be formed simultaneously in the same telescope. The line of sight of such a satellite could be measured relative to nearby star lines of sight with an accuracy of approximately 0.03 arc second. Development of a star catalog with 0.04 arc second rms accuracy and perhaps ten stars per square degree would allow determination of satellite lines of sight with 0.05 arc second rms absolute accuracy, corresponding to 10 m at synchronous altitude. Multiple station time transfers through a communications satellite can provide accurate distances from the satellite to the ground stations. Such observations can, if calibrated for delays, determine satellite orbits to an accuracy approaching 10 m rms
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