Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds

The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construction as a carefully organized surgery on a link. In this paper, we work out the relationship between the twisted face-pairing description of closed 3-manifolds and the more common descriptions by surgery and Heegaard diagrams. We show that all Heegaard diagrams have a natural decomposition into subdiagrams called Heegaard cylinders, each of which has a natural shape given by the ratio of two positive integers. We characterize the Heegaard diagrams arising naturally from a twisted face-pairing description as those whose Heegaard cylinders all have integral shape. This characterization allows us to use the Kirby calculus and standard tools of Heegaard theory to attack the problem of finding which closed, orientable 3-manifolds have a twisted face-pairing description.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-10.abs.htm

Blazar Gamma-Rays, Shock Acceleration, and the Extragalactic Background Light

The observed spectra of blazars, their intrinsic emission, and the underlying populations of radiating particles are intimately related. The use of these sources as probes of the extragalactic infrared background, a prospect propelled by recent advances in TeV-band telescopes, soon to be augmented by observations by NASA's upcoming Gamma-Ray Large Area Space Telescope (GLAST), has been a topic of great recent interest. Here, it is demonstrated that if particles in blazar jets are accelerated at relativistic shocks, then gamma-ray spectra with indices less than 1.5 can be produced. This, in turn, loosens the upper limits on the near infrared extragalactic background radiation previously proposed. We also show evidence hinting that TeV blazars with flatter spectra have higher intrinsic TeV gamma-ray luminosities and we indicate that there may be a correlation of flatness and luminosity with redshift.Comment: Version to appear in ApJ Letters, Vol. 667, 20 Sept. 200

Generalized vegetation map of north Merrit Island based on a simplified multispectral analysis

A simplified system for classification of multispectral data was used for making a generalized map of ground features of North Merritt Island. Subclassification of vegetation within broad categories yielded promising results which led to a completely automatic method and to the production of satisfactory detailed maps. Changes in an area north of Happy Hammocks are evidently related to water relations of the soil and are not associated with the last winter freeze-damage which affected mainly the mangrove species, likely to reestablish themselves by natural processes. A supplementary investigation involving reflectance studies in the laboratory has shown that the reflectance by detached citrus leaves, of wavelengths lying between 400 microns and 700 microns, showed some variation over a period of seven days during which the leaves were kept in a laboratory atmosphere

The high energy limit of the trajectory representation of quantum mechanics

The trajectory representation in the high energy limit (Bohr correspondence principle) manifests a residual indeterminacy. This indeterminacy is compared to the indeterminacy found in the classical limit (Planck's constant to 0) [Int. J. Mod. Phys. A 15, 1363 (2000)] for particles in the classically allowed region, the classically forbiden region, and near the WKB turning point. The differences between Bohr's and Planck's principles for the trajectory representation are compared with the differences between these correspondence principles for the wave representation. The trajectory representation in the high energy limit is shown to go to neither classical nor statistical mechanics. The residual indeterminacy is contrasted to Heisenberg uncertainty. The relationship between indeterminacy and 't Hooft's information loss and equivalence classes is investigated.Comment: 12 pages of LaTeX. No figures. Incorporated into the "Proceedings of the Seventh International Wigner Symposium" (ed. M. E. Noz), 24-29 August 2001, U. of Maryland. Proceedings available at http://www.physics.umd.edu/robo

Serrated trailing edges for improving lift and drag characteristics of lifting surfaces

An improvement in the lift and drag characteristics of a lifting surface is achieved by attaching a serrated panel to the trailing edge of the lifting surface. The serrations may have a saw-tooth configuration, with a 60 degree included angle between adjacent serrations. The serrations may vary in shape and size over the span-wise length of the lifting surface, and may be positioned at fixed or adjustable deflections relative to the chord of the lifting surface