Sweeping the cd-Index and the Toric h-Vector

We derive formulas for the cd-index and the toric h-vector of a convex polytope P from a sweeping by a hyperplane. These arise from interpreting the corresponding S-shelling of the dual of P. We describe a partition of the faces of the complete truncation of P to reflect explicitly the nonnegativity of its cd-index and what its components are counting. One corollary is a quick way to compute the toric h-vector directly from the cd-index. We also propose an "extended toric" h-vector that fully captures the information in the flag h-vector.Comment: 23 page

Some Notes on Heteropteran Trichobothria

Excerpt: There has been much recent interest in the comparative morphology of the Heteroptera. This work has emphasized the land bugs, or Geocorisae, and has been concerned with working out the relationships and taxonomic placement of the higher categories (categories above the genus), and with the phylogenetic lines and sequences of these higher categories. The geocorisine groups with which I have been most concerned are in the closely related superfamilies Lygaeoidea, Pyrrho- coroidea, and Coreoidea (see Schaefer, 1964, for a discussion of the relationships among these groups). Another superfamily, the Pentatomoidea, is less closely related. All four of these superfamilies have arolia and pseudarolia, and all four have trichobothria. Because they possess this last character in common, the four are grouped together under the name Heteroptera Trichophora (Tullgren, 1918), aname of no nomenclatorial standing but nevertheless convenient. Trichobothria are long hairs arising from often darkened sockets on the relatively bald abdominal venter. They are usually easy to distinguish from other hairs, because they are longer, have a darkened base, and are arranged symmetrically in a distinctive pattern on each segment. These patterns and the number of trichobothria in them are characteristic of the higher categories of the Trichophora. Since the trichophoran families are closely related, and since this close relation- ship has been established on evidence from other morphological features than trichobothria, one might look for phylogenetic significance in the variety of patterns. However, very little is known about the function and phylogenetic origin of trichobothria. I shall speculate here on their function and their phylogenetic significance, but more must be learned about trichobothria before speculation becomes knowledge

Correlative studies of astrophysical sources of very high and ultra high energy gamma-rays

During the period of this contract, June 1, 1991 to November 14, 1992, the major results of our research effort have come from the Whipple air shower experiment in Tucson, AZ. The most notable development has been the discovery of TeV photons from the BL Lac object, Markarian 421. This result depended critically on the identification of Mrk 421 by the EGRET team as a source of GeV gamma rays

EMU and the ECB

Monetary unions - European Union countries ; European Central Bank ; European Economic Community

A New Technique for Heterodyne Spectroscopy: Least-Squares Frequency Switching (LSFS)

We describe a new technique for heterodyne spectroscopy, which we call Least-Squares Frequency Switching, or LSFS. This technique avoids the need for a traditional reference spectrum, which--when combined with the on-source spectrum--introduces both noise and systematic artifacts such as ``baseline wiggles''. In contrast, LSFS derives the spectrum directly, and in addition the instrumental gain profile. The resulting spectrum retains nearly the full theoretical sensitivity and introduces no systematic artifacts. Here we discuss mathematical details of the technique and use numerical experiments to explore optimum observing schemas. We outline a modification suitable for computationally difficult cases as the number of spectral channels grows beyond several thousand. We illustrate the method with three real-life examples. In one of practical interest, we created a large contiguous bandwidth aligning three smaller bandwidths end-to-end; radio astronomers are often faced with the need for a larger contiguous bandwidth than is provided with the available correlator.Comment: 37 pages, 8 figure