Hopf Algebras of Heap Ordered Trees and Permutations

It is known that there is a Hopf algebra structure on the vector space with basis all heap-ordered trees. We give a new bialgebra structure on the space with basis all permutations and show that there is a direct bialgebra isomorphism between the Hopf algebra of heap-ordered trees and the bialgebra of permutations.Comment: 10 pages LaTeX, minor revisio

A simple example of modeling hybrid systems using bialgebras: Preliminary version

The authors describe how to construct a hybrid control system using a specific set of data and conditions specified within the paper. Furthermore, they give examples of how to create continuous systems, discrete systems, and simple hybrid systems. Finally, they touch upon Heisenberg and state space representation

Water vapor in Jupiter's atmosphere

High spectral resolution observations of Jupiter at 2.7 and 5 microns acquired from the Kuiper Airborne Observatory were used to infer the vertical distribution of H2O between 0.7 and 6 bars. The H2O mole fraction, qH2O, is saturated for P<2 bars, qH2O = 4x.000001 in the 2 to 4 bar range and it increases to 3x.00001 at 6 bars where T = 288 K. The base of the 5 micron line formation region is determined by pressure-induced H2 opacity. At this deepest accessible level, the O/H ratio in Jupiter is depleted by a factor of 50 with respect to the solar atmosphere. High spatial resolution Voyager IRIS spectra of Jupiter's North Tropical Zone, Equatorial Zone, and Hot Spots in the North and South Equatorial Belt were analyzed to determine the spatial variation of H2O across the planet. The column abundance of H2O above the 4 bar level is the same in the zones as in the SEB Hot Spots, about 20 cm-amgt. A cloud model for Jupiter's belts and zones was developed in order to fit the IRIS 5 micron spectra. An absorbing cloud located at 2 bars whose 5 micron optical thickness varies between 1 in the Hot Spots and 4 in the coldest zones satisfactorily matches the IRIS data

CDM analysis

The C Data Manager (CDM) is an advanced tool for creating an object-oriented database and for processing queries related to objects stored in that database. The CDM source code was purchased and will be modified over the course of the Arachnid project. In this report, the modified CDM is referred to as MCDM. Using MCDM, a detailed series of experiments was designed and conducted on a Sun Sparcstation. The primary results and analysis of the CDM experiment are provided in this report. The experiments involved creating the Long-form Faint Source Catalog (LFSC) database and then analyzing it with respect to following: (1) the relationships between the volume of data and the time required to create a database; (2) the storage requirements of the database files; and (3) the properties of query algorithms. The effort focused on defining, implementing, and analyzing seven experimental scenarios: (1) find all sources by right ascension--RA; (2) find all sources by declination--DEC; (3) find all sources in the right ascension interval--RA1, RA2; (4) find all sources in the declination interval--DEC1, DEC2; (5) find all sources in the rectangle defined by--RA1, RA2, DEC1, DEC2; (6) find all sources that meet certain compound conditions; and (7) analyze a variety of query algorithms. Throughout this document, the numerical results obtained from these scenarios are reported; conclusions are presented at the end of the document