qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

An inlet analysis for the NASA hypersonic research engine aerothermodynamic integration model

A theoretical analysis for the inlet of the NASA Hypersonic Research Engine (HRE) Aerothermodynamic Integration Model (AIM) has been undertaken by use of a method-of-characteristics computer program. The purpose of the analysis was to obtain pretest information on the full-scale HRE inlet in support of the experimental AIM program (completed May 1974). Mass-flow-ratio and additive-drag-coefficient schedules were obtained that well defined the range effected in the AIM tests. Mass-weighted average inlet total-pressure recovery, kinetic energy efficiency, and throat Mach numbers were obtained

Multi-kilowatt modularized spacecraft power processing system development

A review of existing information pertaining to spacecraft power processing systems and equipment was accomplished with a view towards applicability to the modularization of multi-kilowatt power processors. Power requirements for future spacecraft were determined from the NASA mission model-shuttle systems payload data study which provided the limits for modular power equipment capabilities. Three power processing systems were compared to evaluation criteria to select the system best suited for modularity. The shunt regulated direct energy transfer system was selected by this analysis for a conceptual design effort which produced equipment specifications, schematics, envelope drawings, and power module configurations

Early Dust Formation and a Massive Progenitor for SN 2011ja?

SN 2011ja was a bright (I = -18.3) Type II supernova occurring in the nearby edge on spiral galaxy NGC 4945. Flat-topped and multi-peaked H-alpha and H-beta spectral emission lines appear between 64 - 84 days post-explosion, indicating interaction with a disc-like circumstellar medium inclined 30-45 degrees from edge-on. After day 84 an increase in the H- and K-band flux along with heavy attenuation of the red wing of the emission lines are strong indications of early dust formation, likely located in the cool dense shell created between the forward shock of the SN ejecta and the reverse shock created as the ejecta plows into the existing CSM. Radiative transfer modeling reveals both ~1.5 x 10^-4 Msun of pre-existing dust located ~ 10^16.7 cm away and ~ 5 x 10^-5 Msun of newly formed dust. Spectral observations after 1.5 years reveal the possibility that the fading SN is located within a young (3-6 Myr) massive stellar cluster, which when combined with tentative 56Ni mass estimates of 0.2 Msun may indicate a massive (> 25 Msun) progenitor for SN 2011ja.Comment: 13 pages, 8 figures, submitted to MNRAS awaiting final referee repor

Identifying the development in phase and amplitude of dipole and multipole radiation

The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity in such cases where, in consequence of retardation, the character and features significantly and progressively change as radiation propagates onwards, from the near-field and out towards the wave-zone. Readily developed analytical representations of the electric field, cast as a function of distance from the source, provide illuminating insights into the most prominent and distinctive properties of radiant electromagnetic emission. Graphical implementations and animations of the results prove particularly instructive in revealing the spatial form and temporal evolution of the emergent electromagnetic fields

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate