ITERA: IDL Tool for Emission-line Ratio Analysis

We present a new software tool to enable astronomers to easily compare observations of emission line ratios with those determined by photoionization and shock models, ITERA, the IDL Tool for Emission-line Ratio Analysis. This tool can plot ratios of emission lines predicted by models and allows for comparison of observed line ratios against grids of these models selected from model libraries associated with the tool. We provide details of the libraries of standard photoionization and shock models available with ITERA, and, in addition, present three example emission line ratio diagrams covering a range of wavelengths to demonstrate the capabilities of ITERA. ITERA, and associated libraries, is available from \url{http://www.brentgroves.net/itera.html}Comment: Accepted for New Astronomy, 3 figures. ITERA tool available to download from http://www.brentgroves.net/itera.htm

The Marr Conjecture and Uniqueness of Wavelet Transforms

The inverse question of identifying a function from the nodes (zeroes) of its wavelet transform arises in a number of fields. These include whether the nodes of a heat or hypoelliptic equation solution determine its initial conditions, and in mathematical vision theory the Marr conjecture, on whether an image is mathematically determined by its edge information. We prove a general version of this conjecture by reducing it to the moment problem, using a basis dual to the Taylor monomial basis $x^\alpha$ on $\mathbb {R}^n$.Comment: 52 pages, 4 figure

Uniqueness for weak solutions of parabolic equations with a fractional time derivative

We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to the test function.Comment: Accepted version to appear in Contemporary Mathematics. Corrected inaccuracies regarding historical results in the introduction. Also changed the initial condition for the equation and fixed typo

Free boundary on a cone

We study two phase problems posed over a two dimensional cone generated by a smooth curve $\gamma$ on the unit sphere. We show that when $length(\gamma)<2\pi$ the free boundary avoids the vertex of the cone. When $length(\gamma) \geq 2\pi$ we provide examples of minimizers such that the vertex belongs to the free boundary

Spatial de-correlation of the UTRA-FDD radio channel

For smart antenna deployment in Frequency Division Duplex (FDD) applications the downlink weight vector can be derived from the uplink steering vector, assuming a degree of correlation between these channels. It is shown here that de-correlation between uplink and downlink power azimuth spectrums (PAS) is significant for frequency offsets as small as 5MHz in urban environments. Results reported here are computed from measured data taken within the UTRA (UMTS Terrestrial Radio Interface) frequency band for cluttered urba