Interferometric array design: optimizing the locations of the antenna pads

The design of an interferometric array should allow optimal instrumental response regarding all possible source positions, times of integration and scientific goals. It should also take into account constraints such as forbidden regions on the ground due to impracticable topography. The complexity of the problem requires one to proceed by steps. A possible approach is to first consider a single observation and a single scientific purpose. A new algorithm is introduced to solve efficiently this particular problem called the configuration problem. It is based on the computation of pressure forces related to the discrepancies between the model (as determined by the scientific purpose) and the actual distribution of Fourier samples. The flexibility and rapidity of the method are well adapted to the full array design. A software named APO that can be used for the design of new generation interferometers such as ALMA and ATA has been developed.Comment: 9 pages, 7 figure

Estimating Economic Loss from Flash Flooding: A Study of Porter County, IN

This project attempted to determine what kinds of losses occurred during the flash floods of September 2009, caused by Hurricane Ike, in Northwest Indiana. Flash floods are dangerous due to how quickly they can overtake humans, houses, vehicles, and property. Flash floods caused Northwest Indiana to be under a State of Emergency, with drastic human and economic losses. Discovering where the problem is and defining the problem can help to prevent future losses. In addition, geographic software was analyzed for its helpfulness for this kind of problem. It was found that current software, including FEMA\u27s HAZUS-FM, is not suitable for analyzing flash floods for a number of reasons. Adapting the software to flash flood parameters will be the most helpful adjustment for mitigating flood losses. This on-going project was presented at the 2011 Indiana Geographic Information Council Conference

A polynomial invariant for links in lens spaces

We prove the existence of a polynomial invariant that satisfies the HOMFLY skein relation for links in a lens space. In the process we also develop a skein theory of toroidal grid diagrams in a lens space.Comment: 31 pages, 23 figures; final revision for publicatio

Multi-Scale CLEAN deconvolution of radio synthesis images

Radio synthesis imaging is dependent upon deconvolution algorithms to counteract the sparse sampling of the Fourier plane. These deconvolution algorithms find an estimate of the true sky brightness from the necessarily incomplete sampled visibility data. The most widely used radio synthesis deconvolution method is the CLEAN algorithm of Hogbom. This algorithm works extremely well for collections of point sources and surprisingly well for extended objects. However, the performance for extended objects can be improved by adopting a multi-scale approach. We describe and demonstrate a conceptually simple and algorithmically straightforward extension to CLEAN that models the sky brightness by the summation of components of emission having different size scales. While previous multiscale algorithms work sequentially on decreasing scale sizes, our algorithm works simultaneously on a range of specified scales. Applications to both real and simulated data sets are given.Comment: Submitted to IEEE Special Issue on Signal Processin

Abstract carrier space formalism for the irreducible tensor operators of compact quantum group algebras

Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that there are {\em{two}} types of irreducible tensor operator, which may be called `ordinary' and `twisted'. The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner-Eckart theorem for both the ordinary and twisted operators. Examples of irreducible tensor operators for the standard deformation of the function algebra of the compact Lie group $SU(2)$ are described to demonstrate the applicability of the new definitions.Comment: To be published in J.Math.Phys., 32 pages, RevTe

Bennequin type inequalities in lens spaces

We give criteria for an invariant of lens space links to bound the maximal self-linking number in certain tight contact lens spaces. As a corollary we extend the Franks-Williams-Morton inequality to the setting of lens spaces.Comment: 21 pages, 13 figures; International Mathematics Research Notices 201