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Full-Text Articles in Physical Sciences and Mathematics
A Nonexistence Result For Abelian Menon Difference Sets Using Perfect Binary Arrays, K. T. Arasu, James A. Davis, Jonathan Jedwab
A Nonexistence Result For Abelian Menon Difference Sets Using Perfect Binary Arrays, K. T. Arasu, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A Menon difference set has the parameters (4N2, 2N2-N, N2-N). In the abelian case it is equivalent to a perfect binary array, which is a multi-dimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. Suppose that the abelian group H×K×Zpα contains a Menon difference set, where p is an odd prime, |K|=pα, and pj≡−1 (mod exp (H)) for some j. Using the viewpoint of perfect binary arrays we prove that K must be cyclic. A …
Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan
Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan
Department of Math & Statistics Faculty Publications
This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample's exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for …
Research Announcement: Recursive Construction For Families Of Difference Sets, James A. Davis, Jonathan Jedwab
Research Announcement: Recursive Construction For Families Of Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1, d2, ∈ D} contains each nonzero element of G exactly λ times; n = k-λ.