Maximal determinants and saturated D-optimal designs of orders 19 and 37

A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal. For order 19 we find all inequivalent saturated D-optimal designs with maximal determinant, 2^30 x 7^2 x 17, and confirm that the three known designs comprise a complete set. For order 37 we prove that the maximal determinant is 2^39 x 3^36, and find a sample of inequivalent saturated D-optimal designs. Our method is an extension of that used by Orrick to resolve the previously smallest unknown order of 15; and by Chadjipantelis, Kounias and Moyssiadis to resolve orders 17 and 21. The method is a two-step computation which first searches for candidate Gram matrices and then attempts to decompose them. Using a similar method, we also find the complete spectrum of determinant values for {+1,-1} matrices of order 13.Comment: 28 pages, 4 figure

'Sounds of Intent' : Mapping musical behaviour and development in children and young people with complex needs

This article reports on the first year of an Esmae Fairbairn Foundation-funded research project into the design and evaluation of an original 'framework' for mapping the behaviour and development in, and through, music for children with complex needs, specifically those with profound and multiple learning difficulties (PMLD). An initial four-month design and pilot phase critiqued and evaluated a framework that was grounded in video-based iterative analyses of individual case studies that had been collected during the previous two years. The piloting phase was followed by a sustained period of classroom-based music lesson observation in five special schools over a period of seven months. A total of 630 observations were made using the framework for 68 participants whose ages ranged from 4 years 7 months to 19 years 1 month. Subsequent analyses support the general design features of the observational framework and provide new evidence of PMLD musical behaviour and development

Scanning tunneling spectroscopy of lead-substituted bismuth strontium copper oxide

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2007.Includes bibliographical references (leaves 39-43).The hole-doped cuprate Bi ... is doped with lead to the solubility limit of x = 0.38 and studied using STM/STS in the overdoped regime where Tc < 2K. Despite the high lead content, residual supermodulations are observed in the BiO plane. In agreement with previous studies on (Pb,Bi)-2201, there is no separation of the sample into Pb-rich and Pb-poor domains, nor is there a spectral correlation with Pb location. Differential tunneling conductance is modeled using the van Hove scenario, wherein modulated regions are shown to have higher values of EVHS than flat regions. The consistency of parameters matching theoretical predictions to tunneling spectra suggest that EVHS describes a significant part of the density of states.by Michelle Zimmermann.S.B

Die interpersonelle Umverteilung in der Gesetzlichen Krankenversicherung – Status Quo und Perspektiven der Ausgestaltung

Pay-as-you-go, child-related pension, quantity and quality of children