On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

Task profiling : A task-Based approach to measuring the integration of ICT in the classroom

The measurement of ICT (information and communication technology) integration is emerging as an area of research interest with such systems as Education Queensland including it in their recently released list of research priorities. Studies to trial differing integration measurement instruments have taken place within Australia in the last few years, particularly Western Australia (Trinidad, Clarkson, & Newhouse, 2004; Trinidad, Newhouse & Clarkson, 2005), Tasmania (Fitzallen 2005) and Queensland (Finger, Proctor, & Watson, 2005). This paper will add to these investigations by describing an alternate and original methodological approach which was trialled in a small-scale pilot study conducted jointly by Queensland Catholic Education Commission (QCEC) and the Centre of Learning Innovation, Queensland University of Technology (QUT) in late 2005. The methodology described is based on tasks which, through a process of profiling, can be seen to be artefacts which embody the internal and external factors enabling and constraining ICT integration.