The Koebe Domain for Concave Univalent Functions

2000 Mathematics Subject Classification: 30C25, 30C45.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

Teacher leadership : interns crossing to the domain of higher professional learning with mentors?

Over the last two decades, the notion of teacher leadership has emerged as a key concept in both the teaching and leadership literature. While researchers have not reached consensus regarding a definition, there has been some agreement that teacher leadership can operate at both a formal and informal level in schools and that it includes leadership of an instructional, organisational and professional development nature (York-Barr & Duke, 2004). Teacher leadership is a construct that tends not to be applied to pre-service teachers as interns, but is more often connected with the professional role of mentors who collaborate with them as they make the transition to being a beginning teacher. We argue that teacher leadership should be recognised as a professional and career goal during this formative learning phase and that interns should be expected to overtly demonstrate signs, albeit early ones, of leadership in instruction and other professional areas of development. The aim of this paper is to explore the extent to which teacher education interns at one university in Queensland reported on activities that may be deemed to be ‘teacher leadership.’ The research approach used in this study was an examination of 145 reflective reports written in 2008 by final Bachelor of Education (primary) pre-service teachers. These reports recorded the pre-service teachers’ perceptions of their professional learning with a school-based mentor in response to four outcomes of internship that were scaffolded by their mentor or initiated by them. These outcomes formed the bases of our research questions into the professional learning of the interns and included, ‘increased knowledge and capacity to teach within the total world of work as a teacher;’ ‘to work autonomously and interdependently’; to make ‘growth in critical reflectivity’, and the ‘ability to initiate professional development with the mentoring process’. Using the approaches of the constant comparative method of Strauss and Corbin (1998) key categories of experiences emerged. These categories were then identified as belonging to main meta-category labelled as ‘teacher leadership.’ Our research findings revealed that five dimensions of teacher leadership – effective practice in schools; school curriculum work; professional development of colleagues; parent and community involvement; and contributions to the profession – were evident in the written reports by interns. Not surprisingly, the mentor/intern relationship was the main vehicle for enabling the intern to learn about teaching and leadership. The paper concludes with some key implications for developers of preservice education programmes regarding the need for teacher leadership to be part of the discourse of these programmes.