Images inside a reflecting spherical surface with possible application in astronomy

This report studies an algebraic equation whose solution gives the image system of a source of light as seen by an observer inside a reflecting spherical surface. The equation is looked at numerically using GeoGebra. Under the hypothesis that our galaxy is enveloped by a reflecting interface this becomes a possible model for many mysterious extra galactic observations.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Improving daylighting performance of mirrored light pipes

This paper assesses and compares the performances of two daylight collection strategies, one passive and one active, for large-scale mirrored light pipes (MLP) illuminating deep plan buildings. Both strategies use laser cut panels (LCP) as the main component of the collection system. The passive system comprises LCPs in pyramid form, whereas the active system uses a tiled LCP on a simple rotation mechanism that rotates 360° in 24 hours. Performance is assessed using scale model testing under sunny sky conditions and mathematical modelling. Results show average illuminance levels for the pyramid LCP ranging from 50 to 250 lux and 150 to 200 lux for the rotating LCPs. Both systems improve the performance of a MLP. The pyramid LCP increases the performance of a MLP by 2.5 times and the rotating LCP by 5 times, when compared to an open pipe particularly for low sun elevation angles.

Generalising unitary time evolution

In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.

Is there something quantum-like about the human mental lexicon?

Following an early claim by Nelson & McEvoy suggesting that word associations can display `spooky action at a distance behaviour', a serious investigation of the potentially quantum nature of such associations is currently underway. In this paper quantum theory is proposed as a framework suitable for modelling the mental lexicon, specifically the results obtained from both intralist and extralist word association experiments. Some initial models exploring this hypothesis are discussed, and they appear to be capable of substantial agreement with pre-existing experimental data. The paper concludes with a discussion of some experiments that will be performed in order to test these models.

Communicating assessment criteria is not sufficient for influencing students' approaches to assessment tasks – perspectives from a differential equations class

This report presents the findings of an exploratory study into the perceptions held by students regarding the use of criterion-referenced assessment in an undergraduate differential equations class. Students in the class were largely unaware of the concept of criterion referencing and of the various interpretations that this concept has among mathematics educators. Our primary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. Quantitative data and qualitative feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, the manner in which they actually approached the assessment activity was not altered as a result of the use of explicitly communicated grading criteria.

An ingenuous Decision Support System (iDSS) approach for remote area pregnant women

This paper addresses development of an ingenious decision support system (iDSS) based on the methodology of survey instruments and identification of significant variables to be used in iDSS using statistical analysis. A survey was undertaken with pregnant women and factorial experimental design was chosen to acquire sample size. Variables with good reliability in any one of the statistical techniques such as Chi-square, Cronbach’s α and Classification Tree were incorporated in the iDSS. The ingenious decision support system was implemented with Visual Basic as front end and Microsoft SQL server management as backend. Outcome of the ingenious decision support system include advice on Symptoms, Diet and Exercise to pregnant women.

Australian learning and teaching council projects in the mathematical sciences : a retrospective

Since 2004, the Australian Learning and Teaching Council (ALTC) and its predecessor, the Carrick Institute for Learning and Teaching in Higher Education, have funded numerous teaching and educational research-based projects in the Mathematical Sciences. In light of the Commonwealth Government’s decision to close the ALTC in 2011, it is appropriate to take account of the ALTCs input into the Mathe- matical Sciences in higher education. Here we present an overview of ALTC projects in the Mathematical Sciences, as well as report on the contributions they have made to the Discipline.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

Science and subjectivity

Science has been under attack in the last thirty years, and recently a number of prominent scientists have been busy fighting back. Here, an argument is presented that the `science wars' stem from an unreasonably strict adherence to the reductive method on the part of science, but that weakening this stance need not imply a lapse into subjectivity. One possible method for formalising the description of non-separable, contextually dependent complex systems is presented. This is based upon a quantum-like approach.