This study examined whether cortical changes underlying treatment for children with aggressive behaviour problems are related to changes in executive function (EF) performance. Fifty-five 8- to 12-year-old clinically-referred children were tested before and after a 14-week treatment intervention. Performance on four EF tasks varying in affective relevance was assessed at each session. EEG was also used to record peak amplitudes for the “inhibitory” N2, an event-related potential, while the children completed an emotion-induction Go/Nogo task. Results showed that changes in N2 amplitudes significantly predicted changes in performance only for the Iowa Gambling Task (IGT) – an affectively relevant task. Subsequent analysis revealed that only children who improved with treatment displayed significant decreases in N2 amplitudes and significant improvement in IGT performance from pre- to post-treatment. These findings suggest that cortical changes underlying successful treatment for children’s aggressive behaviour problems tap improvement in executive functions recruited for emotionally demanding events.

This study examined whether cortical changes underlying treatment for children with aggressive behaviour problems are related to changes in executive function (EF) performance. Fifty-five 8- to 12-year-old clinically-referred children were tested before and after a 14-week treatment intervention. Performance on four EF tasks varying in affective relevance was assessed at each session. EEG was also used to record peak amplitudes for the “inhibitory” N2, an event-related potential, while the children completed an emotion-induction Go/Nogo task. Results showed that changes in N2 amplitudes significantly predicted changes in performance only for the Iowa Gambling Task (IGT) – an affectively relevant task. Subsequent analysis revealed that only children who improved with treatment displayed significant decreases in N2 amplitudes and significant improvement in IGT performance from pre- to post-treatment. These findings suggest that cortical changes underlying successful treatment for children’s aggressive behaviour problems tap improvement in executive functions recruited for emotionally demanding events.

Spectral geometry is a mathematical discipline that studies the relationship between the geometry of Riemannian manifolds and the spectra of natural differential operators defined on them. The spectra of Laplacians are the ones most studied in this context. A sub-field of this discipline, called inverse spectral geometry, studies how much geometric information one can recover from such spectra. The motivation behind our study of inverse spectral geometry is a physical one. It has recently been proposed that inverse spectral geometry could be the missing mathematical link between quantum field theory and general relativity needed to unify those theories into a single theory of quantum gravity. Unfortunately, this proposed link is not well understood. Most of the efforts in inverse spectral geometry were historically concentrated on the generation of counterexamples to the most general formulation of inverse spectral geometry and the few positive results that exist are quite limited. In order to remedy to that, it has been proposed to linearize the problem, and study an infinitesimal version of inverse spectral geometry. In this thesis, I begin by reviewing the theory of pseudodifferential operators and using it to prove the spectral theorem for elliptic operators. I then define the commonly used Laplacians and survey positive and negative results in inverse spectral geometry. Afterwards, I briefly discuss a coordinate free reformulation of Riemannian geometry via the notion of spectral triple. Finally, I introduce a formulation of inverse spectral geometry adapted for numerical implementations and apply it to the inverse spectral geometry of a particular class of star-shaped domains in ℝ².

The handling of topological aspects in boundary value problems of engineering electromagnetics is often considered to be an engineer's art and not a science. This thesis is an attempt to show that the opposite is true. Through the use of differential forms and rudimentary concepts from homology theory a paradigm variational boundary value problem is formulated and investigated. It is seen that reasoning in terms of the Tonti diagram for this problem may lead to false conclusions if cohomology groups are ignored. As a prelude to this investigation, a suitable orthogonal decomposition of differential forms is derived and the roles played by the long exact homology sequence and topological duality theorems for compact orientable manifolds with boundary are considered in detail.

Graduation date: 2000

The present work studies some aspects of random matrix theory. Its first part is devoted to the asymptotics of random matrices with infinitely divisible, in particular heavy-tailed, entries. Its second part focuses on relations between limiting law in subsequence problems and spectra of random matrices.

The Galois group of a Schubert problem is a subtle invariant that encodes intrinsic structure of its set of solutions. These geometric invariants are difficult to determine in general. However, based on a special position argument due to Schubert and a combinatorial criterion due to Vakil, we show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. The result follows from a particular inequality of Schubert intersection numbers which are Kostka numbers of two-rowed tableaux. In most cases, the inequality follows from a combinatorial injection. For the remaining cases, we use that these Kostka numbers appear in the tensor product decomposition of sl2C-modules. Interpreting the tensor product as the action of certain Toeplitz matrices and using spectral analysis, the inequality can be rewritten as an integral. We establish the inequality by estimating this integral using only elementary Calculus.

Thesis (PhDApSc(MineralsandMaterials))--University of South Australia, 2007.

The unique language of mathematics incorporates words, numbers, symbols and diagrams. These elements and their associated mathematical concepts introduce reading and comprehension requirements that are not experienced in other disciplines. It is the responsibility of teachers to ensure that students are educated about, and encouraged to apply mathematical language in a variety of contexts. This is essential to the development of mathematical problem solving, where word problems often feature in classroom instruction and assessment, and where mathematical language is expected within student responses. Mathematics teachers need to be mindful that the validity of test items used to assess student mathematical problem solving ability are not influenced by other variables such as vocabulary comprehension difficulty. This study discusses the vocabulary which Year 9 students identify as difficult when undertaking word problem tasks in pen and paper test situations. To challenge generalised assumptions that teachers may make, this study focused on development of an instrument to monitor and evaluate the vocabulary comprehension of individual students within the classroom, and with respect to their particular school context. Analyses of findings support the requirement of reading proficiency in mathematics, and in particular, of vocabulary comprehension to student performance on mathematical problem solving assessment comprised of word problems.

Typescript (Photocopy) / Bibliography: leaf 75 / 75 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1985?