Chemical representations play a vital part in the teaching and learning of chemistry. The aim of this research was to investigate students’ understanding of chemical representations and to ascertain the influence of chemical representations on students’ developing mental models of chemical phenomena. Three primary threads flowing through the thesis are models, representations and learning. Each thread was found to play a vital part in students’ learning of chemical content, in their learning of the scientific process and in their learning about the process of learning itself. This research with students from Year 8 to first year university level comprised four studies that provide comparisons between ages, abilities, learning settings and teaching and learning approaches. Students’ modelling ability was observed to develop and improve through instruction and practice and usually coincided with an improvement in their understanding of chemical concepts. While students were observed to actively use models to make predictions and test ideas, some were not aware of the predictive nature of models when asked about it. From the research, five characteristics of scientific models have been identified: scientific models as multiple representations, scientific models as exact replicas, scientific models as explanatory tools, how scientific models are used, and the dynamic nature of scientific models. A theoretical framework relating the four types of models - teaching, scientific, mental and expressed - and a typology of models that highlights the significant attributes of models, support the research results. The data showed that students’ ability to describe the role of the scientific model in the process of science improved with their increasing age and maturity. / The relationship between the three levels of chemical representation of matter - the macroscopic level, the sub-microscopic level and the symbolic level - revealed some complexities concerning the representational and theoretical qualities and the reality of each level. The research data showed that generally most students had a good understanding of the macroscopic and symbolic levels of chemical representation of matter. However, students’ understanding of the sub-microscopic level varied, with some students being able to spontaneously envisage the sub- microscopic view while for others their understanding of the sub-microscopic level of chemical representation was lacking. To make sense of the sub-microscopic level, students’ appreciation of the accuracy and detail of any scientific model, or representation upon which their mental model is built, depended on them being able to distinguish reality from representation, distinguish reality from theory, know what a representation is, understand the role of a representation in the process of science, and understand the role of a theory in the process of science. In considering learning, the importance of an individual’s modelling ability was examined alongside the role of chemical representations and models in providing clear and concise explanations. Examining the links forged between the three levels of chemical representation of matter provided an insight into how students were learning and understanding chemical concepts. Throughout this research, aspects of students’ metacognition and intention were identified as being closely related to their development of mental models. / The research identified numerous factors that influenced learning, including internal factors such as students’ prior chemical and mathematical knowledge, their modelling ability and use of chemical representations, motivation, metacognitive ability and time management as well as external factors such as organisation, assessment, teaching resources, getting feedback and good explanations. The choice of learning strategies by students and instructors appeared to be influenced by those factors that influenced learning. Feedback to students, in the form of discussion with classmates, online quizzes and help from instructors on their understanding was observed to be significant in promoting the learning process. Many first year university non-major chemistry students had difficulties understanding chemical concepts due to a limited background knowledge in chemistry and mathematics. Accordingly, greater emphasis at the macroscopic level of representation of matter with contextual references is recommended. The research results confirmed the theoretical construct for learning chemistry - the rising iceberg - that suggests all chemistry teaching begins at the macroscopic level, with the sub-microscopic and symbolic levels being introduced as needed. More of the iceberg becomes visible as the students’ mental model and depth of understanding increases. In a variety of situations, the changing status of a concept was observed as students’ understanding in terms of the intelligibility, plausibility and fruitfulness of a concept developed. / The research data supported four aspects of learning - epistemological, ontological, social affective and metacognitive - as being significant in the students’ learning and the development of their mental models. Many university students, who are mature and are experienced learners, exhibited strong rnetacognitive awareness and an intentional approach to learning. It is proposed that the intentional and metacognitive learning approaches and strategies could be used to encourage students to be more responsible for their own learning.

This practice-based project explores the photographic phenomenon of ‘moment beyond moment’, which refers to the combined representations of an existing image in an environment, together with the real-life situation at the moment the photograph is taken. I call this photograph an ‘extended photograph’. Employing practical works of extended photographs and focusing on interactions between the moment in real-life and the moment in an existing image, the research explores the transformation of meanings caused by the interactions of these moments in an extended photograph. The research owes its approach to grounded theory, contrary thinking and Chinese Buddhist ‘Sudden Enlightenment’ to further its aim of exploring the unpredictable interaction of these moments, and to disclose the potentials of meaning transformation. My research outcome intends to initiate a discourse with photographic practitioners and theorists on the phenomenon of moment beyond moment in a working environment that is encaged by the excessive existence of displayed images. The thesis is composed as a creative work that consists of a series of photographic images accompanied by an exegesis component. The images represent a nominal 80%, and the exegesis 20% of the final submission.

Une partie de cette thèse étudie des produits tensoriels de deux représentations irreductibles d'un groupes algébrique simple. Il s'agit de comprendre les tenseurs pures dans la componente de Cartan du produit.<br />Une partie étudie la propriété de séparation d'un sous-ensemble dans un espace vectoriel complex.

Soit p un nombre premier et G un groupe classique de type B, C ou D defini sur la cloture algebrique K du corps a p elements (si G est de type B ou D, p est impair). A l'aide de paires duales de groupes et de modules basculants, on trouve le caractere de certaines representations rationnelles irreductibles de G sur K. On obtient tout d'abord des formules en termes de tableaux semi-standards, non couvertes par la conjecture de Lusztig. Puis on determine la dimension et/ou le caractere des representations irreductibles de plus haut poids un poids fondamental, ou une somme de deux poids fondamentaux, suivant G. On en deduit notamment le comportement asymptotique de leur dimension, a p fixe, quand le rang du groupe tend vers l'infini. On dresse enfin la liste des modules de Weyl simples de plus haut poids un poids fondamental quand G est un groupe symplectique, ou de plus haut poids la somme d'un poids fondamental et du plus haut poids de la representation spin quand G est un groupe spin.

When studying the molecular aspect of the life sciences, learners must be introduced to somewhat inaccessible phenomena that occur at the sub-micro scale. Despite the difficulties, students need to be familiar with and understand the highly dynamic nature of molecular processes. Thus, external representations1 (ERs) can be considered unavoidable and essential tools for student learning. Besides meeting the challenge of interpreting external representations, learners also encounter a large array of abstract concepts2, which are challenging to understand (Orgill &amp; Bodner, 2004). Both teachers and learners use metaphorical language as a way to relate these abstract phenomena to more familiar ones from everyday life. Scientific papers, as well as textbooks and popular science articles, are packed with metaphors, analogies and intentional expressions. Like ERs, the use of metaphors and analogies is inevitable and necessary when communicating knowledge concerning molecular phenomena. Therefore, a large body of published research related to metaphors concerns science teachers’ and textbook writers’ interpretation and use of metaphors (Harrison &amp; Treagust, 2006). In this paper we present a theoretical framework for examining metaphorical language use in relation to abstract phenomena and external representations. The framework was verified by using it to analyse students’ meaning-making in relation to an animation representing the sub-microscopic and abstract process of ATP-synthesis in Oxidative Phosphorylation. We seek to discover the animator’s intentions while designing the animation and to identify the metaphors that students use while interacting with the animation. Two of these metaphors serve as examples of a metaphor analysis, in which the characteristics of metaphors are outlined. To our knowledge,  no strategies to identify and understand the characteristics, benefits, and potential pitfalls of particular metaphors have, to date, been presented in science education research. Our aspiration is to contribute valuable insights into metaphorical language use at the interface between external representations, molecular processes, and student learning.

A novel framework based on cluster co-occurrence and graph theory for structure discovery is applied to audio to find new types of audio objects which enable the compression of an input signal. These new objects differ from those found in current object coding schemes as their shape is not restricted by any a priori psychoacoustic knowledge. The framework is novel from an application perspective, as it marks the first time that graph theory is applied to audio, and with regards to theoretical developments, as it involves new extensions to the areas of unsupervised learning algorithms and frequent subgraph mining methods. Tests are performed using a corpus of audio files spanning a wide range of sounds. Results show that the framework discovers new types of audio objects which yield average respective overall and relative compression gains of 15.90% and 23.53% while maintaining a very good average audio quality with imperceptible changes.

W. D. Munn proved that a finite dimensional representation of an inverse semigroup is equivalent to a ⋆-representation if and only if it is bounded. The first goal of this thesis will be to give new analytic proof that every finite dimensional representation of a compact inverse semigroup is equivalent to a ⋆-representation. The second goal is to parameterize all finite dimensional irreducible representations of a compact inverse semigroup in terms of maximal subgroups and order theoretic properties of the idempotent set. As a consequence, we obtain a new and simpler proof of the following theorem of Shneperman: a compact inverse semigroup has enough finite dimensional irreducible representations to separate points if and only if its idempotent set is totally disconnected. Our last theorem is the following: every norm continuous irreducible ∗-representation of a compact inverse semigroup on a Hilbert space is finite dimensional.

Around 1990, Arthur proved a local (ordinary) trace formula for real or p-adic connected reductive groups. The local trace formula is a powerful tool in the local harmonic analysis of reductive groups. One of the aims of this thesis is to establish a local twisted trace formula for certain non-connected reductive groups, which is a twisted version of Arthur’s local trace formula. As an application of the local twisted trace formula, we will prove some twisted orthogonality relations, which are generalizations of Arthur’s results about orthogonality relations for tempered elliptic characters. To establish these relations, we will also give a classification of twisted elliptic representations.

Around 1990, Arthur proved a local (ordinary) trace formula for real or p-adic connected reductive groups. The local trace formula is a powerful tool in the local harmonic analysis of reductive groups. One of the aims of this thesis is to establish a local twisted trace formula for certain non-connected reductive groups, which is a twisted version of Arthur’s local trace formula. As an application of the local twisted trace formula, we will prove some twisted orthogonality relations, which are generalizations of Arthur’s results about orthogonality relations for tempered elliptic characters. To establish these relations, we will also give a classification of twisted elliptic representations.

W. D. Munn proved that a finite dimensional representation of an inverse semigroup is equivalent to a ⋆-representation if and only if it is bounded. The first goal of this thesis will be to give new analytic proof that every finite dimensional representation of a compact inverse semigroup is equivalent to a ⋆-representation. The second goal is to parameterize all finite dimensional irreducible representations of a compact inverse semigroup in terms of maximal subgroups and order theoretic properties of the idempotent set. As a consequence, we obtain a new and simpler proof of the following theorem of Shneperman: a compact inverse semigroup has enough finite dimensional irreducible representations to separate points if and only if its idempotent set is totally disconnected. Our last theorem is the following: every norm continuous irreducible ∗-representation of a compact inverse semigroup on a Hilbert space is finite dimensional.