Le domaine de cette thèse est dans la topologie quantique et son sujet est axé sur l'interaction en- tre la topologie de basse dimension et la théorie des représentations. Ma recherche concerne as- pects différents des invariants quantiques pour les entrelacs et les $3$-variétés, visant a créer des ponts entre les façons algébriques et topologiques de les définir. D'une part, une description al- gébrique et combinatoire pour un concept mathématique, crée l'opportunité de développer des outils de calcul. D'un autre côté, les descriptions topologiques et géométriques ouvrent des per- spectives vers des constructions qui mènent a une compréhension plus profonde et a des théories plus subtiles.Les polynômes de Jones coloriés sont des invariants quantiques d'entrelacs contruits en partant de la théorie des représentations de $U_q(sl(2))$. Le premier invariant de cette séquence est le polynôme de Jones original, qui peut-être caractérisé aussi par la théorie de l'écheveau. Bigelow et Lawrence ont décrit un modèle homologique pour le polynôme de Jones. Ils ont utilisé la représentation de Lawrence, qui est une représentation de groupe de tresses sur l'homologie des revêtements d'espaces de configurations dans le disque pointé, et la nature de l'écheveau de l'in- variant pour la preuve. Contrairement a ce cas, les autres polynômes de Jones coloriés ne peu- vent pas être définis facilement par la théorie de l'écheveau.Dans la premiere partie de cette thèse, nous donnons un modèle topologique pour les polynômes de Jones coloriés. Nous utilisons leur définition comme invariants quantiques et construisons des correspondants topologiques pas à pas. Nous observons d'abord que l'invariant peut être codé par des espaces dits de plus haut poids, puis utiliser un résultat de Kohno, qui identifie ces espaces avec des représentations de Lawrence. Nous prouvons que les polynômes de Jones coloriés peu- vent être obtenus comme une forme d'intersection géométrique gradués entre des classes d'ho- mologie dans certaines couvertures des espaces de configuration de points dans le disque pointé.Les deuxième et troisième parties sont orientées vers les applications de la théorie de la représen- tation des super groupes quantiques aux invariants quantiques. La deuxième partie est une col- laboration avec N. Geer, ou nous construisons des invariants quantiques pour $3$-variétés a par- tir des représentations de $U_q(sl(2|1))$. Turaev-Viro ont défini une méthode de type somme d'état qui donne des invariants de $3$-variétés a partir de $ U_q(sl (2)) $. Pour les super groupes quantiques, cela entraîne l'annulation des invariants. Plus tard, Geer-Pa- tureau-Turaev ont défini une méthode modifiée qui commence par une catégorie avec de bonnes propriétés et conduit à des invariants non-nulls. Notre stratégie consiste a construire une caté- gorie qui peut-être utilisée dans cette méthode modifiée. La troisième partie concerne l'étude des algèbre centralisatrices pour les représentations de $ U_q (sl (2 | 1)) $. Wagner et Marin conjec- turaient les dimensions d'une suite d'algèbres centralisatrices correspondant à la représentation simple standard de $U_q(sl(2|1))$. Nous prouvons cette conjecture en utilisant des techniques combinatoires. / The domain of this thesis is within quantum topology and its subject is focused towards the interaction between low dimensional topology and representation theory. My research con- cerns different aspects of quantum invariants for links and $3$-manifolds, aiming to create bridges between algebraic and topological ways of defining them. On one hand, an algebraic and combinatorial description for a mathematical concept, creates the opportunity to develop computational tools. On the other hand, topological and geometrical descriptions open per- spectives towards constructions that lead to a deeper understanding and more subtle theories.The coloured Jones polynomials are quantum link invariants constructed from the representa- tion theory of $U_q(sl(2))$. The first invariant of this sequence is the original Jones polyno- mial, which can be characterised also by skein theory. Bigelow and Lawrence described a homological model for the Jones polynomial. They used the Lawrence representation, which is a braid group representation on the homology of coverings of configuration spaces in the punctured disk, and the skein nature of the invariant for the proof. In contrast to this case, the other coloured Jones polynomials cannot be defined in an easy manner by skein theory.In the first part of this thesis, we give a topological model for the coloured Jones polynomi- als. We use their definition as quantum invariants and construct step by step topological cor- respondents. We first observe that the invariant can be encoded through so-called highest weight spaces and then use a result by Kohno, which identifies these spaces with Lawrence representations. We prove that the coloured Jones polynomials can be obtained as graded geometric intersection pairings between homology classes in certain coverings of the config- uration spaces of points in the punctured disk.The second and third parts are oriented towards applications of representation theory of super quantum groups to quantum invariants.The second part is a collaboration with N. Geer, where we construct quantum invariants for$3$-manifolds from representations of $U_q(sl(2|1))$. Turaev-Viro defined a state-sum type method that gives $3$-manifold invariants from $U_q(sl(2))$. For super quantum groups, this leads to vanishing invariants. Later on, Geer-Patureau-Turaev defined a modified method which starts with a category with good properties and leads to non-vanishing invariants. Our strategy is to construct a category that fits into the input of this modified method.The third part concerns the study of centralizer algebras for representations of $U_q(sl(2|1))$. Wagner and Marin conjectured the dimensions of a sequence of centralizer algebras corre- sponding to the simple standard $U_q(sl(2|1))$-representation. We prove this conjecture us- ing combinatorial techniques.

Magister Administrationis - MAdmin

Bibliography: p. 285-297. / The following study places the minority-owned business in perspective and seeks to justify the need for a categorical policy for development aimed at correcting the low participation of minorities in general, and Coloured persons in particular, in the business sector.

A fairly general model of the elevator system is presented. Coloured Petri Nets (CPN) and CPN tools are adopted as modeling tools. The model, which is independent of the number of floors and elevators, covers different stages of the elevator system in substantial detail. The model assists simulation-based analysis of different algorithms and rules which govern real elevator systems. The results prove the compatibility and applicability of this model in various situations and demonstrate the expressive power and convenience of CPN. / Thesis / Master of Applied Science (MASc)

Petri nets are a graphical construction with clearly de ned semantics which can model concurrent communicating systems in a formal manner similar to the way that automata theory can model formal language theory(Petri, 1962). As Dr. Carl Petri found the existing automata insu cient or too cumbersome for describing communicating systems others have found Petri Nets to be too cumbersome for e ectively reasoning about sophisticated, real world systems. In some cases these di culties were overcome by extending the theory of Petri Nets. Dr. Kurt Jensen developed the theory of Coloured Petri Nets (Jensen, 1981) for the purpose of generalizing and simplifying complex Petri Net models. This work incorporates Coloured Petri Nets and other theoretical extensions to describe a real world automated steel cutting system. During the course of this investigation the paper will formalize colours in the language of algebras and examine patterns related to timing conditions. / Thesis / Master of Science (MSc) / Petri nets can provide a graphical explanation of computer systems that have sophisticated communications. The graph has a precise mathematical meaning which allows it to be formally analyzed to prove many interesting properites of the net. There have been many extensions of the theory, some of which are incorporated to this model of an automated steel cutting machine. This thesis also presents the idea of colours, or data types, in the language of algebras.

No abstract available. / Thesis (M.A.)-University of Natal, Durban 1991.

Philosophiae Doctor - PhD (Education) / The World Health Organisation defines mental health as "a state of well-being in which the individual realizes her or his own abilities, can work productively and fruitfully, and is able to make a contribution to her or his community" (WHO, 2001, p. 1). There is a paucity of academic research about the mental health status of minority groups, especially women of colour (Moultrie & Kleintjes, 2006). In South Africa too, this gap in research is evident when focussing on the mental health of women, especially Coloured women in South Africa. Women's health and their mental health in particular are often affected by the way society treats and regards them; often they suffer from emotional, mental and physical exhaustions. This study investigated the mental health status of Coloured female teachers working in historically disadvantaged Special Schools in the Cape Metropole of the Western Cape Education Department. This group designation is the designation that was formally used during South Africa's Apartheid past policies of segregation in categorising groups according to pre-determined race categories. Coloureds where then considered to be a minority grouping in South Africa. Reference is still currently made in democratic South Africa to the Apartheid race categorisations in contemporary formal policies that seek to redress the inequities of the past, both in terms of race as well as gender categories (Conway-Smith, 2011; Stromquist, 1998). Given the intimate association between race and identity, especially within a socio-historical context such as that of South Africa, it is reasonable to consider the impact of this association on an individual's mental health status.

Yes / We read with interest the review written by Evans and Allen, and published in the Journal of Optometry, in July, 2016.

Thesis (M.A.)--Rhodes University, 1991. / Facsimile. "Submitted in Fulfilment of the Requirements for the Degree of MASTER OF ART of Rhodes University." Includes bibliographical references.

Modern software systems have increasingly higher expectations on their reliability, in particular if the systems are critical and real-time. The development of these complex software systems requires strong modelling and analysis methods including quantitative modelling and formal verification. Unified Modelling Language (UML) is a widely used and intuitive graphical modelling language to design complex systems, while formal models provide a theoretical support to verify system design models. However, UML models are not sufficient to guarantee correct system designs and formal models, on the other hand, are often restrictive and complex to use. It is believed that a combined approach comprising the advantages of both models can offer better designs for modern complex software development needs. This thesis focuses on the design and development of a rigorous framework based on Model Driven Development (MDD) that facilitates transformations of non-formal models into formal models for design verification. This thesis defines and describes the transformation from UML2 sequence diagrams to coloured Petri nets and proves syntactic and semantic correctness of the transformation. Additionally, we explore ways of adding information (time, probability, and hierarchy) to a design and how it can be added onto extensions of a target model. Correctness results are extended in this context. The approach in this thesis is novel and significant both in how to establish semantic and syntactic correctness of transformations, and how to explore semantic variability in the target model for formal analysis. Hence, the motivation of this thesis establishes: the UML behavioural models can be validated by correct transformation of them into formal models that can be formally analysed and verified.