Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

The purification and characterization of the high and low molecular weight forms of rabbit intestinal adenosine deaminase

Accepted Version

Leveraging lessons learned in organizations through implementing practice-based organizational learning and performance improvement - An opportunity for context-based intelligent assistant support (CIAS)

Organizations that leverage lessons learned from their experience in the practice of complex real-world activities are faced with five difficult problems. First, how to represent the learning situation in a recognizable way. Second, how to represent what was actually done in terms of repeatable actions. Third, how to assess performance taking account of the particular circumstances. Fourth, how to abstract lessons learned that are re-usable on future occasions. Fifth, how to determine whether to pursue practice maturity or strategic relevance of activities. Here, organizational learning and performance improvement are investigated in a field study using the Context-based Intelligent Assistant Support (CIAS) approach. A new conceptual framework for practice-based organizational learning and performance improvement is presented that supports researchers and practitioners address the problems evoked and contributes to a practice-based approach to activity management. The novelty of the research lies in the simultaneous study of the different levels involved in the activity. Route selection in light rail infrastructure projects involves practices at both the strategic and operational levels; it is part managerial/political and part engineering. Aspectual comparison of practices represented in Contextual Graphs constitutes a new approach to the selection of Key Performance Indicators (KPIs). This approach is free from causality assumptions and forms the basis of a new approach to practice-based organizational learning and performance improvement. The evolution of practices in contextual graphs is shown to be an objective and measurable expression of organizational learning. This diachronic representation is interpreted using a practice-based organizational learning novelty typology. This dissertation shows how lessons learned when effectively leveraged by an organization lead to practice maturity. The practice maturity level of an activity in combination with an assessment of an activity’s strategic relevance can be used by management to prioritize improvement effort.

Crystallisation and crystal forms of carbohydrate derivatives

This thesis is focused on the synthesis and solid state analysis of carbohydrate derivatives, including many novel compounds. Although the synthetic chemistry surrounding carbohydrates is well established in the literature, the crystal chemistry of carbohydrates is less well studied. Therefore this research aims to improve understanding of the solid state properties of carbohydrate derivatives through gaining more information on their supramolecular bonding. Chapter One focuses on an introduction to the solid state of organic compounds, with a background to crystallisation, including issues that can arise during crystal growth. Chapter Two is based on glucopyranuronate derivatives which are understudied in terms of their solid state forms. This chapter reports on the formation of novel glucuronamides and utilising the functionality of the amide bond for crystallisation. TEMPO oxidation was completed to form glucopyranuronates by oxidation of the primary alcohol groups of glucosides to the carboxylic acid derivatives, to increase functionality for enhanced crystal growth. Chapter Three reports on the synthesis of glucopyranoside derivatives by O-glycosylation reactions and displays crystal structures, including a number of previously unsolved acetate protected and deprotected crystal structures. More complex glycoside derivatives were also researched in an aim to study the resultant supramolecular motifs. Chapter Four contains the synthesis of aryl cellobioside derivatives including the novel crystal structures that were solved for the acetate protected and deprotected compounds. Research was carried out to determine if 1-deoxycellodextrins could act as putative isostructures for cellulose. Our research displays the presence of isostructural references with 1-deoxycellotriose shown to be similar to cellulose III11, 1-deoxycellotetraose correlates with cellulose IV11 and 1-deoxycellopentose shows isostructurality similar to that of cellulose II. Chapter Five contains the full experimental details and spectral characterisation of all novel compounds synthesised in this project and relevant crystallographic information.

Ontological representation of design science research publications

A search result provided by existing digital library and web search systems typically comprises only a prioritised list of possible publications or web pages that meet the search criteria, possibly with excerpts and possibly with search terms highlighted. The research in progress reported in this poster contributes to a larger research effort to provide a readable summary of search results that synthesise relevant publications or web pages to provide results that meet four C’s: comprehensive, concise, coherent, and correct, as a more useful alternative to un-synthesised result lists. The scope of this research is limited to searching for and synthesising Design Science Research (DSR) publications that present the results of DSR, as an example problem domain.