The purpose of this paper is to investigate some of the more basic properties of peripherally continuous functions, graph maps and connectivity maps.

Although most organisations want to improve quality and reduce costs, the deployment and implementation of continuous improvement methodologies is commonly viewed as a daunting journey. Many organisations fail to properly structure and/or support continuous improvement initiatives, which ultimately doom them to failure. South African Banks are not adopting Lean and/or Six-sigma to the point where it is going to make any sort of significant difference to the bottom line over a significantly meaningful period of time. So where are they going wrong? Often it comes down to key issues that are not addressed effectively as part of the deployment. The research objectives are: • The primary objective is to establish what the mission critical success factors for Lean and/or Six-sigma implementation in South African Banking are. • The secondary objective is to define a list of the sources of benefits for Lean and/or Six-sigma implementations in South African Banking. The research questions/problems to be addressed are: • What are the mission critical success factors for Lean and/or Six-sigma implementations in South African Banking? • How do South African Banks prioritise these critical success factors? • How do South African Banks that are already on the Lean and/or Six-sigma journey perform against these critical success factors? • What are the gaps between the importance’s of the critical success factors versus the banks actual performance against these, and how is this gap impacting on the benefits that the banks are experiencing? • What sources of benefits are South African Banks experiencing? • Can generic guidelines be provided to the South African Banks for successful Lean and/or Six-sigma implementation?

Spatial facility location problems (SFLPs) involve the placement of facilities in continuous demand regions. One approach to solving SFLPs is to aggregate demand into discrete points, and then solve the point-based model as a conventional facility location problem (FLP) according to a surrogate model. Solution performance is measured in terms of the percentage of continuous space actually covered in the original SFLP. In this dissertation I explore this approach and examine factors contributing to solution quality. Three error sources are discussed: point representation spacing, multiple possible solutions to the surrogate point-based model, and round-off errors induced by the computer representation of numbers. Some factors—including boundary region surrogate points and surrogate point location—were also found to make significant contributions to coverage errors. A surrogate error measure using a point-based surrogate model was derived to characterize relationships among spacing, facility coverage area, and spatial coverage error. Locating continuous space facilities with full coverage is important but challenging. Demand surrogate points were initially used as a continuous space for constructing the MIP model, and a point-based surrogate FLP was enhanced for extracting multiple solutions with additional constraints that were found to reduce coverage error. Next, a best initial solution was applied to a proposed heuristic algorithm to serve as an improvement procedure. Algorithm performance was evaluated and applied to a problem involving the location of emergency warning sirens in the city of Dublin, Ohio. The effectiveness of the proposed method for solving this and other facility location/network design problems was demonstrated by comparing the results with those reported in recently published papers.

Cutting operations are important and commonly used operations in the field of manufacturing. Automated machining is today commonly used in CNC-machines. One common drawback with automated machining is that the tool condition is challenging to predict which leads to a conservative tool replacement times. This leads to a low utilisation of the tool economical lifetime and an unnecessary high number of tool replacements. Methods for indirect continuous monitoring of the tool wear exist but usually require retrofitting of external sensors that can be both costly and also interrupt the machine operation due to the additional wiring. It is therefore of interest to investigate the possibility to use the, often high resolution, sensors already fitted in a CNC-machine to extract valuable data that can indirectly give an estimation of the tool condition. This thesis work has, with attention to the X-, Y- and Z-position sensors, resulted in development of algorithms that show relations between tool wear and data acquired from these sensors. The algorithms operate in the frequency domain to determine changes in the dynamic response over the time of tool degradation.

Many strains of Gram-negative bacteria, such as Pseudomonas, are able to utilize a variety of unusual chemicals, including a wide range or aromatic hydrocarbons and their derivatives for growth. Bacteria with the potential to degrade sodium benzoate were isolated, identified and grown as biofilms on sodium benzoate in a laboratory-scale fluidized bed biofilm bioreactor. Four Pseudomonas strains identified as P. aeruginosa (BDS2) P. putida (BDS1 and GR1) and Burkholderia cepecia (GR3FAR) were used in a laboratory-scale FBBR together with two Bacillus strains - Bacillus macroides (SBSY4) and Bacillus simplex (MAR). Sodium benzoate biodegradation capacities of these species were compared under batch and continuous operations. Biofilm and planktonic bacterial growth dynamics were monitored by plate counts, and optical density measurements (230nm) determined benzoate biodegradation. Overall, higher attached and planktonic bacterial counts were determined under batch compared to continuous mode. In addition to this, the ability of attached cells to use sodium benzoate as their sole carbon source was compared to their suspended counterparts in a batch system. There were more attached counts compared to suspended cells and attached cells apparently degraded sodium benzoate better than planktonic cells. Similarly, higher rates of benzoate depletion were found to occur under batch compared to the continuous system. It thus appeared that more cell growth implied more substrate consumption. SEM showed attached cells and microcolonies of all the isolates on GAC, indicating their biofilmforming abilities.

Organisational change has proven to be a major challenge for many businesses worldwide with the pharmaceutical environment being no exception. The pharmaceutical industry is increasingly pressurised by stakeholders who seek reduced cost, higher value and quality. This has resulted in many pharmaceutical businesses attempting to launch various continuous improvement methodologies, which ultimately fail. Whereas failure of continuous improvement undertakings within the pharmaceutical environment is well documented, this study aimed to understand the factors that influence the successful sustainability of such endeavours. The purpose of this study was therefore to identify and create an understanding of the factors that influence a culture of continuous improvement within the pharmaceutical environment. The literature review revealed that factors such as leadership, teamwork, communication, continuous improvement capability and a continuous improvement mind-set contributed to the successful implementation of a culture that embraces continuous improvement. It was recognised that building a culture of continuous improvement is not instantaneous and that it requires all stakeholders to be committed and to acknowledge that changing culture requires time. An empirical study with a questionnaire as data collecting instrument was conducted to assess respondents’ perceptions of the levels of continuous improvement, leadership, teamwork, communication, continuous improvement capability and a continuous improvement mind-set within a selected pharmaceutical manufacturing business. The study revealed that all these factors were related and influenced a culture of continuous improvement. Furthermore, leadership and a continuous improvement mind-set proved to have the most significant relationship with a culture of continuous improvement. Recommendations were provided for the creation of a culture of continuous improvement in pharmaceutical businesses.

This project looks at using diagrammatic reasoning to prove mathematical theorems. The work is motivated by a need for theorem provers whose reasoning is readily intelligible to human beings. It should also have practical applications in mathematics teaching. We focus on the continuous domain of analysis - a geometric subject, but one which is taught using a dry algebraic formalism which many students find hard. The geometric nature of the domain makes it suitable for a diagram-based approach. However it is a difficult domain, and there are several problems, including handling alternating quantifiers, sequences and generalisation. We developed representations and reasoning methods to solve these. Our diagram logic isn't complete, but does cover a reasonable range of theorems. It utilises computers to extend diagrammatic reasoning in new directions – including using animation. This work is tested for soundness, and evaluated empirically for ease of use. We demonstrate that computerised diagrammatic theorem proving is not only possible in the domain of real analysis, but that students perform better using it than with an equivalent algebraic computer system.

A topological group is an abstract group which is also a topological space and in which the group operation are continuous. In group theory the algebraic binary operation of passage to a limit is studied in a similar manner. The two fundamental mathematical concepts of binary operation and passage to a limit are united and interrelated in the concept of topological group. The concept of topological groups arose from the study of continuous transformations. However, topological groups can be studied quite independently from continuous transformations and the latter can be presented as applications of topological groups. The first person to consider topological groups was Lie, but he was concerned with groups defined by analytic operations. Later, around 1900-1910 other men, beginning with Hilbert and Brouwer, studied more general topological groups. The topological group is then -- from a logical point of view only -- a combination of the abstract group and the topological space. Hence, the first and second chapters of this paper will be devoted to the concept of abstract group and topological space respectively, while the third and main chapter will utilize these two concepts in the formation and study of the topological group. Our main source of information will be Leon Pontrjagin's book, "Topological Groups" (1939); however, our approach will be somewhat broader and we will include results from other sources and our own investigations. In order to avoid making this paper to lengthy for its purpose, we will prove only some of the theorems. The rest of them will be simply stated and often followed by a sketch or an outline of the proof. The major definitions and theorems and all the examples will be numbered consecutively as they appear. For instance "Theorem 2.5" is the fifth numbered item in the second chapter.

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The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.