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Die doel van hierdie studie van beperkte omvang is om inligting in te samel oor die probleem van dissipline soos dit manifesteer in Intermediêre Skole in die Namakwa Distrik van die Noord-Kaap Provinsie. Die aandag word toegespits op: * wetgewing met betrekking tot dissipline in skole; * soorte van probleme; * faktore wat aanleiding gee tot probleme; * maatreëls wat gebruik word om dissiplinêre probleme te hanteer en te voorkom. Deur literatuurstudie word begrip en kennis verkry wat as agtergrond dien vir die kwalitatiewe ondersoek waardeur `n kontekstuele begrip verkry word van die ervaring van dissipline en probleme deur `n geselekteerde groep skoolhoofde van Intermediêre Skole in die Namakwa Distrik van die Noord-Kaapprovinsie. Ten slotte word voorstelle gemaak met die oog op die verbetering van `n komplekse situasie. / The aim of this study on a small scale is to gather information about the problem of discipline as manifested in Intermediate Schools in the Namaqua District of the Northern Cape Province. The attention is focused on: * legislation in connection with discipline in schools; * types of problems; * factors that cause problems; * measures to cope and prevent disciplinary problems. The study of literature provides understanding and knowledge that serves as background to the qualitative study by way of which a contextual understanding is developed of the experience of discipline and specific problems by a selected group of principals of Intermediate Schools in the Namaqua District of the Northern Cape Province. In conclusion proposals are made aimed at the improvement of a complex situation. / Educational Studies / M. Ed. (Educational Management)

Summaries in English and Afrikaans / Text in Afrikaans / Key terms in English and Afrikaans / Verskeie tekortkomings is in die bestaande konseptuele model en kwantitatiewe navorsingsliteratuur oor skofwerk geidentifiseer. Ontevredenheid met die oorvereenvoudigde oorsaak-gevolg-verklarings vir getroude vroue se skofwerkervaring het in die studie gelei tot die ontwikkeling van 'n ekologiese model van vroueskofwerk. Hierdie nuwe konseptuele model weerspieel 'n altematiewe benadering waar erkenning gegee word aan die bestaan van meervoudige realiteite wat mense in konsensus deur taal konstrueer. Die oogmerk met die ekologiese model is om, met inagneming van vroueskofwerkers se wyer konteks, patrone te ondersoek van hoe die verskillende beskrywings van getroude vroue se ervaring van skofwerk bymekaar pas. Daarmee kan 'n meer sistemiese begrip verkry word wat die kompleksiteit van menslike interaksie respekteer. Die ekologiese model van vroueskofwerk is ontwikkel as 'n hulpmiddel vir die waamemer om ryk, beskrywende ekologiese verhale te kan konstrueer van hoe getroude vroue se belewing van skofwerk tot sistemiese ontwrigting of behoud kan lei. / Several shortcomings have been identified in the existing conceptual model and quantitative research literature regarding shiftwork. Dissatisfaction with the oversimplified cause-effect-explanations for married women's shiftwork experience has led to the development of an ecological model of women shiftwork in this study. This new conceptual model reflects an alternative approach where recognition is given to the existence of multiple realities which are consensually created by people through language. The aim with the ecological model, by taking into account the broader context of women shiftworkers, is to search for patterns of how the different descriptions of women's experience of shiftwork fit together. This offers a more systemic view that respects the complexity of human interaction. The ecological model for women shiftwork is developed as an aid to the observer to construct rich, descriptive ecological stories about how married women's experience of shiftwork can lead to systemic disruption or conservation. / Psychology / M.A. (Clinical Psychology)

Tikhonov-type regularization of linear and nonlinear ill-posed problems in abstract spaces under sparsity constraints gained relevant attention in the past years. Since under some weak assumptions all regularized solutions are sparse if the l1-norm is used as penalty term, the l1-regularization was studied by numerous authors although the non-reflexivity of the Banach space l1 and the fact that such penalty functional is not strictly convex lead to serious difficulties. We consider the case that the sparsity assumption is narrowly missed. This means that the solutions may have an infinite number of nonzero but fast decaying components. For that case we formulate and prove convergence rates results for the l1-regularization of nonlinear operator equations. In this context, we outline the situations of Hölder rates and of an exponential decay of the solution components.

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The present thesis considers the problem of reconstructing a function f that is defined on the d-dimensional unit sphere from its mean values along hyperplane sections. In case of the two-dimensional sphere, these plane sections are circles. In many tomographic applications, however, only limited data is available. Therefore, one is interested in the reconstruction of the function f from its mean values with respect to only some subfamily of all hyperplane sections of the sphere. Compared with the full data case, the limited data problem is more challenging and raises several questions. The first one is the injectivity, i.e., can any function be uniquely reconstructed from the available data? Further issues are the stability of the reconstruction, which is closely connected with a description of the range, as well as the demand for actual inversion methods or algorithms. We provide a detailed coverage and answers of these questions for different families of hyperplane sections of the sphere such as vertical slices, sections with hyperplanes through a common point and also incomplete great circles. Such reconstruction problems arise in various practical applications like Compton camera imaging, magnetic resonance imaging, photoacoustic tomography, Radar imaging or seismic imaging. Furthermore, we apply our findings about spherical means to the cone-beam transform and prove its singular value decomposition. / Die vorliegende Arbeit beschäftigt sich mit dem Problem der Rekonstruktion einer Funktion f, die auf der d-dimensionalen Einheitssphäre definiert ist, anhand ihrer Mittelwerte entlang von Schnitten mit Hyperebenen. Im Fall d=2 sind diese Schnitte genau die Kreise auf der Sphäre. In vielen tomografischen Anwendungen sind aber nur eingeschränkte Daten verfügbar. Deshalb besteht das Interesse an der Rekonstruktion der Funktion f nur anhand der Mittelwerte bestimmter Familien von Hyperebenen-Schnitten der Sphäre. Verglichen mit dem Fall vollständiger Daten birgt dieses Problem mehrere Herausforderungen und Fragen. Die erste ist die Injektivität, also können alle Funktionen anhand der gegebenen Daten eindeutig rekonstruiert werden? Weitere Punkte sind die die Frage nach der Stabilität der Rekonstruktion, welche eng mit einer Beschreibung der Bildmenge verbunden ist, sowie der praktische Bedarf an Rekonstruktionsmethoden und -algorithmen. Diese Arbeit gibt einen detaillierten Überblick und Antworten auf diese Fragen für verschiedene Familien von Hyperebenen-Schnitten, angefangen von vertikalen Schnitten über Schnitte mit Hyperebenen durch einen festen Punkt sowie Kreisbögen. Solche Rekonstruktionsprobleme treten in diversen Anwendungen auf wie der Bildgebung mittels Compton-Kamera, Magnetresonanztomografie, fotoakustischen Tomografie, Radar-Bildgebung sowie der Tomografie seismischer Wellen. Weiterhin nutzen wir unsere Ergebnisse über sphärische Mittelwerte, um eine Singulärwertzerlegung für die Kegelstrahltomografie zu zeigen.

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Afrikaans text / Die afname in dissipline en dissipline handhawing in skole is 'n omvangryke probleem. Die fokus van hierdie studie is om die aard en omvang van dissiplinêre probleme te ondersoek om sodoende riglyne daar te stel om konstruktiewe dissipline in klaskamers te vestig as 'n sleutel taak van die onderwyser. In hierdie studie maak die navorser gebruik van die gekombineerde benaderingsmetode, naamlik die kwalitatiewe-kwantitatiewe navorsingsmetode. Vraelyste (kwantitatief) en onderhoude (kwalitatief) is as data insamelingstegnieke gebruik om vas te stel wat die aard, omvang en moontlike oplossings is, vir die navorsingsprobleem. Die navorsingstudie is gedoen deur 106 onderwysers in die intermediêre- en senior fase van ses laerskole van die Noordweste van Pretoria te betrek. Daar is ook onderhoude gevoer met ses senior onderwysers wat in beheer was van hul skole se dissiplinêre stelsels. Die navorsingstudie het bevind dat onderwysers, leerders en ouers bydraend is tot dissiplinêre probleme in klaskamers. Positiewe strategieë sluit in kommunikasie en toepassing van klasreëls. Uit die bevindinge van die navorsing is daar ongetwyfeld 'n sterk behoefte aan leiding vir onderwysers om dissiplinêre probleme aan te spreek. Onderwysers moet bemagtig word om konstruktiewe dissipline te ontwikkel, te bevorder en te handhaaf. / The decline in discipline and discipline enforcement in schools is a massive problem. The focus of this study is to examine the nature and extent of discipline problems in order to set guidelines to establish constructive discipline in the classroom as a key task of the teacher. In this study, the researcher makes use of the combined approach method, namely the qualitative - quantitative research methodology. Questionnaires (quantitative) and interviews (qualitative) were used as data collection techniques to determine the nature, extent and The research study was conducted by involving 106 teachers in the intermediate and senior phase of six primary schools of the North West of Pretoria. There were also interviews with six senior teachers who were in charge of their schools' disciplinary systems. The research study found that teachers, pupils and parents are contributing factors to discipline problems in classrooms. Positive strategies include communication and application of rules. From the findings of the research there is undoubtedly a strong need for guidance for teachers to address disciplinary problems. Teachers should be empowered to develop positive, promote, and maintain constructive discipline in the classroom. possible solutions of the research problem. / Educational Management and Leadership / M. Ed. (Education Management)

Infimalfolgen nichtkonvexer Variationsprobleme haben aufgrund feiner Oszillationen häufig keinen starken Grenzwert in Sobolevräumen. Diese Oszillationen haben eine physikalische Bedeutung; Finite-Element-Approximationen können sie jedoch im Allgemeinen nicht auflösen. Relaxationsmethoden ersetzen die nichtkonvexe Energie durch ihre (semi)konvexe Hülle. Das entstehende makroskopische Modell ist degeneriert: es ist nicht strikt konvex und hat eventuell mehrere Minimalstellen. Die fehlende Kontrolle der primalen Variablen führt zu Schwierigkeiten bei der a priori und a posteriori Fehlerschätzung, wie der Zuverlässigkeits- Effizienz-Lücke und fehlender starker Konvergenz. Zur Überwindung dieser Schwierigkeiten erweitern Stabilisierungstechniken die relaxierte Energie um einen diskreten, positiv definiten Term. Bartels et al. (IFB, 2004) wenden Stabilisierung auf zweidimensionale Probleme an und beweisen dabei starke Konvergenz der Gradienten. Dieses Ergebnis ist auf glatte Lösungen und quasi-uniforme Netze beschränkt, was adaptive Netzverfeinerungen ausschließt. Die vorliegende Arbeit behandelt einen modifizierten Stabilisierungsterm und beweist auf unstrukturierten Netzen sowohl Konvergenz der Spannungstensoren, als auch starke Konvergenz der Gradienten für glatte Lösungen. Ferner wird der sogenannte Fluss-Fehlerschätzer hergeleitet und dessen Zuverlässigkeit und Effizienz gezeigt. Für Interface-Probleme mit stückweise glatter Lösung wird eine Verfeinerung des Fehlerschätzers entwickelt, die den Fehler der primalen Variablen und ihres Gradienten beschränkt und so starke Konvergenz der Gradienten sichert. Der verfeinerte Fehlerschätzer konvergiert schneller als der Fluss- Fehlerschätzer, und verringert so die Zuverlässigkeits-Effizienz-Lücke. Numerische Experimente mit fünf Benchmark-Tests der Mikrostruktursimulation und Topologieoptimierung ergänzen und bestätigen die theoretischen Ergebnisse. / Infimising sequences of nonconvex variational problems often do not converge strongly in Sobolev spaces due to fine oscillations. These oscillations are physically meaningful; finite element approximations, however, fail to resolve them in general. Relaxation methods replace the nonconvex energy with its (semi)convex hull. This leads to a macroscopic model which is degenerate in the sense that it is not strictly convex and possibly admits multiple minimisers. The lack of control on the primal variable leads to difficulties in the a priori and a posteriori finite element error analysis, such as the reliability-efficiency gap and no strong convergence. To overcome these difficulties, stabilisation techniques add a discrete positive definite term to the relaxed energy. Bartels et al. (IFB, 2004) apply stabilisation to two-dimensional problems and thereby prove strong convergence of gradients. This result is restricted to smooth solutions and quasi-uniform meshes, which prohibit adaptive mesh refinements. This thesis concerns a modified stabilisation term and proves convergence of the stress and, for smooth solutions, strong convergence of gradients, even on unstructured meshes. Furthermore, the thesis derives the so-called flux error estimator and proves its reliability and efficiency. For interface problems with piecewise smooth solutions, a refined version of this error estimator is developed, which provides control of the error of the primal variable and its gradient and thus yields strong convergence of gradients. The refined error estimator converges faster than the flux error estimator and therefore narrows the reliability-efficiency gap. Numerical experiments with five benchmark examples from computational microstructure and topology optimisation complement and confirm the theoretical results.

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