This thesis is an account of our study of two branches of dynamical systems theory, namely the mean and pointwise ergodic theory. In our work on mean ergodic theorems, we investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space generated by measures on the group. We apply these results to derive general Tauberian theorems that apply to arbitrary locally compact abelian groups acting on a large class of locally convex vector spaces which includes Fr echet spaces. We show how these theorems simplify the derivation of Mean Ergodic theorems. Next we turn to the topic of pointwise ergodic theorems. We analyse the Transfer Principle, which is used to generate weak type maximal inequalities for ergodic operators, and extend it to the general case of -compact locally compact Hausdor groups acting measure-preservingly on - nite measure spaces. We show how the techniques developed here generate various weak type maximal inequalities on di erent Banach function spaces, and how the properties of these function spaces in- uence the weak type inequalities that can be obtained. Finally, we demonstrate how the techniques developed imply almost sure pointwise convergence of a wide class of ergodic averages. Our investigations of these two parts of ergodic theory are uni ed by the techniques used - locally convex vector spaces, harmonic analysis, measure theory - and by the strong interaction of the nal results, which are obtained in greater generality than hitherto achieved. / PhD (Mathematics), North-West University, Potchefstroom Campus, 2014

This thesis is an account of our study of two branches of dynamical systems theory, namely the mean and pointwise ergodic theory. In our work on mean ergodic theorems, we investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space generated by measures on the group. We apply these results to derive general Tauberian theorems that apply to arbitrary locally compact abelian groups acting on a large class of locally convex vector spaces which includes Fr echet spaces. We show how these theorems simplify the derivation of Mean Ergodic theorems. Next we turn to the topic of pointwise ergodic theorems. We analyse the Transfer Principle, which is used to generate weak type maximal inequalities for ergodic operators, and extend it to the general case of -compact locally compact Hausdor groups acting measure-preservingly on - nite measure spaces. We show how the techniques developed here generate various weak type maximal inequalities on di erent Banach function spaces, and how the properties of these function spaces in- uence the weak type inequalities that can be obtained. Finally, we demonstrate how the techniques developed imply almost sure pointwise convergence of a wide class of ergodic averages. Our investigations of these two parts of ergodic theory are uni ed by the techniques used - locally convex vector spaces, harmonic analysis, measure theory - and by the strong interaction of the nal results, which are obtained in greater generality than hitherto achieved. / PhD (Mathematics), North-West University, Potchefstroom Campus, 2014

The aim of the study was to investigate participants’ views on strategies for combating corruption in Zimbabwean public secondary schools with a view to promoting learner academic achievement. The study was undertaken at four (4) selected public secondary schools in Harare Metropolitan Province in Zimbabwe. The study adopted the case study as the principal research design and it was informed by the interpretive paradigm; thus, qualitative research approaches were used. Non-probability and probability sampling techniques were adopted in site and participants’ selection. A representative sample of fifty-four (54) participants was used from a target population of three-hundred and eighteen (318) participants. The study was informed by multiple theories. The study found that most of the participants perceived corruption as a major problem affecting the education of learners in most public secondary schools in Zimbabwe. It was found out that the adoption of a vibrant and robust anti-corruption strategy is the solution/panacea to solve this problem of rampant corrupt practices in educational institutions. The introduction of anti-corruption education in public secondary schools was singled out to be the ‘pivotal’ strategy that policy makers should adopt to disseminate educative anti-corruption information to learners. It was further established that the ‘Zero Tolerance to Corruption’ policy employed by the Government of Zimbabwe should be strongly supported by a multi-agency response to effectively combat corruption within the education system to propel sustainable learner academic achievement. The study findings further revealed that the public secondary schools lack the necessary anticipated formal anti-corruption education curriculum. The study concludes that anti-corruption education and the adoption of multi-strategies play a central role in combating corruption. Therefore, there is need to strengthen the anti-corruption strategies and support mechanisms currently being employed in Zimbabwe to successfully provide an environment that supports sustainable learner academic achievement. In line with the above, the study recommends the introduction of a formal anti-corruption curriculum in Zimbabwean public secondary schools to combat corruption. In addition, the study recommends further research in this seemingly grey area to contribute to the knowledge body regarding instituting good corporate governance in public secondary schools in Zimbabwe. / Die doel van die studie was om deelnemers se menings oor strategieë te ondersoek vir die bestryding van korrupsie in Zimbabwiese openbare sekondêre skole met die oog om leerders se akademiese prestasie se bevorder. Die studie is by vier (4) uitgesoekte openbare sekondêre skole in die Harare Metropolitaanse Provinsie in Zimbabwe onderneem. Die studie het die gevallestudie as die hoofnavorsingsontwerp geneem en dit is gevorm deur die vertolkende paradigma; kwalitatiewe navorsingsbenaderings is dus gebruik. Niewaarskynlikheid- en waarskynlikheidsteekproefnemingtegnieke is gebruik vir ligging en keuse van deelnemers. 'n Verteenwoordigende steekproef van vier-en-vyftig (54) deelnemers is gebruik uit 'n teikenpopulasie van drie-honderd-en-agtien (318) deelnemers. Die studie is gevorm deur verskeie teorieë. Die studie het bevind dat meeste van die deelnemers korrupsie as 'n groot probleem sien wat die onderrig van leerders in die meeste openbare sekondêre skole in Zimbabwe beïnvloed. Daar is bevind dat die gebruik van 'n dinamiese en robuuste teenkorrupsiestrategie die oplossing/kuur is om hierdie probleem van toenemende korrupsiepraktyke in opvoedkundige instellings op te los. Die inleiding tot teenkorrupsie-onderrig in openbare sekondêre skole is uitgesonder as die vernaamste strategie wat beleidmakers moet aanvaar om opvoedkundige teenkorrupsie-inligting onder leerders te versprei. Daar is verder bevind dat die Zimbabwiese regering se 'Zero Tolerance to Corruption'-beleid sterk ondersteun moet word deur reaksie van verskeie agente om korrupsie in die onderwysstelsel doeltreffend te beveg om leerders se volhoubare akademiese prestasie aan te dryf. Die studie se bevindings het verder getoon dat openbare sekondêre skole nie die noodsaaklike verwagte formele teenkorrupsie onderwyskurrikulum het nie. Die studie het tot die gevolgtrekking gekom dat teenkorrupsie-onderrig en die gebruik van verskeie strategieë 'n sentrale rol speel om korrupsie te beveg. Teenkorrupsiestrategieë en ondersteuningsmeganismes wat tans in Zimbabwe gebruik word, moet dus versterk word om 'n omgewing te skep wat volhoubare akademiese prestasie vir leerders ondersteun. Ooreenkomstig hiermee, beveel die studie die bekendstelling van 'n formele teenkorrupsiekurrikulum in Zimbabwiese openbare sekondêre skole aan om korrupsie te beveg. Die studie beveel verdere navorsing in hierdie oënskynlike grys area aan om tot die kennis van goeie korporatiewe beheer in openbare sekondêre skole in Zimbabwe by te dra. / Inhloso yocwaningo ukuphenyisisa ngemibono yababambi-qhaza ngamasu okulwa nenkohlakalo kwezezimali ezikoleni zikahulumeni zamasekondari eZimbabwe ngombono wokuqhubela phambili ukuphumelela kwabafundi kwezemfundo. Ucwaningo lwenziwe ezikoleni zamasekondari zikahulumeni ezingu 4 ezikhethwe endaweni yedolobhakazi leprovinsi, leHarare iHarare Metropolititan Province eZimbabwe. Ucwaningo lusebenzise i-case study njengedizayini enkulu yocwaningo, kanti futhi lwasekelwa ngulwazi ngenqubo ye-interpretive paradigm; ngakho-ke kusetshenziswe inkambiso ye-qualitative research kucwaningo. Kusetshenziswe amathekniki amasampuli e-non probability kanye ne-probability ezindaweni lapho okukhethwe khona ababambi-qhaza. Kusetshenziswe amasampuli angamashumi amahlanu nane (54) ababambi-qhaza, kwisibalo sethagethi yabantu abangamakhulu amathathu neshumi nesishagalombili (318). Ucwaningo lusekelwe ngamathiyori amaningana. Ucwaningo luthole ukuthi ababambi-qhaza babone inkohlakalo kwezezimali njengenkinga enkulu enomthelela kwimfundo yabafundi ezikoleni zikahulumeni zamasekondari eZimbabwe. Kutholakale ukuthi ukwamukelwa kwesu eliphambili nelinomdlandla lokulwa nenkohlakalo, yisixazululo/ikhambi lokuxazulula le nkinga yenkohlakalo kwezezimali kwizikhungo zemfundo. Ukusungulwa kwenqubo yokulwa nenkohlakalo kwizikole zesekondari zemfundo kahulumeni yisu eliphambili abenzi bomgomo okumele balemukele ukusabalalisa kubafundi ulwazi lokufundisa nokulwa nenkohlakalo. Kuphinde futhi kwatholakala nokuthi umgomo wokungabekezeli neze inkohlakalo ngesaga esithi 'Zero Tolerance to Corruption' nguHulumeni weZimbabwe kumele usekelwe zikhungo ezehlukene ukuze kube nempumelelo ekulweni nenkohlakalo kwinqubo yemfundo, ukuze abafundi bakwazi ukuphumelela ezifundweni zabo. Ucwaningo luveze nokuthi, izikole zesekondari azinayo ikharikhyulamu ehleliwe yokulwa nenkohlakalo kwimfundo. Ucwaningo luphetha ngokuthi imfundo yokulwa nenkohlakalo kanye nokwamukelwa kwamasu amaningana kudlala indima ebalulekile ekulweni nenkohlakalo. Ngakho-ke, kunesidingo sokuqinisa amasu okulwa nenkohlakalo kanye nezindlela zokusekela ezisetshenziswa okwamanje eZimbabwe ukusekela ukuthi kube nesimo esisekela impumelelo yabafundi kwezemfundo. Ngokuhambisana nokungenhla, ucwaningo luncoma ukuthi kusungulwe ikharikhyulamu ehleliwe yokulwa nenkohlakalo ezikoleni zamasekondari zikahulumeni eZimbabwe, ukulwa nenkohlakalo. Kanti futhi nangaphezu kwalokho, ucwaningo luncoma ukuthi kwenziwe olunye ucwaningo kulo mkhakha ongacacile kahle ukungezela ulwazi maqondana nenqubo yokuphatha kahle ezikoleni zikahulumeni zamasekondari eZimbabwe. / Educational Foundations / D. Phil. (Sociology of Education)