The present study proposes to use a Conrad probe for transient growth study by measuring the two-dimensional velocity behind an array of roughness elements in the Blasius boundary layer. A look-up table approach is proposed to increase the accuracy of the data reduction process at low velocities, based on the results of the calibration performed in a round jet. A velocity correction method is proposed to minimize the errors due to high velocity shear and wall-proximity in the Blasius boundary layer by comparing Conrad probe results to previous hot-wire data. Measurements of the steamwise velocity perturbation obtained with the Conrad probe agree with previous studies. The measured spanwise perturbation confirms the transport process suggested by simulation. The results show that the perturbation amplitude increases by increasing both the freestream velocity and roughness elements height. However, the mechanism for changing the perturbation amplitude of influence differs for these two parameters.

The present study proposes to use a Conrad probe for transient growth study by measuring the two-dimensional velocity behind an array of roughness elements in the Blasius boundary layer. A look-up table approach is proposed to increase the accuracy of the data reduction process at low velocities, based on the results of the calibration performed in a round jet. A velocity correction method is proposed to minimize the errors due to high velocity shear and wall-proximity in the Blasius boundary layer by comparing Conrad probe results to previous hot-wire data. Measurements of the steamwise velocity perturbation obtained with the Conrad probe agree with previous studies. The measured spanwise perturbation confirms the transport process suggested by simulation. The results show that the perturbation amplitude increases by increasing both the freestream velocity and roughness elements height. However, the mechanism for changing the perturbation amplitude of influence differs for these two parameters.

Health problems of the human beings in a society are one of the main components of the social security systems due to the dimension of the financial burden it might bring on individuals, employers, insurance companies and governments. Morbidity measures, such as incidence and prevalence of a specific disease in a certain population enable researchers to estimate for individuals the probability of being diagnosed or being prone to the diseases. This information is usually not tractable because of the non-availability of the convenient data or recordings for many countries as well as Turkey. Even if it is available, it is commonly limited with largely varying characteristics about the type and coverage of the diseases. In this regard, the pattern that a population follows for an acute disease may not be the same for chronic diseases. Having those indicators determined for a group of insureds will enable underwriters to have more profitable and economical premium calculation and precision on required reserve estimation. v Based on their characteristics such as acute or chronic behaviour, the gender, and the location of residency of people, the diseases show different behaviour on their occurrences. From the insurer

L’objectif de cette thèse est de développer et de proposer de nouvellesméthodes de réduction de dimension pour la construction d’indicateurs composites dequalité de vie à l’échelle communale. La méthodologie statistique développée met l’accentsur la prise en compte de la multidimensionnalité du concept de qualité de vie, avecune attention particulière sur le traitement de la mixité des données (variables quantitativeset qualitatives) et l’introduction des conditions environnementales. Nous optonspour une approche par classification de variables et pour une méthode multi-tableaux(analyse factorielle multiple pour données mixtes). Ces deux méthodes permettent deconstruire des indicateurs composites que nous proposons comme mesure des conditionsde vie à l’échelle communale. Afin de faciliter l’interprétation des indicateurscomposites construits, une méthode de sélection de variables de type bootstrap estintroduite en analyse factorielle multiple. Enfin nous proposons la méthode hclustgeode classification d’observations qui intègre des contraintes de proximité géographiqueafin de mieux appréhender la spatialité des phénomènes mis en jeu. / The purpose of this thesis is to develop and suggest new dimensionreduction methods to construct composite indicators on a municipal scale. The developedstatistical methodology highlights the consideration of the multi-dimensionalityof the quality of life concept, with a particular attention on the treatment of mixeddata (quantitative and qualitative variables) and the introduction of environmentalconditions. We opt for a variable clustering approach and for a multi-table method(multiple factorial analysis for mixed data). These two methods allow to build compositeindicators that we propose as a measure of living conditions at the municipalscale. In order to facilitate the interpretation of the created composite indicators, weintroduce a method of selections of variables based on a bootstrap approach. Finally,we suggest the clustering of observations method, named hclustgeo, which integratesgeographical proximity constraints in the clustering procedure, in order to apprehendthe spatiality specificities better.

The results of mathematics level 3 have always been a problem at TVET colleges as this hampers the certification rate and the progress of the students to level 4. Students who did not do well in the current subject are not allowed to register that subject in the following level. Even though the students are allowed to progress to level 4 they won’t be certificated for both levels until they pass the remaining subject. The above challenges made the researcher to check during the marking and moderation of November / December examination the course of poor results for mathematics level 3. In the process of checking the researcher discovered that rectangular hyperbola is one of the topics that the students of mathematics level 3 are struggling with. This study therefore focuses on exploring the challenges faced by TVET Level 3 NCV students in understanding the hyperbolic function in mathematics. In addition to the literature review, an empirical investigation based on a qualitative approach and involving semi-structured interviews with the students of a TVET college in North West was conducted to collect data. The analysis of documents relevant to the study was also used as the other method. The study used participatory action research, where the researcher, collaborators and students work alongside each other to collect data and to improve practice and follow the spiral pattern of reflection, analysing the results and adapting the action. The research design and methodology was qualitative. This helped the researcher to understand the challenges students faced in the learning of rectangular hyperbola and also came up with ways to minimise those challenges. The data collection methods used was interviewing using semi-structured questions, pre-test and post-tests. During data collection different interventions (IN1 –IN3) was used depending on the understanding of the students. For ethical consideration, ethical clearance was obtained from UNISA. DHET, the principal of the college, collaborators, parents and students will also give written consent on forms which will be sent out explaining what we envisage. Since research was voluntary, an explanation was given that this was not compulsory and that participation was completely voluntary and that they could withdraw at any time. In this study, various methods to empower students were recommended. Recommendations are also made on what was found in this study, as are recommendations for further study. / Mathematics Education / M. Ed. (Mathematics Education)