This research project concerns itself with the three disputed passages of Christian import as preserved in extant manuscripts of the AJ (Ἰουδαϊκὴ Ἀρχαιολογία a.k.a. Antiquitates Judaicae), viz.: AJ, XVIII, 3, 3 / 63 (i.e. the so-called Testimonium Flavianum), AJ, XVIII, 5, 2 / 116 -119 (i.e. the references to John the Baptist) and AJ, XX, 9, 1 / 200 - 203 (i.e. the references to James the brother of Jesus). Within the context of contemporary historicity research outcomes, and employing an interpretist/constructivist episteme, a series of critical analyses was undertaken aimed at verifying to what degree the three passages in question may be deemed to be in any way authentic and/or historically reliable. The result of the investigation proves beyond reasonable doubt that no reliable extra-biblical/scriptural accounts exist to support the historical existence of, inter alia, Jesus of Nazareth, James the Just or John the Baptist. Certainly, no such accounts ever appeared in Josephus’ original texts. Furthermore, and most importantly, the three passages are confirmed to be total forgeries initiated in the first four centuries of the Common Era most likely by Origen and Eusebius respectively. / PhD (Greek), North-West University, Potchefstroom Campus, 2015

In the journey toward optimal spectrum usage, techniques and concepts such as Cognitive Radio and Dynamic Spectrum Access have enjoyed increasing attention in many research projects. Dynamic Spectrum Access introduces the need for real-time RF spectrum information in the form of Radio Environment Maps. This need motivates an investigation into a hybrid approach of sample measurements and spatial interpolation as opposed to using conventional propagation models. Conventional propagation models, both path-general and path-specific, require information of transmitters within the area of interest. Irregular Terrain Models such as the Longley-Rice model, further require topographic information in order to consider the effects of obstacles. The proposed spatial interpolation technique, kriging, requires no information regarding transmitters. Furthermore, Ordinary Kriging requires nothing other than measured samples whereas other kriging variants such as Universal Kriging and Regression Kriging can use additional information such as topographic data to aid in prediction accuracy. This dissertation investigates the performance of the three aforementioned kriging variants in producing Radio Environment Maps of received power. For practical and financial reasons, the received power measurement samples are generated using the Longley-Rice Irregular Terrain Model and are, therefore, simulated measurements. The experimental results indicate that kriging shows great promise as a tool to generate Radio Environment Maps. It is found that Ordinary Kriging produces the most accurate predictions of the three kriging methods and that prediction errors of less than 10 dB can be achieved even when using very low sampling densities. / MSc (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

This research project concerns itself with the three disputed passages of Christian import as preserved in extant manuscripts of the AJ (Ἰουδαϊκὴ Ἀρχαιολογία a.k.a. Antiquitates Judaicae), viz.: AJ, XVIII, 3, 3 / 63 (i.e. the so-called Testimonium Flavianum), AJ, XVIII, 5, 2 / 116 -119 (i.e. the references to John the Baptist) and AJ, XX, 9, 1 / 200 - 203 (i.e. the references to James the brother of Jesus). Within the context of contemporary historicity research outcomes, and employing an interpretist/constructivist episteme, a series of critical analyses was undertaken aimed at verifying to what degree the three passages in question may be deemed to be in any way authentic and/or historically reliable. The result of the investigation proves beyond reasonable doubt that no reliable extra-biblical/scriptural accounts exist to support the historical existence of, inter alia, Jesus of Nazareth, James the Just or John the Baptist. Certainly, no such accounts ever appeared in Josephus’ original texts. Furthermore, and most importantly, the three passages are confirmed to be total forgeries initiated in the first four centuries of the Common Era most likely by Origen and Eusebius respectively. / PhD (Greek), North-West University, Potchefstroom Campus, 2015

In the journey toward optimal spectrum usage, techniques and concepts such as Cognitive Radio and Dynamic Spectrum Access have enjoyed increasing attention in many research projects. Dynamic Spectrum Access introduces the need for real-time RF spectrum information in the form of Radio Environment Maps. This need motivates an investigation into a hybrid approach of sample measurements and spatial interpolation as opposed to using conventional propagation models. Conventional propagation models, both path-general and path-specific, require information of transmitters within the area of interest. Irregular Terrain Models such as the Longley-Rice model, further require topographic information in order to consider the effects of obstacles. The proposed spatial interpolation technique, kriging, requires no information regarding transmitters. Furthermore, Ordinary Kriging requires nothing other than measured samples whereas other kriging variants such as Universal Kriging and Regression Kriging can use additional information such as topographic data to aid in prediction accuracy. This dissertation investigates the performance of the three aforementioned kriging variants in producing Radio Environment Maps of received power. For practical and financial reasons, the received power measurement samples are generated using the Longley-Rice Irregular Terrain Model and are, therefore, simulated measurements. The experimental results indicate that kriging shows great promise as a tool to generate Radio Environment Maps. It is found that Ordinary Kriging produces the most accurate predictions of the three kriging methods and that prediction errors of less than 10 dB can be achieved even when using very low sampling densities. / MSc (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

The field of wireless communication is under massive development and the demands on the cellular system, especially, are constantly increasing as the utilizing devices are increasing in number and diversity. A key component of wireless communication is the knowledge of the channel, i.e, how the signal is affected when sent over the wireless medium. Channel prediction is one concept which can improve current techniques or enable new ones in order to increase the performance of the cellular system. Firstly, this report will investigate the concept of a predictor antenna on new, extensive measurements which represent many different environments and scenarios. A predictor antenna is a separate antenna that is placed in front of the main antenna on the roof of a vehicle. The predictor antenna could enable good channel prediction for high velocity vehicles. The measurements show to be too noisy to be used directly in the predictor antenna concept but show potential if the measurements can be noise-filtered without distorting the signal. The use of low-pass filter and Kalman filter to do this, did not give the desired results but the technique to do this should be further investigated. Secondly, a interpolation technique will be presented which utilizes predictions with different prediction horizon by estimating intermediate channel components using interpolation. This could save channel feedback resources as well as give a better robustness to bad channel predictions by letting fresh, local, channel predictions be used as quality reference of the interpolated channel estimates. For a linear interpolation between 8-step and 18-step Kalman predictions with Normalized Mean Square Error (NMSE) of -15.02 dB and -10.88 dB, the interpolated estimates had an average NMSE of -13.14 dB, while lowering the required feedback data by about 80 %. The use of a warning algorithm reduced the NMSE by a further 0.2 dB. It mainly eliminated the largest prediction error which otherwise could lead to retransmission, which is not desired.

Résumé: Tel que le notent si bien Oliver et al. (1990), la plupart des méthodes d’interpolation classiques sont basées sur les modèles des méthodes numériques différents des modèles probabilistes de variation spatiale. Les distributions des variables des données spatiales se comportent plus comme des variables aléatoires et la théorie des variables régionalisées comporte un ensemble de méthodes stochastiques pour les analyser. Le krigeage et le cokrigeage, basés sur cette théorie, expriment les variations spatiales de variables en termes de variogrammes et ils minimisent les erreurs de prédiction qui sont elles-mêmes estimées. Appliquées aux données des variables pédologiques des champs de la Station de recherches de Lennoxville, les méthodes ou techniques d’interpolation de la géostatistique: les krigeages et cokrigeages ordinaires, universels et par bloc, ainsi dénommées, sont explorées et comparées en vue d’en identifier la méthode appropriée intégrable dans un système d’information géographique, pour obtenir l’optimum de la modélisation, la présentation et celui de l’analyse spatiale. Les valeurs krigées et cokrigées des techniques choisies sont obtenues à l’aide de l’algorithme Cokri (Marcotte, 1991, 1993) et sont comparées aux valeurs initiales dont elles en sont les estimations. Des tests de similarité appliqués à ces données et résultats attestent la similarité de leurs distributions respectives. En d’autres termes, les types de krigeage et de cokrigeage examinés bénéficient de la même homogénéité des données qui est vérifiée par des outils de comparaison visuels et des traitements géostatistiques. De plus l’utilisation de ces méthodes donne des erreurs minimes proches de la réalité. Ainsi, selon la nature spécifique des données spatiales, en l’occurence les données homogènes sans structure spatiale particulière cachée, un estimateur linéaire simple ou la moyenne arithmétique de ces données, suffit pour représenter les variables étudiées.||Abstract: As Oliver et al. (1990) pointed it out so well, most of iraditional methods of interpolation are based on numerical method models as distinct from stochastic models of spatial variation. Spatially distributed data behave more like random variables, however, and regionalized variable theory provides a set of stochastic methods for analyzing them. Kriging and cokriging, based on that theory, depend on expressing spatial variation of the property in terms of variograms, and they minimize the prediction erros which are themselves estimated. Used on pedological parameters data, oridinary, universai and block krigings and cokrigings, geostatistical interpolation methods or techniques, are expiored and compared in order to identify the appropriate method which can be integrated into a Geographic Information System to provide optimum modelting, presentation and spatial analysis. Kriged and cokriged values are obtained by Cokri algorithm (Marcotte, 1991, 1993), and are compared to estimated initial data. Similarity tests applied to these data and values show that their respective distributions are similar. In othe words, the examined kriging and cokriging types perfom equally well. They ail take advantage of the data homogeneity, verified by visual comparison and geostatiatical tools or techniques, for providing doser minimum error terms. Thus, according to the special nature of spatial data, namely the homogeneous ones without a hiden particular spatial structure, a simple linear estimator, such as the data arithmetical mean, is sufficient for representing die variables under consideration.

Computational fluid dynamics has progressed to the point where it is now possible to simulate flows with large eddy turbulence, free surfaces and other complex features. However, the success of these models often depends on the accuracy of the advection scheme supporting them. Two such schemes are the constrained interpolation profile method (CIP) and the interpolated differential operator method (IDO). They share the same space discretisation but differ in their respectively semi-Lagrangian and Eulerian formulations. They both belong to a family of high-order, compact methods referred to as the multi-moment methods. In the absence of sufficient information in the literature, this thesis begins by taxonomising various multi-moment space discretisations and appraising their linear advective properties. In one dimension it is found that the CIP/IDO with order (2N -1) has an identical spectrum and memory cost to the Nth order discontinuous Galerkin method. Tests confirm that convergence rates are consistent with nominal orders of accuracy, suggesting that CIP/IDO is a better choice for smooth propagation problems. In two dimensions, six Cartesian multi-moment schemes of third order are compared using both spectral analysis and time-domain testing. Three of these schemes economise on the number of moments that need to be stored, with one CIP/IDO variant showing improved isotropy, another failing to maintain its nominal order of accuracy, and one of the conservative variants having eigenvalues with positive real parts: it is stable only in a semi-Lagrangian formulation. These findings should help researchers who are interested in using multi-moment schemes in their solvers but are unsure as to which are suitable. The thesis then addresses the question as to whether a multi-moment method could be implemented on a Cartesian cut cell grid. Such grids are attractive for supporting arbitrary, possibly moving boundaries with minimal grid regeneration. A pair of novel conservative fourth order schemes is proposed. The first scheme, occupying the Cartesian interior, has unprecedented low memory cost and is proven to be conditionally stable. The second, occupying the cut cells, involves a profile reconstruction that is guaranteed to be well-behaved for any shape of cell. However, analysis of the second scheme in a simple grid arrangement reveals positive real parts, so it is not stable in an Eulerian formulation. Stability in a hybrid formulation remains open to question.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: See full text / AFRIKAANSE OPSOMMING: Sien volteks

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Cette thèse se place dans le cadre des expériences simulées auxquelles on a recours lorsque des expériences physiques ne sont pas réalisables. Une expérience simulée consiste à évaluer une fonction déterministe type boîte-noire coûteuse qui décrit un modèle physique. Les entrées de ce modèle, entachées d'incertitude, forment un vecteur aléatoire. Cela implique que les sorties que nous souhaitons étudier sont aléatoires. Une technique standard pour rendre possibles de nombreux traitements statistiques, est de remplacer la fonction type boîte-noire par un métamodèle d'évaluation quasi-instantanée l'approchant. Nous nous concentrons plus particulièrement sur les métamodèles d'interpolateurs à noyaux dont nous étudions la construction et l'utilisation. Dans ce cadre, une première contribution est la proposition d'une définition plus générale de noyau conditionnellement positif qui permet une vraie généralisation du concept de noyau défini positif et des théorèmes associés. Nous donnons ensuite, dans une deuxième contribution, un algorithme de construction de plans d'expérience dans des domaines éventuellement non hypercubiques suivant un critère maximin pertinent pour ces métamodèles. Dans une troisième contribution, nous traitons un problème statistique inverse en utilisant un métamodèle d'interpolateurs à noyaux dans un algorithme stochastique EM puisque le modèle liant les entrées aux sorties est de type boîte-noire coûteux. Enfin, nous proposons aussi, dans la dernière contribution, l'utilisation d'un tel métamodèle pour développer deux stratégies d'estimation et de majoration de probabilités d'événements rares dépen\-dant d'une fonction type boîte-noire coûteuse.