In this thesis, I have explored the different approaches towards proving Artin's `primitive root' conjecture unconditionally and the elliptic curve analogue of the same. This conjecture was posed by E. Artin in the year 1927, and it still remains an open problem. In 1967, C. Hooley proved the conjecture based on the assumption of the generalized Riemann hypothesis. Thereafter, the mathematicians tried to get rid of the assumption and it seemed quite a daunting task. In 1983, the pioneering attempt was made by R. Gupta and M. Ram Murty, who proved unconditionally that there exists a specific set of 13 distinct numbers such that for at least one of them, the conjecture is true. Along the same line, using sieve theory, D. R. Heath-Brown reduced this set down to 3 distinct primes in the year 1986. This is the best unconditional result we have so far. In the first part of this thesis, we will review the sieve theoretic approach taken by Gupta-Murty and Heath-Brown. The second half of the thesis will deal with the elliptic curve analogue of the Artin's conjecture, which is also known as the Lang-Trotter conjecture. Lang and Trotter proposed the elliptic curve analogue in 1977, including the higher rank version, and also proceeded to set up the mathematical formulation to prove the same. The analogue conjecture was proved by Gupta and Murty in the year 1986, assuming the generalized Riemann hypothesis, for curves with complex multiplication. They also proved the higher rank version of the same. We will discuss their proof in details, involving the sieve theoretic approach in the elliptic curve setup. Finally, I will conclude the thesis with a refinement proposed by Gupta and Murty to find out a finite set of points on the curve such that at least one satisfies the conjecture.

Web Service technology is one of the most rapidly developing contemporary technologies. Nowadays, Web Services are being used by a large number of projects and academic studies all over the world. As the use of Web service technology is increasing, it becomes harder to find the most suitable web service which meets the Quality of Service (QoS) as well as functional requirements of the user. In addition, quality of the web services (QoS) that take part in the software system becomes very important. In this thesis, we develop a method to track the QoS primitives of Web Services and an algorithm to automatically calculate QoS values for Web Services. The proposed method is realized within a domain specific web service discovery system, namely DSWSD-S, Domain Specific Web Service Discovery with Semantics. This system searches the Internet and finds web services that are related to a domain and calculates QoS values through some parameters. When a web service is queried, our system returns suitable web services with their QoS values. How to calculate, keep track of and store QoS values constitute the main part of this study.

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Nous avons étudié le transfert de chaleur et de matière au cours de l'histoire de la Terre primitive à de multiples échelles en utilisant des modèles numériques. Deux systèmes différents sont abordés. Tout d'abord, nous nous concentrons sur les premiers stades de la formation du noyau terrestre lorsque le fer se sépare des silicates et descend vers l'intérieur de la planète. Au cours de la différenciation, des interactions chimiques et thermiques se produisent entre les gouttes de fer dispersées dans des silicates fondus formant un océan de magma. Nous étudions le transport chimique des éléments traces à l'intérieur et autour des gouttes. Nous tirons quelques relations fonctionnelles dépendante du régime dynamique d'écoulement et montrons que le système tend à être en équilibre chimique extrêmement rapidement par rapport à l'échelle de temps de la descente de la goutte de fer. Peu de temps après la fin de l'accrétion de la Terre, la fusion extensive de son intérieur profond ainsi que la formation d'un océan de magma en surface a lieu. Comme le rayonnement de la chaleur dans l'espace est très efficace, les silicates fondus superficiels cristallisent très rapidement. L'histoire thermique de la couche liquide enterrée, appelée océan de magma basal (OMB), se déroule sur une longue période de temps et il est proposé que ses restes soient aujourd'hui observables sous forme de poches partiellement fondues au dessus de frontière noyau-manteau. Nous déterminons les paramètres régissant un système convectif dans lequel se produit une transition solide/liquide. Les lois d'échelle ainsi obtenues ont été appliquées à l'OMB et indiquent que la différence de température qui peut être maintenue dans les couches limites supérieure et inférieure de l'OMB est infime. Par conséquent, la température du noyau suit la température de liquidus à la base du manteau et ainsi la vitesse de refroidissement de l'OMB doit être la même que celle du noyau de la Terre.

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This research aimed to undertake an investigation into the question of whether after divorce, in the matrilineal customary law marriage in Malawi, women's rights are severely violated. The study showed causes of divorce, how proceedings are done, how issues of property are handled, how the issue of custody of children and maintenance are also handled. All this was weighed against the constitutional provisions and international law.

Rather than the expression of mystical Je^ire tor unity with God, Ignatius' letters are interpreted (using Weber's charismatic type) as the efforts of an 3 ut ho r-ity using his extraordinary position to protect communities from divisive house-church meetings. Protection from false teaching was initiated by reinforcing the position of bishops (the hosts of the common euchanstic assembly).

This dissertation seeks to examine and analyse the healing practices within JMC in relation to health care provided to women during pregnancy. The healing practice performed in this church has made the church become popular and grow numerically. This is also exacerbated by the high cost of medical care in Zimbabwe which is a challenge especially for pregnant women. This is an empirical study which used in-depth interviews with both men and women who are married and are long serving members of JMC. The objective of the study was to find out how the healing practice within JMC contributes to women’s health during pregnancy. The study found out that; one of the teachings of this church is that members are not allowed to seek for medical help from the hospitals. Therefore women who are pregnant are supposed to receive health services only from the church. This is done in form of prayers, prophecy and use of symbols which are directed towards the protection of the mother and child from evil that is perceived to attack them during this period. The church also provides teachings to these mothers to be on how to look after themselves through the use of elderly women who act as birth attendants. The study also found out that some women decided to also seek other forms of medication like visiting hospitals despite the consequences that were put up by the leaders of the church. This study does not claim that religion cannot help women during pregnancy but rather seeks to show that while the church focuses on spiritual healing, there is also a need for a holistic approach to healing that will call on women to visit hospitals, especially when addressing issues relating to pregnancy. / Thesis (M.Th.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Cette thèse porte sur l'étude des atmosphères de Titan et de la Terre primitive avec des modèles de circulation générale (GCM). Tout d'abord, j'ai analysé la structure thermique et la dynamique de la basse troposphère de Titan. Cette étude a abouti à une caractérisation complète de la couche limite et a révélé l'existence d'une circulation de couche limite, qui impacte tous les aspects de la météorologie titanienne (régimes de vents, ondes, formation des dunes et des nuages, échanges de moment cinétique et superrotation). A partir de cette analyse, j'ai proposé une nouvelle hypothèse pour expliquer l'orientation vers l'est des dunes de Titan grâce à un couplage entre les orages tropicaux et la superrotation. Ceci a été validé par des simulations méso-échelles et a permis de proposer un schéma global expliquant la formation des dunes et leurs différentes caractéristiques. J'ai ensuite participé au développement d'un GCM générique, conçu pour étudier tout type d'atmosphère. Je l'ai appliqué aux paléoclimats de Titan pour simuler une période où l'atmosphère a pu être dépourvue de méthane. Dans ce cas, le climat devait être différent d'aujourd'hui avec potentiellement des conséquences géologiques fondamentales notamment pour l'érosion et l'âge de la surface. Finalement, j'ai appliqué ce GCM générique au cas de la Terre primitive. J'ai montré que, malgré un soleil moins lumineux qu'aujourd'hui et des quantités de gaz à effet de serre contraintes par les archives minéralogiques, le climat de la Terre Archéenne a pu être tempérée. En particulier, grâce à une rétro-action nuageuse, la Terre aurait pu éviter une glaciation globale et rester propice au développement de la vie.