With few previous data and literature based on the South African banking sector, the key aim of this study was to contribute further results concerning the effect of operational loss events on the reputation of South African banks. The main distinction between this study and previous empirical research is that a small sample of South African banks listed on the JSE, between 2000 and 2014 was used. Insurance companies fell outside the scope of the study. The study primarily focused on identifying reputational risk among Regal Treasury Bank, Saambou Bank, African Bank and Standard Bank. The events announced by these banks occurred between 2000 and 2014. The precise date of the announcement of the operational events was also determined. Stock price data were collected for those banks that had unanticipated operational loss announcements (i.e. the event). Microsoft Excel models applied to the reputational loss as the difference between the operational loss announcement and the loss in the stock returns of the selected banks. The results indicated significant negative abnormal returns on the announcement day for three of the four banks. For one of the banks it was assumed that the operational loss was not significant enough to cause reputational risk. The event methodology similar to previous literature, furthermore examined the behaviour of return volatility after specific operational loss events using the sample of banks. The study further aimed at making two contributions. Firstly, to analyse return volatility after operational loss announcements had been made among South African banks, and secondly, to compare the sample of affected banks with un-affected banks to further identify whether these events spilled over into the banking industry and the market. The volatility of these four banks were compared to three un-affected South African banks. The results found that the operational loss events for Regal Treasury Bank and Saambou Bank had no influence on the unaffected banks. However the operational loss events for African Bank and Standard Bank influenced the sample of unaffected banks and the Bank Index, indicating systemic risk.

With few previous data and literature based on the South African banking sector, the key aim of this study was to contribute further results concerning the effect of operational loss events on the reputation of South African banks. The main distinction between this study and previous empirical research is that a small sample of South African banks listed on the JSE, between 2000 and 2014 was used. Insurance companies fell outside the scope of the study. The study primarily focused on identifying reputational risk among Regal Treasury Bank, Saambou Bank, African Bank and Standard Bank. The events announced by these banks occurred between 2000 and 2014. The precise date of the announcement of the operational events was also determined. Stock price data were collected for those banks that had unanticipated operational loss announcements (i.e. the event). Microsoft Excel models applied to the reputational loss as the difference between the operational loss announcement and the loss in the stock returns of the selected banks. The results indicated significant negative abnormal returns on the announcement day for three of the four banks. For one of the banks it was assumed that the operational loss was not significant enough to cause reputational risk. The event methodology similar to previous literature, furthermore examined the behaviour of return volatility after specific operational loss events using the sample of banks. The study further aimed at making two contributions. Firstly, to analyse return volatility after operational loss announcements had been made among South African banks, and secondly, to compare the sample of affected banks with un-affected banks to further identify whether these events spilled over into the banking industry and the market. The volatility of these four banks were compared to three un-affected South African banks. The results found that the operational loss events for Regal Treasury Bank and Saambou Bank had no influence on the unaffected banks. However the operational loss events for African Bank and Standard Bank influenced the sample of unaffected banks and the Bank Index, indicating systemic risk.

Ad hoc networks represent the current de-facto alternative for infrastructure-less environments, due to their self-configuring and resilience characteristics. Ad hoc networks flexibility benefits, such as unrestrained computing, lack of centralisation, and ease of deployment at low costs, are tightly bound with relevant deficiencies such as limited resources and management difficulty. Ad hoc networks witnessed high attention from the research community due to the numerous challenges faced when deploying such a technology in real scenarios. Starting with the nature of the wireless environment, which raises significant transmission issues when compared with the wired counterpart, ad hoc networks require a different approach when addressing the data link problems. Further, the high packet loss due to wireless contention, independent of network congestion, requires a different approach when considering quality of service degradation and unfair channel resources distribution among competing flows. Although these issues have already been considered to some extent by researchers, there is still room to improve quality of service by reducing the effect of packet loss and fairly distributing the medium access among competing nodes. The aim of this thesis is to propose a set of mechanisms to alleviate the effect of packet loss and to improve fairness in ad hoc networks. A transport layer algorithm has been proposed to overcome the effects of hidden node collisions and to reduce the impact of wireless link contention by estimating the four hop delay and pacing packet transmissions accordingly. Furthermore, certain topologies have been identified, in which the standard IEEE 802.11 faces degradation in channel utilisation and unfair bandwidth allocation. Three link layer mechanisms have been proposed to tackle the challenges the IEEE 802.11 faces in the identified scenarios to impose fairness in ad hoc networks through fairly distributing channel resources between competing nodes. These mechanisms are based on monitoring the collision rate and penalising the greedy nodes where no competing nodes can be detected but interference exists, monitoring traffic at source nodes to police access to the channel where only source nodes are within transmission range of each other, and using MAC layer acknowledgements to flag unfair bandwidth allocation in topologies where only the receivers are within transmission range of each other. The proposed mechanisms have been integrated into a framework designed to adapt and to dynamically select which mechanism to adopt, depending on the network topology. It is important to note that the proposed mechanisms and framework are not alternatives to the standard MAC protocol but are an enhancement and are triggered by the failure of the IEEE 802.11 protocol to distribute the channel resources fairly. All the proposed mechanisms have been validated through simulations and the results obtained from the experiments show that the proposed schemes fairly distribute channel resources fairly and outperform the performance of the IEEE 802.11 protocol in terms of channel utilisation as well as fairness.

The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.

This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be used as an accessible, stand-alone introduction to the subject of SVMs for the advanced undergraduate. Its second section provides a proof of the positive-definiteness of a certain useful function here called E and dened as follows: Let V be a complex inner product space. Let N be a function that maps a vector from V to its norm. Let p be a real number between 0 and 2 inclusive and for any in V , let ( be N() raised to the p-th power. Finally, let a be a positive real number. Then E() is exp(()). Although the result is not new (other proofs are known but involve deep properties of stochastic processes) this proof is accessible to advanced undergraduates with a decent grasp of linear algebra. Its final section presents an algorithm by Dr. Kallman (preprint), based on earlier Russian work by B.F. Mitchell, V.F Demyanov, and V.N. Malozemov, and proves its convergence. The section also discusses briefly architectural features of the algorithm expected to result in practical speed increases.

This research aims to investigate how particles assemble together through thermodynamic and kinetic control. Particle assembly with thermodynamic control is achieved in part due to electrostatic attraction between particles. Electrostatic attraction between particles can be achieved by functionalizing polystyrene or SiO2 particles with different charges. Particles with different charges will come together in solution slowly and self-assemble to form ordered crystals with different patterns based on size and charge ratios of two oppositely charged particles. Kinetic control of particle assembly is achieved by pattern aided exponential amplification of nanoscale structures. Some of these nanoscale structures are difficult to build with other conventional synthetic methods. On the other hand, as for kinetically controlled particle replication, the patterns can be synthesized by one of two ways i) crystal products which are produced by thermodynamically controlled particle assembly or ii) single particle deposition. Specifically, kinetically controlled particle assembly focuses on constructing SiO2 particles. Exponential replication of SiO2 particles is achieved by growing a "bridge layer", between templates of SiO2 particles and next generation SiO2 replicas. By dissolving the bridge layer, two times the amount of the SiO2 particles with the shape of the original templates can be formed. In the next generation, all the particles serve as template particles. Thus, after n cycles of replication, 2n amount of products can be formed. If successful, particle assembly can be thermodynamic controlled and particle exponential replication can be kinetical controlled, which will enable new ways to build particles with well-defined shapes from readily available building blocks.

Ce mémoire contient quelques résultats sur l'intégration numérique. Ils sont liés à la célèbre formule de quadrature de K. F. Gauss. Une généralisation très intéressante de la formule de Gauss a été obtenue par P. Turán. Elle est contenue dans son article publié en 1948, seulement quelques années après la seconde guerre mondiale. Étant données les circonstances défavorables dans lesquelles il se trouvait à l'époque, l'auteur (Turán) a laissé beaucoup de détails à remplir par le lecteur. Par ailleurs, l'article de Turán a inspiré une multitude de recherches; sa formule a été étendue de di érentes manières et plusieurs articles ont été publiés sur ce sujet. Toutefois, il n'existe aucun livre ni article qui contiennent un compte-rendu détaillé des résultats de base, relatifs à la formule de Turán. Je voudrais donc que mon mémoire comporte su samment de détails qui puissent éclairer le lecteur tout en présentant un exposé de ce qui a été fait sur ce sujet. Voici comment nous avons organisé le contenu de ce mémoire. 1-a. La formule de Gauss originale pour les polynômes - L'énoncé ainsi qu'une preuve. 1-b. Le point de vue de Turán - Compte-rendu détaillé des résultats de son article. 2-a. Une formule pour les polynômes trigonométriques analogue à celle de Gauss. 2-b. Une formule pour les polynômes trigonométriques analogue à celle de Turán. 3-a. Deux formules pour les fonctions entières de type exponentiel, analogues à celle de Gauss pour les polynômes. 3-b. Une formule pour les fonctions entières de type exponentiel, analogue à celle de Turán. 4-a. Annexe A - Notions de base sur les polynômes de Legendre. 4-b. Annexe B - Interpolation polynomiale. 4-c. Annexe C - Notions de base sur les fonctions entières de type exponentiel. 4-d. Annexe D - L'article de P. Turán. / This mémoire contains some results about numerical integration. They are related to the famous quadrature formula of K. F. Gauss. A very interesting generalization of the formula of Gauss was obtained by P.Turán. It is contained in a paper that was published in 1948, only a few years after the second world war. Due to adverse circunstances he was in at the time, the author (Turán) left many details for the reader to fill in. Otherwise, the article of Turán inspired a multitude of research, and his formula has been extended in many ways and several papers have been written on this subject. However, there is no single book or paper where one can nd a clear and comprehensive account of the basic results pertaining to Turán's formula. Thus, I would like my Master's mémoire to contain enough details that can enlighten the reader and present an exposition of much that has been done on this subject. Here is how we have arranged the contents of the mémoire. 1-a. The original formula of Gauss for polynomials - statement along with a proof. 1-b. Turán's point of view - detailed account of the results contained in his paper. 2-a. A formula for trigonometric polynomials analogous to that of Gauss. 2-b. A formula for trigonometric polynomials analogous to that of Turán. 3-a. Two formulae for entire functions of exponential type, analogous to the one of Gauss for polynomials. 3-b. A formula for entire functions of exponential type, analogous to that of Turán. 4-a. Annexe A - Basic facts about Legendre polynomials. 4-b. Annexe B - Polynomial interpolation. 4-c. Annexe C - Basic facts about entire functions of exponential type. 4-d. Annexe D - Paper of P. Turán.

This diploma thesis provides an evaluation of Exponential families of distributions which has a special position in mathematical statistics. Diploma will learn the basic concepts and facts associated with the distribution of exponential type. Especially with focusing on the advantages of exponential families in classical parametric statistics, thus in theory of estimation and hypothesis testing. Emphasis will be placed on one-parameter and multi-parameters systems.

Title: Exponential families in statistical inference Author: Sally Abdel-Maksoud Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Daniel Hlubinka, Ph.D. Supervisor's e-mail address: Daniel.Hlubinka@mff.cuni.cz Abstract: This diploma thesis provides an evaluation of Exponential families of distributions which has a special position in mathematical statistic including appropriate properties for estimation of population parameters, hypothesis testing and other inference problems. Diploma will introduce the basic concepts and facts associated with the distribution of exponential type especially with focusing on the advantages of exponential families in classical parametric statistics, thus in theory of estimation and hypothesis testing. Emphasis will be placed on one-parameter and multi- parameters systems. It also exposes an important concepts about the curvature of a statistical problem including the curvature in exponential families. We will define a quantity that measure how nearly "exponential" the families are. This quantity is said to be the statistical curvature of the family. We will show that the family with a small curvature enjoy the good properties of exponential families Moreover, the properties of the curvature, hypotheses testing and some...

The aim of this diploma thesis is to develop a good teaching tool for study- ing exponential and logarithmic equations at the secondary school. It is not a textbook but an interactive website which contains dynamic elements and tests that can help stu- dents understand this subject matter. The website should mainly serve secondary school students as a supplementary study material. In the first chapter of the work the existing websites devoted to this theme are discussed and evaluated. On the basis of these and other educational sites the autor created a new website.