The introduction of cyber technology, accompanied by its fast developing nature, has not only resulted in numerous advantages to its user and society as a whole but has also produced harmful consequences specifically impacting on cyber crime. One of these harmful effects is cyber stalking. Cyber stalking is the use of the Internet or any electronic medium to stalk, harass and pursue victims. This unwanted perusal has various negative implications for the victim, as cyber stalking can disrupt many aspects of an individual’s lifestyle. In this study, the occurrence, nature and the impact of cyber stalking among the victims of cyber stalking were explored. Additionally, protective measures available to victims of cyber stalking were examined as a way to facilitate the operational efficiency of related legislation. This was done through determining the occurrence, nature and the impact of cyber stalking as well as the extent of the usage of social networks in the commission of cyber stalking. Legislation specific to South Africa and the effectiveness of such legislation were examined. The study implemented a qualitative approach. Twelve research participants who met the requirements of the study were selected by means of purposive and snowball sampling methods. The study was publicised on the Internet through current popular social network sites. In conjunction to the cyber theme of the study, the research participants were requested to complete an online e-mail interview to share their personal cyber stalking victimisation experiences. Within the constraints of the e-mail interview, a semi-structured interview schedule was incorporated in order to guide the research participants in sharing their cyber stalking victimisation experiences. The findings of the study were extensive; ranging from emerged patterns to unique and exclusive experiences. In brief, the study concludes that cyber stalking is occurring in South Africa, its nature and impact is complex and although there are many common themes within cyber stalking, it is uniquely situated to individual cyber stalking incident(s). Although there is no current South African legislation specifically aimed at addressing cyber stalking, South African legislation comprehensively deals with addressing the problem of cyber stalking within various related legislation. It was determined that although cyber stalking is effectively addressed in the drafting of legislation, it is ineffectively administered at grass roots level, where the police act as the gatekeepers and vital role players in the reporting and intervention of crime. Based upon the findings, as guided by the aims and objectives of the study, recommendations for the prevention and intervention of cyber stalking as well as recommendations for future research were made. As derived from the research participants’ responses as well as from current literature, recommendations focused on all victims of cyber stalking while specifically paying attention to young victims and victims who are business users. Recommendations were also made to assist in dealing with cyber stalking as well as recommendations aimed at assisting professional role players. In the final chapter of the study, emphasis is placed on awareness and educational campaigns aimed at informing the cyber community of cyber stalking. / Criminal and Procedural Law / M. A. (Criminology)

Diploma thesis gives a brief description of the traditional technology of preparation of lime mortars for restoration of historical buildings. The theoretical part is focused on the preparation of lime mortars traditional methods, using appropriate materials for making and influence amount of water. Attention is also paid to the events that take place in the setting and hardening of lime mortar. In the experimental part of the research was conducted, which aimed to assess the influence of water-cement ratio and mixing ratio (binder to filler) on the properties of lime mortars. At various times were measured mechanical properties, density, shrinkage, frost resistance and porosity. The mortar was also carried out thermal analysis and found to contain calcium carbonate. Acquired knowledge could help in the reconstruction of historical buildings.

The goal of this thesis is two-fold. On the one hand, it pursues to provide a contribution to the conjugate duality by proposing a new duality concept, which can be understood as an umbrella for different meaningful perturbation methods. On the other hand, this thesis aims to investigate minimax location problems by means of the duality concept introduced in the first part of this work, followed by a numerical approach using epigraphical splitting methods. After summarizing some elements of the convex analysis as well as introducing important results needed later, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of n+1 functions. For this problem we propose a conjugate dual problem, where the functions involved in the objective function of the primal problem are decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach we determine the formulae of the conjugate as well as the biconjugate of the objective function of the primal problem and analyze an optimization problem having as objective function the sum of reciprocals of concave functions. In the second part of this thesis we discuss in the sense of the introduced duality concept three classes of minimax location problems. The first one consists of nonlinear and linear single minimax location problems with geometric constraints, where the maximum of nonlinear or linear functions composed with gauges between pairs of a new and existing points will be minimized. The version of the nonlinear location problem is additionally considered with set-up costs. The second class of minimax location problems deals with multifacility location problems as suggested by Drezner (1991), where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. As the last and third class the classical multifacility location problem with geometrical constraints is considered in a generalized form where the maximum of gauges between pairs of new facilities and the maximum of gauges between pairs of new and existing facilities will be minimized. To each of these location problems associated dual problems will be formulated as well as corresponding duality statements and necessary and sufficient optimality conditions. To illustrate the results of the duality approach and to give a more detailed characterization of the relations between the location problems and their corresponding duals, we consider examples in the Euclidean space. This thesis ends with a numerical approach for solving minimax location problems by epigraphical splitting methods. In this framework, we give formulae for the projections onto the epigraphs of several sums of powers of weighted norms as well as formulae for the projection onto the epigraphs of gauges. Numerical experiments document the usefulness of our approach for the discussed location problems.

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.