As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.

A pesquisa teve como objetivo principal avaliar a incorporação de agregados reciclados de concreto em blocos estruturais de concreto para três classes de resistência (4,5 MPa, 8,0 MPa e 12,0 MPa). O estudo foi desenvolvido basicamente em quatro etapas. A primeira etapa consistiu na análise das propriedades físicas de agregados miúdos e graúdos reciclados de concreto originários de uma fábrica de pré-moldados. Na segunda etapa, foram analisadas as propriedades físicas e mecânicas de corpos-de-prova cilíndricos produzidos com concreto de consistência seca utilizando-se dois tipos de agregados reciclados previamente avaliados. O objetivo foi definir um intervalo de correlação entre a resistência à compressão de corpos-de-prova e blocos, verificar preliminarmente a influência dos agregados reciclados sobre as propriedades físicas e mecânicas e determinar os traços para a próxima etapa. Para a terceira etapa, foi avaliada a viabilidade técnica da produção de blocos com agregados reciclados através da análise de propriedades físicas e mecânicas, sendo também avaliada a viabilidade econômica pela proposição de algumas alternativas para reciclagem. De maneira geral, independentemente do grupo de resistência avaliado, todas as unidades com agregados graúdos reciclados cumpriram os requisitos estabelecidos; já para o estudo econômico, todas as hipóteses atestaram a viabilidade da produção de unidades com agregados reciclados com custos de produção e comercialização inferiores aos das unidades comumente produzidas. Finalmente, a quarta etapa, consistiu na avaliação da retração por secagem em miniparedes, resistência à compressão e módulo de deformação de elementos (prismas e miniparedes) produzidos com as unidades da etapa anterior. Em função dos resultados obtidos, pode-se afirmar que apenas a propriedade de retração por secagem foi afetada pelas unidades com agregados reciclados; nesse caso, a redução da distância entre juntas de controle foi considerada uma medida suficiente para minimizar os efeitos da retração por secagem. / The main goal of the present research project was the evaluation of recycled concrete aggregates incorporation in structural concrete blocks of three different levels of compressive strength (4,5 MPa, 8,0 MPa and 12,0 MPa). The study was developed in four stages. The first stage analyzed the physical properties of fine and coarse concrete aggregates derived from a precast concrete plant. In the second stage, physical and mechanical properties of dry consistency concrete cylindrical specimens were analyzed using two types of recycled aggregates. The aim was to define a correlation interval between the compressive strength of cylindrical specimens and concrete blocks, verify the influence of recycled aggregates on the physical and mechanical properties, and determine the better compositions to be used in the next stage. The third stage involved the technical viability of producing concrete blocks, and also the economic viability of some recycling alternatives. As a whole, independently of the strength class, the recycled coarse aggregate blocks fulfilled the required specifications; additionally the economic hypotheses confirmed the viability of producing recycled aggregate units with both production and market costs lower than those of the conventional units. Finally, the fourth stage dealt with the drying shrinkage of mini-walls, the compressive strength and the elasticity modulus of elements (prisms and mini-walls) built with units defined in the former stage. Based on the obtained results, the study showed that only the drying shrinkage property was affected by the recycled aggregates units; the reduction of the distance between two adjacent control joints was an adequate procedure to minimize the effects of the drying shrinkage in this case.

O presente trabalho trata do desenvolvimento de formulações numéricas para avaliar o comportamento mecânico de estruturas compostas planas, no contexto de elasticidade linear e mecânica da fratura não linear. As formulações propostas são baseadas no Método dos Elementos de Contorno (MEC), por meio das representações integrais singular e hiper singular dos problemas elastostáticos. A técnica de multi-regiões é considerada para acoplar a interface de sólidos multifásicos. O MEC é uma técnica numérica robusta e precisa para analisar o fenômeno da fratura em sólidos. Esse método numérico apresenta uma natural redução na dimensionalidade do problema, tornando mais simples a modelagem das superfícies de fratura. Além disso, essa redução de dimensionalidade faz também com que o tratamento de interfaces materiais em estruturas compostas seja uma tarefa menos árdua. Com o uso da solução fundamental de Kelvin nas representações integrais, materiais isotrópicos podem ser considerados para constituir as estruturas compostas. Por outro lado, utilizando a solução fundamental de Cruse & Swedlow, também é possível lidar, de maneira geral, com materiais anisotrópicos em estruturas compostas. Nessas estruturas, as fraturas são assumidas como ocorrendo ao longo das interfaces e o comportamento não linear é introduzido pelo modelo coesivo de fratura, o qual é aplicável a materiais quase frágeis. Nessas análises, o sistema não linear de equações pode ser solucionado utilizando dois distintos algoritmos de resolução iterativa. O primeiro sempre leva em consideração a rigidez elástica da estrutura e é, portanto denominado Operador Constante (OC). Já o segundo é denominado Operador Tangente (OT), pois considera uma rigidez tangente à resposta estrutural não linear, o que resulta em melhores taxas de convergência em comparação ao OC. Como aplicações das formulações, estruturas compostas teóricas foram analisadas em regime elástico. Além disso, testes experimentais de fratura em espécimes de concreto e madeira também foram simulados. A comparação dos resultados com as referências demonstrou que, as formulações foram efetivas e precisas para avaliar respostas mecânicas de estruturas, seja em regime elástico linear ou nos testes de fratura quase frágil. / The present work deals the development of numerical formulations to evaluate the mechanical behaviour of plane composed structures, in the context of linear elasticity and nonlinear fracture mechanics. The proposed formulations are based on the Boundary Element Method (BEM), through its classical singular and hyper singular integral equations. The multi-region technique is adopted to couple the interfaces of non-homogeneous multiphase bodies. The BEM is a robust and accurate numerical technique to analyse fracture phenomena in solids. This numerical method presents a mesh dimensionality reduction, which makes easier the modelling of cracks surfaces. Besides, this dimensionality reduction also makes the treatment of interfaces in composed structures a less complex task. Considering the use of Kelvin fundamental solutions at the integrals equations, isotropic materials can be represent as parts of the composed structures. On the other hand, using Cruse & Swedlow fundamental solution it is also possible to deal with general anisotropic materials. At the composed structures, cracks can propagate along the materials interfaces and the cohesive crack model is responsible for the nonlinear structural behaviour of the quasi-brittle failures. The nonlinear system of equations at the fracture analyses is solved using two different algorithms for iterative resolution. The first always takes into account the structure elastic strength and, hence it is called Constant Operator (CO). On the other hand, the second is denominated Tangent Operator (TO) due to the fact that it considers strengths at the tangent directions of the nonlinear structural response. Therefore, convergence rates are faster when compared with the CO. As applications, composed structures were analysed with the developed formulations in linear elastic range. In addition, experimental fracture testes performed in concrete and wood specimens were also analysed. The confront of obtained results with the reference ones show that, the formulation was effective and accurate to evaluate the mechanical responses of composed structures in linear elastic range, and also to perform nonlinear quasi-brittle fracture tests.

This dissertation discusses the potential of the snare drum as a solo concert instrument. Four pieces from a collection entitled The Noble Snare are used for demonstration ("Homily" by Milton Babbitt, "Composed Improvisation for Snare Drum" by John Cage, "Peeping Tom" by Dan Senn, and "The Noble Snare" by Stuart Saunders Smith). In the absence of many traditional musical devices (i.e. melody and harmony), alternative means of expression are used by the composer. Each piece is discussed with regard to its distinctive compositional approach and inherent performance issues. Information is also given pertaining to the background of the Noble Snare series. This includes: the inspiration for the project, editorial issues, and its influence on snare drum performance. Much of this research was completed through interviews by with author with Sylvia Smith, publisher of The Noble Snare and owner of Smith Publications.

The goal of this work is to present a conjugate duality treatment of composed programming as well as to give an overview of some recent developments in both scalar and multiobjective optimization. In order to do this, first we study a single-objective optimization problem, in which the objective function as well as the constraints are given by composed functions. By means of the conjugacy approach based on the perturbation theory, we provide different kinds of dual problems to it and examine the relations between the optimal objective values of the duals. Given some additional assumptions, we verify the equality between the optimal objective values of the duals and strong duality between the primal and the dual problems, respectively. Having proved the strong duality, we derive the optimality conditions for each of these duals. As special cases of the original problem, we study the duality for the classical optimization problem with inequality constraints and the optimization problem without constraints. The second part of this work is devoted to location analysis. Considering first the location model with monotonic gauges, it turns out that the same conjugate duality principle can be used also for solving this kind of problems. Taking in the objective function instead of the monotonic gauges several norms, investigations concerning duality for different location problems are made. We finish our investigations with the study of composed multiobjective optimization problems. In doing like this, first we scalarize this problem and study the scalarized one by using the conjugacy approach developed before. The optimality conditions which we obtain in this case allow us to construct a multiobjective dual problem to the primal one. Additionally the weak and strong duality are proved. In conclusion, some special cases of the composed multiobjective optimization problem are considered. Once the general problem has been treated, particularizing the results, we construct a multiobjective dual for each of them and verify the weak and strong dualities. / In dieser Arbeit wird, anhand der sogenannten konjugierten Dualitätstheorie, ein allgemeines Dualitätsverfahren für die Untersuchung verschiedener Optimierungsaufgaben dargestellt. Um dieses Ziel zu erreichen wird zuerst eine allgemeine Optimierungsaufgabe betrachtet, wobei sowohl die Zielfunktion als auch die Nebenbedingungen zusammengesetzte Funktionen sind. Mit Hilfe der konjugierten Dualitätstheorie, die auf der sogenannten Störungstheorie basiert, werden für die primale Aufgabe drei verschiedene duale Aufgaben konstruiert und weiterhin die Beziehungen zwischen deren optimalen Zielfunktionswerten untersucht. Unter geeigneten Konvexitäts- und Monotonievoraussetzungen wird die Gleichheit dieser optimalen Zielfunktionswerte und zusätzlich die Existenz der starken Dualität zwischen der primalen und den entsprechenden dualen Aufgaben bewiesen. In Zusammenhang mit der starken Dualität werden Optimalitätsbedingungen hergeleitet. Die Ergebnisse werden abgerundet durch die Betrachtung zweier Spezialfälle, nämlich die klassische restringierte bzw. unrestringierte Optimierungsaufgabe, für welche sich die aus der Literatur bekannten Dualitätsergebnisse ergeben. Der zweite Teil der Arbeit ist der Dualität bei Standortproblemen gewidmet. Dazu wird ein sehr allgemeines Standortproblem mit konvexer zusammengesetzter Zielfunktion in Form eines Gauges formuliert, für das die entsprechenden Dualitätsaussagen abgeleitet werden. Als Spezialfälle werden Optimierungsaufgaben mit monotonen Normen betrachtet. Insbesondere lassen sich Dualitätsaussagen und Optimalitätsbedingungen für das klassische Weber und Minmax Standortproblem mit Gauges als Zielfunktion herleiten. Das letzte Kapitel verallgemeinert die Dualitätsaussagen, die im zweiten Kapitel erhalten wurden, auf multikriterielle Optimierungsprobleme. Mit Hilfe geeigneter Skalarisierungen betrachten wir zuerst ein zu der multikriteriellen Optimierungsaufgabe zugeordnetes skalares Problem. Anhand der in diesem Fall erhaltenen Optimalitätsbedingungen formulieren wir das multikriterielle Dualproblem. Weiterhin beweisen wir die schwache und, unter bestimmten Annahmen, die starke Dualität. Durch Spezialisierung der Zielfunktionen bzw. Nebenbedingungen resultieren die klassischen konvexen Mehrzielprobleme mit Ungleichungs- und Mengenrestriktionen. Als weitere Anwendungen werden vektorielle Standortprobleme betrachtet, zu denen wir entsprechende duale Aufgaben formulieren.

With this thesis we bring some new results and improve some existing ones in conjugate duality and some of the areas it is applied in. First we recall the way Lagrange, Fenchel and Fenchel - Lagrange dual problems to a given primal optimization problem can be obtained via perturbations and we present some connections between them. For the Fenchel - Lagrange dual problem we prove strong duality under more general conditions than known so far, while for the Fenchel duality we show that the convexity assumptions on the functions involved can be weakened without altering the conclusion. In order to prove the latter we prove also that some formulae concerning conjugate functions given so far only for convex functions hold also for almost convex, respectively nearly convex functions. After proving that the generalized geometric dual problem can be obtained via perturbations, we show that the geometric duality is a special case of the Fenchel - Lagrange duality and the strong duality can be obtained under weaker conditions than stated in the existing literature. For various problems treated in the literature via geometric duality we show that Fenchel - Lagrange duality is easier to apply, bringing moreover strong duality and optimality conditions under weaker assumptions. The results presented so far are applied also in convex composite optimization and entropy optimization. For the composed convex cone - constrained optimization problem we give strong duality and the related optimality conditions, then we apply these when showing that the formula of the conjugate of the precomposition with a proper convex K - increasing function of a K - convex function on some n - dimensional non - empty convex set X, where K is a k - dimensional non - empty closed convex cone, holds under weaker conditions than known so far. Another field were we apply these results is vector optimization, where we provide a general duality framework based on a more general scalarization that includes as special cases and improves some previous results in the literature. Concerning entropy optimization, we treat first via duality a problem having an entropy - like objective function, from which arise as special cases some problems found in the literature on entropy optimization. Finally, an application of entropy optimization into text classification is presented.

As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.

Prognostiziert durch Konzepte der Industrie 4.0 und den Cyber-Physischen-Systemen, können autonome Systeme zukünftig dynamisch auf Datenquellen in ihrer Umgebung zugreifen. Während die gemeinsame Nutzung solcher Datenquellen ein enormes Performanzpotenzial bietet, stellt die benötigte Systemarchitektur vorherrschende Sicherheitsprozesse vor neue Herausforderungen. Die vorliegende Arbeit motiviert zunächst, dass diese nur zur Laufzeit des Systems adressiert werden könne, bevor sie daraus zwei zentrale Ziele ableitet und verfolgt. Zum einen wird ein Beschreibungsmodel für die Darstellung von Fehlercharakteristika gemeinsam genutzter Daten vorgestellt. Dieses generische Fehlermodell erlaubt es zum anderen eine Sicherheitsanalyse zu definieren, die eine spezifische, dynamische Systemkomposition zur Laufzeit mit Hinblick auf die zu erwartenden Unsicherheiten bewerten kann. Die als Region of Safety betitelte Analysestrategie erlaubt, in Kombination mit dem generischen Fehlermodell, die Sicherheit der auf gemeinsam genutzten Daten basierenden Kollisionsvermeidungsstrategie zweier Roboter noch zur Designzeit zu garantieren, obwohl die spezifischen Fehlercharakteristika der Daten erst zur Laufzeit bekannt werden.:List of Acronyms List of Theorems List of Definitions List of Figures List of Tables 1. Introduction – Safety in Future Smart Industries 1.1. The Example of Smart Warehouses 1.2. Functional Safety Standards 1.2.1. Overview of Functional Safety Standards 1.2.2. IEC 61508 1.3. Scope of this Thesis 1.3.1. Objectives 1.3.2. Contributions 1.3.3. Outline 1.4. Related Publications by the Author 1.5. Mathematical Notation 2. State of the Art 2.1. State of the Art in Run-Time Safety Assessment 2.1.1. Approaches at the Functional Level 2.1.2. Approaches at the Technical Level 2.1.3. Conclusions 2.2. State of the Art in Failure Modeling 2.2.1. The Definition of (Sensor) Failure Model 2.2.2. Interval-Based Failure Modeling 2.2.3. Distribution-Based Failure Modeling 2.2.4. Failure-Type-Based Failure Modeling 2.2.5. Conclusions 2.3. Conclusions from the State of the Art 3. Generic Failure Model 3.1. Defining the Generic Failure Model 3.1.1. Time- and Value-Correlated Random Distribution 3.1.2. A Failure Type’s Failure Amplitudes 3.1.3. A Failure Type’s State Function 3.1.4. Polynomial Representation of a Failure Type 3.1.5. Discussion on the Fulfillment of the Predefined Criteria 3.2. Converting a Generic Failure Model to an Interval 3.2.1. Converting a Time- and Value-Correlated Random Distribution 3.2.2. A Failure Type’s Interval 3.3. Processing Chain for Generating Generic Failure Models 3.3.1. Identifying Failure Types 3.3.2. Parameterizing Failure Types 3.3.3. Confidence Calculation 3.4. Exemplary Application to Artificial Failure Characteristics 3.4.1. Generating the Artificial Data Set – Manually Designing GFMs 3.4.2. Identifying Failure Types 3.4.3. Parameterizing Failure Types 3.4.4. Confidence Calculation 3.4.5. Comparison to State-of-the-Art Models 3.5. Summary 4. Region of Safety 4.1. Explicitly Modeling Uncertainties for Dynamically Composed Systems 4.2. Regions of Safety for Dynamically Composed Systems 4.2.1. Estimating Regions of Attraction in Presence of Uncertainty 4.2.2. Introducing the Concept of Region of Safety 4.2.3. Discussion on the Fulfillment of the Predefined Criteria 4.3. Evaluating the Concept of Region of Safety 4.3.1. Defining the Scenario and Considered Uncertainties 4.3.2. Designing a Control Lyapunov Function 4.3.3. Determining an Appropriate Value for λc 4.3.4. The Effect of Varying Sensor Failures on Regions of Safety 4.4. Summary 5. Evaluation and Integration 5.1. Multi-Robot Collision Avoidance 5.1.1. Assumptions 5.1.2. Design of the Circle and Navigation Scenarios 5.1.3. Kinematics 5.1.4. Control Policy 5.1.5. Intention Modeling by Model Uncertainty 5.1.6. Fusing Regions of Safety of Multiple Stability Points 5.2. Failure Modeling for Shared Data – A Marker Detection Failure Model 5.2.1. Data Acquisition 5.2.2. Failure Model Generation 5.2.3. Evaluating the Quality of the Failure Model 5.3. Safe Handling of Shared Data in a Collision Avoidance Strategy 5.3.1. Configuration for Region of Safety Estimation 5.3.2. Estimating Regions of Safety 5.3.3. Evaluation Using the Circle Scenario 5.3.4. Evaluation Using the Navigation Scenario 5.4. Summary 6. Conclusions and Future Work 6.1. Summary 6.2. Limitations and Future Work 6.2.1. Limitations and Future Work on the Generic Failure Model 6.2.2. Limitations and Future Work on Region of Safety 6.2.3. Future Work on Safety in Dynamically Composed Systems Appendices A. Defining Factors of Risk According to IEC 61508 B. Evaluation Results for the Identification Stage C. Overview of Failure Amplitudes of Marker Detection Results Bibliography / The concepts of Cyber-Physical-Systems and Industry 4.0 prognosticate autonomous systems to integrate sources of shared data dynamically at their run-time. While this promises substantial increases in their performance, the openness of the required system architecture poses new challenges to processes guaranteeing their safety. This thesis firstly motivates that these can be addressed only at their run-time, before it derives and pursues two corresponding goals. Firstly, a model for describing failure characteristics of shared data is presented. Secondly, this Generic Failure Model is built upon to define a run-time safety assessment methodology that enables analyzing dynamic system compositions integrating shared data with respect to the expected uncertainties at run-time. This analysis strategy, entitled Region of Safety, allows in combination with the generic failure model to guarantee the safety of robots sharing position data for collision avoidance already at design-time, although specific failure characteristics become available only at run-time.:List of Acronyms List of Theorems List of Definitions List of Figures List of Tables 1. Introduction – Safety in Future Smart Industries 1.1. The Example of Smart Warehouses 1.2. Functional Safety Standards 1.2.1. Overview of Functional Safety Standards 1.2.2. IEC 61508 1.3. Scope of this Thesis 1.3.1. Objectives 1.3.2. Contributions 1.3.3. Outline 1.4. Related Publications by the Author 1.5. Mathematical Notation 2. State of the Art 2.1. State of the Art in Run-Time Safety Assessment 2.1.1. Approaches at the Functional Level 2.1.2. Approaches at the Technical Level 2.1.3. Conclusions 2.2. State of the Art in Failure Modeling 2.2.1. The Definition of (Sensor) Failure Model 2.2.2. Interval-Based Failure Modeling 2.2.3. Distribution-Based Failure Modeling 2.2.4. Failure-Type-Based Failure Modeling 2.2.5. Conclusions 2.3. Conclusions from the State of the Art 3. Generic Failure Model 3.1. Defining the Generic Failure Model 3.1.1. Time- and Value-Correlated Random Distribution 3.1.2. A Failure Type’s Failure Amplitudes 3.1.3. A Failure Type’s State Function 3.1.4. Polynomial Representation of a Failure Type 3.1.5. Discussion on the Fulfillment of the Predefined Criteria 3.2. Converting a Generic Failure Model to an Interval 3.2.1. Converting a Time- and Value-Correlated Random Distribution 3.2.2. A Failure Type’s Interval 3.3. Processing Chain for Generating Generic Failure Models 3.3.1. Identifying Failure Types 3.3.2. Parameterizing Failure Types 3.3.3. Confidence Calculation 3.4. Exemplary Application to Artificial Failure Characteristics 3.4.1. Generating the Artificial Data Set – Manually Designing GFMs 3.4.2. Identifying Failure Types 3.4.3. Parameterizing Failure Types 3.4.4. Confidence Calculation 3.4.5. Comparison to State-of-the-Art Models 3.5. Summary 4. Region of Safety 4.1. Explicitly Modeling Uncertainties for Dynamically Composed Systems 4.2. Regions of Safety for Dynamically Composed Systems 4.2.1. Estimating Regions of Attraction in Presence of Uncertainty 4.2.2. Introducing the Concept of Region of Safety 4.2.3. Discussion on the Fulfillment of the Predefined Criteria 4.3. Evaluating the Concept of Region of Safety 4.3.1. Defining the Scenario and Considered Uncertainties 4.3.2. Designing a Control Lyapunov Function 4.3.3. Determining an Appropriate Value for λc 4.3.4. The Effect of Varying Sensor Failures on Regions of Safety 4.4. Summary 5. Evaluation and Integration 5.1. Multi-Robot Collision Avoidance 5.1.1. Assumptions 5.1.2. Design of the Circle and Navigation Scenarios 5.1.3. Kinematics 5.1.4. Control Policy 5.1.5. Intention Modeling by Model Uncertainty 5.1.6. Fusing Regions of Safety of Multiple Stability Points 5.2. Failure Modeling for Shared Data – A Marker Detection Failure Model 5.2.1. Data Acquisition 5.2.2. Failure Model Generation 5.2.3. Evaluating the Quality of the Failure Model 5.3. Safe Handling of Shared Data in a Collision Avoidance Strategy 5.3.1. Configuration for Region of Safety Estimation 5.3.2. Estimating Regions of Safety 5.3.3. Evaluation Using the Circle Scenario 5.3.4. Evaluation Using the Navigation Scenario 5.4. Summary 6. Conclusions and Future Work 6.1. Summary 6.2. Limitations and Future Work 6.2.1. Limitations and Future Work on the Generic Failure Model 6.2.2. Limitations and Future Work on Region of Safety 6.2.3. Future Work on Safety in Dynamically Composed Systems Appendices A. Defining Factors of Risk According to IEC 61508 B. Evaluation Results for the Identification Stage C. Overview of Failure Amplitudes of Marker Detection Results Bibliography

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 & Procedural Law / Masters of Arts (Criminology)

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.