In this thesis, we study two problems. The first problem is to introduce the general version of Abramovich-Wickstead type spaces and investigate its order properties. In particular, we study the ideals, order bounded sets, disjointness properties, Dedekind completion and the norm properties of this Riesz space. We also define a new concrete example of Riesz space-valued uniformly continuous functions, denoted by CDr0 which generalizes the original Abramovich-Wickstead space. It is also shown that similar spaces CD0 and CDw introduced earlier by Alpay and Ercan are decomposable lattice-normed spaces. The second problem is related to analytic representations of different classes of dominated operators on these spaces. Our main representation theorems say that regular linear operators on CDr0 or linear dominated operators on CD0 may be represented as the sum of integration with respect to operator-valued measure and summation operation. In the case when the operator is order continuous or bo-continuous, then these representations reduce to discrete parts.

Autonomous mobile robots - both aerial and terrestrial vehicles - have gained immense importance due to the broad spectrum of their potential military and civilian applications. One of the indispensable requirements for the autonomy of a mobile vehicle is the vehicle's capability of planning and executing its motion, that is, finding appropriate control inputs for the vehicle such that the resulting vehicle motion satisfies the requirements of the vehicular task. The motion planning and control problem is inherently complex because it involves two disparate sub-problems: (1) satisfaction of the vehicular task requirements, which requires tools from combinatorics and/or formal methods, and (2) design of the vehicle control laws, which requires tools from dynamical systems and control theory. Accordingly, this problem is usually decomposed and solved over two levels of hierarchy. The higher level, called the geometric path planning level, finds a geometric path that satisfies the vehicular task requirements, e.g., obstacle avoidance. The lower level, called the trajectory planning level, involves sufficient smoothening of this geometric path followed by a suitable time parametrization to obtain a reference trajectory for the vehicle. Although simple and efficient, such hierarchical separation suffers a serious drawback: the geometric path planner has no information of the kinematic and dynamic constraints of the vehicle. Consequently, the geometric planner may produce paths that the trajectory planner cannot transform into a feasible reference trajectory. Two main ideas appear in the literature to remedy this problem: (a) randomized sampling-based planning, which eliminates altogether the geometric planner by planning in the vehicle state space, and (b) geometric planning supported by feedback control laws. The former class of methods suffer from a lack of optimality of the resultant trajectory, while the latter class of methods makes a restrictive assumption concerning the vehicle kinematic model. In this thesis, we propose a hierarchical motion planning framework based on a novel mode of interaction between these two levels of planning. This interaction rests on the solution of a special shortest-path problem on graphs, namely, one using costs defined on multiple edge transitions in the path instead of the usual single edge transition costs. These costs are provided by a local trajectory generation algorithm, which we implement using model predictive control and the concept of effective target sets for simplifying the non-convex constraints involved in the problem. The proposed motion planner ensures "consistency" between the two levels of planning, i.e., a guarantee that the higher level geometric path is always associated with a kinematically and dynamically feasible trajectory. We show that the proposed motion planning approach offers distinct advantages in comparison with the competing approaches of discretization of the state space, of randomized sampling-based motion planning, and of local feedback-based, decoupled hierarchical motion planning. Finally, we propose a multi-resolution implementation of the proposed motion planner, which requires accurate descriptions of the environment and the vehicle only for short-term, local motion planning in the immediate vicinity of the vehicle.

This paper is concerned with the numerical analysis of the autoconvolution equation $x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone functions are added. The paper is completed by a numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y.

Both real-time virtualization and recursive virtualization are desirable properties of a virtual machine monitor (or hypervisor). Although the prospect for virtualization and even recursive virtualization has become better as the PC hardware becomes faster, the real-time systems community so far has not been able to reap much benefits. This is because no existing virtualization mechanism can properly support the stringent timing requirements needed by real-time systems. It is hard to do real-time virtualization, and it is even harder to do it recursively. In this dissertation, we propose a framework whereby the hypervisor is capable of running real-time guests and participating in recursive virtualization. Such a hypervisor is called a real-time hierarchical hypervisor. We first look at virtualization of abstract resource types from the real-time systems perspective. Unlike the previous work on recursive real-time partitioning that assumes fully-preemptable resources, we concentrate on other and often more practical types of scheduling constraints, especially the non-preemptive and limited-preemptive ones. Then we consider the current x86 architecture and explore the problems that need to be addressed for real-time recursive virtualization. We drill down on the problem that affects timing properties the most, namely, the recursive forwarding and delivery of interrupts, exceptions and intercepts. We choose the x86 architecture because it is popular and readily available, but it is by no means the only architecture of choice for real-time recursive virtualization. We conclude the research with an architecture-independent discussion on future possibilities in real-time recursive virtualization. / text

A new method to perform direct numerical simulations of wall-bounded flows has been developed and implemented. The method uses high-order compact finite differences in wall-normal (for channel flow) or radial direction (for pipe flow) on a collocated grid, which gives high-accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid. The use of compact finite differences means that extreme clustering near the wall leading to small time steps in high-Reynolds number simulations is avoided. The influence matrix method is used to ensure a completely divergence-freesolution and all systems of equations are solved in banded form, which ensures an effcient solution procedure with low requirements for data storage. The method is unique in the sense that exactly divergence-free solutions on collocated meshes are calculated using arbitrary dffierence matrices. The code is validated for two flow cases, i.e. turbulent channel and turbulent pipe flow at relatively low Reynolds number. All tests show excellent agreement with analytical and existing results, confirming the accuracy and robustness ofthe method. The next step is to eciently parallelise the code so that high-Reynolds number simulations at high resolution can be performed. We furthermore investigated rare events occurring in the near-wall region of turbulent wall-bounded flows. We find that negative streamwise velocities and extreme wall-normal velocity uctuations are found rarely (on the order of 0:01%), and that they occur more frequently at higher Reynolds number. These events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall-bounded flows. / <p>QC 20150303</p>

Dans ce mémoire, nous traiterons du théorème de Lebesgue, un des plus frappants et des plus importants de l'analyse mathématique ; à savoir qu'une fonction à variation bornée est dérivable presque partout. Le but de ce travail est de fournir, à part la démonstration souvent proposée dans les cours de la théorie de la mesure, d'autres démonstrations élaborées avec des outils mathématiques plus simples. Ma contribution a consisté essentiellement à détailler et à compléter ces démonstrations, puis à inclure la plupart des figures pour une meilleure lisibilité. Nous allons maintenant, pour ce théorème qui se présente sous d'autres variantes, en proposer l'historique et trois démonstrations différentes. / In this dissertation, we will be handling a theorem of Lebesgue, one of the most stricking and ultimate of mathematical analysis ; namely a function with bounded variation has a derivative almost everywhere. The aim of our research is to provide, apart from the proof usually offered in measure theory courses, other demontrations achieved with more simple mathematical tools. My contribution was primarily to simplify and to complete these demonstrations, to include the most of the drawings in order to visualize what is being said. For this theorem, which has other presentations, we will give now the history and three different demonstrations.

This thesis presents two classes of models of boundedly rational decision makers - one with application to finance and the other to pricing. It consists of three parts. The first part of the thesis investigates the impact of investors' boundedly rational forecasting on asset price bubbles. We present a class of models, called extrapolation-correction models, of boundedly rational investor behavior. That is, the investors in our model, quite reasonably, use data available to them, i.e. past price data, to form forecasts about future prices. We relate the model parameters to various behavioral aspects like investor memory, caution/confidence, and panic. We present the resulting dynamical system model of asset price bubbles and relate the behavior of the dynamical system to the parameters capturing investor forecasting behavior. We show that, depending on the behavioral parameters, the associated dynamical system can converge to the fundamental value, go into predictable price cycles, or go into unpredictable price cycles. In particular, we find that the greater the weight investors' forecasts put on the most recent observations, the greater the tendency for the asset prices to exhibit cycles, forming positive and negative bubbles. We also find that when forecasts are strongly affected by recent prices, the price process becomes chaotic and it becomes increasingly difficult to forecast future prices accurately. The second part of the thesis addresses the question: How do investors make their price forecasts? We present the design of an experiment where investors participate in a virtual asset market run over a computer network. During the course of the experiment, the participants report their price forecasts and enter buy and sell orders. The computer software determines the market clearing prices. Despite full disclosure of the assets' dividends and the fundamental value, the price trajectories in all three experimental sessions exhibited cycles. We calibrated various models, including rational expectations based models and the extrapolation-correction family of models presented in the first part of the thesis. The results indicate that rational expectations hypothesis does not provide an accurate model of forecast formation. Moreover, a simple one-parameter exponential smoothing model is much better at modeling forecast formation, with the extrapolation-correction models making the fit slightly better. The third part of the thesis explores a different aspect of customer rationality - that of customer impatience - and its effect on pricing of product versions. We consider a setting in which impatient customers are faced with frequent product introductions, for example, products like Apple iPhones. This raises the following questions regarding customers: Given the pricing strategy of the firm, what are the optimal buying behaviors of the customers? How does customer buying behavior change in relation to impatience? We consider two settings. In the first setting, the firm offers a trade-in price for existing customers and a higher full price for new customers. In the second setting, the firm offers the same prices to new and existing customers, however there is an introductory full price and a discounted price later in the product cycle. We model the customer's problem in these two settings and characterize their optimal actions as a function of the price parameters. We also analyze the bilevel program for the firm's pricing decisions. We see that in both settings considered there are certain well-defined regions in the price space wherein the firm's optimal decision lies. We also provide some numerical computations to study the behavior of the optimal prices as the cost per unit increases.

We characterize the structure of the domain of a pure jump-type Dirichlet form which is given by a Beurling–Deny formula. In particular, we obtain su cient conditions in terms of the jumping kernel guaranteeing that the test functions are a core for the Dirichlet form and that the form is a Silverstein extension. As an application we show that for recurrent Dirichlet forms the extended Dirichlet space can be interpreted in a natural way as a homogeneous Dirichlet space. For reflected Dirichlet spaces this leads to a simple purely analytic proof that the active reflected Dirichlet space (in the sense of Chen, Fukushima and Kuwae) coincides with the extended active reflected Dirichlet space. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

Il presente lavoro si è proposto di indagare il concetto di razionalità limitata nel contesto delle scelte mediche. Sono stati reclutati 80 adulti, senza una storia clinica particolare a cui è stato dapprima somministrato un test virtuale che richiedeva di prendere delle decisioni su alcuni trattamenti e, successivamente, è stata somministrata una intervista semi-strutturata per approfondire il tema della scelta. I principali risultati: in primis, le persone adottano l’uso di euristiche veloci e frugali. In particolare, le persone adottano l’euristica del “Prendi il meglio” considerando, per ogni scelta, un numero limitato di caratteristiche. In secondo luogo, l'uso di euristiche è legato a una razionalità ecologica che adatta le strategie decisionali alla struttura delle informazioni disponibili del contesto ambientale. In questo contesto, se il consiglio del o le informazioni rispetto ai rischi/effetti indesiderati sono disponibili allora essi saranno sempre valutati perché sono caratteristiche fondamentali del processo di scelta. Il consiglio del medico è espressione della fiducia tra medico e paziente. La fiducia è rappresentata da segnali semplici e onesti che il medico è capace di trasmettere e questi segnali formano un canale di comunicazione tra le persone. Infine un altro risultato riguarda la comprensione del rischio associato al consumo di un farmaco che è risultato di difficile comprensione e rappresentazione. / This research aimed at applying the concept of bounded rationality in common medical choices in order to analyse the process by which laypersons make decisions in the field of health. Eighty adults, without a particular disease history were recruited and they were asked to manage both some virtual situations of medical choices and to discuss face to face about their past experiences in medical choices.Three major findings emerged. Firstly, people often use fast and frugal heuristics. In particular, people adopt the rule of the ‘take the best” considering, for each choice, a very limited number of elements to make their decisions. Secondly, the use of heuristics is related with the principle of ecological rationality in which strategies are chosen in connection with the available information of the environmental context. In this context, if “doctor’s advice” as well as “side effects information” are available, they will be always considered because they represent fundamental features of the decision making process. Doctor’s advice is expression of the trust between patient-doctor relationship. Trust is represented by simple and honest signals that the doctor communicates and these signals form an unconscious channel of communication between people. Thirdly, we found that risks associated with treatments are not easy to be conceived by laypersons. It was that people have not in mind a clear definition of the risk implied by medicines and treatment and they show, in average, a scarce interest in risk comprehension.

De senaste åren kan vi se ett ökat intresse för lärande i organisationer och kompetensutveckling. Detta menar många forskare och beslutsfattare är en väsentlig del för produktivitet, konkurrenskraft och innovation. ( Kock, Gill &amp; Ellström, 2008) Innovationer är vanligtvis en frukt av flera olika personers kreativa förmåga, deras samarbete, erfarenheter och kompletterande kunskaper (Leonard &amp; Swap, 1999). 96,3% av företagen i Sverige är småföretag (www.scb.se). Småföretag och entreprenörer ses som särskilt viktiga för sysselsättning och tillväxt i näringslivet. Trots många initiativ, saknas lösningar i samhället som är väl anpassade till deras speciella behov och förutsättningar. (http://www.regeringen.se). Denna examensuppsats är en kvalitativ studie bestående av semistrukturerade intervjuer som syftar till att undersöka ett kompetensutvecklingsprojekt för småföretagare, vilket syftar till att stödja småföretagares utveckling genom att möjliggöra samverkan och kompetensutveckling. Hansson (2005) beskriver kompetensutveckling som ett mål att förse kompetens till företaget. Dalin (1997) och Hansson (2005) beskriver samverkan som en aspekt av kompetens. För att småföretag ska kunna frodas bör de utveckla externa relationer med andra aktörer som har förmågan att stötta företaget i dess företagsutvecklande. Ska småföretagare kunna flytta sina positioner mot ökad framgång och lönsamhet krävs externa resurser. (Street &amp; Ann-Frances, 2007) Under intervjuerna framkommer respondenternas upplevelser av samverkan under projektets gång och upplevelsen av möjlighet till kommande samverkan som delad. Några av respondenterna uttrycker att samverkan har till viss del stärkt de band som redan funnits genom att mötet har gett en större inblick i de andra företagens verksamhet. Enligt hälften av respondenterna upplevs de för företaget specifika kompetensutvecklingsaktiviteterna som företaget varit i behov av som det viktigaste bidraget till verksamheten. / Over the last couple of years an increased interest of learning in organizations and competence development has been noticed. Many researchers and decitionmakers are of the opinion that this is an important part of productivity, competitiveness and innovation. (Kock, Gill &amp; Ellström, 2008) Innovations are usually the fruit of several individuals creative ability, their cooperation, experiences and their additional knowledge (Leonard &amp; Swap, 1999). 96.3% of the companies in Sweden are small business.(www.scb.se) Small business and entrepreneurs are seen as especially importance of employment and the growth of the economy in spite of many initiatives there is a lack of solutions in the society that are well adjusted to the specific needs and prerequisites (http://www.regeringen.se). This essay is a qualitative study consisting of semi structured interviews with the purpose of exanimating a project of competence development with the aim of supporting small business development through enabling interaction and competence development. Hansson (2005) describes competence development as an objective for providing. Dalin (1997) and Hansson (2005) describe interaction as an aspect of competence. On order for small business to be able to thrive external relations with other businesses with the ability to support the company in its development should be developed. In order for small businesses to be more successful and profitable external resources are needed. (Street &amp; Ann-Frances, 2007) During the interviews it was revealed that the respondents experiences of interaction during the course of the project and the experience of the possibilities for future interaction was parted. Some of the respondents expresses that the interaction to some extent has strengthened existing bonds of interaction by enlarged insight in the other companies business. According to half of the respondents the specific activities of competence development witch the respondent was in need of is experienced as the most important contribution to the business.