We look at the mixed boundary value problem for elliptic operators in a bounded C1,1(ℝn) domain. The boundary is decomposed into disjoint parts, D and N, with Dirichlet and Neumann data, respectively. Expanding on work done by Ott and Brown, we find a larger range of values of p, 1 < p < n/(n-1), for which the Lp mixed problem has a unique solution with the non-tangential maximal function of the gradient in Lp(∂Ω).

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

In this thesis, we study robust combinatorial problems with interval data. We introduce several new measures of robustness in response to the drawbacks of existing measures of robustness. The idea of these new measures is to ensure that the solutions are satisfactory for the decision maker in all scenarios, including the worst case scenario. Therefore, we have introduced a threshold over the worst case costs, in which above this threshold, solutions are no longer satisfactory for the decision maker. It is, however, important to consider other criteria than just the worst case. Therefore, in each of these new measures, a second criteria is used to evaluate the performance of the solution in other scenarios such as the best case one. We also study the robust deviation p-elements problem. In fact, we study when this solution is equal to the optimal solution in the scenario where the cost of each element is the midpoint of its corresponding interval. Then, we finally formulate the robust combinatorial problem with interval data as a bicriteria problem. We also integrate the decision maker's preferences over certain types of solutions into the model. We propose a method that uses these preferences to find the set of solutions that are never preferred by any other solution. We call this set the final set. We study the properties of the final sets from a coherence point of view and from a robust point of view. From a coherence point of view, we study necessary and sufficient conditions for the final set to be monotonic, for the corresponding preferences to be without cycles, and for the set to be stable. Those that do not satisfy these properties are eliminated since we believe these properties to be essential. We also study other properties such as the transitivity of the preference and indifference relations and more. We note that many of our final sets are included in one another and some are even intersections of other final sets. From a robust point of view, we compare our final sets with different measures of robustness and with the first- and second-degree stochastic dominance. We show which sets contain all of these solutions and which only contain these types of solutions. Therefore, when the decision maker chooses his preferences to find the final set, he knows what types of solutions may or may not be in the set. Lastly, we implement this method and apply it to the Robust Shortest Path Problem. We look at how this method performs using different types of randomly generated instances.

With the financial crisis, many firms suffered from liquidity shortages and needed to quickly change their way of working to release capital from the operations. Scholars argue that firms should handle immediate crisis with short-term measures first, and then change the underlying organizational routines to prevent recurrence. The management of working capital has received increased attention amongst corporate managers as a result of the crisis, whereby it is interesting to understand how firms can reduce their working capital in a sustainable way. By using the problem-finding and problem-solving approach, this study explores how successful firms have found and solved problems to make them sustainable. To answer the research question a multiple-case study is performed, where five firms are explored through interviews with key respondents. The study indicates that urgency is the main driver for both introducing and increasing the focus on working capital management. Different strategies for obtaining sustainable working capital management are found, where focus and commitment from the top management is suggested to be the glue that makes it last. It is furthermore suggested that managers have two main tools for creating and sustaining desired routines and practices; communication and control.

The purpose of the present study was to examine cognitive abilities and problem solving processes of young and older adults. Specifically, three areas of inquiry were investigated: possible age-related differences in problem solving cognitive abilities, possible differences in cognitive processes used during problem solution, and possible differences in determinants of problem solving cognitive processes.

O objetivo desta dissertação é estudar o problema de autovalor de Dirichlet para variedades riemannianas completas. Mais precisamente, pretendemos estudar uma cota por baixo para o -ésimo autovalor de um domínio limitado em uma variedade riemanniana completa. Tal cota é obtida fazendo-se uso de uma fórmula de recorrência de Cheng e Yang e um teorema de Nash. Ademais, pretendemos estudar uma desigualdade universal para os autovalores no espaço hiperbólico. / The goal of this dissertation is to study the Dirichlet eigenvalue problem for a complete riemannian manifold. More accurately, we intend to investigate a lower-bound for the -ℎ eigenvalue on a bounded domain in a complete riemannian manifold. Such a bound is obtained by making use of a recursion formula of Cheng and Yang and Nash’s Theorem. Furthermore, we study a universal inequality for eigenvalues of the Dirichlet eigenvalue problem on a bounded domain in a hyperbolic space (−1).

Denna systematiska litteraturstudie är uppdelad i två huvuddelar. Den första delen handlar om problemlösning där resultatet betonar vad som kännetecknar ett matematiskt problem och hur begreppet problemlösning definieras. Vidare redovisas resultat av vad olika forskare skriver om hur ett arbete med problemlösning bör användas i klassrummet och vilka fördelar som finns med detta arbetssätt. Den andra huvuddelen är inriktad på öppna problem. Denna del följer samma struktur där först en definition av begreppet öppna problem framkommer. Resultatet visar på många olika fördelar med ett arbete genom problemlösning och främst öppna problem i det matematiska klassrummet. Studien avser vara en hjälp till lärare som arbetar med problemlösning för att skapa en tydlighet i hur ett arbete genom problemlösning och öppna problem bör se ut.

Few and many-body systems usually feature interesting and novel behaviors compared with their counterparts in three dimensions. On one hand, low dimensional physics presents challenges due to strong interactions and divergences in the perturbation theory; On the other hand, there exist powerful theoretical tools such as the renormalization group and the Bethe ansatz. In this thesis, I discuss two examples: three interacting bosons in two dimensions and interacting bosons/fermions in one dimension. In both examples, there are intraspecies repulsion as well as interspecies attraction, producing a rich spectrum of phenomena. In the former example, a universal curve of three-body binding energies versus scattering lengths is obtained efficiently by evolving a matrix renormalization group equation. In the latter example, exact solutions for the BCS-BEC crossover are obtained and the unexpected robust features in their excitation spectra are explained by a comprehensive semiclassical analysis.

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The study challenges current literature, which views the notion of problem-finding as the initial identification of a problem to be solved. The concept of problem-finding in this study is that problem-finding continues throughout the problem-solving process and is not distinct from it. This thesis aims to develop a better understanding of problem-finding by examining high school students using problem-finding to solve industrial design problems. The study seeks to find out what types of problem-finding exist and what roles they play in solving design problems. To explore problem-finding, this study uses a Think Aloud methodology to examine the thinking of three high school industrial design students and one high school industrial design teacher solving an authentic industrial design problem. Protocol data was gathered from the subjects and then transcribed, segmented and analysed in three ways, each of which became progressively more specific: Firstly, a macroscopic examination which identified problem-finding episodes occurring throughout the design process; secondly, a microscopic examination which identified four categories of problem-finding; and lastly, a microscopic examination which looked at the role played by the different problem-finding categories in solving design problems. The findings of this study are fourfold. Firstly, problem-finding was found to be used throughout the entire design process. Secondly, there were four categories of problemfinding. Thirdly, each category played an important role predominantly through interaction with other categories. Lastly, the more experienced a person was, the more able they were to use problem-finding effectively to solve design problems. Many current practices use trial and error methods to solve design problems. The importance of this study is that through a better understanding of problem-finding, designers may be able to use metacognitive strategies more efficiently in the process. Similarly, in educational practice, high school design students may be able to learn to think about the methods they use to solve design problems, and this may result in more creative designs.