918 resultados para Hausdorff dimension
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We study which topology have an immediate predecessor in the poset of Sigma(2) of Hausdorff topologies on set X. We show that certain classes of H-closed topologies, do have predecessors. and we give examples of second countable H-closed topologies which are not upper Sigma(2.)
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In this dissertation, an educational perspective called the moral dimension of teaching is developed. The work includes a theoretically informed discussion from a pragmatist point of view in which the concept of pedagogical rhythm is introduced. The concept captures the need for teachers to regularly shift their intentions and occasionally act in contradictory ways as a consequence of the moral which emerges from interaction in pedagogical situations. Using this perspective, criteria are developed for the characteristics of discussions of the work of teachers, which are desirable in order for students in pre-service teacher education to have opportunities to develop their teachership. Secondly, the educational perspective as it is conceptualised serves as a theoretical framework for a study of discussions taking place in net-based seminars among students in teacher education. The study consists of 14 recorded seminars in which discussions of the work of teachers are analysed in terms of content and direction for reflection. The result of the analysis is a construction of four different focal points for processes of making judgements: existential, performative, critical and professional. Mainly the performative, and to some extent the critical, focal points appear to be supported by the net-based environment, although potential for the professional focal point is found when available tools in net-based settings are used in deliberate ways. Finally, based on these four focal points, possible future predispositions among student teachers are deliberated. Student teachers’ future opportunities to develop a moral and epistemological authority are discussed, as well as teachers’ general opportunities to exercise professional responsibility. The conclusion emphasises that a perspective such as the one developed in the dissertation is important, as it creates an understanding for the need to educate student teachers to exercise a form of responsibility that goes beyond being accountable to society.
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Why did house prices fall in 2007‐2009? This is the fundamental question to most Americans, and to those who lent them money. Most homeowners did not care why residential real estate prices rose. They assumed prices always rose, and they should simply enjoy their good fortune. It was not until prices began to fall that people were left searching for answers. How much did regulation or lack thereof play in the role of the devastation? To what degree did greed and unrealistic consumer expectation have on the real estate bubble? Using existing literature as well as face to face interviews of experienced leaders within the real estate industry in California who experienced both the up and down of the real estate cycle, the overarching purpose of this study is to investigate the opinions and beliefs of the leaders and drivers within the real estate industry about the cause of the real estate bubble that occurred sharply in 2008 . Specifically, this project will focus on the opinions of real estate industry leaders who worked in the center of the subprime universe located in Irvine, California, during 2004‐2008. Comparing the mainstream beliefs with the interviewees it is fair to say that the main finding in the mainstream beliefs are reflected very well with the finding of the subject’s opinion. The thesis is divided into 6 chapters starting with “introduction”, followed by chapter 2 “Literature Review”. Chapter 3 is “Research Methodology” followed by chapter 4 “Data Presentation”. Finally, the results are discussed in chapter 5 “Analysis and Discussion” and conclusions in Chapter 6.
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Nota: A autora agradece à Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) pela concessão de bolsa de estudos para o desenvolvimento deste projeto de pesquisa.
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Orientador Louis Marmoz
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points
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The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl.
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Bloch and Wannier functions of the Kohn type for a quite general one-dimensional Hamiltonian with inversion symmetry are studied. Important clarifications on null minigaps and the symmetry of those functions are given, with emphasis on the Kronig-Penney model. The lack of a general selection rule on the miniband index for optical transitions between edge states in semiconductor superlattices is discussed. A direct method for the calculation of Wannier-Kohn functions is presented.
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In this work we present the principal fractals, their caracteristics, properties abd their classification, comparing them to Euclidean Geometry Elements. We show the importance of the Fractal Geometry in the analysis of several elements of our society. We emphasize the importance of an appropriate definition of dimension to these objects, because the definition we presently know doesn t see a satisfactory one. As an instrument to obtain these dimentions we present the Method to count boxes, of Hausdorff- Besicovich and the Scale Method. We also study the Percolation Process in the square lattice, comparing it to percolation in the multifractal subject Qmf, where we observe som differences between these two process. We analize the histogram grafic of the percolating lattices versus the site occupation probability p, and other numerical simulations. And finaly, we show that we can estimate the fractal dimension of the percolation cluster and that the percolatin in a multifractal suport is in the same universality class as standard percolation. We observe that the area of the blocks of Qmf is variable, pc is a function of p which is related to the anisotropy of Qmf
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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This study analyzes an accident in which two maintenance workers suffered severe burns while replacing a circuit breaker panel in a steel mill, following model of analysis and prevention of accidents (MAPA) developed with the objective of enlarging the perimeter of interventions and contributing to deconstruction of blame attribution practices. The study was based on materials produced by a health service team in an in-depth analysis of the accident. The analysis shows that decisions related to system modernization were taken without considering their implications in maintenance scheduling and creating conflicts of priorities and of interests between production and safety; and also reveals that the lack of a systemic perspective in safety management was its principal failure. To explain the accident as merely non-fulfillment of idealized formal safety rules feeds practices of blame attribution supported by alibi norms and inhibits possible prevention. In contrast, accident analyses undertaken in worker health surveillance services show potential to reveal origins of these events incubated in the history of the system ignored in practices guided by the traditional paradigm.