Diss. (sammanfattning) Stockholm : Karol. inst., 2006. / Härtill 4 uppsatser.

Diss. (sammanfattning) Stockholm : Karol. inst., 2006. / Härtill 4 uppsatser.

Dissertation (Ph.D.) --University of Texas Graduate School of Biomedical Sciences at San Antonio, 2008. / Vita. Includes bibliographical references.

Nós estudamos a dinâmica do operador de renormalização atuando no espaço de pares (?, t), onde ? é um difeomorfismo e t ? [0, 1], interpretados como aplicações unimodais ? o qt, onde qt(x) = -2t|x|? + 2t - 1. Estabelecemos cotas complexas a priori para pares suficientemente renormalizáveis com combinatória limitada e então a utilizamos para mostrar que quando o expoente crítico ? está próximo de um número par, o operador de renormalização tem um único ponto fixo, o qual é hiperbólico e possui uma variedade estável de codimensão um que contém todos os pares infinitamente renormalizáveis / We study the dynamics of the renormalization operator acting on the space of pairs (?, t), where ? is a diffeomorphism and t ? [0, 1], interpretated as unimodal maps ? o qt, where qt(x) = -2t|x|? + 2t - 1. We prove the so called complex bounds for sufficiently renormalizable pairs with bounded combinatorics. This allows us to show that if the critical exponent ? is close to an even number then the renormalization operator has a unique fixed point. Furthermore this fixed point is hyperbolic and its codimension one stable manifold contains all infinitely renormalizable pairs

The use of bidentate ligands in organometallic chemistry is best illustrated by the successful application in homogeneous catalysis1 and bio-medical2 systems. For catalytic systems the use of bidentate phosphines have revolutionised the way in which homogeneous catalysis is viewed, with the use of functionalised organic ligands to induce favourable catalytic product formation such as the production of L-Dopa3. To this end, the investigation of tropolone type ligands and complexes will be discussed further in this chapter. The possible application of tropolone systems will be investigated in the context of possible catalytic and bio-medical applications. In 1945 Dewar4 predicted that 2-hydroxy-2,4,6-cycloheptatrien-one (Tropolone, Eq. 1.1.I), would show certain aromatic properties; he specifically referred to the natural products known at that time, stipitatic acid and colchicine5 as representative of this class of compounds. Thus Dewar was the first person to point to a new field in organic chemistry, which to date has not been fully explored due to the diversity of uses of tropolone and its derivatives. / Prof. A. Roodt

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This thesis is an investigation into the makings of a successful youth baseball facility. Youth sports is a multi-billion dollar industry in the United States, and much of the competition follows a tournament, or "travel league" format. This is especially true in youth baseball. Despite this growing trend towards travel play, facilities that host these tournaments were designed and constructed in an age where the primary format was not tournament play, but rather a recreational structure where single games were played individually. These facilities do not meet the needs of the typical park user: players and their families. The parts of the following investigation are the Author's research, including a literature review and four case studies of facilities that are representational of a larger sample. This is followed by the identification of a list of universial challenges faced by many facilities which led to a development of a list of design criteria to correct the issue of under-performing parks, identification of a fundamental design question, and specific goals and objectives. Finally, identification of a site to be studied is introduced and analyzed, and the development of the Author's concept for a new design is reported and then analyzed. The Master Plan is then presented and discussed in detail. The master plan for the new Rockville School Park has been developed based on the list of design criteria developed by the Author, based largely on field research. A large effort was made to identify literature directly regarding the questions presented in this thesis. The literature used has been included within the references section at the end of this document. / Master of Landscape Architecture / This thesis is an investigation into the makings of a successful youth baseball facility. Youth sports is a multi-billion dollar industry in the United States, and much of the competition follows a tournament, or "travel league" format. This is especially true in youth baseball. Despite this growing trend towards travel play, facilities that host these tournaments were designed and constructed in an age where the primary format was not tournament play, but rather a recreational structure where single games were played individually. These facilities do not meet the needs of the typical park user: players and their families. The parts of the following investigation are the Author's research, including a literature review and four case studies of facilities that are representational of a larger sample. This is followed by the identification of a list of universial challenges faced by many facilities which led to a development of a list of design criteria to correct the issue of under-performing parks, identification of a fundamental design question, and specific goals and objectives. Finally, identification of a site to be studied is introduced and analyzed, and the development of the Author's concept for a new design is reported and then analyzed. The Master Plan is then presented and discussed in detail. The master plan for the new Rockville School Park has been developed based on the list of design criteria developed by the Author, based largely on field research. A large effort was made to identify literature directly regarding the questions presented in this thesis. The literature used has been included within the references section at the end of this document.

Yes / In CAD, when considering the question of new designs of complex mechanical parts, such as engine pistons, a parametric representation of the design is usually defined. However, in general there is a lack of efficient tools to create and manipulate such parametrically defined shapes. In this paper, we show how the geometry of complex mechanical parts can be parameterised efficiently enabling a designer to create and manipulate such geometries within an interactive environment. For surface generation we use the PDE method which allows surfaces to be defined in terms of a relatively small number of design parameters. The PDE method effectively creates surfaces by using the information contained at the boundaries (edges) of the surface patch. An interactively defined parameterisation can then be introduced on the boundaries (which are defined by means of space curves) of the surface. Thus, we show how complex geometries of mechanical parts, such as engine pistons, can be efficiently parameterised for geometry manipulation allowing a designer to create alternative designs.

The Fundamental Theorem of Algebra is a useful tool in determining the number of zeros of complex-valued polynomials and rational functions. It does not, however, apply to complex-valued harmonic polynomials and rational functions generally. In this thesis, we determine behaviors of the family of complex-valued harmonic functions $f_{c}(z) = z^{n} + \frac{c}{\overline{z}^{k}} - 1$ that defy intuition for analytic polynomials. We first determine the sum of the orders of zeros by using the harmonic analogue of Rouch\'e's Theorem. We then determine useful geometry of the critical curve and its image in order to count winding numbers by applying the harmonic analogue of the Argument Principle. Combining these results, we fully determine the number of zeros of $f_{c}$ for $c > 0$.

Brilleslyper et al. analyzed a one-parameter family of harmonic trinomials, and Brooks and Lee analyzed a one-parameter family of harmonic functions with poles. Each family was explored to find the relationship between the size of the parameter and the number of zeros of the harmonic function. In this thesis, we examine convex combinations of members of these families. We determine conditions under which the critical curves separating the sense-preserving and sense-reversing regions are circular. We show that the number of zeros of a convex combination can be greater than the maximum number of zeros of either part.