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The central object of the study in this thesis is ΩO(<I>n</I>), the space of closed continuous loops on an orthogonal group O(<I>n</I>) based at the identity-element 1 Ε O(<I>n</I>). The space ΩO(<I>n</I>) carries a group structure given by pointwise multiplication of paths in the group O(<I>n</I>). This makes it an infinite dimensional Lie group. A filtration of ΩO(<I>n</I>), more precisely of the subspace of 'polynomial' loops, is constructed. This can be thought of as the 'real' analogue of the Mitchell-Richter filtration of ΩSU(<I>n</I>). Our filtration of ΩO(<I>n</I>) splits stably and O(<I>n</I>)-equivariantly in the cases <I>n</I> = 3, 4. We obtain: In contrast to the complex case no general splitting result can hold (this follows from work by Hopkins on stable indecomposability of ΩSp(2)). The thesis also investigates the topology of the loopspace of a real Stiefel-manifold. A stable O(<I>n</I>)-equivariant splitting for the fibrewise loop-space of a projective bundle is used to give a splitting for the free loop-space LRP<I>ⁿ</I> on a real projective space.

This thesis verified that metric spaces can be constructed using ultrametrics d and D, where d(x,y) = 0 if x = y and d(x,y) = (1/2) k if x not equal to y, such that x-y = 2k(a/b) for a,b relatively prime to 2, and where D(A,B)= max(d(al,bl); d(a2,b2)) for A = (al,a2) and B = (bl,b2).Assuming that a line is represented by some linear equation, a one-dimensional point was defined as an element of Q and a two-dimensional point as an element of Q x Q. There was an investigation of one-dimensional points with respect to the behavior of segments, midpoints, and distances as measured by d. The function D demonstrated the behavior of midpoints, medians, and triangles, as well as the congruence relation. The study necessitated the introduction of pseudomidpoints and pseudomedians, and an unorthodox definition of angle measurement.

Cooling and ventilation of office spaces by displacement ventilation and chilled ceiling panel systems is potentially more energy efficient than conventional air conditioning systems. Heat transfer in this type of system is characterised by the presence of vertical temperature gradients and significant radiant asymmetry. The room heat transfer models used in current building simulation methods do not allow adequate representation of this type of system due to their reliance on a single node to define the internal air temperature. The overall aim of the work described in the thesis has been to develop a model of this type of system that is suitable for use in annual building energy simulation. The model presented, is intermediate in complexity between a CFD numerical model and the current single air node models, having ten air nodes. The operating characteristics of displacement ventilation systems, used both with and without chilled ceiling panels, have been studied by making experimental measurements in a test chamber and by reference to published experimental data. Numerical calculations of the flow and temperature fields have been made with a coupled flow and radiant exchange CFD code. Steady state calculations have been made of displacement ventilation using a conjugate heat transfer method. Interesting oscillations in the flow and temperature field of displacement ventilation operating with a chilled ceiling have been found through adopting a fully transient calculation procedure. The thesis describes how the experimental and numerical data has been used to develop the structure and define the parameters of a simplified nodal model. The logical development of the model structure, from the most elementary model to one which is able to capture the effects of the temperature gradients and incomp1ete mixing of the air in the room is described. A method is also presented whereby the parameters of the model are found directly from the experimental data by solving the heat and mass balance equations of the nodal model. The parameters of the model have been generalised by analysing these calculations and by making use of established convection coefficient correlations. The performance of the model is demonstrated by firstly making comparisons of the experimental and numerical data under steady state conditions, and also by demonstrating that the model is able to reproduce the characteristics of displacement ventilation and chilled ceiling systems under different operating conditions.

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This thesis is an analysis of convergence results on Fourier series. Convergence of Fourier series is studied in two ways in this thesis. The first way is in the context of Banach spaces, where the set of functions is restricted to a certain Banach space. Then the problem is in determining whether the Fourier series of a function can be represented as an element of that Banach space. The second way is in the context of pointwise convergence. Here, the problem is in determining what conditions need to be placed on an arbitrary function for its Fourier series to converge at a point.

This document examines the public spaces created by the built environment of the city and asks: How is it that the apparently benign and benevolent activity of designing public space can in fact reinforce values that effectively marginalise and exclude significant groups of people? It contrasts the consequences of design decisions that are based on a value system of ???either/or??? with the possibility for designs based on ???both/and???. The perception of boundaries, the desire to dwell, the need to belong and the relationship of these phenomena to an understanding of ???self???, is proposed as the key means for analysing how public space is experienced by the user. The document uses the language of barriers and boundaries to interrogate how the value systems of those with the control over resources is manifest in the built environment of the city, and examines the impact such environments have on the user???s desire to ???dwell??? and need to belong. The potential for an alternate paradigm based on a system that recognises ???both/and??? to produce beneficial outcomes is then proposed, with a focus on an ethic of care to complement the ethic of justice that currently guides design decisions for public space. Personal interviews with architects, town planners, representatives from relevant government agencies, and users of public space, participation in public meetings and systematic observation of specific sites have been used to inform the argument and assess the validity of claims. The document is extended by a body of visual work that further interrogates the need to belong and broader issues of the primal significance of ???sanctuary??? to the ability to ???dwell???. The making and maintaining of boundaries, necessary to form a sanctuary, is portrayed as a process fraught with insecurities and vulnerabilities necessitating, in circumstances where personal power or the ability to influence one???s environment is diminished, the use of subversive tactics in order to create a space in which one can belong.

Thesis (M.A.)--York University, 2006. Graduate Programme in Geography. / Typescript. Includes bibliographical references (leaves 166-171). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR19639