Thesis. 1978. M.Arch--Massachusetts Institute of Technology. Dept. of Architecture. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Bibliography: leaves 109-110. / M.Arch

In this thesis, we consider the recent definition of gravitational energy at the quasi-local level provided by Mu-Tao Wang and Shing-Tung Yau. Their definition poses a variational question predicated on isometric embedding of Riemannian surfaces into the Minkowski space; as such, there is a naturally associated Euler-Lagrange equation, which is a fourth-order system of partial differential equations for the embedding functions. We prove a perturbation result for solutions of this Euler-Lagrange equation.

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The purpose of this paper is to examine the important topological properties of the function spaces BC(X,Y) and C(X,Y). Emphasis is given to the relationship between the metrizability of X and the separability of these function spaces. The paper is divided into three major parts: the preliminary definitions and theorems; the relationship between the topological properties of X and BC (X ,Y), for compact X; and the extension of the results of Part II for X not compact and for the case when we have C(X, Y).

Latin American research has addressed the role of urban landscapes in contributing to a sense of community, to social relationships, to the quality of urban life and to community development. This thesis analyses, compares and evaluates spatial practice in two local parks of Bogotá, Colombia. Spatial practice in this research is defined according to Lefebvre’s writing on the production of space. Spatial practice refers to the sensorial level of spatial phenomena; it involves uses, interactions, perceptions, influences and transformations in the everyday relationships between space and people. The two parks under investigation are located in and belong to different socioeconomic areas and the cross-class comparison of parks and spatial practice is important in a highly segregated city such as Bogotá. Locally, the two parks are part of the innovative municipal government program, ‘Parks for Learning How to Live,’ (1998-2000).This project transformed public space physically as well as residents’ perceptions of public space, parks, and outdoor recreation and leisure. The research design was qualitative because it sought information on perceptions, uses and feelings of park users.The findings identified that despite the two parks being similar in terms of their physical characteristics, they display different spatial practices that in turn reflect the socio-economic status, history, and expectations of the communities that use them. This research provides an in-depth analysis of the spatial practice in these two parks in order to start building a bottom-up framework that may be instrumental for future planning. / Doctor of Philosophy (PhD)

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.S.)--University of Delaware, 2006. / Principal faculty advisor: Robert E. Lyons, Dept. of Plant & Soil Sciences. Includes bibliographical references.

No description available.

Résumé de la thèse : ce travail porte sur la notion d'espace symétrique symplectique extrinsèque. Ces espaces sont des espaces symétriques symplectiques dont la structure est induite par le plongement dans variété symplectique ambiante munie d'une connexion. Par analogie à la théorie standard des espaces symétriques, nous démontrons un théorème d'équivalence entre les espaces symétriques symplectiques extrinsèques d'une variété qui est elle-même un espace symétrique symplectique. La définition d'un espace symétrique symplectique extrinsèque fait intervenir l'existence d'affinités globales de la variété ambiante, les ``symétries extrinsèques', qui induisent la structure symétrique de la sous-variété ; ceci mène à poser une question du type : quelles sont les variétés possédant ``beaucoup' de ces affinités~? Une question précise ainsi qu'une réponse sont fournies dans un contexte où la variété ambiante est seulement supposée munie d'une structure symplectique et d'une connexion symplectiques. Nous considérons également le cas où ces symétries commutent avec un champ $K$ d'endomorphismes symplectiques fixé de la variété, de carré $pmId$. Nous définissons une notion de courbure sectionnelle pour plans $K$-stables et montrons que les espaces à $K$-courbure sectionnelle constantes sont localement symétriques de type Ricci. Par suite nous étudions les espaces symétriques symplectiques extrinsèques dans un espace vectoriel symplectique. Nous montrons par exemple qu'un tel espace, s'ils est de dimension deux, est forcément intrinsèquement plat (c.-à-d. à courbure intrinsèque nulle), mais que son image n'est pas forcément un plan affin de l'espace vectoriel ambiant. Nous décrivons en fait explicitement tous les espaces symétriques symplectiques extrinsèques, dans un espace vectoriel, dont la courbure intrinsèque s'annule identiquement. Nous décrivons également une famille d'exemples d'espaces extrinsèques, dont nous montrons qu'elle fournit la totalité des espaces extrinsèques de codimension $2$, dans un espace vectoriel. Enfin, nous décrivons quelques exemples d'espaces symétriques symplectiques extrinsèques qui sont totalement géodésiques, dans un espace de type Ricci particulier.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 51-52).