We present important results from Hilbert space and functional analysis for understanding the subject ofReproducing kernel Hilbert spaces. We then showcase the underlying theory and properties of Reproducingkernel Hilbert Spaces. Finally, we show how the theory of reproducing kernel Hilbert spaces is applicable inboth interpolation and machine learning.

This work is dealing with almost-compact embeddings of function spaces, in particular, the class of classical and weak Lorentz spaces with a norm given by a general weight fuction is studied. These spaces are not Banach function spaces in general, thus the almost-compact em- bedding is defined for more general sturctures of rearrangement-invariant lattices. A general characterization of when an r.i. lattice is almost-compactly embedded into a Lorentz space, involving an optimal constant of a certain continuous embedding, is proved. Based on this the- orem and appropriate known results about continuous embeddings, explicit characterizations of mutual almost-compact embeddings of all subtypes of Lorentz spaces are obtained. 1

In this thesis we focus on generalized Gamma spaces GΓ(p, m, v) and classify some of their intrinsic properties. In an article called Relative Re- arrangement Methods for Estimating Dual Norm (for details see references), the authors attempted to characterize their associate norms but obtained only several one-sided estimates. Equipped with these, they further showed reflexivity of gener- alized Gamma spaces for p ≥ 2 and m > 1 under an additional restriction that the underlying measure space is of finite measure. However, the full characterization of the associate norm and of the reflexivity of such spaces for 2 > p > 1 remained an open problem. In this thesis we shall fill this gap. We extend the theory to a σ-finite measure space. We present a complete characterization of the associate norm, and we find necessary and sufficient conditions for the reflexivity of such spaces. 1

Esta dissertação de mestrado versa sobre os Espaços Públicos Abertos e o conceito de Infra-Estrutura Verde para a cidade de Sorocaba, localizada a 100 km da metrópole de São Paulo, na região sudoeste do Estado de São Paulo. Lida com as questões dos recursos naturais do suporte biofísico da região, a configuração de seus Espaços Públicos Abertos, a morfologia urbana, as áreas a serem preservadas, o planejamento ambiental para uma cidade grande que polarizou na última década recursos financeiros expressivos e populações em uma região que comparada ao restante do Estado de São Paulo, com taxas de urbanização e de riqueza baixas. Cita como exemplo o Parque Vitória Régia, localizado numa área de várzea do Rio Sorocaba, para a utilização do conceito de Infra-Estrutura Verde utilizando o planejamento, o projeto e ações de implementação que podem ser aplicados em varias escalas, como conceito e como processo. / This paper is about the Open Public Spaces and Green Infrastructure concept for the city of Sorocaba, located about 60 miles from the São Paulo City, in the southwest part of São Paulo State. Natural resources, the fisiography of the region, the public open spaces evolution, urban morphology, the green areas to be preserved, flooding areas, the landscape planning possible, are studied about a great city (more than 500 mil inhabitants) which drew an expressive amount of financial resources and other population to this particular region, still one of those less developed and less rich of Sao Paulo State. Talks about The Vitoria Régia Park, a citys public space installed in an open area of Sorocaba River, which received an intervation to stop its environemental pollution, and to use the approach of Green Infrastructure, using the project, planning and management which can be used as a concept and as a process to preserve the open lands still full of life.

Lam Li. / "Architecture Department, Chinese University of Hong Kong, Master of Architecture Programme 2001-2002, design report." / Includes bibliographical references (leaves [93]-[95]). / Acknowledgment --- p.2 / Chapter 1 --- Thesis Statement --- p.3 / Chapter 1.1 --- Hypothesis / Chapter 1.2 --- Statement / Chapter 1.3 --- Objectives / Chapter 1.4 --- Scope of Work / Chapter 2 --- Research --- p.5 / Chapter 2.1 --- "Reading on Spirit of Place : < Genius Loci>, Christian" / Chapter 2.2 --- "Reading on the <Image of City>, Kevin Lynch" / Chapter 2.3 --- Reflections on the Two Readings / Chapter 2.4 --- Studies on the Recent History of City Planning / Chapter 2.5 --- Precedent Study: An Art City - Paris / Chapter 2.5.1 --- Haussmann: Paris Transformed / "The Rebuilding of Paris, 1852-1870" / Chapter 2.5.2 --- "The Place Louis-XV, 1757-90" / Chapter 2.5.3 --- New development scheme for Paris by Henry Bernard (1965-67) / Chapter 2.5.4 --- The new city centre - les Forum des halles by C. Vasconi - G. Pencreac'h 1982 / Chapter 2.6 --- Research on Public Art / Chapter 2.7 --- Writing: <An Urban Pubic Space - The Hong Kong Culture Centre> / Chapter 3 --- Special Studies on Piazza Delia Signoria and Uffizi Gallery in Florence --- p.43 / Chapter 3.1 --- The City: Florence / Chapter 3.2 --- Piazza Delia Signoria / Chapter 3.3 --- Uffizi Gallery / Chapter 4 --- Site Analysis --- p.48 / Chapter 4.1 --- The City: Hong Kong / Chapter 4.1.1 --- Landscape / Chapter 4.1.2 --- Major Site Influences / Chapter 4.1.3 --- Victoria Harbour / Chapter 4.1.4 --- West Kowloon New Cultural District Competition / Chapter 4.2 --- "The District: Neighborhoods: Kowloon City District, Wong Tai Sin District and Kowoon Bay District" / Chapter 4.3 --- The Region: Old Kai Tak Airport / Chapter 4.3.1 --- History / Chapter 4.3.2 --- Character / Chapter 4.3.3 --- East Kowloon Development Proposal / Chapter 4.4 --- Ma Tau Kok / Chapter 4.5 --- Cattle Depot Artist Village / Chapter 5 --- Design Development --- p.72 / Chapter 5.1 --- Planning Strategy 1: Preliminary Proposal of Master Layout Plan / Chapter 5.2 --- Planning Strategy 2: The Organisation of art institutions in Hong Kong / Chapter 5.3 --- Planning Strategy 3: The Artists' Path and the Nodes - the Cattle Artist new Cultural area in Kai Tak / Chapter 5.4 --- Preliminary Design / Chapter 5.5 --- Final Design / Chapter 6.2.1 --- Street Design / Chapter 6.2.2 --- Theatre Design / Chapter 5.6 --- Final Presentation / Chapter 6 --- Bibliography --- p.91 / Chapter 7 --- Reference --- p.92

Esta dissertação de mestrado versa sobre os Espaços Públicos Abertos e o conceito de Infra-Estrutura Verde para a cidade de Sorocaba, localizada a 100 km da metrópole de São Paulo, na região sudoeste do Estado de São Paulo. Lida com as questões dos recursos naturais do suporte biofísico da região, a configuração de seus Espaços Públicos Abertos, a morfologia urbana, as áreas a serem preservadas, o planejamento ambiental para uma cidade grande que polarizou na última década recursos financeiros expressivos e populações em uma região que comparada ao restante do Estado de São Paulo, com taxas de urbanização e de riqueza baixas. Cita como exemplo o Parque Vitória Régia, localizado numa área de várzea do Rio Sorocaba, para a utilização do conceito de Infra-Estrutura Verde utilizando o planejamento, o projeto e ações de implementação que podem ser aplicados em varias escalas, como conceito e como processo. / This paper is about the Open Public Spaces and Green Infrastructure concept for the city of Sorocaba, located about 60 miles from the São Paulo City, in the southwest part of São Paulo State. Natural resources, the fisiography of the region, the public open spaces evolution, urban morphology, the green areas to be preserved, flooding areas, the landscape planning possible, are studied about a great city (more than 500 mil inhabitants) which drew an expressive amount of financial resources and other population to this particular region, still one of those less developed and less rich of Sao Paulo State. Talks about The Vitoria Régia Park, a citys public space installed in an open area of Sorocaba River, which received an intervation to stop its environemental pollution, and to use the approach of Green Infrastructure, using the project, planning and management which can be used as a concept and as a process to preserve the open lands still full of life.

In this paper we give a characterization theorem for the reciprocal Dunford-Pettis property as defined by Grothendieck. The relationship of this property to Pelczynski's property V is examined. In particular it is shown that every Banach space with property V has the reciprocal Dunford-Pettis property and an example is given to show that the converse fails to hold. Moreover the characterizations of property V and the reciprocal Dunford-Pettis property lead to the definitions of property V* and property RDP* respectively. Me compare and contrast results for the reciprocal Dunford-Pettis property and property RDP* with those for properties V and V*. In the final chapter we use a result of Brooks to obtain a characterization for the Radon-Nikodým property.

Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.

Let X be a Polish space and Q a measurable partition of X into Gδ equivalence classes. In 1978, S. M. Srivastava proved the existence of a Borel cross section for Q. He asked whether more can be concluded in case each equivalence class is uncountable. This question is answered here in the affirmative. The main result of the author is a proof that shows the existence of a Castaing Representation for Q.

Typescript (photocopy). / Digitized by Kansas Correctional Industries