published_or_final_version / Urban Planning / Master / Master of Science in Urban Planning

Thesis (Ph.D.)--Ohio University, June, 2009. / Includes bibliographical references (leaves 146-149)

Thesis (Ph.D.)--Ohio University, June, 2009. / Title from PDF t.p. Includes bibliographical references (leaves 146-149)

Thesis (M.U.D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 77-78).

This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. We study different structural, integrability, and smoothness properties of functions satisfying certain mixed norm conditions. Conditions of this type are determined by the behaviour of linear sections of functions. The work in this direction originates in a paper due to Gagliardo (1958), and was further developed by Fournier (1988), by Blei and Fournier (1989), and by Kolyada (2005). Here we continue these studies. We obtain some refinements of known embeddings for certain mixed norm spaces introduced by Gagliardo, and we study general properties of these spaces. In connection with these results, we consider a scale of intermediate mixed norm spaces, and prove intrinsic embeddings in this scale. We also consider more general, fully anisotropic, mixed norm spaces. Our main theorem states an embedding of these spaces to Lorentz spaces. Applying this result, we obtain sharp embedding theorems for anisotropic Sobolev-Besov spaces, and anisotropic fractional Sobolev spaces. The methods used are based on non-increasing rearrangements, and on estimates of sections of functions and sections of sets. We also study limiting relations between embeddings of spaces of different type. More exactly, mixed norm estimates enable us to get embedding constants with sharp asymptotic behaviour. This gives an extension of the results obtained for isotropic Besov spaces by Bourgain, Brezis, and Mironescu, and for anisotropic Besov spaces by Kolyada. We study also some basic properties (in particular the approximation properties) of special weak type spaces that play an important role in the construction of mixed norm spaces, and in the description of Sobolev type embeddings. In the last chapter, we study mixed norm spaces consisting of functions that have smooth sections. We prove embeddings of these spaces to Lorentz spaces. From this result, known properties of Sobolev-Liouville spaces follow.

Thesis (M.U.D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 77-78) Also available in print.

The purpose of this master's thesis is to explore how creative spaces in libraries function, their goals and how they affect the role of their host libraries by undertaking a qualitative multi-case study in three public libraries in Dublin Ireland .This uses the four spaces model as a theoretical framework in analysing the empirical data which was gathered from semi-structured interviews of librarians and an events planner in the spaces as well as a document analysis of related strategic documents. The results of the study show that creative spaces offer a way for libraries to attract more and diverse groupings of patrons to their service and primarily have a role as learning and inspirational spaces. They enable libraries in particular to help give equal access to STEM resources and encourage experience based learning in all age groups from young to old. Each space has an individual character and its content and role is dependent on the host library and can act as a force multiplier for the various goals and roles of the library itself.

In this thesis, we discuss three main projects which are related to Polish groups and their actions on standard Borel spaces. In the first part, we show that the complexity of the classification problem of continua is Borel bireducible to a universal orbit equivalence relation induce by a Polish group on a standard Borel space. In the second part, we compare the relative complexity of various types of classification problems concerning subspaces of [0,1]^n for all natural number n. In the last chapter, we give a topological characterization theorem for the class of locally compact two-sided invariant non-Archimedean Polish groups. Using this theorem, we show the non-existence of a universal group and the existence of a surjectively universal group in the class.

The thesis is composed by three sections, each devoted to the study of a specific problem in the setting of PI spaces. The problem analyzed are: a C^m Lusin approximation result for horizontal curves in the Heisenberg group, a limit result in the spirit of Burgain-Brezis-Mironescu for Orlicz-Sobolev spaces in Carnot groups and the differentiability of Lipschitz functions in Laakso spaces.

The property B(P,∝)-refinability is studied and is used to obtain new covering characterizations of paracompactness, collectionwise normality, subparacompactness, d-paracompactness, a-normality, mesocompactness, and related concepts. These new characterizations both generalize and unify many well-known results. The property B(P,∝)-refinability is strictly weaker than the property Θ-refinability. A B(P,∝)-refinement is a generalization of a σ-locally finite-closed refinement. Here ∝ is a fixed ordinal which dictates the number of "levels" in a given refinement, and P represents a property such as discreteness or local finiteness which each "level" must satisfy relative to a certain subspace. / Ph. D. / incomplete_metadata