One problem, considered important in Banach space theory since at least the 1970’s, asks for intrinsic characterizations of subspaces of a Banach space with an unconditional basis. A more general question is to give necessary and sufficient conditions for operators from Lp (2 < p < 1) to factor through `p. In this dissertaion, solutions for the above problems are provided. More precisely, I prove that for a reflexive Banach space, being a subspace of a reflexive space with an unconditional basis or being a quotient of such a space, is equivalent to having the unconditional tree property. I also show that a bounded linear operator from Lp (2 < p < 1) factors through `p if and only it satisfies an upper-(C, p)-tree estimate. Results are then extended to operators from asymptotic lp spaces.

Thesis (Ph. D.)--Oregon State University, 1990. / Typescript (photocopy). Includes bibliography (leaf 42). Also available on the World Wide Web.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 276-279).

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

Algebraic geometry is the study of solutions in polynomial equations using objects and shapes. Differential geometry is based on surfaces, curves, and dimensions of shapes and applying calculus and algebra. Desingularizing the singularities of a variety plays an important role in research in algebraic and differential geometry. Toroidal Embedding is one of the tools used in desingularization. Therefore, Toroidal Embedding and desingularization will be the main focus of my project. In this paper, we first provide a brief introduction on Toroidal Embedding, then show an explicit construction on how to smooth a variety with singularity through Toroidal Embeddings.

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 46-47).

Word embeddings is a useful method that has shown enormous success in various NLP tasks, not only in open domain but also in biomedical domain. The biomedical domain provides various domain specific resources and tools that can be exploited to improve performance of these word embeddings. However, most of the research related to word embeddings in biomedical domain focuses on analysis of model architecture, hyper-parameters and input text. In this paper, we use SemMedDB to design new sentences called `Semantic Sentences'. Then we use these sentences in addition to biomedical text as inputs to the word embedding model. This approach aims at introducing biomedical semantic types defined by UMLS, into the vector space of word embeddings. The semantically rich word embeddings presented here rivals state of the art biomedical word embedding in both semantic similarity and relatedness metrics up to 11%. We also demonstrate how these semantic types in word embeddings can be utilized.

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No description available.