2 resultados para Sobolev Spaces Besov Spaces Carnot Groups Sub-Laplacians

em Digital Commons - Michigan Tech


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Personal photographs permeate our lives from the moment we are born as they define who we are within our familial group and local communities. Archived in family albums or framed on living room walls, they continue on after our death as mnemonic artifacts referencing our gendered, raced, and ethnic identities. This dissertation examines salient instances of what women “do” with personal photographs, not only as authors and subjects but also as collectors, archivists, and family and cultural historians. This project seeks to contribute to more productive, complex discourse about how women form relationships and engage with the conventions and practices of personal photography. In the first part of this dissertation I revisit developments in the history of personal photography, including the advertising campaigns of the Kodak and Agfa Girls and the development of albums such as the Stammbuch and its predecessor, the carte-de-visite, that demonstrate how personal photography has functioned as a gendered activity that references family unity, sentimentalism for the past, and self-representation within normative familial and dominant cultural groups, thus suggesting its importance as a cultural practice of identity formation. The second and primary section of the dissertation expands on the critical analyses of Gillian Rose, Patricia Holland, and Nancy Martha West, who propose that personal photography, marketed to and taken on by women, double-exposes their gendered identities. Drawing on work by critics such as Deborah Willis, bell hooks, and Abigail Solomon-Godeau, I examine how the reconfiguration, recontextualization, and relocation of personal photographs in the respective work of Christine Saari, Fern Logan, and Katie Knight interrogates and complicates gendered, raced, and ethnic identities and cultural attitudes about them. In the final section of the dissertation I briefly examine select examples of how emerging digital spaces on the Internet function as a site for personal photography, one that both reinscribes traditional cultural formations while offering new opportunities for women for the display and audiencing of identities outside the family.

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In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.