This dissertation argues that the waters of the English Channel and North Sea constituted a coherent region of political, geographical, and human life in the late sixteenth and early seventeenth centuries. It examines a large corpus of manuscript and printed maps, sea-charts, portolan charts, navigation manuals, and other works of geography to determine what the Channel was named, when, and by whom, demonstrating how nomenclature and systems of toponyms were wielded as political tools by nationalist cartographers. It traces changes in how the region was known and represented over two centuries, and how cartographic practices and sailing technology shifted along with those changes, to the benefit of domestic and overseas trade and nascent empire-building for England, France, and the Netherlands. It posits the existence of at least two ‘maritime states’ on and next to Channel waters, as the Dutch Sea Beggars and the Brittany port town of Saint-Malo sought to carve out nationhood for themselves based almost solely on the deployment of marine power. Finally, it considers how events and experiences in the Channel can inform and support current developments in the field of the ‘blue humanities.’ Many aspects of the work seek to complicate, and in some places to undermine, the common truism that ‘knowledge is power,’ asking what representations of knowledge might have produced what sort(s) of power on early modern European maps.

Large quantum computers have the potential to vastly outperform any classical computer. The biggest obstacle to building quantum computers of such size is noise. For example, state of the art superconducting quantum computers have average decoherence (loss of information) times of just microseconds. Thus, the field of quantum error correction is especially crucial to progress in the development of quantum technologies. In this research, we study quantum error correction for general noise, which is given by a linear Hermitian map. In standard quantum error correction, the usual assumption is to constrain the errors to completely positive maps, which is a special case of linear Hermitian maps. We establish constraints and sufficient conditions for the possible error correcting codes that can be used for linear Hermitian maps. Afterwards, we expand these sufficient conditions to cover a large class of general errors. These conditions lead to currently known conditions in the limit that the error map becomes completely positive. The later chapters give general results for quantum evolution maps: a set of weak repeated projective measurements that never break entanglement and the asymmetric depolarizing map composed with a not completely positive map that gives a completely positive composition. Finally, we give examples.

The purpose of the thesis was to examine the extent to which geography is integrated into history courses. This was done through analyses of the maps in eighth and tenth grade history books. Every map in each book was tabulated according to its purpose, characteristics, and cartographic techniques. The statistics which were gathered from these tabulations were then used as a basis for percentages of the maps devoted to various purposes. In addition to this, twenty-five maps were analyzed in detail, with an examination not only of the map, but of the accompanying text, and the method in which the map was integrated into the written portion of the book. Through these analyses, it was discovered that maps are very poorly utilized in these textbooks. Many maps were used which were not in an appropriate scale for the subject they were to portray. Also, it was common to see a map which appeared to be useful for illustrating one idea, applied in an entirely different manner. Often maps were not incorporated with the text, or located in appropriate sections of the books. Most books had some maps which were excellent, and used advantageously; these same books also misused maps. There was a great deal of inconsistency in the quality of maps, and how they were used. The conclusion drawn is a recommendation that more studies be done in this field, in an endeavor to further analyze the problem as it exists new, so that it can be corrected.

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Old maps are valuable research tools in many fields. Finding and identifying them, however, is often difficult. This annotated cartobibliography attempts to identify all maps of Utah printed before 1900. Entries give the distinguishing features, peculiarities, inaccuracies, and a general description as well as the map's provenance and citations in other lists and bibliographies. The maps are listed chronologically and include all maps located in research collections in Utah, and in the catalogs of the Library of Congress and the Bancroft Library. Although the first entry is dated 1777, the first map of Utah made from actual observation, earlier maps are discussed as they relate to explorers' and cartographers' perceptions of the area. This cartobibliography augments and carries forward the work of Carl I. Wheat.

In 1882, the United States Geological Survey began its National Mappping Program designed to map the nation using a series of several thousand topographic quadrangles. Since that date, the program and the maps themselves have undergone many changes due mainly to technological advances in mapping methods. The use of data collected from historic U.S.G.S. topographic maps in modem day applications necessitates a general knowledge of the potentials and limitations of these data. This study compares representations of terrain features on historic maps compiled using plane table methods with the same features as represented on more accurate modem maps compiled using photogrammetry. Using the modem map as a standard, errors in the old maps were identified and defined using statistical procedures. Measures of closed contour lines recorded the angularity of the line, the length of the line, the area within the contour, the shape of the feature and spatial relationships between contour pairs. The analysis attempts to relate errors to these geometric components of contour lines and to predict the occurrence of error. Due to practices of smoothing and generalization of contour lines in plane table surveys, measures of both angularity and shape were significantly different between older and newer maps. Systematic errors, a consistent displacement of contour lines in a similar direction, were also identified on the historic maps. Based on these results, several suggestions for continuation of the research are given. / Master of Science

<p> In this thesis we study extensive subcategories of various categories of Hausdorff spaces and continuous maps, and of Hausdorff uniform spaces and uniformly continuous maps, In particular, we obtain new methods to construct extensive subcategories which can be applied to many categories and give us an inclusive relationship between reflective subcategories of Haus and coreflective subcategories of Top. We consider perfect onto projectivity in those categories. The relationships between n-compact spaces and topologically complete spaces are discussed. </p> / Thesis / Doctor of Philosophy (PhD)

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