In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n-1, which yields permutations of labels for the edges of Stn taken from the set of integers {1,..., [n/2c]}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n) in Stn. The search for edge-disjoint Hamilton cycles in star graphs is important for the design of interconnection network topologies in computer science. All our results improve on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs.

Eighteenth-century Scottish bibliography is a vast subject still awaiting exploration. There are, however, some landmarks to look for and guides to employ. I am thinking particularly, in the context of my own interests, of the writings of Philip Gaskell, and a work that should open up new sources, Robert H. Carnie’s awaited dictionary of the Scottish Book trade. The national Library of Scotland is in the early stages of compliling a catalogue of its eighteenth-century Scottish books which, no matter what form it takes, will provide scholars with a major tool. The description of books has been and doubtless will continue to be a controvertial subject, but those students who have much to identify can take encouragement, I believe from David Foxon’s ‘Thoughts on the History and future of Bibliographical Description’. In this work I map some particular and general areas of Scottish publishing history by examining the partnership of Gavin Hamilton and John Balfour, and the association they formed with the printer Patrick Neill. I study the partners in their own right as booksellers, publishers and printers, but I am concerned also with the larger bibliographical background. Hamilton and Balfour were strong-willed individuals who bought the force of their personal and private interests to bear on their professional lives; Hamilton, especially, in the period under consideration, saw little difference between his duty as a Scottish gentleman and his activities as a Scottish publisher. He and Balfour were far-sighted and adventurous, and deserve to be thought of as central figures in the story of the Edinburgh book trade.

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This thesis examines concrete poetry in England and Scotland from 1962 to 1975. Through the 1950s-70s, international concrete poetry evolved away from constructivist influenced, “classical” ideals of minimalism and iconic visual effect towards principles owing more to Dadaism and Futurism: spontaneity, maximalism, sonority and an emphasis on intermedial expression. Against this backdrop, using close textual analysis supported by primary research, I engage with four poets whose work collectively exemplifies the wide range of values which concrete poetry represented in England and Scotland during the period in question. A movement away from classical ideals can be tracked across the oeuvres of Finlay, Morgan, Houédard and Cobbing; but many aspects of their work cannot be accounted for by this general rubric. Finlay saw concrete poetry as a means of casting off Scottish literary tradition, but also of embodying an immutable vision of aesthetic and ethical order, using a marriage of the visual and linguistic to emphasise links between disparate ideas and things. However, his restless reconfiguration of poetry’s visual-physical aspects ultimately resulted in a re-separation of word and image which, together with an increasing historical-mindedness, ended his attachment to the style. Morgan, by contrast, used concrete poetry to redefine rather than repel Scottish literary culture, and was a more context-focused poet, using concrete grammar – whose sonic possibilities he exploited more than Finlay – to depict specific communicative scenarios, and thus to register ethical and political imperatives, often reflecting Scottish nationalist ideals. The emphasis on semantics common to Morgan and Finlay’s work, reflecting relative fidelity to classical principles, is overridden in Houédard’s concrete poetry, which came to employ a grammar of abstract visual motifs in which linguistic meaning was subsumed, related as much to apophatic theology as to classical concrete. For Cobbing too, concrete became a means of evading language, in his case to access a transcendent realm of “intermedial” poetry equally related to language’s sonic and visual dimensions, and influenced by various contemporary artforms, and by counter-cultural ideals. However, Cobbing’s emphasis on performing poems, and the reintegration of semantics into his work throughout this period, led by the early 1970s to an alternative poetic ideal of relativity.

This thesis investigates how the mapping of Africa by British institutions between c.1880 and c.1915 was more complex and variable than is traditionally recognised. The study takes three ‘cuts’ into this topic, presented as journal papers, which examine: the Bartholomew map-publishing firm, the cartographic coverage of the Second Boer War, and the maps associated with Sir Harry H. Johnston. Each case-study focuses on what was produced – both quantitative output and the content of representations – and why. Informed by theories from the history of cartography, book history and the history of science, particular attention is paid to the concerns and processes embodied in the maps and map-making that are irreducible to simply ‘imperial’ discourse; these variously include editorial processes and questions of authorship, concerns for credibility and intended audiences, and the circulation and ‘life-cycles’ of maps. These findings are also explored in relation to the institutional geography of cartography in Britain: the studies illustrate the institutional contingency of such factors and how this gave rise to highly variable representations of Africa. These three empirical papers represent the first sustained studies of each of the topics. By connecting their findings, the thesis also offers broader reconceptualisations of the British mapping of Africa between c.1880 and c.1915: with respect to cartographic representations, maps as objects, and the institutions producing them. Maps did not simply reflect ‘imperial’ discourse; they were highly variable manifestations of multifaceted and institutionally contingent factors and were mobile and mutable objects that were re-used and re-produced in different ways across different settings. Mapmaking institutions were discrete but interconnected sites that not only produced different representations, but played different roles in the mapping of Africa. By illuminating the institutional provenance, ‘life-cycles’ and content of the maps studied, this thesis extends current knowledge of British mapping of Africa during the late nineteenth and early twentieth centuries and raises questions for further research incorporating its lessons, sources and theories.

Let G be a graph and k be an integer greater than or equal to the chromatic number of G. The k-colouring graph of G is the graph whose vertices are k-colourings of G, with two colourings adjacent if they colour exactly one vertex differently. We explore the Hamiltonicity and connectivity of such graphs, with particular focus on the k-colouring graphs of complete multipartite graphs. We determine the connectivity of the k-colouring graph of the complete graph on n vertices for all n, and show that the k-colouring graph of a complete multipartite graph K is 2-connected whenever k is at least the chromatic number of K plus one. Additionally, we examine a conjecture that every connected k-colouring graph is 2-connected, and give counterexamples for k greater than or equal to 4. As our main result, we show that for all k greater than or equal to 2t, the k-colouring graph of a complete t-partite graph is Hamiltonian. Finally, we characterize the complete multipartite graphs K whose k-colouring graphs are Hamiltonian when k is the chromatic number of K plus one. / Graduate

We propose a discontinuous Galerkin finite element method (DGFEM) for fully nonlinear elliptic Hamilton--Jacobi--Bellman (HJB) partial differential equations (PDE) of second order with Cordes coefficients. Our analysis shows that the method is both consistent and stable, with arbitrarily high-order convergence rates for sufficiently regular solutions. Error bounds for solutions with minimal regularity show that the method is generally convergent under suitable choices of meshes and polynomial degrees. The method allows for a broad range of hp-refinement strategies on unstructured meshes with varying element sizes and orders of approximation, thus permitting up to exponential convergence rates, even for nonsmooth solutions. Numerical experiments on problems with nonsmooth solutions and strongly anisotropic diffusion coefficients demonstrate the significant gains in accuracy and computational efficiency over existing methods. We then extend the DGFEM for elliptic HJB equations to a space-time DGFEM for parabolic HJB equations. The resulting method is consistent and unconditionally stable for varying time-steps, and we obtain error bounds for both rough and regular solutions, which show that the method is arbitrarily high-order with optimal convergence rates with respect to the mesh size, time-step size, and temporal polynomial degree, and possibly suboptimal by an order and a half in the spatial polynomial degree. Exponential convergence rates under combined hp- and τq-refinement are obtained in numerical experiments on problems with strongly anisotropic diffusion coefficients and early-time singularities. Finally, we show that the combination of a semismooth Newton method with nonoverlapping domain decomposition preconditioners leads to efficient solvers for the discrete nonlinear problems. The semismooth Newton method has a superlinear convergence rate, and performs very effectively in computations. We analyse the spectral bounds of nonoverlapping domain decomposition preconditioners for a model problem, where we establish sharp bounds that are explicit in both the mesh sizes and polynomial degrees. We then go beyond the model problem and show computationally that these algorithms lead to efficient and competitive solvers in practical applications to fully nonlinear HJB equations.

This research examines the emergence of cycling-supportive land-use and transportation policies in Ontario and Hamilton, Ontario between 1990 and 2016. The focus of this thesis is on two questions that have been unexplored in previous research: (1) what cycling-supportive policies emerged in Provincial and Municipal government during this time?; and (2) what role, if any, did the Provincial position on cycling play in the development of Hamilton, Ontario cycling policies? A primary and secondary document review was undertaken to identify patterns between historical Provincial and Municipal policies. Three types of results are presented: (1) an examination of amendments to the Ontario Planning Act, emphasizing its effect on the role of policy in Ontario, the structure of the Ontario planning system, and on Municipal conformity; (2) a detailed review of emergent cycling-supportive policies and trends in Ontario and Hamilton, Ontario between 1990 and 2016; and (3) an analysis of evidence showing the influence of Provincial cycling-supportive policies on Hamilton plan policies. This research concludes that (1) novel cycling-supportive policies have emerged at both the Municipal and Provincial levels during the research period, and (2) evidence exists that Provincial land-use and transportation policies have influenced Hamilton’s cycling policy over the research period. / February 2017

I became interested in Marcel Duchamp's work at an early stage of my art history studies. His then most important piece, The Bride Stripped Bare by her Bachelors, Even, particularly fascinated me and I wished to understand the complexity of the work itself. I also wanted to learn more about the personality and psyche of this artist.For several years I lived in Philadelphia, and spent many Sunday afternoons in the Philadelphia Museum of Art studying, evaluating and appreciating Duchamp's works which can be found in the Arensberg Collection. I obtained Richard Hamilton's translation of the Green Box1 and used it as Duchamp wished--reading it along with a visual study of The Bride Stripped Bare.During my residence in Philadelphia and, shortly after his death, Duchamp's final work was unveiled. Upon further study of his total work and the writings about him, I experienced in several dimensions the message of his art and felt that this new writing, this thesis, needed to be done. I could not accept the frustration, castration, negation, and non-aesthetic that was read into his work by many critics. Duchamp was a revolutionary in art, yes--but there was an erotic joy, a sensuous aesthetic sensitivity to his form, be it created or found, and a continuous desire on his part to extend man's aesthetic awareness to new areas of life experience.This thesis presents a critical re-evaluation of Marcel Duchamp's two works: first, The Bride Stripped Bare by her Bachelors, Even; and secondly, Etant Donnés: 1° la chute d'eau, 2° le gaz d'éclairage, which is the concern of chapter two.Because of the nature of these two works of art, it was necessary to discuss and analyse iconographically, in chapter one, various other works -- following their development and recurrences as symbolic images. Several statements by writers and critics are also re-evaluated, mainly those referring to an erotic pessimism reflected in Duchamp's work.An important guide line for this study has been the Green Box. It, along with other writings and staements, revels Duchamp as a sensitive, highly intellectual artist ready for constant changes. From the material within the Green Box is woven the thread for the final content -- the positive, erotic message and the aesthetic experience.1 Duchamp saved all of the notes, sketches, and drawings related to The Bride Stripped Bare in a green box, which he later published, titled the Green Box. A typographic version of the notes, translated by George Heard Hamilton, was prepared by Richard Hamilton, titled The Bride Stripped Bare by her Bachelors, Even (London: Percy Lund, Humphries and Co. Ltd., 1960).

The thesis analyzes the origins and the formative period of Virginia’s historical marker program. It shows that historical markers were critical to the success of Harry Flood Byrd’s administration and his Commission on Conservation and Development. The thesis also examines how Virginia’s marker program set the standard for roadside commemoration across the entire United States. Lastly, the work appraises the influence of Dr. Hamilton James Eckenrode, his pioneering methods of historical commemoration, and his central role in the success of Virginia’s marker program.