Thesis (M. Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 135-140).

published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 35). Also available in electronic version.

Thesis (M. Phil.)--University of Hong Kong, 1992.

Thesis (M.Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 135-140). Also available in print.

The research addresses the problem of maximizing a zero-one quadratic function. The report falls into three main sections. The first section uses results from Hammer [12] and Picard and Ratliff [23] to develop a new test for fixing the value of a variable in some solution and to provide a means for calculating a new upper bound on the maximum of the function. In addition the convergence of the method of calculation for the bounds is explored in an investigation of its sharpness. The second section proposes a branch and bound algorithm that uses the ideas of the first along with a heuristic solution procedure. It is shown that one advantage of this is that it may now be possible to identify how successful this algorithm will be in finding the maximum of a specified problem. The third section gives a basis for a new heuristic solution procedure. The method defines a concept of gradient which enables a simple steepest ascent technique to be used. It is shown that in general this will find a local maximum of the function. A further procedure to help distinguish between local and global maxima is also given. / Business, Sauder School of / Graduate

The purpose of this thesis is to discuss Markoff Numbers, their associated binary quadratic forms, together with the units in the associated real quadratic field. Relations betweeen the Markoff Numbers, the explicit structure of the automorph group of the forms, generators of the Commutator Subgroup Γ’ of SL₂(Z) = Γ and the lengths of geodesies on certain Riemann Surfaces are conveyed. A conjecture combining these relations is formulated and expressed at the end of this paper. / Science, Faculty of / Mathematics, Department of / Graduate

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaf 98).

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