Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

My overall claim in this paper is twofold: Firstly, the activity of developing arguments in favour of the existence of the Christian God is tenable and worthwhile and, secondly, the “infinite God objection” fails to undermine the kalam cosmological argument. Concerning the former, it is often claimed that the very activity of developing arguments in favour of God’s existence is futile. I argue, however, that such theistic arguments play an important role in the philosophy of religion, natural theology, and apologetics. Concerning the latter claim, I will attempt to show how the infinite God objection fails to undermine a notable theistic argument, namely, the kalam cosmological argument. As regards this objection, the proponents of the kalam cosmological argument face a dilemma – either an actual infinity cannot exist or God’s knowledge cannot be infinite. More specifically, this objection claims that God’s omniscience entails the existence of an actual infinity with God knowing an actual infinite number of future events and mathematical truths. My solution to this problem is that (1) God’s omniscience should be understood as maximal knowledge; (2) the existence of abstract objects (such as numbers and propositions) should be denied; and (3) God’s knowledge is non-propositional in nature. / MPhil, North-West University, Potchefstroom Campus, 2014

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains xiii, 110 p.; also includes graphics (some col.) Includes bibliographical references (p. 104-110). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xiii, 96 p.; also includes graphics Includes bibliographical references (p. 92-96). Available online via OhioLINK's ETD Center

Thesis (Ph.D.)--University of Central Florida, 2009. / Adviser: Chengying Xu. Includes bibliographical references (p. 118-126).

Thesis (Ph. D.)--University of Hong Kong, 1997. / Includes bibliographical references (leaf 131-138).

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2005. / On t.p. "2" is lower case and "[infinity]" appears as the infinity symbol. Includes bibliographical references (leaves 110-116). Also available in electronic version.

We choose a generator G of the derived category of coherent sheaves on a smooth curve X of genus g which corresponds to a choice of g distinguished points P1, . . . , Pg on X. We compute the Hochschild cohomology of the algebra B = Ext (G,G) in certain internal degrees relevant to extending the associative algebra structure on B to an A1-structure, which demonstrates that A1-structures on B are finitely determined for curves of arbitrary genus. When the curve is taken over C and g = 1, we amend an explicit A1-structure on B computed by Polishchuk so that the higher products m6 and m8 become Hochschild cocycles. We use the cohomology classes of m6 and m8 to recover the j-invariant of the curve. When g 2, we use Massey products in Db(X) to show that in the A1-structure on B, m3 is homotopic to 0 if and only if X is hyperelliptic and P1, . . . , Pg are chosen to be Weierstrass points. iv

This thesis investigates Bicoprime Factorisations (BCFs) and their possible uses in robust control theory. BCFs are a generalisation of coprime factorisations, which have been well known and widely used by the control community over the last few decades. Though they were introduced at roughly the same time as coprime factorisations, they have been largely ignored, with only a very small number of results derived in the literature. BCFs are first introduced and the fundamental theory behind them is developed. This includes results such as internal stability in terms of BCFs, parametrisation of the BCFs of a plant and state space constructions of BCFs. Subsequently, a BCF uncertainty structure is proposed, that encompasses both left and right coprime factor uncertainty. A robust control synthesis procedure is then developed with respect to this BCF uncertainty structure. The proposed synthesis method is shown to be advantageous in the following two aspects: (1) the standard assumptions associated with H-infinity control synthesis are directly fulfilled without the need of loop shifting or normalisation of the generalised plant and (2) any or all of the plant's unstable dynamics can be ignored, thus leading to a reduction in the dimensions of the Algebraic Riccati Equations (AREs) that need to be solved to achieve robust stabilisation. Normalised BCFs are then defined, which are shown to provide many advantages, especially in the context of robust control synthesis. When using a normalised BCF of the plant, lower bounds on the achievable BCF robust stability margin can be easily and directly computed a priori, as is the case for normalised coprime factors. Although the need for an iterative procedure is not completely avoided when designing an optimal controller, it is greatly simplified with the iteration variable being scalar. Unlike coprime factorisations where a single ARE needs to be solved to achieve normalisation, two coupled AREs must be satisfied for a BCF to be normalised. Two recursive methods are proposed to solve this problem. Lastly, an example is presented where the theory developed is used in a practical scenario. A quadrotor Unmanned Aerial Vehicle (UAV) is considered and a normalised BCF controller is designed which in combination with feedback linearisation is used to control both the attitude and position of the vehicle.

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