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

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Thesis advisor: Patrick Byrne / In the late 19th century, Georg Cantor opened up the mathematical field of set theory with his development of transfinite numbers. In his radical departure from previous notions of infinity espoused by both mathematicians and philosophers, Cantor created new notions of transcendence in order to clearly described infinities of different sizes. Leading the opposition against Cantor's theory was Leopold Kronecker, Cantor's former mentor and the leading contemporary German mathematician. In their lifelong dispute over the transfinite numbers emerge philosophical disagreements over mathematical existence, consistency, and freedom. This thesis presents a short summary of Cantor's controversial theories, describes Cantor and Kronecker's philosophical ideas, and attempts to state clearly their differences of opinion. In the end, the author hopes to present the shock caused by Cantor's work and an appreciation of the two very different philosophies of mathematics represented by Cantor and Kronecker. / Thesis (BA) — Boston College, 2005. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Philosophy. / Discipline: College Honors Program.

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For a long time determining the stability issue of characteristic polynomials has played avery important role in Control System Engineering. This thesis addresses the traditionalcontrol issues such as stabilizing a system with any certain controller analyzingcharacteristic polynomial, yet a new perspective to solve them. Particularly, in this thesis,Proportional-Integral-Derivative (PID) controller is considered for a fixed structuredcontroller. This research aims to attain controller gain set satisfying given performancespecifications, not from the exact mathematical model, but from the empirical data of thesystem. Therefore, instead of a characteristic polynomial equation, a speciallyformulated characteristic rational function is investigated for the stability of the systemin order to use only the frequency data of the plant. Because the performance satisfactionis highly focused on, the characteristic rational function for the investigation of thestability is mainly dealt with the complex coefficient polynomial case rather than realone through whole chapters, and the mathematical basis for the complex case is prepared.For the performance specifications, phase margin is considered first since it is avery significant factor to examine the system’s nominal stability extent (nominal performance). Second, satisfying H norm constraints is handled to make a more robustclosed loop feedback control system. Third, we assume undefined, but bounded outsidenoise, exists when estimating the system’s frequency data. While considering theseuncertainties, a robust control system which meets a given phase margin performance, isattained finally (robust performance).In this thesis, the way is explained how the entire PID controller gain setssatisfying the given performances mentioned in the above are obtained. The approachfully makes use of the calculating software e.g. MATLAB® in this research and isdeveloped in a systematically and automatically computational aspect. The result ofsynthesizing PID controller is visualized through the graphic user interface of acomputer.

For a long time determining the stability issue of characteristic polynomials has played avery important role in Control System Engineering. This thesis addresses the traditionalcontrol issues such as stabilizing a system with any certain controller analyzingcharacteristic polynomial, yet a new perspective to solve them. Particularly, in this thesis,Proportional-Integral-Derivative (PID) controller is considered for a fixed structuredcontroller. This research aims to attain controller gain set satisfying given performancespecifications, not from the exact mathematical model, but from the empirical data of thesystem. Therefore, instead of a characteristic polynomial equation, a speciallyformulated characteristic rational function is investigated for the stability of the systemin order to use only the frequency data of the plant. Because the performance satisfactionis highly focused on, the characteristic rational function for the investigation of thestability is mainly dealt with the complex coefficient polynomial case rather than realone through whole chapters, and the mathematical basis for the complex case is prepared.For the performance specifications, phase margin is considered first since it is avery significant factor to examine the system’s nominal stability extent (nominal performance). Second, satisfying H norm constraints is handled to make a more robustclosed loop feedback control system. Third, we assume undefined, but bounded outsidenoise, exists when estimating the system’s frequency data. While considering theseuncertainties, a robust control system which meets a given phase margin performance, isattained finally (robust performance).In this thesis, the way is explained how the entire PID controller gain setssatisfying the given performances mentioned in the above are obtained. The approachfully makes use of the calculating software e.g. MATLAB® in this research and isdeveloped in a systematically and automatically computational aspect. The result ofsynthesizing PID controller is visualized through the graphic user interface of acomputer.

Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, September 1990. / Thesis Advisor(s): Collins, Daniel J. Second Reader: Schmidt, Louis V. "September 1990." Description based on title screen as viewed on December 29, 2009. DTIC Identifier(s): Flight control systems, control theory, computer files, theses, input output processing, F-18 aircraft. Author(s) subject terms: Modern control theory, H infinity control theory, H2 control theory, multivariable robustness, F-18 control design or synthesis, super augmented aircraft. Includes bibliographical references (p. 110). Also available in print.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2003. / On t.p. "[infinity]" appears as the infinity symbol. Includes bibliographical references (leaves 88-92). Also available in electronic version. Access restricted to campus users.

Includes bibliographical references (p. 121-124).

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy