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We generalise the study of cyclotomic matrices - those with all eigenvalues in the interval [-2; 2] - from symmetric rational integer matrices to Hermitian matrices with entries from rings of integers of imaginary quadratic fields. As in the rational integer case, a corresponding graph-like structure is defined. We introduce the notion of `4-cyclotomic' matrices and graphs, prove that they are necessarily maximal cyclotomic, and classify all such objects up to equivalence. Six rings OQ( p d) for d = -1;-2;-3;-7;-11;-15 give rise to examples not found in the rational-integer case; in four (d = -1;-2;-3;-7) we recover infinite families as well as sporadic cases. For d = -15;-11;-7;-2, we demonstrate that a maximal cyclotomic graph is necessarily 4- cyclotomic and thus the presented classification determines all cyclotomic matrices/graphs for those fields. For the same values of d we then identify the minimal noncyclotomic graphs and determine their Mahler measures; no such graph has Mahler measure less than 1.35 unless it admits a rational-integer representative.

Thesis advisor: Richard Kearney / The present study seeks to address the general question of the relation between Levinas's ethics and his account of religion. The specific questions pursued here include the following: Is his ethics secular or religious, and in what sense is it so, either way? Does his ethics depend on religion? How does Levinas himself understand 'religion'? This thesis will show that any interpretation of Levinas's ethics cannot be separated from its religious dimension, namely, the openness to exteriority as Desire for the Infinite. Religion, despite all consolations it may bring, cannot dispense with this ethical demand. / Thesis (PhD) — Boston College, 2010. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Philosophy.

This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=?igtriangleup x_i?igtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured entropy of a system but the maximum entropy remains constant due to the uncertainty principle. By taking $h_u ightarrow 0^+$ an infinite unobservable entropy is attained leading to an infinite unobservable energy per particle and an unobservable chemical equilibrium between all particles. The amount of heat fluxing though measurement apparatus is formulated as a function of $h_I$ for systems in steady state equilibrium as well as the number of measured particles or sub-particles so any system can be described as unitary or composite in number. Some example systems are given using variable $h_I$.

by Chi-Kwan Leung. / "July 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 106-109). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

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In this thesis, the root-locus theory for a class of diffusion systems is studied. The input and output boundary operators are co-located in the sense that their highest order derivatives occur at the same endpoint. It is shown that infinitely many root-locus branches lie on the negative real axis and the remaining finitely many root-locus branches lie inside a fixed closed contour. It is also shown that all closed-loop poles vary continuously as the feedback gain varies from zero to infinity.

In this thesis, the root-locus theory for a class of diffusion systems is studied. The input and output boundary operators are co-located in the sense that their highest order derivatives occur at the same endpoint. It is shown that infinitely many root-locus branches lie on the negative real axis and the remaining finitely many root-locus branches lie inside a fixed closed contour. It is also shown that all closed-loop poles vary continuously as the feedback gain varies from zero to infinity.

Ordinary life oscillates between dichotomies: from work to leisure, from reality to fantasy, from private to public. These are distinct worlds that bring order to the chaos of experience; their boundaries contain what philosopher James Carse calls finite games. As we move from game to game, we find ourselves in perpetual motion. SUPER ORDINARY explores Carse‚s other type of game: the infinite game. It is an architectural investigation of its potential to transcend the serious and experience the truly playful, an attempt to manifest a place without boundaries in a world defined by them. Lamport Stadium is the setting for this journey. In this theatre of finite games, our experiences are limited to its rules and boundaries. However, where we truly play, we liberate personal narratives from finite games. Architecture, rather than categorizing experience, is instead redefined through experience. Ergo, rather than the site of finite games, SUPER ORDINARY imagines Lamport Stadium as an infinite game. The dichotomies of finite play˜field and bleacher, player and observer, inside and out, and so on˜are dissolved, and the stadium becomes a place of possibility and adventure; here, we can at once submit to the ecstasy of the place while forging our own narratives. It is a building that is never quite finished, but always open to our imaginations.

Infinite dimensional systems such as flexible airplane wings and Vertical Axis Wind Turbine (VAWT) blades may require control to improve performance. Traditional control techniques use position and velocity information feedback, but velocity information for infinite dimensional systems is not easily attained. This research investigates the use of reduced-sensing control for these applications. Reduced-sensing control uses feedback of position measurements and an associated filter state to stabilize the system dynamics. A filter state is a nonphysical entity that appends an additional ordinary differential equation to the system dynamics. Asymptotic stability of a system using this control approach is confirmed through a sequence of existing mathematical tools. These tools include equilibrium point solutions, Lyapunov functions for stability and control, and Mukherjee and Chen's Asymptotic Stability Theorem. This thesis research investigates the stability of a beam representing an airplane wing or a VAWT blade controlled using feedback of position and filter state terms only. Both of these infinite dimensional systems exhibit asymptotic stability with the proposed reduced-sensing control design. Additionally, the analytical stability response of the VAWT is verified through numerical simulation.