The issue of downtown revitalization has been much studied over the past several decades. However, much of the existing knowledge base pertains to our largest urban centres. This leaves a significant information gap with regards to mid-size cities. As a result, past renewal attempts in these cities have often been scaled down versions of what has worked in larger cities. In most cases, this has resulted in detrimental rather than reviving effects. The current trend in cities of all sizes is the implementation of Creative City Theory. This thesis seeks to study this trend and its specific relevance to the mid-size city. The scope of research will then build on the current theory by exploring the effects of well-designed public spaces and their ability to not only unleash the creative spirit but to revitalize the post-industrial mid-size city downtown. This information will then be applied to a design study for Hamilton, Ontario where failed renewal attempts have crippled the city’s downtown. The design will concentrate on Jackson Square (formerly known as Civic Square), a superblock within the very centre of downtown Hamilton. Through a redesign of Jackson Square, the thesis proposes to create a place that not only fosters creativity, but is once again meaningful and significant to Hamilton citizens. While the application of research to Hamilton is specific, the goal is to produce a body of work with principles that can be applied to any number of mid-size cities across the post-industrial world.

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In this thesis, we consider receiver design problems in a multi-cell MIMO system using the coordinated multi-point transmission/reception technique. The linear minimum mean square error (LMMSE) receiver, which involves the inverse operation, is adopted. By the Cayley-Hamilton theorem, the matrix inverse can be represented by weighted sum of power of matrices. Given an order of the matrix power, we calculate the best weight in sense of the minimum mean square error. Both the uplink and the downlink scenarios are considered. Also, given a target signal to interference and noise ratio (SINR), we consider the best weight design problem in the downlink scenario. This problem can be formulated as the second-order cone programming (SOCP) and semidefinite relaxation (SDR) programming. By computer simulations, we show that the SDR and SOCP are equivalent.

<p>This thesis concerns the approximation of optimally controlled partial differential equations for applications in optimal design and reconstruction. Such optimal control problems are often ill-posed and need to be regularized to obtain good approximations. We here use the theory of the corresponding Hamilton-Jacobi-Bellman equations to construct regularizations and derive error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method where the first, analytical, step is to regularize the Hamiltonian. Next its stationary Hamiltonian system, a nonlinear partial differential equation, is computed efficiently with the Newton method using a sparse Jacobian. An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its<em> L</em>² projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems. In the thesis we present solutions to applications such as optimal design and reconstruction of conducting materials and elastic structures.</p>

The first part of this work gives an introduction into aperiodic order in general and the lines of research pursued. The second part consists of eight manuscripts.

Das Thema dieser Arbeit ist die spektraltheoretische Untersuchung von zufälligen Operatoren, die zu einem minimal ergodischen bzw. strikt ergodischen Delone dynamischen System assoziiert sind. Es werden kontinuierliche sowie diskrete Modelle untersucht. Diese Modelle sind mathematische Modelle zur Beschreibung von Festkörpern, bei denen die Punkte der einzelnen, in einem Delone dynamischen System enthaltenen, Delone-Mengen die Atompositionen eines Festkörpers beschreiben. Delone-Mengen, die in einem minimal ergodischen Delone dynamischen System enthalten sind weisen eine sehr hohe Ordnungsstruktur auf, sind aber nicht notwendigerweise periodisch. Sie können daher zur Modellierung von Quasikristallen verwendet werden. In dieser Arbeit wird das Spektrum der assoziierten Operatoren im kontinuierlichen sowie im diskreten Fall untersucht.

Es wird Anderson-Lokalisierung und starke dynamische Lokalisierung für Quantengraphen mit Gitterstruktur mit Multiskalenanalyse bewiesen. Für eine weitere Klasse von Quantengraphen wird eine lineare Wegner-Abschätzung gezeigt, woraus die Lipschitz-Stetigkeit der integrierten Zustandsdichte folgt.

Es wird Anderson-Lokalisierung und starke dynamische Lokalisierung für Quantengraphen mit Gitterstruktur mit Multiskalenanalyse bewiesen. Für eine weitere Klasse von Quantengraphen wird eine lineare Wegner-Abschätzung gezeigt, woraus die Lipschitz-Stetigkeit der integrierten Zustandsdichte folgt.

We consider large and sparse eigenproblems where the spectrum exhibits special symmetries. Here we focus on Hamiltonian symmetry, that is, the spectrum is symmetric with respect to the real and imaginary axes. After briefly discussing quadratic eigenproblems with Hamiltonian spectra we review structured Krylov subspace methods to aprroximate parts of the spectrum of Hamiltonian operators. We will discuss the optimization of the free parameters in the resulting symplectic Lanczos process in order to minimize the conditioning of the (non-orthonormal) Lanczos basis. The effects of our findings are demonstrated for several numerical examples.

Texte remanié de : Thèse de doctorat : Mathématiques : Lyon, École normale supérieure (sciences) : 2007. / Bibliogr. p. [243]-251.