Thesis advisor: Mark Reeder / A polynomial is said to be invariant for a group of linear fractional transformations G if its roots are permuted by G. We begin by using a simple group of linear fractional transformations that is isomorphic to S_{3} and finding its invariant polynomials to build up the tools necessary to attack a larger group. We then follow a construction from Toth of the icosahedral group I, and derive a general formula for all polynomials of degree 60 that are invariant under I. / Thesis (BA) — Boston College, 2004. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Mathematics. / Discipline: College Honors Program.

"In the design of any antenna radiator, single or multi-element, a significant amount of time and resources is spent on impedance matching. There are broadly two approaches to impedance matching; the first is the distributed impedance matching approach which leads to modifying the antenna geometry itself by identifying appropriate degrees of freedom within the structure. The second option is the lumped element approach to impedance matching. In this approach instead of modifying the antenna geometry a passive network attempts to equalize the impedance mismatch between the source and the antenna load. This thesis introduces a new technique of impedance matching using lumped circuits (passive, lossless) for electrically small (short) non-resonant dipole/monopole antennas. A closed form upper-bound on the achievable transducer gain (and therefore the reflection coefficient) is derived starting with the Bode-Fano criterion. A 5 element equalizer is proposed which can equalize all dipole/monopole like antennas. Simulation and experimental results confirm our hypothesis. The second contribution of this thesis is in the design of broadband, small size, modular arrays (2, 4, 8 or 16 elements) using the distributed approach to impedance matching. The design of arrays comprising a small number of elements cannot follow the infinite array design paradigm. Instead, the central idea is to find a single optimized radiator (unit cell) which if used to build the 2x1, 4x1, 2x2 arrays, etc. (up to a 4x4 array) will provide at least the 2:1 bandwidth with a VSWR of 2:1 and stable directive gain (not greater than 3 dB variation) in each configuration. Simulation and experimental results for a solution to the 2x1, 4x1 and 2x2 array configurations is presented. "

Since the first robotic surgical intervention was performed in 1985 using a PUMA industrial manipulator, development in the field of surgical robotics has been relatively fast paced, despite the tremendous costs involved in developing new robotic interventional devices. This is due to the clear advantages to augmented a clinicians skill and dexterity with the precision and reliability of computer controlled motion. A natural extension of robotic surgical intervention is the integration of image guided interventions, which give the promise of reduced trauma, procedure time and inaccuracies. Despite magnetic resonance imaging (MRI) being one of the most effective imaging modalities for visualizing soft tissue structures within the body, MRI guided surgical robotics has been frustrated by the high magnetic field in the MRI image space and the extreme sensitivity to electromagnetic interference. The primary contributions of this dissertation relate to enabling the use of direct, live MR imaging to guide and assist interventional procedures. These are the two focus areas: creation both of an integrated MRI-guided development platform and of a stereotactic neural intervention system. The integrated series of modules of the development platform represent a significant advancement in the practice of creating MRI guided mechatronic devices, as well as an understanding of design requirements for creating actuated devices to operate within a diagnostic MRI. This knowledge was gained through a systematic approach to understanding, isolating, characterizing, and circumventing difficulties associated with developing MRI-guided interventional systems. These contributions have been validated on the levels of the individual modules, the total development system, and several deployed interventional devices. An overview of this work is presented with a summary of contributions and lessons learned along the way.

Thesis. 1978. M.Arch.A.S.--Massachusetts Institute of Technology. Dept. of Architecture. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Bibliography: leaves 87-88. / M.Arch.A.S.

Thesis. 1975. M.Arch.A.S.--Massachusetts Institute of Technology. Dept. of Architecture. / M.Arch.A.S.

Thesis (M.Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Includes bibliographical references. / by Jin Kyoon Kim. / M.Arch.

Thesis. 1975. M.Arch.A.S.--Massachusetts Institute of Technology. Dept. of Architecture. / Bibliography: leaf 62. / by Shyng Miin Chen. / M.Arch.A.S.

Dans ma thèse j'etude les variétés abéliennes ordinaires définies avec multiplication réelle maximale. Je définis des polynômes modulaires dans ce situation et je donne un algorithme pour calculer sur les nombres complexes et pour les surfaces sur des corps finis. Je donne aussi un théorème de structure pour les graphs des isogénies dans ce contexte. Je donne une généralisation de Schoof-Elkies-Atkin aux courbes de genre 2 avec multiplication réelle maximale fixe en utilisant les polynômes modulaires. / My thesis looks at ordinary abelian varieties defined with maximal real multiplication. I define modular polynomials in this setting and give an algorithm to compute them over the complex numbers, and for surfaces over finite fields. I also give a structure theorem for isogeny graphs in this setting. I give a generalisation of Schoof-Elkies-Atkin to genus 2 curves with fixed maximal real multiplication using the modular polynomials.

We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and Jenkins. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also demonstrate congruences for Fourier coefficients of some level 4 modular functions.

Tese de mestrado integrado. Engenharia Civil (Área de Especialização de Construções). Faculdade de Engenharia. Universidade do Porto. 2012