S(5,8,24) is one of the largest known Steiner systems and connects combinatorial designs, error-correcting codes, finite simple groups, and sphere packings in a truly remarkable way. This thesis discusses the underlying structure of S(5,8,24), its construction via the (24,12) Golay code, as well its automorphism group, which is the Mathieu group M24, a member of the sporadic simple groups. Particular attention is paid to the calculation of the size of automorphism groups of Steiner systems using the Orbit-Stabilizer Theorem. We conclude with a section on the sphere packing problem and elaborate on how the 8-sets of S(5,8,24) can be used to form Leech's Lattice, which Leech used to create the densest known sphere packing in 24-dimensions. The appendix contains code written for Matlab which has the ability to construct the octads of S(5,8,24), permute the elements to obtain isomorphic S(5,8,24) systems, and search for certain subsets of elements within the octads. / Master of Science

Oil and gas exploitation in deep waters has become more than just a profit business to be a daily necessity, since the world energy matrix is based on fossil components. Risers are offshore structures that are intimately linked with oil and gas exploitation and those are subjected to a great variety of effects in field, e.g., marine currents, Vortex Induced Vibration (VIV), heave motion caused by gravitational waves, non-linear contact with the sea floor, and many others. Riser dynamics is essentially non-linear and experimental tests in real scale are almost impossible due to a great variety of control parameters acting concomitantly. Small-scale models are a better experimental approach. Nevertheless, there are many structural and hydrodynamical parameters to be evaluated. Considering only vertical risers in the present work, Galerkin\'s modal decomposition is used in order to reduce the dynamics of a vertical flexible cylinder to a few linear modes in which the majority of energy and information are contained. From the modal analysis, added mass and structural parameters damping of a vertical flexible cylinder using data obtained from free-decay tests performed both in water and in air are evaluated. Finally, a modal Mathieu-Hill oscillator with non-linear damping is constructed and, based on aStrutt diagram, modal stability under parametric resonance is discussed. / Exploração de óleo e gás em bacias de águas profundas tem-se tornado mais do que apenas uma economia lucrativa, para ser uma necessidade diária, já que a matriz energética mundial está baseada em componentes fósseis. Risers são estruturas offshore ligadas intimamente com a exploração de óleo e gás e essas estão sujeitas a uma grande variedade de efeitos na operação, e.g., correntes marítimas, Vibrações Induzidas por Vórtices (VIV), movimento de heave causado por ondas gravitacionais, contato não-linear com o solo marinho, entre outros. Dinâmica de risers é essencialmente não-linear e testes experimentais em escala real são praticamente impossíveis devido a uma enorme variedade de parâmetros de controle agindo concomitantemente. Modelos em escala reduzida são uma abordagem experimental mais conveniente. Não obstante, há muitos parâmetros estruturais e hidrodinâmicos a serem determinados. Considerando apenas risers verticais no trabalho presente, a decomposição modal de Galerkin é usada a fim de reduzir a dinâmica de um cilindro fléxivel vertical a alguns modos lineares em que a maior parte da energia e informação estão contidos. A partir da análise modal, parâmetros de massa adicional e amortecimento estrutural de um cilindro flexível vertical são obtidos usando testes de decaimento livre conduzidos na água e no ar. Finalmente, um oscilador modal de Mathieu-Hill com amortecimento não-linear é proposto e, baseado em um diagrama de Strutt, a estabilidade modal sob excitação de ressonânica paramétrica é discutida.

Oil and gas exploitation in deep waters has become more than just a profit business to be a daily necessity, since the world energy matrix is based on fossil components. Risers are offshore structures that are intimately linked with oil and gas exploitation and those are subjected to a great variety of effects in field, e.g., marine currents, Vortex Induced Vibration (VIV), heave motion caused by gravitational waves, non-linear contact with the sea floor, and many others. Riser dynamics is essentially non-linear and experimental tests in real scale are almost impossible due to a great variety of control parameters acting concomitantly. Small-scale models are a better experimental approach. Nevertheless, there are many structural and hydrodynamical parameters to be evaluated. Considering only vertical risers in the present work, Galerkin\'s modal decomposition is used in order to reduce the dynamics of a vertical flexible cylinder to a few linear modes in which the majority of energy and information are contained. From the modal analysis, added mass and structural parameters damping of a vertical flexible cylinder using data obtained from free-decay tests performed both in water and in air are evaluated. Finally, a modal Mathieu-Hill oscillator with non-linear damping is constructed and, based on aStrutt diagram, modal stability under parametric resonance is discussed. / Exploração de óleo e gás em bacias de águas profundas tem-se tornado mais do que apenas uma economia lucrativa, para ser uma necessidade diária, já que a matriz energética mundial está baseada em componentes fósseis. Risers são estruturas offshore ligadas intimamente com a exploração de óleo e gás e essas estão sujeitas a uma grande variedade de efeitos na operação, e.g., correntes marítimas, Vibrações Induzidas por Vórtices (VIV), movimento de heave causado por ondas gravitacionais, contato não-linear com o solo marinho, entre outros. Dinâmica de risers é essencialmente não-linear e testes experimentais em escala real são praticamente impossíveis devido a uma enorme variedade de parâmetros de controle agindo concomitantemente. Modelos em escala reduzida são uma abordagem experimental mais conveniente. Não obstante, há muitos parâmetros estruturais e hidrodinâmicos a serem determinados. Considerando apenas risers verticais no trabalho presente, a decomposição modal de Galerkin é usada a fim de reduzir a dinâmica de um cilindro fléxivel vertical a alguns modos lineares em que a maior parte da energia e informação estão contidos. A partir da análise modal, parâmetros de massa adicional e amortecimento estrutural de um cilindro flexível vertical são obtidos usando testes de decaimento livre conduzidos na água e no ar. Finalmente, um oscilador modal de Mathieu-Hill com amortecimento não-linear é proposto e, baseado em um diagrama de Strutt, a estabilidade modal sob excitação de ressonânica paramétrica é discutida.

This thesis considers four nonlinear systems with parametric forcing. The first problem involves an inverted pendulum with asymmetric elastic restraints subjected to harmonic vertical base excitation. On linearizing trigonometric terms the pendulum is governed by an asymmetric Mathieu equation. Solutions to this equation are scaleable. The stability regions in the parameter plane are studied numerically. Periodic solutions at the boundaries of stable regions in the parameter plane are found numerically and then their existence is proved theoretically. The second problem involves use of the method of multiple scales to elucidate the dynamics associated with early and delayed ejection of ions from Paul traps. A slow flow equation is developed to approximate the solution of a weakly nonlinear Mathieu equation to describe ion dynamics in the neighborhood of the nominal stability boundary of ideal traps. Since the solution to the unperturbed equation involves linearly growing terms, some care in identification and elimination of secular terms is needed. Due to analytical difficulties, harmonic balance approximations are used within the formal implementation of the method. The third problem involves the attenuation, caused by weak damping, of harmonic waves through a discrete, periodic structure with wave frequency nominally within the Propagation Zone. Adapting the transfer matrix method and using the harmonic balance for nonlinear terms, a four-dimensional map governing the dynamics is obtained. This map is analyzed by applying the method of multiple scales upto first order. The resulting slow evolution equations give the amplitude decay rate in the structure. The fourth problem involves the dynamic response of a strongly nonlinear single-degree-of-freedom oscillator under a constant amplitude, parametric, periodic, impulsive forcing, e.g., a pendulum with strongly nonlinear torsional spring that is periodically struck in the axial direction. Single-term harmonic balance gives an approximate, but explicit, 2-dimensional map governing the dynamics. The map exhibits many fixed points (both stable and unstable), higher period orbits, transverse intersections of stable and unstable manifolds of unstable fixed points, and chaos.

La spectrométrie de masse, en particulier le couplage HPLC/MRM3, est un outil bien adapté au diagnostic in vitro, particulièrement en microbiologie clinique. L’utilisation en routine de cette technologie est cependant tributaire de sa sensibilité et de sa spécificité. Ce travail de thèse a pour objectif d’étudier la possibilité d’éjecter et de détecter simultanément et de façon sélective des ions de ratio masse/charge donnés, ceux-ci étant confinés dans un piège ionique quadrupolaire. Cette approche permet de supprimer les étapes de balayage en masse et d’intégration mathématique du signal en mode MRM3 ce qui permet de gagner à la fois en sensibilité et en spécificité (en diminuant le temps de cycle et en diminuant le rapport signal sur bruit). Cet objectif a été poursuivi premièrement par une étude théorique approfondie des équations du mouvement des ions dans un piège radiofréquence ; deuxièmement par une étude numérique de la stabilité de ces équations et enfin troisièmement par une validation expérimentale de ces résultats théoriques. La présentation de ces trois approches fait l’objet du présent mémoire / Mass spectrometry, and more specifically HPLC/MRM3, is a very suitable tool for in vitro diagnostic. Nevertheless high sensitivity and specificity has to be reached for one to use mass spectrometry as a routine technique in clinical microbiology. The objective of this work is to study the possibility of ejecting, and thus detecting, simultaneously ions several desired m/z ratio stored in a quadrupolar ion trap. This approach allows suppressing altogether the mass scan and mathematical integration stages, leading to an improvement of the signal-to-noise ratio and a decrease of the cycle time which increase both sensitivity and specificity. This objective was carried out by an extensive mathematical and numerical study of the stability of the ions’ motion equation comforted by experimental data

Syftet med denna uppsats är att belysa hur litteratur kan användas i ett integrerat värdegrundsarbete i svenskundervisning på gymnasiet, utifrån exemplet Jennifer Mathieus roman Moxie (2021), med fokus på jämställdhet mellan könen. Genom att analysera romanen utifrån genus- och feministisk teori har värdefulla delar ur romanen lyfts fram. Detta ställdes sedan i relation till kursplanen för svenska (Skolverket, u.å.) och tidigare forskning kring litteratursamtal, både som arbetssätt och i ett värdegrundsarbete. Analysen visar att Moxie gestaltar och problematiserar patriarkala mönster och maktsystem, och hur en feministisk rörelse kan bidra till att förbättra kvinnornas ställning i samhället. Analysen visar också att dessa delar fungerar som ett bra material i litteratursamtal, och att detta i sin tur agerar som ett viktigt verktyg i ett integrerat värdegrundsarbete i svenskundervisningen. / The aim of this study is to illustrate how literature can be used in an integrated work on fundamental values in Swedish education at upper secondary school, with the example Jennifer Mathieu’s novel Moxie (2021), with focus on gender equality. By analyzing the novel based on gender- and feminist theory valuable parts from the novel have been highlighted. This was then put in relation to the syllabus for Swedish (Skolverket, u.å.) and previous research on book talk, both as an approach on work methods and as a part in a work on fundamental values. The analysis shows that Moxie portrays and problematizes patriarchal patterns and power structures, and how a feminist movement can contribute to improving the position of women in society. The analysis also shows that these parts serve as good material in book talks, and at the same time acts as an important tool in an integrated work on basic values in Swedish education.

André Mathieu (1929-1968), a Canadian composer and performer, received acclaim in Europe, Canada and United States from his earliest years. He revealed brilliant pianistic skill, and critics hailed him as the "young Canadian Mozart". Mathieu's early solo piano works, written mostly in ternary form, reveal an abundance of compositional ideas based on the influences of Romantic and Impressionist styles. However, when he began composing Piano Concerto No. 3, a much larger work, his lack of compositional training became evident. Formal weakness resulted in a disconnection between themes and lack of thematic and motivic development. Not until Mathieu studied with Swiss composer Arthur Honegger did he develop and clearly display a concept of formal structure. In this study, I will demonstrate that, through compositional studies with Arthur Honegger, André Mathieu assimilated a new approach to form, resulting in the discovery of his mature compositional voice found for the first time in the Piano Concerto No. 4. The synthesis of Romantic and Impressionistic styles in this concerto further contributes to the unique nature of this mature voice.This document is organized in six chapters. Chapter I reviews current literature on André Mathieu and his music and points out both the values and the limitations of this literature. Chapter II relates Mathieu's biography. Chapter III provides background information on Mathieu's solo piano works and four concerti, as well as the difficult pianistic techniques composed into those works. Chapter IV discusses the influences of Romantic and Impressionist styles in Piano Concerto No. 4 and how Mathieu synthesized both styles. Chapter V analyzes the form, motivic and thematic material, and rhythmic design of all three movements of Piano Concerto No. 4 and compares them with that of Piano Concerto No. 3. Honegger's influence also is discussed in Chapter V. Chapter VI is the conclusion. Musical examples throughout will illustrate points made.

Real neurons, and their networks, are far too complex to be described exactly by simple deterministic equations. Any description of their dynamics must therefore incorporate noise to some degree. It is my thesis that the nervous system is organized in such a way that its performance is optimal, subject to this constraint. I further contend that neuronal dynamics may even be enhanced by noise, when compared with their deterministic counter-parts. To support my thesis I will present and analyze three case studies. I will show how noise might (i) extend the dynamic range of mammalian cold-receptors and other cells that exhibit a temperature-dependent discharge; (ii) feature in the perception of ambiguous figures such as the Necker cube; (iii) alter the discharge pattern of single cells.

Frank Dobbins in memoriam In 1976 Louise Litterick proposed that Cambridge, Magdalene College, Pepys Library MS 1760 was originally prepared for Louis XII and Anne of Brittany of France but was gifted to Henry VIII of England in 1509. That the manuscript actually was prepared as a wedding gift from Louis to his third wife Mary Tudor in 1514, however, is indicated by its decorative and textual imagery, which mirrors the decoration of a book of hours given by Louis to Mary and the textual imagery used in her four royal entries. Analysis of the manuscript’s tabula and texts suggests that MS 1760 was planned by Louis’s chapelmaster Hilaire Bernonneau (d. 1524) at the king’s behest. The new theory elucidates the content and significance of Gascongne’s twelve-voice canon Ista est speciosa, which appeared beneath an original portrait of Mary Tudor and was intended to mirror the perfection of the Blessed Virgin and her ‘godchild’ Mary.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.