In this thesis we study the optimal stochastic control problem of the drift of a Lévy process. We show that, for a broad class of Lévy processes, the partial integro-differential Hamilton-Jacobi-Bellman equation for the value function admits classical solutions and that control policies exist in feedback form. We then explore the class of Lévy processes that satisfy the requirements of the theorem, and find connections between the uniform integrability requirement and the notions of the score function and Fisher information from information theory. Finally we present three different numerical implementations of the control problem: a traditional dynamic programming approach, and two iterative approaches, one based on a finite difference scheme and the other on the Fourier transform. / text

This thesis proposes that astronomical ideas and forces structured the poetic, religious and philosophical imaginings of William Wordsworth and Samuel Taylor Coleridge. Despite the widespread scholarly predilection for interdisciplinary enquiry in the field of literature and science, no study has been undertaken to assess the impact and imaginative value of mathematics and astronomy upon Wordsworth and Coleridge. Indeed, it is assumed they had neither the resources available to access this knowledge, nor the capacity to grasp it fully. This is not the case. I update the paradigm that limits their familiarity with the physical sciences to the education they received at school and at Cambridge, centred principally on Euclid and Newton, by revealing their attentiveness to the new world views promulgated by William Herschel, William Rowan Hamilton, Pierre-Simon Laplace, and the mathematicians of Trinity College, Cambridge, including John Herschel, George Peacock, and George Biddell Airy, amongst others. The language of astronomy wielded a vital, analogical power for Wordsworth and Coleridge; it conditioned the diurnal rhythms of their thought as its governing dynamic. Critical processes were activated, at the level of form and content, with a mixture of cosmic metaphors and nineteenth-century discoveries (such as infra-red). Central models of Wordsworth’s and Coleridge’s literary and metaphysical inventions were indissociable from scientific counterparts upon which they mutually relied. These serve as touchstones for creative endeavour through which the mechanisms of their minds can be traced at work. Exploring the cosmological charge contained in the composition of their poems, and intricately patterned and pressed into their philosophical and spiritual creeds, stakes a return to the evidence of the Romantic imagination. The incorporation of astrophysical concepts into the moulds of Wordsworth’s and Coleridge’s constructions manifests an intelligent plurality and generosity which reveals the scientific valency of their convictions about, variously, the circumvolutions of memory and the idea of psychic return; textual revision, specifically the ways in which language risks becoming outmoded; prosody, balance, and the minute strictures modifying metrical weight; volubility as an axis of conversation and cognition; polarity as the reconciling tool of the imagination; and the perichoretic doctrine of the Holy Trinity. The ultimate purpose is to show that astronomy provided Wordsworth and Coleridge with a scaffold for thinking, an intellectual orrery which ordered artistic consciousness and which they never abandoned.

O ensaio de simples reconhecimento de solos (SPT) é a ferramenta de investigação de solos mais utilizada no mundo. Devido ao grande número de parâmetros que influenciam os seus resultados, a medida de sua eficiência passa a ser indispensável à transposição de experiências entre as práticas desenvolvidas em diferentes locais. Infelizmente, a medida da eficiência através da instrumentação do impacto do martelo é economicamente inviável para a maioria das empresas de sondagem no Brasil. Este trabalho apresenta uma metodologia para a determinação da eficiência do SPT baseada no princípio de Hamilton e na realização de prova de carga estática sobre o amostrador, que pode ser uma alternativa para sanar esta situação. / The standard penetration test (SPT) is the most used soil investigation tool in the world. Due to the great number of variables that influences its results, the measurement of the efficiency becomes imperative to the transposition of experiences between developed practices in different places. Unfortunately, the measurement of the efficiency through the instrumentation of the hammer impact is economically inpracticable to most of the soil investigation firms in Brazil. This work presents a methodology to determinate the SPT efficiency based on the Hamilton\'s principle and on the execution of static load test over the sampler, what seems to be a good alternative to end this situation.

Orientador: Bruto Max Pimentel Escobar / Resumo: Neste trabalho apresentamos o formalismo Hamiltoniano de Dirac para sistemas singulares, analisando inclusive a construção do gerador de transformações de gauge. A seguir discutimos brevemente a generalização, já conhecida, desse formalismo para o caso de Lagrangeanos singulares de segunda ordem fazendo também uma análise da estrutura de vínculos presente em tais teorias. Desenvolvemos então o formalismo de Hamilton-Jacobi para sistemas singulares fazendo sua generalização para Lagrangeanos de segunda ordem. Por último, ambos formalismos são aplicados à Eletrodinâmica de Podols y e os resultados obtidos são comparados. / Abstract: In this work we study Dirac's Hamiltonian formulation for singular systems including the construction of the gauge transformations generator. Next we briefy discuss the generalization, already developed, of this formalism for singular second order La grangians. Besides that we also make an anlysis of the constrains structure present in such theories. Then we develop the Hamilton-Jacobi formalism for singular systems making its generalization for the case of second order Lagrangians. Finally, both formalisms are applied to Podols y's eletrodynamics and the obtained results are comparad. / Mestre

Cette thèse concerne les jeux différentiels à somme nulle et à deux joueurs avec information incomplète. La structure de l'information est liée à un signal que reçoivent les joueurs. Cette information est dite symétrique quand la connaissance du signal est la même pour les deux joueurs (le signal est public), et asymétrique quand les signaux reçus par les joueurs peuvent être différents (le signal est privé).Ces signaux sont révélés au cours du jeu. Dans plusieurs situations de tels jeux, il est montré dans cette thèse, l'existence d'une valeur du jeu et sa caractérisation comme unique solution d'une équation aux dérivées partielles.Un type de structure d'information concerne le cas symétrique où le signal est réduit à la connaissance par les joueurs de l'état du système au moment où celui-ci atteint une cible donnée (les données initiales inconnues sont alors révélées). Pour ce type du jeu, nous avons introduit des stratégies non anticipatives qui dépendent du signal et nous avons obtenu l'existence d'une valeur.Comme les fonctions valeurs sont en général irrégulières (seulement continues), un des points clefs de notre approche est de prouver des résultats d'unicité et des principes de comparaison pour des solutions de viscosité lipschitziennes de nouveaux types d'équation d'Hamilton-Jacobi-Isaacs associées aux jeux étudiés. / In this thesis we investigate two-person zero-sum differential games with incomplete information. The information structure is related to a signal communicated to the players during the game.In such games, the information is symmetric if both players receive the same signal (namely it is a public signal). Otherwise, if the players could receive different signals (i.e. they receive private signals), the information is asymmetric. We prove in this thesis the existence of value and the characterization of the value function by a partial differential equation for various types of such games.A particular type of such information structure is the symmetric case in which the players receive as their signal the current state of the dynamical system at the moment when the state of the dynamic hits a fixed target set (the unknown initial data are then revealed to both players). For this type of games, we introduce the notion of signal-depending non-anticipative strategies with delay and we prove the existence of value with such strategies.As the value functions are in general irregular (at most continuous), a crucial step of our approach is to prove the uniqueness results and the comparison principles for viscosity solutions of new types of Hamilton-Jacobi-Isaacs equation associated to the games studied in this thesis.

Charles Jennens (1700-1773), the librettist of 'Saul', 'Messiah', 'Belshazzar', the final part of 'L'Allegro, il Penseroso ed il Moderato', and probably 'Israel in Egypt', amassed a huge library of music that forms the bulk of what is now known as the Aylesford collection. Jennens's collection of Handel's music was unique among those of his contemporaries, not only because it includes part-books, but also because it is unusually comprehensive. The dissertation focuses on his copies of the sacred oratorios beginning with 'Saul' (1739) because most of the collection was copied in the 1740s, the sacred oratorios were the works that Jennens was most interested in, and 'Saul' was his first collaboration with Handel. As many of these manuscripts have not been the focus of modern scholarly attention, I first establish how, when, and by whom each manuscript was copied, in order to achieve a greater understanding of how and when Jennens assembled his collection, and what his reasons were for doing so. This close study of the manuscripts reveals that Jennens made extensive alterations to the verbal text, the structure, and the music of several oratorios in his collection. His amendments to 'Saul' and 'Belshazzar' shed light on his collaboration with Handel; and his amendments to 'Samson' and 'Joseph and his Brethren' provide insights into his attitude to Handel in the mid-1740s, his approach to word-setting, his views on the adaptation of Scripture for oratorio, and his beliefs and commitments. Jennens was a highly educated man whose activities were informed by two deeply held, conflicting allegiances: to the Anglican Church and to the deposed Stuarts. An examination of how he harnessed Handel's music to deliver his religious and political messages leads to a richer and more profound understanding of the works, of the relationship between Jennens, Handel, and Handel's music, and of their place in the religious and political context of the mid-eighteenth century.

Esta tese apresenta, o projeto de uma perfuratriz que permite a execução de cinco tipos de fundação profunda, e o desenvolvimento de um ensaio de campo que possibilita avaliar as resistências por atrito lateral desenvolvidas entre o instrumento envolvido pelo solo escavado e o terreno natural. A perfuratriz foi projetada para executar estacas dos tipos hélice contínua monitorada, escavadas com trado mecânico, hélice segmentada monitorada, raiz e hollow-auger. As estacas dos tipos hélice contínua monitorada e as escavadas com trado mecânico são muito utilizadas no Brasil; as estacas raiz e hollow-auger são utilizadas em situações especiais e a estaca hélice segmentada monitorada é mais recente, mas sua aplicação tem tido um crescimento importante nos últimos dez anos. Para a perfuratriz multifuncional são apresentados cálculos e desenhos básicos dos principais conjuntos. Para a nova investigação de campo, denominada FDT - Full Displacement Test, é apresentado um desenvolvimento teórico com base no princípio universal da conservação de energia que, em termos práticos, resulta na obtenção da parcela de atrito lateral, denominado atrito lateral unitário equivalente (fse). Os resultados obtidos a partir dos dados aquisitados pelo sistema de monitoramento eletrônico da perfuratriz apresentaram-se concordantes entre si, indicando a possibilidade de praticamente se conseguir a repetibilidade do ensaio. Entre os diversos ensaios realizados, foi dada ênfase aos ensaios realizados no campo experimental de Fundações e Geotecnia da Faculdade de Engenharia Agrícola FEAGRI, da Universidade de Campinas - UNICAMP e foram feitas correlações com as resistências obtidas nas provas de carga estáticas realizadas no local por Albuquerque (2001), a partir dos ajustes feitos para o nível instrumentado na profundidade de 11,70 m para o qual foi determinado um fator (G2), para cada tipo de estaca ensaiada (escavada, hélice contínua e ômega). A partir dos ajustes feitos para o nível 11,70 m foram feitas previsões de capacidade de carga por atrito lateral para os outros níveis instrumentados (5,00 m; 11,10 m e 12,00 m), sendo que os resultados apresentaram-se concordantes. / This thesis presents the design of a drilling rig that allows the execution of five types of deep foundation, and the development of a field test that allows measuring the skin friction resistance developed between the instrument involved by the excavated ground and the natural soil. The drilling rig was designed to make continuous flight auger, bored pile, continuous flight auger with segmented auger, root pile and hollow-auger pile. The continuous flight auger and bored piles are widely used in Brazil; the root pile and hollow-auger pile are used for in special conditions, and the continuous flight auger with segmented auger, is although more recent, but its application has had increased application grown in over the last ten years. For the multifunctional drilling rig, calculations and basic designs of the main sets are presented. For the new field test denominated FDT - Full Displacement Test, a theoretical development based on the universal principle of energy conservation was made carried out resulting and the result, in practical terms, was to obtain in the attainment of the skin friction defined in this thesis as equivalent unit skin friction (fse). The results obtained from the data acquired by the electronic monitoring system of drilling rigs were consistent among themselves, indicating the possibility of practically achieve the repeatability of the test. Among the various tests performed, emphasis was given to tests in the experimental field of foundations and geotechnics, of the College of Agricultural Engineering FEAGRI, Campinas University UNICAMP, and were correlated to the skin friction resistance obtained from the static load tests performed on site by Albuquerque (2001), based on the adjustments done to the instrumented level depth of 11.70 m, for which a factor (G2) was given in each type tested (bored, C.F.A and omega). From the adjustments made to the 11,70 m level, load-bearing capacity of skin friction predictions were made for other instrumented levels (5.00 m; 11.10 m and 12.00 m) presenting consistent results.

The thesis focuses on portraying historical events in musical theatre pieces. It explores especially the historical musical Hamilton that became a phenomenon in the field. The musical narrates the story of Alexander Hamilton and historical events that led to the foundation of the United States of America. The first part of the thesis analyses how the musical Hamilton portrays historical phenomena, events and personalities. It also explores various methods how they are staged. The results of this analysis will be used for comparison of musical Hamilton with other contemporary musicals. In the final part the thesis points out the possibilities of usage of modern musical theatre in history education.

Dans cette thèse nous nous intéressons à des inégalités fonctionnelles comme les inégalités de Poincaré, Sobolev logarithmique, Sobolev, et celles appelées inégalités de transport. Dans un premier temps, nous étudions les inégalités de Poincaré et de Sobolev logarithmique pour des modèles de mécanique statistique. Cette étude nous permet de donner une nouvelle classe de phases telle que les mesures de Gibbs associées satisfassent à ces deux inégalités. Nous étudions dans un second temps, les inégalités de Sobolev logarithmique et de Sobolev par le biais des équations de Hamilton-Jacobi. Nous montrons, de la même façon que Gross en 1975 pour les semi-groupes de diffusion, l'équivalence entre l'inégalité de Sobolev logarithmique et l'hypercontractivité des solutions des équations de Hamilton-Jacobi. Cette équivalence permet de montrer, par une nouvelle méthode que celle utilisée par Otto et Villani, que l'inégalité de Sobolev logarithmique implique une inégalité de transport quadratique. De la même manière que Varopoulos en 1985 pour les semi-groupes de diffusion, nous donnons le lien entre l'inégalité de Sobolev et l'ultracontractivité des solutions des équations de Hamilton-Jacobi. Pour finir nous étudions les inégalités de transport dans un cadre général. Cette étude permet d'une part de donner le lien entre des inégalités de Sobolev logarithmiques modifiées et des inégalités de transport particulières et d'autre part de donner un exemple d'inégalité de transport quadratique pour une mesure en dimension infinie, la mesure de Wiener.

Le travail présenté dans ce mémoire est divisé en deux parties. La première partie est consacrée aux calculs des fonctions d'appui de la Jacobienne généralisée de Clarke et de son enveloppe plénière, associées à une fonction localement lipschtizienne à valeurs vectorielles. Clarke avait établi en 1975 que la fonction d'appui du sous-différentiel généralisé était une dérivée directionnelle généralisée. Il est donc satisfaisant de constater que la fonction d'appui de la Jacobienne généralisée est une sorte de "divergence directionnelle généralisée". Dans la seconde partie, nous présentons un certain nombre d'applications de techniques issues de l'Analyse non lisse à la résolution d'équations de Hamilton-Jacobi du premier ordre. Ainsi nous utilisons la dualité convexe et le calcul sous-différentiel pour prouver que les formules dites de Hopf-Lax définissent des solutions explicites des équations de Hamilton-Jacobi associées (avec données initiales semicontinues inférieurement). Nous n'utilisons ni le fameux principe de comparaison de la théorie des solutions de viscosité ni régularisation. Nous traitons successivement le cas de la dimension finie et de la dimension infinie. Ces résultats nous permettent de trouver des estimations des solutions d'équations dont l'hamiltonien est la différence de deux fonctions convexes. Enfin, nous nous attachons à l'étude des solutions sci dans des espaces de Banach dits ``lisses''. Le théorème de la valeur moyenne de Clarke et Ledyaev nous permet de montrer un résultat d'``enveloppe'' : nous construisons une solution sci pour une équation dont l'hamiltonien est le supremum d'une famille d'hamiltoniens. Nous appliquons enfin les mêmes techniques pour prouver l'existence d'une solution sci minimale sous des hypothèses plus faibles que celles que l'on recontre généralement dans la littérature.