This thesis considers two isoperimetric inequalities for the eigenvalues of the Laplacian on a family of spherically symmetric Riemannian manifolds. The Payne-Pólya-Weinberger Conjecture (PPW) states that for a bounded domain Ω in Euclidean space Rn, the ratio λ1(Ω)/λ0(Ω) of the first two eigenvalues of the Dirichlet Laplacian is bounded by the corresponding eigenvalue ratio for the Dirichlet Laplacian on the ball BΩof equal volume. The Szegö-Weinberger inequality states that for a bounded domain Ω in Euclidean space Rn, the first nonzero eigenvalue of the Neumann Laplacian μ1(Ω) is maximized on the ball BΩ of the same volume. In the first three chapters we will look at the known work for the manifolds Rn and Hn. Then we will take a family a spherically symmetric manifolds given by Rn with a spherically symmetric metric determined by a radially symmetric function f. We will then give a PPW-type upper bound for the eigenvalue gap, λ1(Ω) − λ0(Ω), and the ratio λ1(Ω)/λ0(Ω) on a family of symmetric bounded domains in this space. Finally, we prove the Szegö-Weinberger inequality for this same class of domains.

This thesis serves as documentation of my efforts to define accurately my creative process as an actor in creating the role of Doc Gibbs in Our Town by Thornton Wilder. This includes research, rehearsal journal, character analysis and evaluation of my performance. Our Town was produced by the University of New Orleans Department of Film, Theatre and Communication Arts in New Orleans, Louisiana. The play was performed in the Robert E. Nims Theatre of the Performing Arts Center at 7:30 pm on the evenings of April 22 through April 24, 2010 and April 29 through May 1, 2010 as well as one matinee at 2:30 pm on Sunday, May 2, 2010.

The rhetoric of W.E.B. Du Bois contributed both to a sense of group failure among blacks and a sense of individual failure. Du Bois also created a need to explain the reasons for the failure of the group, as well as that of individuals within the group, specifically those within a segment of the black population deemed the talented tenth. Today the talented tenth is more generally spoken of as those occupying positions within the black middle class. Explanations for failure among blacks as a group are generally of two kinds. The first posits that the failure blacks experience as a group is due to the failure of the talented tenth to provide adequate leadership of the race. The second posits that the failure blacks experience as a group is due to the failure of American society to commit itself to establishing not only legal equality but also social, political, and economic equality for all Americans. Members of the talented tenth, not understanding that the root of the problem lies with the impossible situation Du Bois placed them in as saviors of the race begin to attribute perceived failures among blacks to American society. Instead of questioning Du Bois's goal and the possibility for complete 'racial uplift,' members of the talented tenth begin to question American society's commitment to realize the goals of the civil rights movement. Rather than optimism, one finds pessimism among blacks in the post-civil rights era. I examine Shelby Steele, Derrick Bell, and Randall Robinson's texts as rhetorical discourses that respond to the notion of a debt owed to the race, and evidence a sense of group failure among blacks. I illustrate how David Payne's topoi of therapeutic rhetoric provide a context for understanding not only the arguments these authors make about the nature of failure among blacks, but also the possible solutions these authors pose as avenues for consolation and/or compensation.

Grâce à leur propriété d'amortissement, les élastomères chargés sont couramment utilisés dans l'industrie pour réaliser des pièces anti-vibratoires. Cependant, des phénomènes complexes et couplés, comme l'effet Mullins et l'effet Payne, rendent le comportement de ces matériaux fortement non-linéaire. Peu de modèles permettent de prédire la réponse dynamique de ces pièces quelle que soit la sollicitation appliquée.<br/ >L'objectif principal de cette étude est de proposer un modèle de comportement mécanique du matériau intégrant la prise en compte de l'effet Payne afin de mieux prévoir la réponse dynamique de pièces anti-vibratoires en élastomère chargé et de permettre notamment une meilleure conception de ces pièces en fonction de leur utilisation (fréquence à atténuer, charge statique supportée ...). Ensuite, nous avons développé une chaîne de modèles allant du modèle de comportement matériau au modèle de substitution de la liaison souple intégrable dans un modèle dynamique de grand système, comme un avion par exemple. Pour cela, une méthode de réduction d'ordre de modèle a notamment été développée pour résoudre efficacement le problème paramétrique relatif à la construction du modèle de substitution.<br/ >Ainsi, dans un premier temps, une campagne d'essais dynamiques, caractérisés par une fréquence, une amplitude de déformation et une déformation statique, sur éprouvettes à la fois en cisaillement puis en compression a été menée. Ceux-ci ont notamment permis de caractériser l'effet Payne vis à vis de ces différents paramètres.<br/ >Ensuite, nous avons cherché à développer un modèle de comportement matériau permettant de simuler ces essais et donc de prédire la réponse dynamique de la liaison souple, notamment en terme de rigidité et de dissipation, quelles que soient les sollicitations statiques et dynamiques appliquées. Pour cela, un modèle de comportement hyperviscoplastique : le modèle DyMPPlEC, basé sur celui de Qi-Boyce, a été enrichi au Centre des Matériaux. Les paramètres matériau, associés au modèle développé, ont été identifiés à partir des données expérimentales sur un élément de volume représentatif puis le modèle a été validé sur une structure réelle.<br/ >Enfin, la capacité de ce modèle à prévoir l'effet Payne même pour des sollicitations dynamiques de déformation statique non nulle tout en intégrant l'effet Mullins a été mise en avant.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Humanidades, Departamento de Filosofia, Programa de Pós-Gradução, 2006. / Submitted by Alexandre Marinho Pimenta (alexmpsin@hotmail.com) on 2009-10-03T21:22:19Z No. of bitstreams: 1 2006_Maurício Mota Saboya Pinheiro.pdf: 636303 bytes, checksum: 3bcded7e63dbd24f927677f883f1da39 (MD5) / Approved for entry into archive by Guimaraes Jacqueline(jacqueline.guimaraes@bce.unb.br) on 2009-10-05T12:02:21Z (GMT) No. of bitstreams: 1 2006_Maurício Mota Saboya Pinheiro.pdf: 636303 bytes, checksum: 3bcded7e63dbd24f927677f883f1da39 (MD5) / Made available in DSpace on 2009-10-05T12:02:21Z (GMT). No. of bitstreams: 1 2006_Maurício Mota Saboya Pinheiro.pdf: 636303 bytes, checksum: 3bcded7e63dbd24f927677f883f1da39 (MD5) Previous issue date: 2006-07 / Esta dissertação analisa a relação entre experiência religiosa e credenciais epistêmicas das crenças teístas, com base principalmente nas obras de William Alston (Perceiving God) e Alvin Plantinga (Warranted Christian Belief). Após passar em revista os conceitos clássicos de experiência religiosa, examinam-se em profundidade os argumentos de Alston e de Plantinga em defesa do teísmo para, em seguida, serem criticados e comparados esses autores. A análise comparativa entre ambos sugere vários pontos de complementaridade que poderiam conduzir a futuros aperfeiçoamentos nos trabalhos de cada um. Em particular, uma alternativa indicada por McLeod – um holismo epistemológico de base externalista – parece ser bastante promissora no sentido de se alcançar uma síntese e uma superação de Alston e Plantinga. Tanto os conceitos centrais de prática doxástica (Alston) quanto de aparato cognitivo (Plantinga) poderiam ser integrados em uma estrutura de formação de crenças cujos dados de entrada seriam as experiências do sujeito – considerado tanto individual quanto coletivamente. Nesse esquema, a experiência religiosa ou mística teria um papel meramente causal (ou de “catalisação”) na formação das crenças teístas e estas seriam credenciadas de acordo com os critérios do holismo epistemológico, a saber: o compromisso e o poder de ordenamento do mundo, dentre outros. _________________________________________________________________________________________ ABSTRACT / This dissertation aims at analyzing the bearings between religious experience and the theistic beliefs epistemic credentials, on the basis of the works of William Alston (Perceiving God) and Alvin Plantinga (Warranted Christian Belief). After surveying the classical concepts of religious experience, one deeply examines the arguments of Alston and Plantinga for the theism and, after that, one criticizes and compares both authors. The comparative analysis suggests various complementary points that could lead to improvements in each other’s works. In particular, an alternative pointed out by McLeod – an externalist epistemological holism – looks quite promising in order to attain both a synthesis and an overriding of Alston and Plantinga. The crucial concepts of doxastic practice (Alston) and of cognitive apparatus (Plantinga) could be integrated in a structure of belief formation whose inputs would be the subject’s experiences – this considered both from individual and collective points of view. Under such scheme, religious or mystical experience would have a merely causal role in the formation of theistic beliefs; these beliefs would be credentialed according to the epistemological holism criteria: the commitment and the ordering-world power, among others.

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Des élastomères renforcés modèles sont étudiés afin de mettre en relation leur structure microscopique avec leur comportement mécanique macroscopique. Tout d'abord, la dynamique des chaînes de polymères est étudiée par RMN. Nous mettons en évidence l'existence d'un gradient de température de transition vitreuse autour des charges solides. Nous interprétons ainsi le comportement de plusieurs échantillons à différentes températures avec simplement deux paramètres : l'épaisseur due aux greffons et la taille caractéristique du gradient. Ce modèle de gradient reste valable lors de l'ajout de solvant et permet également d'interpréter les résultats de calorimétrie des échantillons. Par ailleurs, les propriétés mécaniques des échantillons sont mesurées en cisaillement sinusoïdal. En plus de l'effet Payne classiquement observé pour les élastomères renforcés, une non harmonicité des signaux est détectée. Leur analyse montre la présence d'un raidissement et d'une rhéofluidification à l'intérieur de chaque cycle de sollicitation. Par comparaison avec des simulations obtenues par le modèle de renforcement par ponts vitreux, nous pouvons attribuer ce comportement à la cinétique de destruction - reformation des ponts vitreux au cours des sollicitations. Enfin, l'arrangement des particules dans chaque échantillon est déterminé grâce à des simulations Monte-Carlo inverses à partir de résultats de diffusion de neutrons. En faisant le lien avec les mesures de dynamique, nous montrons qu'en plus de la couche de polymère vitreux autour des particules, il existe une fraction de polymère plus faiblement ralenti qui joue un rôle non négligeable dans l'effet Payne.

This work aims at enhancing the understanding and to provideimproved models of the dynamic behavior of rubber vibrationisolators which are widely used in mechanical systems.Initially, a time domainmodel relating compressions tocomponent forces accounting for preload effects, frequency anddynamic amplitude dependence is presented. The problem ofsimultaneously modelling the elastic, viscoelastic and frictionforces are removed by additively splitting them, where theelastic force response is modelled either by a fully linear ora nonlinear shape factor based approach, displaying resultsthat agree with those of a neo-Hookean hyperelastic isolatorunder a long term precompression. The viscoelastic force ismodelled by a fractional derivative element, while the frictionforce governs from a generalized friction element displaying asmoothed Coulomb force. This is a versatile one-dimensionalcomponent model effectively using a small number of parameterswhile exhibiting a good resemblance to measured isolatorcharacteristics. Additionally, the nonlinear excitationeffects on dynamic stiffness and damping of a filled rubberisolator are investigated through measurements. It is shownthat the well-known Payne effect - where stiffness is high forsmall excitation amplitudes and low for large amplitudes whiledamping displays a maximum at intermediate amplitudes -evaluated at a certain frequency, is to a large extentinfluenced by the existence of additional frequency componentsin the signal. Finally, a frequency, temperature and preloaddependent dynamic stiffness model is presented covering theranges from 20 to 20 000 Hz, -50 to +50 °C at 0 to 20 %precompression. A nearly incompressible, thermo-rheologicallysimple material model is adopted displaying viscoelasticitythrough a time - strain separable relaxation tensor with asingle Mittag-Leffler function embodying its time dependence.This fractional derivative based function successfully fitsmaterial properties throughout the whole audible frequencyrange. An extended neo-Hookean strain energy function, beingdirectly proportional to the temperature and density, isapplied for the finite deformation response with componentproperties solved by a nonlinear finite element procedure. Thepresented work is thus believed to enlighten workingconditions’impact on the dynamic properties of rubbervibration isolators, while additionally taking some of thesemost important features into account in the presentedmodels.

<p>This work aims at enhancing the understanding and to provideimproved models of the dynamic behavior of rubber vibrationisolators which are widely used in mechanical systems.Initially, a time domainmodel relating compressions tocomponent forces accounting for preload effects, frequency anddynamic amplitude dependence is presented. The problem ofsimultaneously modelling the elastic, viscoelastic and frictionforces are removed by additively splitting them, where theelastic force response is modelled either by a fully linear ora nonlinear shape factor based approach, displaying resultsthat agree with those of a neo-Hookean hyperelastic isolatorunder a long term precompression. The viscoelastic force ismodelled by a fractional derivative element, while the frictionforce governs from a generalized friction element displaying asmoothed Coulomb force. This is a versatile one-dimensionalcomponent model effectively using a small number of parameterswhile exhibiting a good resemblance to measured isolatorcharacteristics. Additionally, the nonlinear excitationeffects on dynamic stiffness and damping of a filled rubberisolator are investigated through measurements. It is shownthat the well-known Payne effect - where stiffness is high forsmall excitation amplitudes and low for large amplitudes whiledamping displays a maximum at intermediate amplitudes -evaluated at a certain frequency, is to a large extentinfluenced by the existence of additional frequency componentsin the signal. Finally, a frequency, temperature and preloaddependent dynamic stiffness model is presented covering theranges from 20 to 20 000 Hz, -50 to +50 °C at 0 to 20 %precompression. A nearly incompressible, thermo-rheologicallysimple material model is adopted displaying viscoelasticitythrough a time - strain separable relaxation tensor with asingle Mittag-Leffler function embodying its time dependence.This fractional derivative based function successfully fitsmaterial properties throughout the whole audible frequencyrange. An extended neo-Hookean strain energy function, beingdirectly proportional to the temperature and density, isapplied for the finite deformation response with componentproperties solved by a nonlinear finite element procedure. Thepresented work is thus believed to enlighten workingconditions’impact on the dynamic properties of rubbervibration isolators, while additionally taking some of thesemost important features into account in the presentedmodels.</p>