We study compensation functions for an infinite-to-one factor code $\pi : X \to Y$ where $X$ is a shift of finite type. The $p$-Dini condition is given as a way of measuring the smoothness of a continuous function, with $1$-Dini corresponding to functions with summable variation. Two types of compensation functions are defined in terms of this condition. Given a fully-supported invariant measure $\nu$ on $Y$, we show that the relative equilibrium states of a $1$-Dini function $f$ over $\nu$ are themselves fully supported, and have positive relative entropy. We then show that there exists a compensation function which is $p$-Dini for all $p > 1$ which has relative equilibrium states supported on a finite-to-one subfactor. / Graduate / 0405 / antoniol@uvic.ca

Mathematics is defined as an abstract way of thinking. Abstraction ranks among the least accessible mental activities. In an educational context the encounter with mathematical abstraction is the crucial step of the transition from informal school mathematics to the formalism of university mathematics. This transition is characterised by cognitive tensions. This study aimed at the identification and exploration of the tensions in the novice mathematician's encounter with mathematical abstraction. For this purpose twenty first-year mathematics undergraduates were observed in their weekly tutorials in four Oxford Colleges during Michaelmas and Hilary Term of Year 1. Tutorials were tape-recorded and fieldnotes kept during observation. The students were also interviewed at the end of each term of observation. The recordings of the observed tutorials and the interviews were transcribed and submitted to an analytical process of filtering out episodes that illuminate the novices' cognition. An analytical framework consisting of cognitive and sociocultural theories on learning was applied on sets of episodes within the mathematical areas of Foundational Analysis, Calculus, Linear Algebra and Group Theory. This topical analysis was followed by a cross-topical synthesis of themes that were found to characterise the novices' cognition. The novices' encounter with mathematical abstraction was described as a personal meaning-construction process and as an enculturation process: the new culture is Advanced Mathematics introduced by an expert, the tutor. The novices' interaction with the new concept definitions was obstructed by their unstable previous knowledge. Concept image construction was described as a construction of meaningful metaphors and an exploration of the 'raison-d'-être' of the new concepts and the new reasoning and was characterised by the tension between the Informal/Intuitive/Verbal and the Formal/Abstract/Symbolic — which was discussed in terms of semantics and reasoning. The novices were in difficulty with the mechanics of formal mathematical reasoning as well as with applying these mechanics in a contextualised manner. This decontextualised behaviour was linked to the fragility of their knowledge with regard to the nature of rigour in formal mathematics.

Thesis (Ph. D.)--University of Chicago, Dept. of Slavic Languages and Literatures, June 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Universidade Federal do Paraná, (2002?). / Includes bibliographical references.

The Casimir effect refers to the primarily attractive force between material bodies due to quantum fluctuations in the electromagnetic field. The Casimir effect is difficult to calculate in general, since it is sensitive to the exact shapes of the bodies and involves contributions from all frequencies. As a result, calculating the Casimir effect between general bodies usually requires a numerical approach. The worldline method computes Casimir energies by creating an ensemble of space-time paths corresponding to a virtual particle interacting with the bodies. This method was originally developed for a scalar fields coupled to an idealized background potential, rather than the vector electromagnetic field interacting with media. This thesis presents work on extending the worldline method to account for the material properties of the interacting bodies, and the polarizations of electromagnetism. This thesis starts by covering background material on path integrals, and quantizing the electromagnetic field in media. The electromagnetic field is decomposed in terms of two scalar fields for planar bodies, where these scalar fields correspond to the transverse-electric and transverse-magnetic polarizations of the electromagnetic field. The worldline path integrals are developed for both polarizations, and solved analytically. Next, numerical methods are developed and tested in the context of planar bodies. The starting positions, and scale of the paths, and shape of the paths are sampled via Monte Carlo methods. The transverse-magnetic path integral also requires specialized methods for estimating derivatives, and path construction. The analytical and numerical results for both worldline path integrals are in agreement with known solutions. Finally, specialized methods are developed for computing derivatives of the worldline Casimir-energy path integrals, allowing for efficient numerical computations of Casimir forces and torques.

Made available in DSpace on 2014-06-11T19:22:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-10-25Bitstream added on 2014-06-13T19:08:28Z : No. of bitstreams: 1 araujo_jcb_me_sjrp.pdf: 676720 bytes, checksum: ec12d48a0e70f3225d98b32f48a1f86d (MD5) / Neste trabalho é apresentado o formalismo supersimétrico que consiste em uma generalização do método de fatorização para se encontrar a solução da equação de Schrödinger. O oscilador harmônico e o átomo de hidrogênio são resolvidos através deste formalismo. Para o potencial de Lennard-Jones (12,6) é utilizado o método variacional, onde utilizamos a supersimetria para encontrar uma função de onda que se assemelhe com a função real, este procedimento é feito através da escolha de um superpotencial que gere um potencial efetivo que se aproxima do potencial original. Com isto as autofunções e os autovalores para o estado fundamental e o primeiro estado excitado são encontrados. Alguns resultados numéricos obtidos são comparados com outros encontrados na literatura. / In this work it is presented the supersymmetrical formalism that consists of a generalization of the factorization method to find the solution of Schrödinger equation. The harmonic oscillator and the hydrogen atom are decided through this formalism. For the potential of Lennard-Jones (12,6) the variational method is used, where we use the supersymmetry to find a wave function that is similar to the real function, this procedure is made through the choice of a superpotential that generates an effective potential that approaches to the original potential. With this the autofunctions and the autovalues for the fundamental state and the first state excited are found. Some gotten numerical results are compared with others found in the literature.

Safety assessment is a rational and systematic process for assessing the risk associated with the usage of a product. While the safety assessment process is important even when making a simple product, the true importance of this process comes into light when designing for example an aircraft, where a failure could possibly lead to the loss of human lives. However,even though this process is vital for certain industries, it is plagued by a lack of tools. The existing tools are focused on specific parts of the process and do not make use of work done in earlier steps of the process which often means that the safety engineer needs to manually do work that could have been calculated automatically from information that is already present from an earlier step in the process. This thesis shows that by creating a model of the product that can be present and augmented throughout every step in the process, many calculations that are currently done by hand can be automated or semi-automated by examining this shared model. The thesis proposes a specification for a modeling formalism that is simple enough to be used as early as the requirements phase of a project, but powerful enough to provide important information all the way throughout the safety assessment process. The thesis also specifically shows how this model can be used to help in the creation and updating process of Failure Mode and Effects Analysis (FMEA) documents as a proof-of concept implementation based on Sörman Information AB’s product “Uptime BPC Standard”.Algorithms for synchronizing between the model and the FMEA representation, as well as algorithms for automatically calculating the next level effect and global level effect of failure modes based on the hierarchy and connections made in the model are also presented. The prototype implementation shows that even though the entire safety assessment process cannot be automated it is possible to extract information from the model by analyzing its hierarchy and connections. While more work still needs to be done before the entire safety assessment process can be encompassed, the initial results shows that the proposed modeling formalism allows us to create models from which relevant information that can be used to support the safety assessment process can be calculated.

L’objet de ce travail de thèse consiste à utiliser un formalisme vibratoire pour la détermination de contraintes dans les dépôts à l’aide de la méthode dynamique résonante. Ceci a nécessité le développement d’un formalisme vibratoire adapté aux massifs revêtus, en reliant le niveau de contrainte à la variation des fréquences de résonance mesurées. L’étude a été effectuée en menant trois approches en parallèle : numérique, analytique et expérimentale. En premier lieu, nous avons réalisé des simulations numériques par éléments finis, afin de déterminer la distribution de contraintes dans l’épaisseur d’une poutre composite contrainte et d’évaluer l’effet de ces profils de contraintes sur la fréquence de résonance. Les résultats numériques ont permis d’optimiser le développement d’un nouveau formalisme vibratoire analytique. Pour valider ce dernier formalisme, il nous a fallu l’appliquer sur des dépôts réels,en confrontation avec les résultats d’autres méthodes de mesures de contraintes (DRX/Stoney). Cette confrontation numérique-analytique/expérimentale a révélé que la méthode dynamique résonante est pertinente pour des systèmes de dépôts ayant des rapports d’épaisseur supérieur à0,01. / The aim of this work is to use a new vibratory formalism in order to determine the level of internal stresses in coated materials using the dynamic resonant method. This requires the improvement of vibratory formalism, which allows to link the stress level to the variation of resonance frequency in free flexural mode. This study was conducted by doing three different approaches: numerical, analytical and experimental measurements in real coating. Numerical simulations were conducted by finite element method in static mode to determine the stress distribution in depth. Furthermore, we made other numerical simulations in dynamic mode to evaluate the effect of these static results on the resonant frequency, in comparison with those of coated material without stress. At this stage, these numerical studies let us to develop the vibratory formalism analytically. To validate this latter formalism, we applied it in a real coating for measuring the stress level and we made comparisons with results from others methods(DRX/Stoney). This confrontation (numerical-analytical/experimental measurements) found that dynamic resonant method is efficient for coated material having a thickness ratio moreimportant than 0,01.

M.A. (English) / This dissertation begins by examining the central tenets of Russian Formalism and American New Criticism. Although it is a term coined by the Russian Formalists, both these schools of thought, in their own ways, are concerned with literariness – that is, that which distinguishes the literary work from other forms of writing. This study traces the ways in which these two critical movements account for the specifically literary language that they claim characterises literary works. Based on the principles derived from these two schools I analyse aspects of Virginia Woolf’s Mrs Dalloway and demonstrate that defamiliarization is at work on various levels of this novel. Thereafter, I examine criticism pertaining to Woolf and illustrate that there are numerous illuminating parallels that can be drawn between recent critics’ studies on Woolf and the principles of the formalists. In particular, I attempt to show that the principle of estranged form continues to inform our critical thought about Woolf’s works. I focus primarily on the arguments posited in two critical studies: Edward Bishop’s Virginia Woolf (1991) and Oddvar Holmesland’s Form as Compensation for Life: Fictive Patterns in Virginia Woolf’s Novels (1998). These studies were selected because they centre on questions of language and form and, as such, coincide in a number of interesting ways with the tenets of formalism.

How do we understand our encounter with ambivalent or visceral aesthetic feelings—textual environments, moods, and atmospheres—if they do not solely belong to the representation of individual or collective emotions? This dissertation proposes a concept of “the feeling of form” to approach these aesthetic feelings as formal dynamics, such as restless orientations and rhythmic intensities. How can literary forms have feelings, and where—or is it necessary—to locate the textual body and the subject of these feelings? The goal of my dissertation is not to show what specific neurological procedures are involved in the emotive-cognitive entanglement between the text and the reader, but to understand “form” as a verb—forming, shaping, mediating, transmitting—whose dynamics and actions manifest the narrative form’s visceral aesthetic feelings, and to examine how such feelings bear significant cultural and political currency. Reading formal dynamics as aesthetic feelings also invites us to adjust our usual gaze at “form” away from categories coined by various formalisms, such as “genre,” “structure,” “focalization,” or “style.” In doing so, we are able to reimagine these categories as part of the dynamics of formal reorientations, rhythms, and syntactic intensities, and to open ourselves up to the impersonal agency and criticality of literary forms. Based on these convictions, my dissertation argues that reading for the feeling of form allows us to experience how literary forms transmit and regenerate volatile experiences of history in ways that complicate, supplement, or subvert the explicit representation of historical events and temporality in a literary text. In this dissertation, I focus on the relationship between the feeling of form and the experience of various histories in Ford Madox Ford’s Parade’s End (1924–1928), Lewis Grassic Gibbon’s A Scots Quair (1932–1934), Lawrence Durrell’s The Alexandria Quartet (1957–60), and Kazuo Ishiguro’s single-volume novel The Unconsoled (1995). Chapter One traces how nauseous form in Parade’s End allows us to experience wartime and postwar anxiety through Christopher Tietjens’s self-revolting and incoherent consciousness. Chapter Two examines how the deterioration of rhythm in A Scot’s Quair transmits a historical experience of gradual suffocation intricately linked with Scotland’s political and ecological disasters. In a brief Coda, I conclude my project by looking at how The Alexandria Quartet and The Unconsoled manifest weakened and depleted feelings of form, and how these feelings prompt us to rethink the relationship of the feeling of form to European heteronormative ideology and the ethics of community formation. The Unconsoled (1995), in particular, serves as a twofold limit case of the feeling of form: first, as a limit case of the futile feeling of form, and second, as a limit case of the distinction between the novel form and the novel series form. This twofold limit case speaks to its own historical experience of futility at the end of history, and responds to the aesthetic and ideological legacies of early twentieth-century experimental novel series. / Graduate / 2021-05-12