Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

The architecture of influence: Paul Rudolph's Art and Architecture Building at Yale

Focussing on Paul Rudolph’s Art & Architecture Building at Yale, this thesis demonstrates how the building synthesises the architect’s attitude to architectural education, urbanism and materiality. It tracks the evolution of the building from its origins – which bear a relationship to Rudolph’s pedagogical ideas – to later moments when its occupants and others reacted to it in a series of ways that could never have been foreseen. The A&A became the epicentre of the university’s counter culture movement before it was ravaged by a fire of undetermined origins. Arguably, it represents the last of its kind in American architecture, a turning point at the threshold of postmodernism. Using an archive that was only made available to researchers in 2009, this is the first study to draw extensively on the research files of the late architectural writer and educator, C. Ray Smith. Smith’s 1981 manuscript about the A&A entitled “The Biography of a Building,” was never published. The associated research files and transcripts of discussions with some thirty interviewees, including Rudolph, provide a previously unavailable wealth of information. Following Smith’s methodology, meetings were recorded with those involved in the A&A including, where possible, some of Smith’s original interviewees. When placed within other significant contexts – the physicality of the building itself as well as the literature which surrounds it – these previously untold accounts provide new perspectives and details, which deepen the understanding of the building and its place within architectural discourse. Issues revealed include the importance of the influence of Louis Kahn’s Yale Art Gallery and Yale’s Collegiate Gothic Campus on the building’s design. Following a tumultuous first fifty years, the A&A remains an integral part of the architectural education of Yale students and, furthermore, constitutes an important didactic tool for all students of architecture.

Genes, race, and the ethics of belief.

A Troublesome Inheritance, by Nicholas Wade, should be read by anyone interested in race and recent human evolution. Wade deserves credit for challenging the popular dog-ma that biological differences between groups either don't exist or cannot ex-plain the relative success of different groups at different tasks. Wade's work should be read alongside another re-cent book, The 10,000 Year Explosion: How Civilization Accelerated Human Evolution, by Gregory Cochran and Henry Harpending. Together, these books represent a ma-jor turning point in the public debate about the speed with which relatively isolated groups can evolve: both books suggest that small genetic differences between members of different groups can have large impacts on their abilities and propensities, which in turn affect the outcomes of the societies in which they live.

When a trauma becomes a key to identity: Enhanced integration of trauma memories predicts posttraumatic stress disorder symptoms

The Centrality of Event Scale (CES) measures the extent to which a traumatic memory forms a central component of personnal identity, a turning point in the life story and a reference point for everyday inferences. In two studies, we show that the CES is positively correlated with severity of PTSD symptoms, even when controlling for measures of anxiety, depression, dissociation and self-consciousness. The findings contradict the widespread view that poor integration of the traumatic memory into one's life story is a main cause of PTSD symptoms. Instead, enhanced integration appears to be a key issue. Copyright © 2006 John Wiley & Sons, Ltd.

Living sustainably: changing cultures and behaviours

2007 was a turning point on what sustainability meant for the construction industry with its new regulation and initiatives. The Government defined sustainability in terms of environmental objectives that can be measured, monitored and met. Last year was also the introduction of the Code for Sustainable Homes. This seminar explores the lessons learnt and the next stage of sustainability in terms of policy and practice.

The origins of the control of information in war coverage

The conflict’s coverage, since its inception, has been closely linked to the relationship that both the military and the media have. The freedom they maintained during their first conflicts, although not without problems, though they suffered strict censorship suffered during World War I, and lastly the straitjacket treatment that they have endured during recent wars. The Vietnam War marked a turning point in this relationship, and after the invasion of Grenada, the military would launch new information guidelines, called Department of Defense National Media Pool. The lack of clear guidance of both control and space, has made for a complicated relationship between media and military, so the rules have evolved after every conflict shaping the future of press coverage and thus, war reporting.

Semiclassical treatment of Wannier's theory when the exponent diverges

We consider a non-standard application of the Wannier model. A physical example is the single ionization of a hydrogenic beryllium ion with a fully stripped beryllium ion, where the ratio of the charge of the third particle to the charges of the escaping particles is 1/4; we investigate the single ionization by an electron of an atom comprising an electron and a nucleus of charge 1/4. An infinite exponent is obtained suggesting that this process is not tractable within the Wannier model. A modified version of Crothers' uniform semiclassical wavefunction for the outgoing particles has been adopted, since the Wannier exponents and are infinite for an effective charge of Z = 1/4. We use Bessel functions to describe the Peterkop functions u and u and derive a new turning point ?. Since u is well behaved at infinity, there exists only the singularity in u at infinity, thus we employ a one- (rather than two-) dimensional change of dependent variable, ensuring that a uniform solution is obtained that avoids semiclassical breakdown on the Wannier ridge. The regularized final-state asymptotic wavefunction is employed, along with a continuum-distorted-wave approximation for the initial-state wavefunction to obtain total cross sections on an absolute scale. © 2006 IOP Publishing Ltd.

Zipf and Type-Token rules for the English, Spanish, Irish and Latin languages

The Zipf curves of log of frequency against log of rank for a large English corpus of 500 million word tokens, 689,000 word types and for a large Spanish corpus of 16 million word tokens, 139,000 word types are shown to have the usual slope close to –1 for rank less than 5,000, but then for a higher rank they turn to give a slope close to –2. This is apparently mainly due to foreign words and place names. Other Zipf curves for highlyinflected Indo-European languages, Irish and ancient Latin, are also given. Because of the larger number of word types per lemma, they remain flatter than the English curve maintaining a slope of –1 until turning points of about ranks 30,000 for Irish and 10,000 for Latin. A formula which calculates the number of tokens given the number of types is derived in terms of the rank at the turning point, 5,000 for both English and Spanish, 30,000 for Irish and 10,000 for Latin.

The Architecture of Seduction: An Analysis on Digital Architectures within Consumer Society

Currently new digital tools used in architecture are often at the service of a conception of architecture as a consumer society’s cultural good. Within this neoliberal cultural frame, architects’ social function is no longer seen as the production of urban facts with sense of duty, but as a part within the symbolic logic that rules the social production of cultural values as it was defined by Veblen and developed by Baudrillard. As a result, the potential given by the new digital tools used in representation has shifted from an instrument used to verify a built project to two different main models: At the one hand the development of pure virtual architectures that are exclusively configured within their symbolic value as artistic “images” easily reproducible. On the other hand the development of all those projects which -even maintaining their attention to architecture as a built fact- base their symbolic value on the author’s image and on virtual aesthetics and logics that prevail over architecture’s materiality. Architects’ sense of duty has definitely reached a turning point.

Foraging-farming transitions at the Niah Caves, Sarawak, Borneo

The Niah Caves in Sarawak, Borneo, have captured evidence for people and economies of 8000 and 4000 years ago. Although not continuous on this site, these open two windows on to life at the cultural turning point, broadly equivalent to the transition from Mesolithic to Neolithic. They have much in common, inferring that the occupants, perhaps belonging to an older maritime dispersal, had a choosy appetite for the Neolithic package.

Developing an integrated hydrograph separation and lumped modelling approach to quantifying hydrological pathways in Irish river catchments

An appreciation of the quantity of streamflow derived from the main hydrological pathways involved in transporting diffuse contaminants is critical when addressing a wide range of water resource management issues. In order to assess hydrological pathway contributions to streams, it is necessary to provide feasible upper and lower bounds for flows in each pathway. An important first step in this process is to provide reliable estimates of the slower responding groundwater pathways and subsequently the quicker overland and interflow pathways. This paper investigates the effectiveness of a multi-faceted approach applying different hydrograph separation techniques, supplemented by lumped hydrological modelling, for calculating the Baseflow Index (BFI), for the development of an integrated approach to hydrograph separation. A semi-distributed, lumped and deterministic rainfall runoff model known as NAM has been applied to ten catchments (ranging from 5 to 699 km2). While this modelling approach is useful as a validation method, NAM itself is also an important tool for investigation. These separation techniques provide a large variation in BFI, a difference of 0.741 predicted for BFI in a catchment with the less reliable fixed and sliding interval methods and local minima turning point methods included. This variation is reduced to 0.167 with these methods omitted. The Boughton and Eckhardt algorithms, while quite subjective in their use, provide quick and easily implemented approaches for obtaining physically realistic hydrograph separations. It is observed that while the different separation techniques give varying BFI values for each of the catchments, a recharge coefficient approach developed in Ireland, when applied in conjunction with the Master recession Curve Tabulation method, predict estimates in agreement with those obtained using the NAM model, and these estimates are also consistent with the study catchments’ geology. These two separation methods, in conjunction with the NAM model, were selected to form an integrated approach to assessing BFI in catchments.

1916-2016. The 1916 Easter Rising

Commissioned by An Post to commemorate the centenary of the Easter Rising, this illustrated book draws on eye-witness accounts to assess this key turning-point in modern Irish history. Leading historian Fearghal McGarry explores the impact of events at the General Post Office, as well as setting the rebellion in its wider historical context. His account concludes with an assessment of the Rising's commemoration since 1916 and a commentary on the definitive stamps issued by An Post to mark the formative event in the emergence of an independent Irish nation.

Walter Benjamin and the Inhumanities: Towards a Pedagogical Anti-Nietzscheanism

The following discussion is intended as a critical intervention into recent debates about the “crisis of the humanities,” reading the symptomaticity of crisis in the medical sense of a turning point. It does so from the perspective of the work of Walter Benjamin, whose own transdisciplinary practice of thought has been characterized as a “philosophy directed against philosophy” and a “philosophizing beyond philosophy,” and stands as a model for the kind of intellectual and para-academic activity evoked here. Historically re-situating Benjamin’s famous allegory of the Angel of History from the twentieth-century context of the “crisis of culture” to the contemporary “crisis of education,” it attempts to reconstruct a dialectical understanding of pedagogization within Benjamin’s work, which is used to sketch out the contours of a critically reimagined pedagogy of the Inhumanities.

Scott Misener Steamships Co. Ltd. Records, 1965, 1967, 1972-1977, 1987, n.d.

Ontario Editorial Bureau (O.E.B.)

Dynamic Performance Evaluation of Canadian Fixed-Income Funds using Markov Regime Switching Models

This thesis examines the performance of Canadian fixed-income mutual funds in the context of an unobservable market factor that affects mutual fund returns. We use various selection and timing models augmented with univariate and multivariate regime-switching structures. These models assume a joint distribution of an unobservable latent variable and fund returns. The fund sample comprises six Canadian value-weighted portfolios with different investing objectives from 1980 to 2011. These are the Canadian fixed-income funds, the Canadian inflation protected fixed-income funds, the Canadian long-term fixed-income funds, the Canadian money market funds, the Canadian short-term fixed-income funds and the high yield fixed-income funds. We find strong evidence that more than one state variable is necessary to explain the dynamics of the returns on Canadian fixed-income funds. For instance, Canadian fixed-income funds clearly show that there are two regimes that can be identified with a turning point during the mid-eighties. This structural break corresponds to an increase in the Canadian bond index from its low values in the early 1980s to its current high values. Other fixed-income funds results show latent state variables that mimic the behaviour of the general economic activity. Generally, we report that Canadian bond fund alphas are negative. In other words, fund managers do not add value through their selection abilities. We find evidence that Canadian fixed-income fund portfolio managers are successful market timers who shift portfolio weights between risky and riskless financial assets according to expected market conditions. Conversely, Canadian inflation protected funds, Canadian long-term fixed-income funds and Canadian money market funds have no market timing ability. We conclude that these managers generally do not have positive performance by actively managing their portfolios. We also report that the Canadian fixed-income fund portfolios perform asymmetrically under different economic regimes. In particular, these portfolio managers demonstrate poorer selection skills during recessions. Finally, we demonstrate that the multivariate regime-switching model is superior to univariate models given the dynamic market conditions and the correlation between fund portfolios.