Thesis (MA)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: This study examines the relationship between history and literature, with specific reference to the Afrikaans novels Verliesfontein (1998) by Karel Schoeman and Op soek na generaal Mannetjies Mentz (1998) by Christoffel Coetzee. Both novels are framed against the background of the Anglo Boer War and both take a postmodern approach to that history, amongst other things. First, Chapter 2 reviews the historical background to the relationship between history and literature through the ages (the classical era, and the eighteenth, nineteenth and twentieth centuries), with a view to indicating how this tradition adheres to the postmodern spirit of contemporary times. Thereafter, Chapter 3 presents a theoretical investigation into the postmodern view of historiography and historical fiction. Special reference is made to Hutcheon's theory of historiographic metafiction as an important theoretical point of departure in the discussion of historical fiction. Political and ideological meaning implicit in historiography is discussed. Chapter 4 explores the current trend in South Africa of rereading and reappraising the past, of questioning traditional historiography in a postapartheid South African context (both in Afrikaans fiction and in historical writing). The revisiting of the Anglo Boer War in contemporary South Africa and in Afrikaans fiction is investigated, and an attempt is made to establish the significance of its reappraisal. Against this background the two texts, Verliesfontein and Op soek na generaal Manntjies Mentz, are discussed in Chapter 5. The two novels amply illustrate the possibility for interaction between history and literature, fact and fiction. How may these texts be read in view of postmodern theory? What lessons for present-day South Africans did Schoeman and Coetzee have in mind with their postmodern questioning of traditional historiography and their unconventional reconstruction of the past? Reappraising conventional accounts of history and exploring personal histories as these texts do, Verliesfontein and Op soek na generaal Mannetjies Mentz are part of the dominant discourse that is taking form in the multicultural society of a postapartheid South Africa today. / AFRIKAANSE OPSOMMING: In hierdie studie is 'n ondersoek onderneem na die verhouding tussen geskiedenis en literatuur, met spesifieke verwysing na Karel Schoeman se roman Verliesfontein (1998) en Christoffel Coetzee se roman Op soek na generaal Mannetjies Mentz (1998). In hierdie twee tekste, wat die Anglo-Boereoorlog as hul raamwerk het, is onder andere 'n postmodernistiese benadering tot die geskiedenis benut. Eerstens word in hoofstuk 2 oorsigtelik gekyk na die historiese agtergrond van die verhouding tussen geskiedenis en literatuur met verloop van die tyd (die klassieke tyd, agtiende eeu, negentiende eeu en twintigste eeu), om aan te dui hoe dié tradisie by die heersende tydsgees van die postmodernisme aansluit. Hierna verskaf hoofstuk 3 'n teoretiese ondersoek na die postmodernistiese manier waarop geskiedskrywing en historiese fiksie gesien word. Die teorie van Hutcheon se historiografiese metafiksie word veral in die bespreking van historiese fiksie betrek as 'n belangrike teoretiese uitgangspunt. Vervolgens kom politieke en ideologiese implikasies in geskiedskrywing onder bespreking. Daarna (hoofstuk 4) word die Suid-Afrikaanse kontemporêre tendens om die verlede te herlees en te herwaardeer uiteengesit, en die ondermyning van die tradisionele geskiedskrywing in die post-apartheid Suid-Afrikaanse konteks (sowel in Afrikaanse fiksie as in geskiedskrywing) word ondersoek. Daar word gefokus op die her-bedenking van die Anglo-Boereoorlog in die hedendaagse Suid-Afrika en in Afrikaanse fiksie, en daar word ook probeer om die betekenis van dié herwaardering te soek. Teen bostaande agtergrond kom die twee tekste, Verliesfontein en Op soek na generaal Manntjies Mentz onder bespreking (hoofstuk 5). Die romans is goeie voorbeelde van die interaksie-moontlikhede tussen geskiedenis en literatuur, feit en fiksie, en daar word ondersoek hoe hierdie twee tekste aan die hand van postmodernistiese teorieë gelees kan word. Uiteindelik word daar besin oor watter lesse Schoeman en Coetzee met die postmodernistiese problematisering van geskiedskrywing en die onkonvensionele rekonstruksie van die verlede aan kontemporêre Suid-Afrikaners wou oordra. Met die herbesinning van die konvensionele weergawe van die geskiedenis en veral deur die verkenning van persoonlike geskiedenisse, vorm Verliesfontein en Op soek na generaal Mannetjies Mentz deel van die heersende diskoers wat vandag in 'n multikulturele samelewing van die post-apartheid Suid-Afrika aan die ontwikkel is.

Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2018-03-15T13:27:07Z No. of bitstreams: 2 Dissertação - Milton Javier Cárdenas Mendez - 2018.pdf: 1063682 bytes, checksum: ab9f203ee1a315ae8756973bcd7c0789 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-16T11:08:51Z (GMT) No. of bitstreams: 2 Dissertação - Milton Javier Cárdenas Mendez - 2018.pdf: 1063682 bytes, checksum: ab9f203ee1a315ae8756973bcd7c0789 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-16T11:08:51Z (GMT). No. of bitstreams: 2 Dissertação - Milton Javier Cárdenas Mendez - 2018.pdf: 1063682 bytes, checksum: ab9f203ee1a315ae8756973bcd7c0789 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-02-26 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / First objective will revise the hyperbolic Gauss map for hypersurfaces Mn C Hn+1 and its relation with tangent horospheres. We will introduce horospherical ovaloids as compact hypersurfaces with regular hyperbolic Gauss map and analyze their properties, analyzes the possible formulations of the Christoffel problem in Hn+1 and that this leads to the notion of hyperbolic curvature radii. Second objective we will prove that the Nirenberg problem on Sn is equivalent to the Christoffel problem in Hn+1. This equivalence is made explicit by means of a representation formula for hypersurfaces in terms of the hyperbolic Gauss map and the horospherical support function. / Nosso primeiro objetivo é revisar a aplicação hiperbólica de Gauss para hipersuperfícies Mn C Hn+1 e sua relação com as horoesferas tangentes, vamos apresentar ovaloides horoesfericos como hipersuperfícies compactas com aplicação regular hiperbólica de Gauss, além disso, queremos dar uma possível formulação do problema de Christoffel em H n+1 com a noção de raios de curvatura hiperbólica. Nosso segundo objetivo é mostrar que o problema de Christoffel em Hn+1 é equivalente ao problema de Nirenberg em Sn, isso é equivalente, dar uma parametrizacão de uma hipersuperfície em termos da aplicão hiperbólica de Gauss e da função suporte horoesferica.

Les textures directionnelles forment la classe particulière des images texturées représentant des hypersurfaces (lignes dermiques, fibres de matériaux, horizons sismiques, etc.). Pour ce type de textures, la reconstruction d'hypersurfaces permet ainsi d'en décrire la géométrie et la structure. À partir du calcul préalable du champ d'orientation, des reconstructions peuvent être obtenues au moyen de la minimisation d'une équation aux dérivées partielles sous contraintes, linéarisée et résolue itérativement de manière optimale dans le domaine de Fourier.Dans ce travail, les reconstructions d'hypersurfaces sont considérées comme un moyen de description à la fois amont et aval de la géométrie des textures directionnelles. Dans une démarche amont, la reconstruction de faisceaux locaux et denses d'hypersurfaces conduit à un modèle de transformation d'espace permettant de déplier localement la texture ou son champ de gradient et d'améliorer l'estimation du champ d'orientation par rapport au classique tenseur de structure. Dans une démarche aval, des reconstructions d'hypersurfaces effectuées sur des supports polygonaux quelconques, isolés ou imbriqués, permettent d'obtenir des reconstructions plus pertinentes que par les méthodes existantes. Les démarches proposées mettent en œuvre des chaînes de transformations d'espace conformes (transformation de Schwarz-Christoffel, de Möbius, etc.) afin de respecter les contraintes et d'accéder à des schémas de résolution rapide. / Directional textures are the particular class of textured images representing hypersurfaces (dermal lines, material fibers, seismic horizons, etc.). For this type of textures, the reconstruction of hypersurfaces describes their geometry and structure. From the preliminary estimation of the orientation field, reconstructions can be obtained by means of the minimization of a partial differential equation under constraints, linearized and iteratively resolved in the Fourier domain.In this work, the reconstructions of hypersurfaces are considered as means of description both upstream and downstream of the geometry of the directional textures. In an upstream approach, the reconstruction of local and dense streams of hypersurfaces leads to a spatial transformation model to locally unfold the texture or its gradient field and to improve the estimation of the orientation field compared with the classic tensor structure. In a downstream approach, reconstructions of hypersurfaces carried out on any polygonal supports, either isolated or imbricated, lead to more accurate reconstructions than existing methods. The proposed approaches implement chains of conformal space transformations (transformation of Schwarz-Christoffel, Möbius, etc.) in order to respect the constraints and to access fast PDE solution schemes.

No description available.

This thesis is primarily focused on flow-field upstream of hydropower intakes, with emphasis on the use of temperature control curtains and predicting the flow acceleration zone. By reviewing the available literature, it is concluded that the flow-field upstream of hydropower intake systems can be modeled by potential flow theory. The understanding of near intake flow-field can be useful in fish entrainment studies and in designing fish repulsion systems. To control downstream river temperatures, a flexible curtain was installed upstream of several dams in California. Flow downstream of the curtain was analyzed using a Computational Fluid Dynamic (CFD) solver with rigorous validation by experimental data. The experiment was conducted with a 4 beam Acoustic Doppler Velocimeter (ADV) probe. The study shows that wall jet properties downstream of the curtain are affected by the water depth and the inlet Reynolds number. Empirical expressions were developed to predict jet properties and the wall shear stress. Flow upstream of the curtain was analyzed using potential flow theories with validation by the CFD solver. In this part, a theory based on Schwarz-Christoffel transformation was developed to predict the flow-field upstream of the curtain without accounting for any density stratification in the water body. It is observed that the acceleration zone upstream of the curtain can be affected by sink opening size, its location and water depth. The effect of boundaries on flow upstream of a line sink and the interaction of multiple sinks were analyzed. The effect of stratification on a line sink is also analyzed. A theory is developed to predict the incipient withdrawal condition when a sink is located on the horizontal bottom. The theory is also extended to a tilted bottom. The effect of boundaries on the incipient withdrawal condition is analyzed. When only one layer is being withdrawn, it is shown that a homogenous equation can be applied to a stratified condition by assuming an upper layer boundary at the interface. In addition to these works, a despike algorithm for ADV data is developed, and a numerical analysis on central difference scheme is presented. / Water Resources Engineering

Made available in DSpace on 2016-06-02T20:28:22Z (GMT). No. of bitstreams: 1 DissSCC.pdf: 580893 bytes, checksum: 668c123be16c687965e925ea0bd5d17b (MD5) Previous issue date: 2004-04-15 / Universidade Federal de Minas Gerais / In this work we develop the transformation theory for isothermic surfaces in Euclidean space IR3 due to Darboux and Bianchi. As a consequence, we describe a method for constructing new solutions of the nonlinear system of partial diferential equations associated to an isothermic surface in IR3 starting from a given one. / Neste trabalho apresentamos a teoria de transformações entre superfícies isotérmicas no espaço Euclidiano IR3 devida a Darboux e Bianchi. Descrevemos, como consequência, um método de obter novas soluções do sistema não linear de equações diferenciais parciais associado a uma superfície isotérmica em IR3, a partir de uma dada.

Dans cette thèse j’étudie l’impact de la géométrie de micro et nano-domaines biologiques sur les propriétés d'électrodiffusion, ceci à l'aide des équations aux dérivées partielles de Poisson-Nernst-Planck. Je considère des domaines non-triviaux ayant une forme cuspide ou elliptique. Mon objectif est de développer des modèles ainsi que des méthodes mathématiques afin d'étudier les caractéristiques électriques de ces nano/micro-domaines, et ainsi mieux comprendre comment les signaux électriques sont modulés à ces échelles. Dans la première partie j’étudie le voltage à l'équilibre pour un électrolyte dans un domaine borné, et ayant un fort excès de charges positives. Je montre que le premier temps de sortie dans une boule chargée dépend de la surface et non du volume. J’étudie ensuite la géométrie composées d'une boule à laquelle est attachée un domaine cuspide. Je construis ensuite une solution asymptotique pour le voltage dans les cas 2D et 3D et je montre qu’ils sont donnés au premier ordre par la même expression. Enfin, j’obtiens la même conclusion en considérant une géométrie formée d'une ellipse, dont je construis une solution asymptotique du voltage en 2D et 3D. La seconde partie porte sur la modélisation de la compartimentalisation électrique des épines dendritiques. A partir de simulations numériques, je mets en évidence le lien entre la polarisation de concentration dans l'épine et sa géométrie. Je compare ensuite mon modèle à des données de microscopie. Je développe une méthode de déconvolution pour extraire la dynamique rapide du voltage à partir des données de microscopie. Enfin j’estime la résistance du cou et montre que celle-ci ne suit pas la loi d'Ohm. / In this PhD I study how electro-diffusion within biological micro and nano-domains is affected by their shapes using the Poisson-Nernst-Planck (PNP) partial differential equations. I consider non-trivial shapes such as domains with cusp and ellipses. Our goal is to develop models, as well as mathematical tools, to study the electrical properties of micro and nano-domains, to understand better how electrical neuronal signaling is regulated at those scales. In the first part I estimate the steady-state voltage inside an electrolyte confined in a bounded domain, within which we assume an excess of positive charge. I show the mean first passage time in a charged ball depends on the surface and not on the volume. I further study a geometry composed of a ball with an attached cusp-shaped domain. I construct an asymptotic solution for the voltage in 2D and 3D and I show that to leading order expressions for the voltage in 2D and 3D are identical. Finally, I obtain similar conclusion considering an elliptical-shaped domain for which I construct an asymptotic solution for the voltage in 2D and 3D. In the second part, I model the electrical compartmentalization in dendritic spines. Based on numerical simulations, I show how spines non-cylindrical geometry leads to concentration polarization effects. I then compare my model to experimental data of microscopy imaging. I develop a deconvolution method to recover the fast voltage dynamic from the data. I estimate the neck resistance, and we found that, contrary to Ohm's law, the spine neck resistance can be inversely proportional to its radius.

<p>Inom många tillämpningar används konforma avbildningar för att transformera tvådimensionella områden till områden med enklare utseende. Ett exempel på ett sådant område är en kanal av varierande tjocklek begränsad av en kontinuerligt deriverbar kurva. I de tillämpningar som har motiverat detta arbete, är det viktigt att dessa egenskaper bevaras i det område en approximativ konform avbildning producerar, men det är också viktigt att begränsningskurvans riktning kan kontrolleras, särkilt i kanalens båda ändar.</p><p>Denna avhandling behandlar tre olika metoder för att numeriskt konstruera konforma avbildningar mellan ett enkelt standardområde, företrädesvis det övre halvplanet eller enhetscirkeln, och ett område begränsat av en kontinuerligt deriverbar kurva, där begränsningskurvans riktning kan kontrolleras, exakt eller approximativt.</p><p>Den första metoden är en utveckling av en idé, först beskriven av Peter Henrici, där en modifierad Schwarz-Christoffel-avbildning avbildar det övre halvplanet konformt på en polygon med rundade hörn.</p><p>Med utgångspunkt i denna idé skapas en algoritm för att konstruera avbildningar på godtyckliga områden med släta randkurvor.</p><p>Den andra metoden bygger också den på Schwarz-Christoffel-avbildningen, och utnyttjar det faktum att om enhetscirkeln eller halvplanet avbildas på en polygon kommer ett område Q i det inre av dessa, som till exempel en cirkel med centrum i origo och radie mindre än 1, eller ett område i övre halvplanet begränsat av två strålar, att avbildas på ett område R i det inre av polygonen begränsat av en slät kurva. Vi utvecklar en metod för att hitta ett polygonalt område P, utanför det Omega som man önskar att skapa en avbildning för, sådant att den Schwarz-Christoffel-avbildning som avbildar enhetscirkeln eller halvplanet på P, avbildar Q på Omega.</p><p>I båda dessa fall används tangentpolygoner för att numeriskt bestämma den önskade avbildningen.</p><p>Slutligen beskrivs en metod där en av Don Marshalls så kallade zipper-algoritmer används för att skapa en avbildning mellan det övre</p><p>halvplanet och en godtycklig kanal, begränsad av släta kurvor, som i båda ändar går mot oändligheten som räta parallella linjer.</p> / <p>In many applications, conformal mappings are used to transform two-dimensional regions into simpler ones. One such region for which conformal mappings are needed is a channel bounded by continuously differentiable curves. In the applications that have motivated this work, it is important that the region an approximate conformal mapping produces, has this property, but also that the direction of the curve can be controlled, especially in the ends of the channel.</p><p>This thesis treats three different methods for numerically constructing conformal mappings between the upper half-plane or unit circle and a region bounded by a continuously differentiable curve, where the direction of the curve in a number of control points is controlled, exact or approximately.</p><p>The first method is built on an idea by Peter Henrici, where a modified Schwarz-Christoffel mapping maps the upper half-plane conformally on a polygon with rounded corners. His idea is used in an algorithm by which mappings for arbitrary regions, bounded by smooth curves are constructed.</p><p>The second method uses the fact that a Schwarz-Christoffel mapping from the upper half-plane or unit circle to a polygon maps a region Q inside the half-plane or circle, for example a circle with radius less than 1 or a sector in the half--plane, on a region Omega inside the polygon bounded by a smooth curve. Given such a region Omega, we develop methods to find a suitable outer polygon and corresponding Schwarz-Christoffel mapping that gives a mapping from Q to Omega.</p><p>Both these methods use the concept of tangent polygons to numerically determine the coefficients in the mappings.</p><p>Finally, we use one of Don Marshall's zipper algorithms to construct conformal mappings from the upper half--plane to channels bounded by arbitrary smooth curves, with the additional property that they are parallel straight lines when approaching infinity.</p>

Inom många tillämpningar används konforma avbildningar för att transformera tvådimensionella områden till områden med enklare utseende. Ett exempel på ett sådant område är en kanal av varierande tjocklek begränsad av en kontinuerligt deriverbar kurva. I de tillämpningar som har motiverat detta arbete, är det viktigt att dessa egenskaper bevaras i det område en approximativ konform avbildning producerar, men det är också viktigt att begränsningskurvans riktning kan kontrolleras, särkilt i kanalens båda ändar. Denna avhandling behandlar tre olika metoder för att numeriskt konstruera konforma avbildningar mellan ett enkelt standardområde, företrädesvis det övre halvplanet eller enhetscirkeln, och ett område begränsat av en kontinuerligt deriverbar kurva, där begränsningskurvans riktning kan kontrolleras, exakt eller approximativt. Den första metoden är en utveckling av en idé, först beskriven av Peter Henrici, där en modifierad Schwarz-Christoffel-avbildning avbildar det övre halvplanet konformt på en polygon med rundade hörn. Med utgångspunkt i denna idé skapas en algoritm för att konstruera avbildningar på godtyckliga områden med släta randkurvor. Den andra metoden bygger också den på Schwarz-Christoffel-avbildningen, och utnyttjar det faktum att om enhetscirkeln eller halvplanet avbildas på en polygon kommer ett område Q i det inre av dessa, som till exempel en cirkel med centrum i origo och radie mindre än 1, eller ett område i övre halvplanet begränsat av två strålar, att avbildas på ett område R i det inre av polygonen begränsat av en slät kurva. Vi utvecklar en metod för att hitta ett polygonalt område P, utanför det Omega som man önskar att skapa en avbildning för, sådant att den Schwarz-Christoffel-avbildning som avbildar enhetscirkeln eller halvplanet på P, avbildar Q på Omega. I båda dessa fall används tangentpolygoner för att numeriskt bestämma den önskade avbildningen. Slutligen beskrivs en metod där en av Don Marshalls så kallade zipper-algoritmer används för att skapa en avbildning mellan det övre halvplanet och en godtycklig kanal, begränsad av släta kurvor, som i båda ändar går mot oändligheten som räta parallella linjer. / In many applications, conformal mappings are used to transform two-dimensional regions into simpler ones. One such region for which conformal mappings are needed is a channel bounded by continuously differentiable curves. In the applications that have motivated this work, it is important that the region an approximate conformal mapping produces, has this property, but also that the direction of the curve can be controlled, especially in the ends of the channel. This thesis treats three different methods for numerically constructing conformal mappings between the upper half-plane or unit circle and a region bounded by a continuously differentiable curve, where the direction of the curve in a number of control points is controlled, exact or approximately. The first method is built on an idea by Peter Henrici, where a modified Schwarz-Christoffel mapping maps the upper half-plane conformally on a polygon with rounded corners. His idea is used in an algorithm by which mappings for arbitrary regions, bounded by smooth curves are constructed. The second method uses the fact that a Schwarz-Christoffel mapping from the upper half-plane or unit circle to a polygon maps a region Q inside the half-plane or circle, for example a circle with radius less than 1 or a sector in the half--plane, on a region Omega inside the polygon bounded by a smooth curve. Given such a region Omega, we develop methods to find a suitable outer polygon and corresponding Schwarz-Christoffel mapping that gives a mapping from Q to Omega. Both these methods use the concept of tangent polygons to numerically determine the coefficients in the mappings. Finally, we use one of Don Marshall's zipper algorithms to construct conformal mappings from the upper half--plane to channels bounded by arbitrary smooth curves, with the additional property that they are parallel straight lines when approaching infinity.

Universiẗat, Diss., 1999--Konstanz. / Gedr. Ausg. im Verl. Der Andere Verl., Bad Iburg.