Masters of Science / The main purpose of this thesis is to study the interplay between relational structures and topology, and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between the categories of topological spaces, closure spaces and relational structures. We study the 4-point non-Hausdorff model S4 weakly homotopy equivalent to the circle s'. We study pairings of some objects in the category of relational structures, similar to the multiplication of Hopf spaces in topology. The multiplication S4 x S4 ---7 S4 fails to be order preserving for posets. Nevertheless, applying a single barycentric subdivision on S4 to get Ss, an 8-point model of the circle enables us to define an order preserving poset map Ss x Ss ---7 S4' Restricted to the axes, this map yields weak homotopy equivalences Ss ---7 S4' Hence it is a pairing. Further, using the non-Hausdorff join Ss ® Ss, we obtain a version of the Hopf map Ss ® Ss ---7 §S4. This model of the Hopf map is in fact a map of non-Hausdorff double mapping cylinders.

A realtor faces valuations of houses and apartments almost every day, but one thing that is not as common is valuation of plots. We think that the absence of parameters, which the valuation is based on, would aggravate the valuation of the plot in comparison to valuation of a settled property. How do the local plan’s terms affect the value of the plot and do the prospective buyers get discouraged by high costs, such as costs to build roads in the community, which apply to the price of the plot? How does the valuation process differentiate from the agency process? Do the municipality’s terms differ from each other and how do these affect the plot value? The knowledge regarding valuation is important to a future realtor and real estate developer, which are our future professions. The reason why the essay is focused on plots is based on the fact that plots are not as common as house properties. To demonstrate the valuables, which affect the value the most, is both crucial and interesting due to the fact that valuation of solely plots is not as common in professional life, as mentioned early. The results of the interviews show that the location is the parameter which affects the value the most, regarding plots. The location is closely followed by the plot’s construction rights. The deficiency of parameters to proceed from when valuating does not seem to be an aggravating fact for the realtors. Additional costs which are difficult to evaluate, such as blasting costs, do however complicate the work. The value of a property is not necessarily equal to the selling price due to the fact that the value is an estimated probable price, while the selling price is an actual observation on the market. To get the highest price possible when selling a plot, you need to find the right buyer, at the right place, at the right time. This scenario is very hard to achieve and leads to the fact that the market value is the most suitable value to proceed from when selling a plot. / En mäklare stöter på värderingar av småhus och bostadsrätter nästintill varje dag, men någonting som inte är riktigt lika vanligt förekommande är värdering av tomter. Att det förekommer betydligt färre parametrar vid tomtvärdering, än vid värdering av en bebyggd fastighet, borde göra att det inte är fullt så enkelt att bedöma en tomts värde. Hur påverkar en detaljplans bestämmelser tomtvärdet och avskräcks spekulanter om höga kostnader, såsom gatukostnadsavgifter, tillkommer efter köpet? Och hur skiljer sig värderings- och förmedlingsprocesserna åt? Skiljer sig kommunernas bestämmelser åt och hur påverkar dessa i så fall tomternas värde? Som blivande fastighetsmäklare och fastighetsutvecklare är kunskap om värdering viktig och vi valde att fokusera arbetet på just tomter eftersom dessa inte är vanligast förekommande bland de olika fastighetstyperna. Att påvisa vilka faktorer som är de mest betydande gällande värdet är både viktigt och intressant p.g.a. att rent tomvärderingsförfarande, följaktligen, inte är lika vanligt förekommande i yrkeslivet. Efter intervjuerna har det visat sig att ett bra läge är den absolut viktigaste faktorn ur värdesynpunkt, tätt följd av vilken byggrätt fastigheten innehar. Avsaknaden av parametrar, vid värderingen, verkar inte vara något som försvårar arbetet. Däremot komplicerar tillkommande och svårbedömda kostnader värderingen. Tillkommande och svårbedömda kostnader är exempelvis sprängningskostnader, vilket blir aktuellt på en bergig tomt. Värdet behöver inte vara detsamma som slutpriset, då värdet är ett bedömt sannolikt pris utifrån en värderingsmetod, jämfört med slutpriset som är en faktisk observation på marknaden. För att få ut högsta möjliga tomtpris vid en försäljning, rör det sig i slutänden om att hitta rätt köpare, på rätt plats, vid rätt tidpunkt. Detta scenario är mycket svårt att uppnå, varför marknadsvärdet, framtaget genom ortsprismetoden, är det lämpligaste värdet att utgå från vid en kommande tomtförsäljning.

This work focuses on generating approximations of complex T-spline surfaces with similar but less complex T-splines. Two approaches to simplifying T-splines are proposed: a bottom-up approach that iteratively refines an over-simple T-spline to approximate a complex one, and a top-down approach that evaluates existing control points for removal in producing an approximations. This thesis develops and compares the two simplification methods, determining the simplification tasks to which each is best suited. In addition, this thesis documents supporting developments made to T-spline research as simplification was developed.

Denna uppsats undersöker hur gymnasieelever på estetiska programmets spetsutbildning i musik uppfattar polyrytmiska övningar i ensemble samt eventuella samband mellan polyrytmiska övningar och pulskänsla. Syftet är att få mer kunskap om gymnasieelevers uppfattningar om polyrytmik. Denna uppsats bygger på en kvalitativ studie med inspiration av aktionsforskning och har gjorts med filmade ensembleövningar där förstaårselever på gymnasiet har fått bekanta sig med det polyrytmiska förhållandet 3:4 och därefter intervjuats enskilt. Studien har använt sig av ett fenomenografiskt teoretiskt perspektiv och visar att polyrytmik uppfattas på olika sätt, men att ett renodlat rytmiskt fokus kan stärka rytmisk förståelse, pulskänsla samt i vissa fall samspel. Den visar också i enlighet med tidigare forskning att en binär underdelning är det vanligaste sättet att uppfatta ett polyrytmiskt förhållande. Vidare forskning skulle kunna göras på referensrytmer och specifika instrumentgruppers uppfattningar om polyrytmik för att ge mer kunskap om hur pulskänsla och polyrytmik uppfattas. / This thesis investigates how polyrhythmic practice within music ensemble in cutting edge education in upper secondary school is perceived. It also investigates the connection between rhythmic stability and polyrhythmic studies. The purpose is to get more knowledge about music students’ perception of polyrythmic practice in music ensemble. The research subjects got acquainted with the polyrhythmic ratio of 3:4. The data which consisted of film and one to one interviews with two ensembles was done in a small-scale quality analysis through a fenomenographic theory method. It showed that polyrhythms are perceived in many ways, but that a rhythmic focus can enhance the understanding of complex rhythms, pulse feel and, in some cases, musical interplay. The study confirmed previous research that binary subdivision is the most common way to perceive pulse within polyrhythmic ratios. Further research could be done on reference rhythms and specific instrumentalists’ perception of polyrhythms to further investigate how the sense of pulse and polyrythmic understanding is perceived.

Finding the shortest tour visiting all given points at least ones belongs to the most famous optimization problems until today [travelling salesman problem (TSP)]. Optimal solutions exist formany problems up to several ten thousand points. Themajor difficulty in solving larger problems is the required computational complexity. This shifts the research from finding the optimum with no time limitation to approaches that find good but sub-optimal solutions in pre-defined limited time. This paper proposes a new approach for two-dimensional symmetric problems with more than a million coordinates that is able to create good initial tours within few minutes. It is based on a hierarchical clustering strategy and supports parallel processing. In addition, a method is proposed that can correct unfavorable paths with moderate computational complexity. The new approach is superior to state-of-the-artmethods when applied to TSP instances with non-uniformly distributed coordinates.

This thesis will study the resident’s perceptions of a community park in the new urbanism community of Mt Laurel, Alabama by evaluating the thirteen principles established by William Hollingsworth Whyte for creating successful urban parks. The thirteen principles established by Whyte for creating successful spaces are: •The parks proximity/relationship to the street •Location of the sidewalks to the street •Its ability to consistently sustain a constant flow of people through its boundaries •Its amount of defined spaces rather than large open spaces •Its amount of sitable space, in terms of ledges, steps, planters, chairs etc. •The parks sense of security among its users •The incorporation of water features within the parks boundaries •The extent of tree canopies within the park for shading purposes •The availability of food concessions •The parks number of waste receptacles •Routine performers •Outdoor cafes in the park •Occasional art and music exhibits

An investigation into the light scattering properties of Saharan dust grains is presented. An electrodynamic trap has been used to levitate single dust particles. By adjusting the trap parameters, partial randomisation of the particle orientation has been introduced. While levitated, the particles were illuminated by a laser, and a rotating half-wave retarder enabled selection of vertically or horizontally polarized incident light. A laser diffractometer and linear photodiode array have been used to measure intensity at scattering angles between 0.5° and 177°. Combining these measurements with Fraunhofer diffraction as calculated for a range of appropriately-sized apertures allows the calculation of the phase function and degree of linear polarization. The phase functions and degree of linear polarisation for four case study particles are presented - the phase functions are found to be featureless across most of the scattering region, with none of the halo features or rainbow peaks associated with regularly shaped particles such as hexagonal columns or spheres. Particle models comprised of large numbers of facets have been constructed to resemble the levitated particles. Utilizing Gaussian random sphere methods, increasing levels of roughness have been added to the surfaces of these models. A Geometric Optics model and a related model, Ray Tracing with Diffraction on Facets, have been modified to calculate scattering on these particle reconstructions. Scattering calculations were performed on each of these reconstructions using a range of refractive indices and two rotation regimes – one where the orientations of the reconstructed particle were limited to match those observed when the particle was levitated, and one where the orientation was not limited. Qualitative comparisons are performed on the phase functions and degree of linear polarization, where it is observed that the addition of roughness to the modelled spheroids causes the computed phase functions to increasingly resemble those from the levitated particles. Limiting the orientation of the particles does not affect the scattering noticeably. The addition of a very small absorption coefficient does not change the comparisons considerably. As the absorption coefficient is increased, however, the quality of the comparisons decreases rapidly in all cases but one. The phase functions are quantitatively compared using RMS errors, and further comparison is performed using the asymmetry parameter.

La question de déterminer si un modèle géométrique a des intersections non prévues est commune à plusieurs domaines : simulations numériques, CAO/DAO, animation, infographie, etc. C’est un problème dont la complexité varie avec la représentation choisie pour créer le modèle. Pour les surfaces paramétriques c’est un problème difficile à résoudre, mais pour lequel plusieurs solutions ont été proposées. Ces solutions diffèrent les unes des autres dans leurs angles d’approche, leur complexité et la justesse de leurs résultats. Dans ce mémoire, nous tenterons de comparer certaines de ces méthodes. Nous nous concentrerons sur les méthodes dites failsafe, c’est-à-dire qui permettent assurément de détecter la possibilité d’une intersection s’il y en a une. Ces méthodes sont celles utilisées pour toutes les applications critiques, donc pour lesquelles un modèle mal formé aurait des conséquences importantes. Ce mémoire est à teneur principalement théorique. Nous comparerons les méthodes, dans un premier temps, sur leur puissance de résolution. Nous discuterons, dans un deuxième temps, de coût calculatoire. Nous avons finalement fait quelques implémenta- tions pour appuyer nos observations théoriques, mais nous n’avons pas fait une analyse empirique approfondie des coûts calculatoires. Ceci reste à faire. Nous verrons entre autre qu’il existe un ordre partiel entre certaines des méthodes, mais pas toutes. Par exemple, la méthode test-point est strictement plus puissante que la séparation des enveloppes convexes, mais elle est ni plus ni moins puissante que la méthode Volino-Thalmann. / The question of determining if a given geometric model has extraneous intersections is common to many domains: numerical simulation, CAD/CAM, animation, computer graphics, etc. The complexity of this problem varies with the representation chosen to generate the model. For parametric surfaces, it is a hard problem, but for which many solutions have been proposed. Those solutions differ from one another by their underlying ideas, their complexity and the exactitude of the result they give. In this thesis, we will try to compare some of these methods. We will concentrate on the class of methods we call failsafe, the methods that will surely detect the possibility of an intersection if there is one. Those are the methods used in all critical applications, the applications in which a malformed model would have important consequences. The work of this thesis is mostly theoretical. First, we will compare the different techniques on their power of resolution. Then, we will discuss the execution cost of the different methods. We did some implementations while working on this thesis, but only as a way to support our theoretical observations. A complete empirical study of the execution times of the different methods would be left to do. We will see that there is a partial order between some of the methods in their strength, but not all of them. For example, the test-point method is strictly stronger than the separation of the convex hulls method, but is neither stronger nor weaker than the Volino- Thalmann method.

This work deals with ray tracing technique, focused to rendering of chess scene with procedural texture materials. Based on this knowledge, program that displays specified chess set is designed.

O uso das ferritas de manganês zinco em fontes de potência de carregadores de bateria vem crescendo nos últimos anos, devido a suas baixas perdas magnéticas em induções da ordem de 0,2 T. Estas ferritas pertencem à categoria de ferritas moles, são óxidos ferrimagnéticos, policristalinos com estrutura cúbica tipo espinélio. Pós desse material foram compactados em prensa uniaxial e em prensa automática de produção para anel e toróide, respectivamente. Foram realizados dois ciclos de queima variando o teor de oxigênio entre 5 e 15%, no patamar de sinterização, com o propósito de avaliar seu efeito na densidade, microestrutura, perdas magnéticas em altas induções (0,2 T) e permeabilidade. Amostras sinterizadas em posições mais quentes do forno resultaram em maior densidade e maior tamanho de grão, conforme esperado, mas resultaram em maiores perdas a 25 °C. O aumento do teor de oxigênio entre 5 e 15% não alterou sistematicamente a densidade, mas resultou num pequeno aumento do tamanho de grão. Já a correlação entre teor de oxigênio e perdas foi complexa. Foi observado que existe uma temperatura de mínimo nas perdas totais por volta de 60 °C. O mesmo comportamento foi observado na curva da perda histerética, compatível com a variação da constante de anisotropia magnetocristalina (K1). Foram realizados ensaios de curvas de histerese a partir de 25 até 100 °C, a 0,2 T com o objetivo de avaliar o efeito da temperatura nas duas parcelas da perda histerética. Amostras sinterizadas a 1290 °C com a menor pressão de oxigênio apresentaram menor temperatura de mínimo de perda. As técnicas de análise química do teor de Fe2+ não foram capazes de estabelecer, inequivocamente, a esperada relação entre essa variável e o teor de oxigênio da atmosfera de sinterização. / The use of manganese zinc ferrite in power sources of battery chargers is growing, due to its low magnetic power losses at inductions around 0.2 T. These ferrites belong to the soft magnetic materials group, they are polycrystalline ferromagnetic oxides with face centered cubic structure. Powders of this material were compacted in uniaxial press and in automatic press of production, by ring and toroidal form, respectively. Two firing cycles, varying the atmosphere oxygen content between 5 and 15%, were applied to evaluate its effect on microstructure, density, magnetic losses in high induction and permeability. Samples sintered in warmer positions inside the furnace resulted in higher density and larger grain size, as expected, but higher losses at 25 °C were achieved. Increasing the atmosphere oxygen content from 5 to 15% did not alter density significantly, but resulted in a slight increase in grain size. On the other hand, the correlation between oxygen content and losses was complex. There are lower losses, at 60 °C. Similar behavior was observed with hysteresis loss, which is compatible with the change in magnetocrystalline magnetic anisotropy (K1). Measurements were performed from 25 to 100 °C, at 0.2 T, aiming at the evaluation of the effect of temperature on the two parcels of hysteresis loss. Samples sintered at 1290 °C with low atmosphere oxygen content showing a minimum on the losses versus temperature curve. The available techniques to analyze Fe2+ content were not capable of establishing, unequivocally, the expected relation between this variable and the oxygen content of the sintering atmosphere.