Ultra-thin solar cells that incorporate earth-abundant and non-toxic materials are promising candidates in the endeavor toward sustainable energy harvesting. Methods to counteract the inevitable low absorption of thinner semiconductor layers are of high interest and have raised considerable attention in the research society. In an attempt to increase the absorption of these types of assemblies, optical coupling effects between the localized surface plasmon resonances (LSPR) of disordered Au nanostructures and a Fabry-Pérot cavity were studied using a previously established absorber/spacer/reflector stack. The disordered Au array was fabricated by evaporating a thin Au film on a substrate with a 55 nm SiO2 dielectric spacer and a 100 nm Al reflecting film, followed by thermal annealing. Nominal Au film thicknesses in the range of 5-25 Å and annealing temperatures of 200-500 oC were investigated. In situ spectroscopic ellipsometry measurements during the subsequent atomic layer deposition (ALD) of tin monosulfide (SnS) allowed analysis of how the optical properties of the SnS/Au absorber layer changed as a function of the growing SnS layer thickness. By employing the Transfer Matrix Method with the estimated optical properties from the in situ analysis, the absorptance of the absorber/spacer/reflector stacks was simulated as a function of the spacer thickness, revealing any signs of the characteristic anti-crossing behavior. It was discovered that a nominal Au film thickness of 25 Å, annealed at 450 oC, and coated with a SnS film of ∼13 nm primed toward the π-phase, resulted in strong optical coupling between the cavity mode and the LSPR. The energy difference at the avoided crossing in the specular reflectance measurement gave an estimated Rabi-splitting energy of 537 meV. This corresponded to about 40% of the original LSPR energy, placing itself within the ultra-strong coupling regime. To evaluate the relevance of the thin-layered structure in photovoltaic applications, more advanced computational methods are required to estimate the useful absorption that occurs in the SnS layer. Nevertheless, these results elucidate the realization of strong optical coupling effects between disordered Au nanostructures and a Fabry-Pérot cavity, and further the possibility of using scalable fabrication methods for this type of ultra-thin absorber/spacer/reflector stack.

In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.

Cette thèse se concentre sur l'étude de quelques propriétés arithmétiques de certaines variétés algébriques qui sont ``les plus simples'' en un sens géométrique et qui sont définies sur des corps de type géométrique. Elle se compose de trois chapitres. Dans le premier chapitre, indépendant des deux autres, on s'intéresse à la propriété d'approximation faible pour une variété projective lisse rationnellement connexe X définie sur le corps de fonctions K=k(C) d'une courbe algébrique C sur un corps k. Supposons que X possède un K-point rationnel. En utilisant des méthodes géométriques, on démontre que X(K) est Zariski dense dans X si k est un corps fertile, et que l'approximation faible en un certain ensemble de places de bonne réduction vaut pour X sous des hypothèses supplémentaires convenables. Lorsque k est un corps fini, on obtient l'approximation faible en une place quelconque de bonne réduction pour une surface cubique lisse sur K ainsi qu'un résultat sur l'approximation faible d'ordre zéro pour des hypersurfaces cubiques de dimension supérieure sur K.Les deux autres chapitres forment la seconde partie de la thèse, où on travaille sur le corps des fractions K d'un anneau intègre local R, hensélien, excellent de dimension 2 dont le corps résiduel k est souvent supposé fini et où on emploie des outils plus algébriques. On étudie d'abord la ramification et la cyclicité des algèbres à division sur un tel corps K. On démontre en particulier que toute classe de Brauer d'ordre n premier à la caractéristique résiduelle sur K est d'indice divisant n^2 et que la cyclicité d'une classe de Brauer d'ordre premier peut être testée localement sur les corps complétés par rapport aux valuations discrètes de K. Ces résultats sont appliqués dans le dernier chapitre pour étudier l'arithmétique des formes quadratiques sur K. On montre que toute forme quadratique de rang \ge 9 sur K possède un zéro non trivial. Si K est le corps des fractions d'un anneau de séries formelles A[[t]] sur un anneau de valuation discrète complet A, on a prouvé le principe local-global pour toute forme quadratique de rang \ge 5 sur K. Pour K général on a établi le principe local-global pour les formes de rang 5. Le cas des formes de rang 6,7 ou 8 est ouvert. / This thesis is concerned with the study of some arithmetic properties of certain algebraic varieties which are ``simplest'' in some geometric sense and which are defined over fields of geometric type. It consists of three chapters. In the first chapter, which is independent of the other two, we consider the weak approximation property for a smooth projective rationally connecte d variety X defined over the function field K=k(C) of an algebraic curve C over a field k. Suppose that X admits a K-rational point. Using geometric methods we prove that X(K) is Zariski dense in X if k is a large field, and that under suitable hypotheses weak approximation with respect to a set of places of good reduction holds for X. When k is a finite field, we obtain weak approximation at any given place of good reduction for a smooth cubic surface over K as well as a zero-th order weak approximation result for higher dimensional cubic hypersurfaces over K.The second part of the thesis consists of the last two chapters, where we work over the fraction field K of a 2-dimensional, excellent, henselian local domain R whose residue field k is often assumed to be finite, and where we use more algebraic tools. We first study the ramification and the cyclicity of division algebras over such a field K. We show in particular that every Brauer class over K of order n, which is prime to the residue characteristic, has index dividing n^2, and that the cyclicity of a Brauer class of prime order can be tested locally over the completions of K with respect to discrete valuations. These results are used in the last chapter to study the arithmetic of quadratic forms over K. We prove that every quadratic form of rank \ge 9 over K has a nontrivial zero. When K is the fraction field of a power series ring A[[t]] over a complete discrete valuation ring A, we prove the local-global principle for quadratic forms of rank \ge 5 over K. For general K we prove the local-global principle for quadratic forms of rank 5. The local-global principle for quadratic forms of rank 6, 7 or 8 is still open in the general case.

Neste trabalho, apresentamos os modelos simétricos parcialmente lineares AR(1), que generalizam os modelos parcialmente lineares para a presença de erros autocorrelacionados seguindo uma estrutura de autocorrelação AR(1) e erros seguindo uma distribuição simétrica ao invés da distribuição normal. Dentre as distribuições simétricas, podemos considerar distribuições com caudas mais pesadas do que a normal, controlando a curtose e ponderando as observações aberrantes no processo de estimação. A estimação dos parâmetros do modelo é realizada por meio do critério de verossimilhança penalizada, que utiliza as funções escore e a matriz de informação de Fisher, sendo todas essas quantidades derivadas neste trabalho. O número efetivo de graus de liberdade e resultados assintóticos também são apresentados, assim como procedimentos de diagnóstico, destacando-se a obtenção da curvatura normal de influência local sob diferentes esquemas de perturbação e análise de resíduos. Uma aplicação com dados reais é apresentada como ilustração. / In this master dissertation, we present the symmetric partially linear models with AR(1) errors that generalize the normal partially linear models to contain autocorrelated errors AR(1) following a symmetric distribution instead of the normal distribution. Among the symmetric distributions, we can consider heavier tails than the normal ones, controlling the kurtosis and down-weighting outlying observations in the estimation process. The parameter estimation is made through the penalized likelihood by using score functions and the expected Fisher information. We derive these functions in this work. The effective degrees of freedom and asymptotic results are also presented as well as the residual analysis, highlighting the normal curvature of local influence under different perturbation schemes. An application with real data is given for illustration.

Neste trabalho, apresentamos os modelos simétricos parcialmente lineares AR(1), que generalizam os modelos parcialmente lineares para a presença de erros autocorrelacionados seguindo uma estrutura de autocorrelação AR(1) e erros seguindo uma distribuição simétrica ao invés da distribuição normal. Dentre as distribuições simétricas, podemos considerar distribuições com caudas mais pesadas do que a normal, controlando a curtose e ponderando as observações aberrantes no processo de estimação. A estimação dos parâmetros do modelo é realizada por meio do critério de verossimilhança penalizada, que utiliza as funções escore e a matriz de informação de Fisher, sendo todas essas quantidades derivadas neste trabalho. O número efetivo de graus de liberdade e resultados assintóticos também são apresentados, assim como procedimentos de diagnóstico, destacando-se a obtenção da curvatura normal de influência local sob diferentes esquemas de perturbação e análise de resíduos. Uma aplicação com dados reais é apresentada como ilustração. / In this master dissertation, we present the symmetric partially linear models with AR(1) errors that generalize the normal partially linear models to contain autocorrelated errors AR(1) following a symmetric distribution instead of the normal distribution. Among the symmetric distributions, we can consider heavier tails than the normal ones, controlling the kurtosis and down-weighting outlying observations in the estimation process. The parameter estimation is made through the penalized likelihood by using score functions and the expected Fisher information. We derive these functions in this work. The effective degrees of freedom and asymptotic results are also presented as well as the residual analysis, highlighting the normal curvature of local influence under different perturbation schemes. An application with real data is given for illustration.

In this thesis, geometry is used as a basis for conducting experiments aimed at growing and arranging inorganic minerals on curved interfaces. Mineralisation is directed using crystalline and liquid-crystalline metallic soaps and surfactant/water systems as templates.¶ A review of the history, syntheses, structure and liquid crystallinity of metallic soaps and other amphiphiles is presented as a foundation to understanding the interfacial architectures in mesostructured template systems in general.¶ In this study, a range of metallic soaps of varying chain length and cation type are synthesised and characterised to find potentially useful templates for mineral growth. These include alkaline-earth, transition metal, heavy metal and lanthanide soaps. These are systematically characterised using a variety of analytical techniques, including chemical analyses, x-ray diffraction (XRD) infrared spectroscopy (IR) and differential scanning calorimetry (DSC). Their molecular and crystal structures are studied using transmission electron microscopy (TEM), cryo-TEM, electron diffraction (ED), electron paramagnetic spin resonance (EPR), absorption spectroscopy (UV-VIS), high resolution laser spectroscopy, atomic force microscopy (AFM), nuclear magnetic resonance spectroscopy, scanning electron microscopy (SEM), electron dispersive x-ray analysis (EDXA), thermal gravimetric analysis (TGA) and magnetic measurements. Models for the molecular and crystal structures of metallic soaps are proposed. The soaps are predominantly lamellar crystalline or liquid crystalline lamellar rotor phases with tilted and/or untilted molecular constituents. These display evidence of varying degrees of headgroup organisation, including superstructuring and polymerisation. A single crystal structure is presented for a complex of pyridine with cobalt soap. Simple models for their structure are discussed in terms of their swelling properties in water and oils. Experiments are also presented to demonstrate the sorbent properties of aluminium soaps on oil spills.¶ The thermotropic liquid crystallinity of alkaline earth, transition metal, heavy metal and lanthanide soaps is investigated in detail. This is done to assess their suitability as templates, and to document their novel thermotropic behaviour, particularly the relatively unknown lanthanide soaps. Liquid crystalline behaviours are studied using high-temperature XRD (HTXRD), hot-stage optical microscopy and DSC. Models for a liquid crystalline phase progression from crystals to anisotropic liquids are discussed in terms of theories of self-assembly and interfacial curvature. The terminology required for this is drawn from various nomenclature systems for amphiphilic crystals and liquid crystals. General agreement with previous studies is reported for known soaps, while liquid crystallinity is demonstrated in the lanthanide and some non-lanthanide soaps for the first time. A general phase progression of crystalline lamellar through liquid crystalline lamellar to non-lamellar liquid crystalline is discussed in terms of models concerned with the molecular and crystal structures of the soaps and their phase transitions via headgroup and chain re-arrangements.¶ Experiments aimed at guiding growth of metal sulfides using metallic soaps as templates are described, and a model for this growth is discussed. Metal sulfides have been successfully grown by reacting crystalline and liquid crystalline transition metal and heavy metal soaps with H2S gas at room temperature and at elevated temperature. These have been characterised using XRD, TEM, ED and IR. Sulfide growth is demonstrated to be restricted and guided by the reacting soap template architecture. Zinc, cadmium, indium and lead soaps formed confined nanoparticles within the matrix of their reacting soap template. In contrast, curved and flat sheet-like structures, some resembling sponges were found in the products of sulfided iron, cobalt, nickel, copper, tin and bismuth soaps. A model to explain this behaviour is developed in terms of the crystal and liquid crystal structures of the soaps and the crystal structures of the metal sulfide particles.¶ Liquid crystalline iron soaps have been subjected to controlled thermal degradation yielding magnetic iron oxide nanoparticles. Some XRD and TEM evidence has been found for formation of magnetic mesostructures in heat-treated iron soaps. Models for the molecular and liquid crystalline structure of iron soaps, their thermotropic phase progression and eventual conversion to these magnetic products are discussed. Systematic syntheses of mesoporous silicates from sheeted clays are discussed.¶The templates that have been used are cationic surfactants and small, organic molecular salts. Experiments are reported where a cooperative self-assembly of surfactant/water/kanemite plus or minus salt and oils yields 'folded sheet materials' (FSM'S). Templating of kanemite has also been achieved using cobalt cage surfactants. A theoretical prediction of the specific surface areas and specific volumes of homologous sets of FSM's gave excellent agreement with measured values. The geometry and topology of the mesostructures are discussed. A theoretical model is also discussed regarding the curvature found in the sheets of natural clays , and results of templating clays and silica using metallic soaps are presented. Experiments and a model for low temperature nucleation and growth of microporous silicalite-1 are described in terms of silica templating by water clathrates.¶ Finally, the problem of finding minimal surface descriptions of crystal networks is addressed. Combinatoric methods are used to disprove the existence of possible embeddings of type I and II clathrate networks in non-self intersecting periodic minimal surfaces. The crystal network of the clathrate silicate, melanophlogite is successfully embedded in the WI-10 self-intersecting surface. Details of a previously unreported, genus-25 periodic surface with symmetry Im3m are discussed.

本文採用可加性模型分析法建立台灣地區小型商用車市場之需求模型，並 引進Box-Jenkins時間序列模型處理具自我相關之誤差項，以利進行拔靴 推論設計時，能拔靴白干擾(bootstrapping white noise)，即重抽樣白 干擾的經驗分配。在此次研究過程中，除配適Box-Jenkins時間序列模型 外，所有分析步驟都是完全自動的，不須作假設和檢驗的工作，所以可降 低傳統上因統計人員主觀判斷錯誤所造成的估計偏誤。可加性模型改進傳 統迴歸模型須先假設模型形式的限制，可從商用車實證分析中，直接由資 料配適平滑函數，顯見其合理性。拔靴法免除傳統推論程序須強使隨機干 擾項分配為常態分配或漸近常態分配之束縛，改由殘差經驗分配模擬隨機 干擾項分配行為，在推論商用車市場上，也獲得不錯的結果。

<p>A new kind of lipid/polymer composite particle, consisting of a biodegradable polymer matrix with well-defined lipid domains, has been created. The lipid used is the water-swelling lipid monoolein (MO), which forms a reversed bicontinuous cubic diamond structure in aqueous solutions. The polymer is poly(d,l-lactide-co-glycolide) (PLG), which degrades into water-soluble monomers through hydrolysis. This new particle might be a good alternative for encapsulation of active substances intended to be released over a longer period of time, i.e. sustained/retained/controlled release.</p><p>To prepare such particles can be difficult. Suitable phase behaviour and a solvent with the right properties are needed. For this reason, the phase behaviours of several different lipid/polymer/solvent/water systems have been explored. From the phase behaviour of a suitable system (i.e. MO/PLG/ethyl acetate/water), a route for formation of lipid/polymer composite particles has been deduced. Particles have been formed and distinct, water-swelling, lipid domains have been confirmed by characterization by means of confocal laser scanning probe microscopy (CLSM). </p><p>The sample preparation process has been automated and a method based on using a robotic liquid handler has been developed. Phase diagrams have been determined by examination of macroscopic behaviours and the microstructures of the phases have been studied by small- and wide-angle X-ray scattering (L₃, V₂, L_α, L), nuclear magnetic resonance self-diffusion (L, L₃), viscosimetry (L) and rheology (L). Several different theoretical models have been applied for interpretation of the results. For example, the swelling of the reversed bicontinuous cubic phases and the sponge phase have been modelled by applying the theory of infinite periodical minimal surfaces, the sponge phase has been shown to be bicontinuous according to the theory of interconnected rods and the phase behaviour of the polymer has been described by the Flory-Huggins theory. The main focus of this work (4/5) concerns phase studies in multicomponent systems from a physical-chemical point of view.</p>

A new kind of lipid/polymer composite particle, consisting of a biodegradable polymer matrix with well-defined lipid domains, has been created. The lipid used is the water-swelling lipid monoolein (MO), which forms a reversed bicontinuous cubic diamond structure in aqueous solutions. The polymer is poly(d,l-lactide-co-glycolide) (PLG), which degrades into water-soluble monomers through hydrolysis. This new particle might be a good alternative for encapsulation of active substances intended to be released over a longer period of time, i.e. sustained/retained/controlled release. To prepare such particles can be difficult. Suitable phase behaviour and a solvent with the right properties are needed. For this reason, the phase behaviours of several different lipid/polymer/solvent/water systems have been explored. From the phase behaviour of a suitable system (i.e. MO/PLG/ethyl acetate/water), a route for formation of lipid/polymer composite particles has been deduced. Particles have been formed and distinct, water-swelling, lipid domains have been confirmed by characterization by means of confocal laser scanning probe microscopy (CLSM). The sample preparation process has been automated and a method based on using a robotic liquid handler has been developed. Phase diagrams have been determined by examination of macroscopic behaviours and the microstructures of the phases have been studied by small- and wide-angle X-ray scattering (L3, V2, Lα, L), nuclear magnetic resonance self-diffusion (L, L3), viscosimetry (L) and rheology (L). Several different theoretical models have been applied for interpretation of the results. For example, the swelling of the reversed bicontinuous cubic phases and the sponge phase have been modelled by applying the theory of infinite periodical minimal surfaces, the sponge phase has been shown to be bicontinuous according to the theory of interconnected rods and the phase behaviour of the polymer has been described by the Flory-Huggins theory. The main focus of this work (4/5) concerns phase studies in multicomponent systems from a physical-chemical point of view.

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