In the first part of this thesis, we present the first non-trivial small value estimate that applies to an algebraic group of dimension 2 and which involves large sets of points. The algebraic group that we consider is the product ℂ× ℂ*, of the additive group ℂ by the multiplicative group ℂ*. Our main result assumes the existence of a sequence (PD)D ≥1 of non-zero polynomials in ℤ [X1, X2] taking small absolute values at many translates of a fixed point (ξ, η) in ℂ × ℂ* by consecutive multiples of a rational point (r, s) ∈ (ℚ*)2 with s = ±1. Under precise conditions on the size of the coefficients of the polynomials PD, the number of translates of (ξ, η) and the absolute values of the polynomials PD at these points, we conclude that both ξ and η are algebraic over ℚ. We also show that the conditions that we impose are close from being best possible upon comparing them with what can be achieved through an application of Dirichlet’s box principle. In the second part of the thesis, we consider points of the form θ = (1,θ1 , . . . ,θd-1 ,ξ) where {1,θ1 , . . . ,θd-1 } is a basis of a real number field K of degree d ≥ 2 over ℚ and where ξ is a real number not in K. Our main results provide sharp upper bounds for the uniform exponent of approximation to θ by rational points, denoted λ ̂(θ), and for its dual uniform exponent of approximation, denoted τ ̂(θ). For d = 2, these estimates are best possible thanks to recent work of Roy. We do not know if they are best possible for other values of d. However, in Chapter 2, we provide additional information about rational approximations to such a point θ assuming that its exponent λ ̂(θ) achieves our upper bound. In the course of the proofs, we introduce new constructions which are interesting by themselves and should be useful for future research.

Fried foods are delicious and enjoyed by almost everyone. However, they are not the healthiest foods to eat because of the amount of oil they contain. This thesis, sponsored by Moaero Company founder, Mr. Harrish Bhutani, intends to determine whether a simply designed centrifuge system can remove a reasonable amount of oil from fried foods after it has been deep fried without adversely affecting the texture of the fried food. Due to a large variety in the texture as well as the type of fried foods, and in order to keep the scope of this thesis more focused and feasible, the focus of this investigation will be French fries. Three variables are tested: the type of fry, the angular velocity of the centrifuge, and the time spent in the centrifuge. Multiple designs for the centrifuge system were made on SolidWorks. Engineer Equation Solver (EES) was used to aid steady state and transient heat transfer calculations. Minitab was used for statistical analysis. The impact of various parameters on the change in mass of the French fries, as a measure for evaluating the oil content, were studied. The results indicate whether a centrifuge will remove a reasonable amount of oil while also considering the integrity of the fries. The study concludes that centrifugation is be a cost-effective method for removing oil from fried foods.

This paper analyzes how the COVID-19 pandemic has affected the Swedish housing market, and in particular prices and shifts in trends. Different classes of housing objects in various counties are investigated. Combining web scraped housing data for the entirety of Sweden between 2016-01-01 and 2021-03-31, including economic, demographic, socioeconomic and locational data, a hedonic regression model is used to estimate how different variables influence the housing price. The base model is subsequently used to investigate if statistically significant structural breaks exist in relation to the COVID-19 pandemic for the different object types in the entire Swedish market and in certain specific counties. Structural breaks are found for the housing object types ‘Fritidshus’, ‘Lägenhet’ and ‘Radhus’ in the entire Swedish market and for “Villa” in Stockholm county shortly after the pandemic outbreak, suggesting there is evidence for a pandemic infused shift in housing price regime on the Swedish housing market for these object types in stated areas. Splitting the hedonic regression model into three, one pooled regression, one before and one after the identified breaks, and comparing the shifts in impact of the housing price determinants suggests different pandemic effects on different object types. The result indicates that for the object types ‘Lägenhet’ in the entire country and for ‘Villa’ in Stockholm county, living area has an increased impact on the price while the locational variable population density has a decreased impact after the breakpoint date compared to before. This could suggest that for permanent housing objects in these regions, living area might have become increasingly valued over location during the pandemic. The results further indicate the direct opposite effect on the shifted impact in living area and the population density for the price of the temporary housing type Fritidshus in entire Sweden. However, an indication for increased impact of the areas socioeconomic level is noted for all these three object types. These results hold as a ground for further research in the subject.

The Chow/Van der Waerden approach to algebraic cycles via resultants is elaborated and used to give a purely algebraic proof for the algebraicity of the complex suspension over arbitrary fields. The algebraicity of the join pairing on Chow varieties then follows over the complex numbers. The approach implies a more algebraic proof of Lawson´s complex suspension theorem in characteristic 0. The continuity of the action of the linear isometries operad on the group completion of the stable Chow variety is a consequence. Further Hoyt´s proof of the independence of the algebraic-continuous homeomorphism type of Chow varieties on embeddings is rectified and worked out over arbitrary fields.

The global financial crisis that started in the USA affected several countries around the world. This study focuses on only three countries; the USA, Sweden, and Italy, which are examples of economies with three different labor market models. The purpose of this study is to investigate if and in that case how Okun's law was affected by the global financial crisis in the three countries’ labor market models and if there are any differences in the correlations before and after the global financial crisis. Okun’s difference version was used in this study. Quarterly time series data was used in this study during the time period 1985-2019. The Chow test was used to test the hypothesis. The results show that the global financial crisis affected Okun’s law after the crisis in all three countries. The USA, Sweden, and Italy were affected differently

O objetivo específico da presente dissertação é estimar a elasticidade-PIB do Imposto de Renda Pessoa Física (IRPF) e Imposto Renda Pessoa Jurídica (IRPJ) no Brasil entre 1986 e 2012. A pesquisa também incorpora em seus objetivos uma análise técnica a respeito da tributação e seus impactos sobre o sistema econômico, tanto a nível microeconômico e macroeconômico, além de abordar o IRPF e IRPJ em seu aspecto econômico e jurídico. No tratamento metodológico são utilizados modelos de Vetor de Correção de erros (VEC) para estimar as elasticidades-PIB do IRPF e IRPJ. Os resultados apontam uma elasticidade-PIB, tanto para IRPF quanto IRPJ, acima da unidade, na maioria dos modelos estimados, e existem períodos determinados que impactam consideravelmente sobre à arrecadação desses tributos. / This dissertation estimates the GDP elasticity of income tax revenue for individuals (IRPF) and corporations (IRPJ) between 1986 and 2012. Additionally the research incorporates an analysis of the macroeconomic and microeconomic effects of taxation. IRPF and IRPJ are analyzed in great detail, including economic as well as legal aspects. An Error Correction Model is estimated to obtain the elasticities. The results show that both elasticities are higher than unit and that reforms that took place in some periods have a significant impact on tax collection.

O objetivo específico da presente dissertação é estimar a elasticidade-PIB do Imposto de Renda Pessoa Física (IRPF) e Imposto Renda Pessoa Jurídica (IRPJ) no Brasil entre 1986 e 2012. A pesquisa também incorpora em seus objetivos uma análise técnica a respeito da tributação e seus impactos sobre o sistema econômico, tanto a nível microeconômico e macroeconômico, além de abordar o IRPF e IRPJ em seu aspecto econômico e jurídico. No tratamento metodológico são utilizados modelos de Vetor de Correção de erros (VEC) para estimar as elasticidades-PIB do IRPF e IRPJ. Os resultados apontam uma elasticidade-PIB, tanto para IRPF quanto IRPJ, acima da unidade, na maioria dos modelos estimados, e existem períodos determinados que impactam consideravelmente sobre à arrecadação desses tributos. / This dissertation estimates the GDP elasticity of income tax revenue for individuals (IRPF) and corporations (IRPJ) between 1986 and 2012. Additionally the research incorporates an analysis of the macroeconomic and microeconomic effects of taxation. IRPF and IRPJ are analyzed in great detail, including economic as well as legal aspects. An Error Correction Model is estimated to obtain the elasticities. The results show that both elasticities are higher than unit and that reforms that took place in some periods have a significant impact on tax collection.

Cette thèse comporte deux parties. Dans la première partie on étudie le motif de Chow d’un fibré en quadriques de dimension relative impaire sur une surface. On montre que ce motif admet une décomposition qui fait intervenir le motif de Prym du revêtement double de la courbe discriminante. Dans la deuxième partie on s’intéresse à des fibrations lagrangiennes, obtenues comme jacobiennes intermédiaires relatives des familles de variétés de Fano de dimension trois contenant une surface K3 fixée, et à l’existence d’une compactification symplectique. Dans un cas particulier, on étudie une compactification partielle en utilisant des calculs avec le logiciel Macaulay2. / This thesis consists of two parts. In the first part we study the Chow motive of a quadric bundle of odd relative dimension over a surface. We show that this motive admits a decomposition which involves the Prym motive of the double covering of the discriminant curve.In the second part, we consider Lagrangian fibrations, obtained as relative intermediate Jacobians of families of Fano threefolds containing a fixed K3 surface, and the existence of a symplectic compactification. In a particular case, we study a partial compactification using calculations with the software system Macaulay2.

<p>It is rarely possible to use an optimal classifier. Often the classifier used for a specific problem is an approximation of the optimal classifier. Methods are presented for evaluating the performance of an approximation in the model class of Bayesian Networks. Specifically for the approximation of class conditional independence a bound for the performance is sharpened.</p><p>The class conditional independence approximation is connected to the minimum description length principle (MDL), which is connected to Jeffreys’ prior through commonly used assumptions. One algorithm for unsupervised classification is presented and compared against other unsupervised classifiers on three data sets.</p> / Report code: LiU-TEK-LIC 2006:11.

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