This work explores mechanisms for pattern formation through coupled bulksurface partial differential equations of reaction-diffusion type. Reaction-diffusion systems posed both in the bulk and on the surface on stationary volumes are coupled through linear Robin-type boundary conditions. In this framework we study three different systems as follows (i) non-linear reactions in the bulk and surface respectively, (ii) non-linear reactions in the bulk and linear reactions on the surface and (iii) linear reactions in the bulk and non-linear reactions on the surface. In all cases, the systems are non-dimensionalised and rigorous linear stability analysis is carried out to determine the necessary and sufficient conditions for pattern formation. Appropriate parameter spaces are generated from which model parameters are selected. To exhibit pattern formation, a coupled bulk-surface finite element method is developed and implemented. We implement the numerical algorithm by using an open source software package known as deal.II and show computational results on spherical and cuboid domains. Theoretical predictions of the linear stability analysis are verified and supported by numerical simulations. The results show that non-linear reactions in the bulk and surface generate patterns everywhere, while non-linear reactions in the bulk and linear reactions on the surface generate patterns in the bulk and on the surface with a pattern-less thin boundary layer. However, linear reactions in the bulk do not generate patterns on the surface even when the surface reactions are non-linear. The generality, robustness and applicability of our theoretical computational framework for coupled system of bulk-surface reaction-diffusion equations set premises to study experimentally driven models where coupling of bulk and surface chemical species is prevalent. Examples of such applications include cell motility, pattern formation in developmental biology, material science and cancer biology.

This thesis is concerned with the study of the Blow-up phenomena for parabolic problems, which can be defined in a basic way as the inability to continue the solutions up to or after a finite time, the so called blow-up time. Namely, we consider the blow-up location in space and its rate estimates, for special cases of the following types of problems: (i) Dirichlet problems for semilinear equations, (ii) Neumann problems for heat equations, (iii) Neumann problems for semilinear equations, (iv) Dirichlet (Cauchy) problems for semilinear equations with gradient terms. For problems of type (i), (ii), we extend some known blow-up results of parabolic problems with power and exponential type nonlinearities to problems with nonlinear terms, which grow faster than these types of functions for large values of solutions. Moreover, under certain conditions, some blow-up results of the single semilinear heat equation are extended to the coupled systems of two semilinear heat equations. For problems of type (iii), we study how the reaction terms and the nonlinear boundary terms affect the blow-up properties of the blow-up solutions of these problems. The noninuence of the gradient terms on the blow-up bounds is showed for problems of type (iv).

No description available.

As estatinas são substâncias que inibem a síntese de colesterol. Por não existir métodos analíticos simples e de baixo custo para determinação quantitativa de pravastatina sódica, fluvastatina sódica, atorvastatina cálcica e rosuvastatina cálcica, o objetivo desta pesquisa foi desenvolver, validar e comparar os métodos por cromatografia líquida de alta eficiência e espectrofotometria direta e derivada no ultravioleta para a determinação quantitativa de estatinas em comprimidos. Os métodos cromatográficos foram realizados em coluna LiChrospher® RP-18 com fase móvel composta de metanol-água e pH ajustado a 3,0 com ácido fosfórico. Os métodos espectrofotométricos foram validados utilizando NaOH 0,1 M como solvente. A análise estatística com os testes t e F, não mostraram diferença significativa entre os métodos propostos ao nível de confiança de 95%. Os métodos são simples, eficientes e podem ser utilizados em análises de rotina para o controle de qualidade de estatinas em comprimidos. / The statins are substances that inhibit the synthesis of cholesterol. There is no simple and low cost analytical methods for quantitative determination of pravastatin sodium, fluvastatin sodium, atorvastatin calcium and rosuvastatin calcium; the objective of this research was to develop, to validate and to compare the methods as high performance liquid chromatography and ultraviolet direct and derivative spectrophotometry for quantitative determination of statins in tablets. The chromatographic methods were carried out with a LiChrospherB RP-18 column with a mobile phase composed of methanol-water and pH adjusted to 3.0 with phosphoric acid. The spectrophotometric methods were validated using NaOH 0.1 M as solvent. The statistical analysis using tests t and F, did not show significant difference between the methods considering the 95% confidence level. The methods are simple, efficient and can be used in routine analyses for quality control of statins in tablets.

This study investigated the effectiveness of various analytical methods used for estimating R2 shrinkage in multiple regression analysis. Two categories of analytical formulae were identified: estimators of the population squared multiple correlation coefficient (ρ2), and estimators of the population cross-validity coefficient (ρc2). To avoid possible confounding factors that might be associated with a real data set such as data nonnormality, lack of precise population parameters, different degrees of multicollinearity among the predictor variables, and so forth, the Monte Carlo method was used to simulate multivariate normal sample data, with prespecified population parameters such as the squared multiple correlation coefficient (ρ2), number of predictors, different sample sizes, known degree of multicollinearity, and controlled data normality conditions. Five hundred replicates were simulated within each cell of the sampling conditions. Various analytical formulae were applied to the simulated data in each sampling condition, and the "adjusted" coefficients were obtained and then compared to their corresponding population parameters (ρ2 and ρc2). Analysis of the results indicates that the currently most widely used (in both SAS and SPSS) "Wherry" formula is probably not the most effective analytical formula in estimating ρ2. Instead, the Pratt formula appeared to outperform other analytical formulae across most of these sampling conditions. Among the analytical formulae designed to estimate ρc2, the Browne formula appeared to be the most effective and stable in minimizing statistical bias across different sampling conditions. The study also concludes that it is the n/p (sample size/number of predictor variables) ratio that affects the performances of these analytical formulae the most; different degrees of multicollinearity among predictor variables do not have dramatic influence on the performances of these analytical formulae. Further replicants on both real and simulated data re still needed to investigate the effectiveness of these analytical formulae.

<p>The aim of this thesis was to verify the indicated occurrence of acrylamide formation in heating of food, to identify factors affecting the formation, and to identify important sources of acrylamide exposure from food. As a prerequisite for the studies, gas- and liquid-chromatographic methods with mass spectrometric detection were developed for the analysis of acrylamide in food. The developed methods showed a high correlation coefficient (0.99), high sensitivity and reproducibility. Acrylamide was demonstrated to occur in heated food products, with unexpectedly high levels in potato products (up to mg/kg level in potato crisps) and in beetroot. The identity of acrylamide was confirmed by the developed methods. </p><p>With potato as a food model, different factors affecting the acrylamide formation were tested. It was shown that the addition of asparagine and fructose, as well as heating temperature and time had a large impact on the formation. Other factors affecting the acrylamide content were pH, addition of other amino acids apart from asparagine, protein and other reducing sugars. No significant effects were observed from addition of neither antioxidant nor radical initiators. It was discovered that acrylamide could be formed during heating of biological materials similar to food, also at temperatures below 100 ˚C. Furthermore, it was demonstrated that a fraction of acrylamide evaporates during heating, similar to conditions for cooking in household kitchens, and during dry matter determinations in laboratories (65-130 ˚C). This constitutes an earlier unobserved source of exposure to acrylamide.</p><p>The method for extraction of food was studied with regard to yield of acrylamide. It was shown that the yield at pH ≥12 increases 3 - 4 times compared to normal water extraction for some foods products. Extraction at acidic pH or with enzymatic treatment was also tested, showing no effect on yield.</p><p>In a study with mice the bioaviability of acrylamide extracted with the normal water extration and at alkaline pH was compared. It was shown that the extra acrylamide released at alkaline pH gave insignificant contributions to the in vivo dose, measured by hemoglobin adducts.</p>

The aim of this thesis was to verify the indicated occurrence of acrylamide formation in heating of food, to identify factors affecting the formation, and to identify important sources of acrylamide exposure from food. As a prerequisite for the studies, gas- and liquid-chromatographic methods with mass spectrometric detection were developed for the analysis of acrylamide in food. The developed methods showed a high correlation coefficient (0.99), high sensitivity and reproducibility. Acrylamide was demonstrated to occur in heated food products, with unexpectedly high levels in potato products (up to mg/kg level in potato crisps) and in beetroot. The identity of acrylamide was confirmed by the developed methods. With potato as a food model, different factors affecting the acrylamide formation were tested. It was shown that the addition of asparagine and fructose, as well as heating temperature and time had a large impact on the formation. Other factors affecting the acrylamide content were pH, addition of other amino acids apart from asparagine, protein and other reducing sugars. No significant effects were observed from addition of neither antioxidant nor radical initiators. It was discovered that acrylamide could be formed during heating of biological materials similar to food, also at temperatures below 100 ˚C. Furthermore, it was demonstrated that a fraction of acrylamide evaporates during heating, similar to conditions for cooking in household kitchens, and during dry matter determinations in laboratories (65-130 ˚C). This constitutes an earlier unobserved source of exposure to acrylamide. The method for extraction of food was studied with regard to yield of acrylamide. It was shown that the yield at pH ≥12 increases 3 - 4 times compared to normal water extraction for some foods products. Extraction at acidic pH or with enzymatic treatment was also tested, showing no effect on yield. In a study with mice the bioaviability of acrylamide extracted with the normal water extration and at alkaline pH was compared. It was shown that the extra acrylamide released at alkaline pH gave insignificant contributions to the in vivo dose, measured by hemoglobin adducts.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniversitet, 2009. / Härtill 5 uppsatser.

Diss. (sammanfattning). Uppsala : Sveriges lantbruksuniv., 2003. / Härtill 8 uppsatser.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniversitet, 2005. / Härtill 6 uppsatser.