Besov spaces and the Laplacian on fractal H-sets

Nesta tese são estudados espaços de Besov de suavidade generalizada em espaços euclidianos, numa classe de fractais designados conjuntos-h e em estruturas abstractas designadas por espaços-h. Foram obtidas caracterizações e propriedades para estes espaços de funções. Em particular, no caso de espaços de Besov em espaços euclidianos, foram obtidas caracterizações por diferenças e por decomposições em átomos não suaves, foi provada uma propriedade de homogeneidade e foram estudados multiplicadores pontuais. Para espaços de Besov em conjuntos-h foi obtida uma caracterização por decomposições em átomos não suaves e foi construído um operador extensão. Com o recurso a cartas, os resultados obtidos para estes espaços de funções em fractais foram aplicados para definir e trabalhar com espaços de Besov de suavidade generalizada em estruturas abstractas. Nesta tese foi também estudado o laplaciano fractal, considerado a actuar em espaços de Besov de suavidade generalizada em domínios que contêm um conjunto-h fractal. Foram obtidos resultados no contexto de teoria espectral para este operador e foi estudado, à custa deste operador, um problema de Dirichlet fractal no contexto de conjuntos-h.

The analysis of political will and its role in leadership: a study of portuguese mayors

This thesis analyses the concept of Political Will, suggests its operationalization and establishes a typological theory that provides the necessary support for the diverse strategies of action of a leader. It claims that political leadership styles articulate a choice of action that results from the Political Will of a leader, which is determined by his intention and his discerned possibilities to act. One main research question guided our research: How does a political leader select and change his leadership style? The most illustrative literature on political leadership is reviewed and the characteristics of democratic governance are analyzed. This is followed by an overview of the most noteworthy theories on the theme and a claim for the need of concept coherence, given the multiplicity of the existent standpoints. After that, we concentrate on leadership styles, with a focus on the local governance context. Human action and intentionality are addressed with particular attention, as well as the motivational drivers for action, in order to advance a conceptualization of Political Will through two dimensions: intention and possibility. This analysis led to a number of relevant propositions: (1) Political Will ‘exists’ when the agent has the intent and the possibility to act; (2) these two dimensions ‘translate’ simultaneously what the agent believes he must do and can do; (3) Intention and possibility reflect diverse but limited worldviews; (4) political leadership styles result from the agent’s Political Will; (5) different combinations of the expected and actual worldviews result in different leadership styles; and (6) political leadership styles can change accordingly to several strategies which allow conformity or reflect reaction to worldviews. We suggested the operationalization of the two dimensions of Political Will through the analytical tool of Grid-group Theory, which provided the identification of the heuristic devices that allowed further comprehension on the subjectivity of the agent’s choice. Four standard property spaces – representing four types of leadership styles – result from a preliminary approach to this process. Afterwards, and because these dimensions operate simultaneously, we advance on the analysis and suggest some plausible heuristical conflicts to happen and describe which consequences, strategies and type migrations are conceivable. An inclusive and more complete set of resulting property spaces renders fourteen different types of leadership styles and sixty different predictable causal paths that result from the expected migration strategies. Case-studies were conducted as plausibility probes designed to provide improvements to our theoretical claims and addressed the cases we selected for research purposes: Portuguese Mayors. The findings from five case studies are discussed and the probable impact and congruence of each with the theoretical claims are assessed. The communalities of the causal mechanisms related to the function of intention and possibility as the dimensions of Political Will and their role in explaining different leadership styles are, finally, addressed. To conclude, we advance some repercussions, mainly in the public policies field of research, and suggest a number of different and necessary paths for further work.

Volatile terpenoids and C13 norisoprenoids in wines: development of rapid methods of analysis and evaluation of the sesquiterpenoids biological potential

Vitis vinifera L., the most widely cultivated fruit crop in the world, was the starting point for the development of this PhD thesis. This subject was exploited following on two actual trends: i) the development of rapid, simple, and high sensitive methodologies with minimal sample handling; and ii) the valuation of natural products as a source of compounds with potential health benefits. The target group of compounds under study were the volatile terpenoids (mono and sesquiterpenoids) and C13 norisoprenoids, since they may present biological impact, either from the sensorial point of view, as regards to the wine aroma, or by the beneficial properties for the human health. Two novel methodologies for quantification of C13 norisoprenoids in wines were developed. The first methodology, a rapid method, was based on the headspace solid-phase microextraction combined with gas chromatography-quadrupole mass spectrometry operating at selected ion monitoring mode (HS-SPME/GC-qMS-SIM), using GC conditions that allowed obtaining a C13 norisoprenoid volatile signature. It does not require any pre-treatment of the sample, and the C13 norisoprenoid composition of the wine was evaluated based on the chromatographic profile and specific m/z fragments, without complete chromatographic separation of its components. The second methodology, used as reference method, was based on the HS-SPME/GC-qMS-SIM, allowing the GC conditions for an adequate chromatographic resolution of wine components. For quantification purposes, external calibration curves were constructed with β-ionone, with regression coefficient (r2) of 0.9968 (RSD 12.51 %) and 0.9940 (RSD of 1.08 %) for the rapid method and for the reference method, respectively. Low detection limits (1.57 and 1.10 μg L-1) were observed. These methodologies were applied to seventeen white and red table wines. Two vitispirane isomers (158-1529 L-1) and 1,1,6-trimethyl-1,2-dihydronaphthalene (TDN) (6.42-39.45 μg L-1) were quantified. The data obtained for vitispirane isomers and TDN using the two methods were highly correlated (r2 of 0.9756 and 0.9630, respectively). A rapid methodology for the establishment of the varietal volatile profile of Vitis vinifera L. cv. 'Fernão-Pires' (FP) white wines by headspace solid-phase microextraction combined with comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (HS-SPME/GCxGC-TOFMS) was developed. Monovarietal wines from different harvests, Appellations, and producers were analysed. The study was focused on the volatiles that seem to be significant to the varietal character, such as mono and sesquiterpenic compounds, and C13 norisoprenoids. Two-dimensional chromatographic spaces containing the varietal compounds using the m/z fragments 93, 121, 161, 175 and 204 were established as follows: 1tR = 255-575 s, 2tR = 0,424-1,840 s, for monoterpenoids, 1tR = 555-685 s, 2tR = 0,528-0,856 s, for C13 norisoprenoids, and 1tR = 695-950 s, 2tR = 0,520-0,960 s, for sesquiterpenic compounds. For the three chemical groups under study, from a total of 170 compounds, 45 were determined in all wines, allowing defining the "varietal volatile profile" of FP wine. Among these compounds, 15 were detected for the first time in FP wines. This study proposes a HS-SPME/GCxGC-TOFMS based methodology combined with classification-reference sample to be used for rapid assessment of varietal volatile profile of wines. This approach is very useful to eliminate the majority of the non-terpenic and non-C13 norisoprenic compounds, allowing the definition of a two-dimensional chromatographic space containing these compounds, simplifying the data compared to the original data, and reducing the time of analysis. The presence of sesquiterpenic compounds in Vitis vinifera L. related products, to which are assigned several biological properties, prompted us to investigate the antioxidant, antiproliferative and hepatoprotective activities of some sesquiterpenic compounds. Firstly, the antiradical capacity of trans,trans-farnesol, cis-nerolidol, α-humulene and guaiazulene was evaluated using chemical (DPPH• and hydroxyl radicals) and biological (Caco-2 cells) models. Guaiazulene (IC50= 0.73 mM) was the sesquiterpene with higher scavenger capacity against DPPH•, while trans,trans-farnesol (IC50= 1.81 mM) and cis-nerolidol (IC50= 1.48 mM) were more active towards hydroxyl radicals. All compounds, with the exception of α-humulene, at non-cytotoxic levels (≤ 1 mM), were able to protect Caco-2 cells from oxidative stress induced by tert-butyl hydroperoxide. The activity of the compounds under study was also evaluated as antiproliferative agents. Guaiazulene and cis-nerolidol were able to more effectively arrest the cell cycle in the S-phase than trans,trans-farnesol and α-humulene, being the last almost inactive. The relative hepatoprotection effect of fifteen sesquiterpenic compounds, presenting different chemical structures and commonly found in plants and plant-derived foods and beverages, was assessed. Endogenous lipid peroxidation and induced lipid peroxidation with tert-butyl hydroperoxide were evaluated in liver homogenates from Wistar rats. With the exception of α-humulene, all the sesquiterpenic compounds under study (1 mM) were effective in reducing the malonaldehyde levels in both endogenous and induced lipid peroxidation up to 35% and 70%, respectively. The developed 3D-QSAR models, relating the hepatoprotection activity with molecular properties, showed good fit (R2LOO > 0.819) with good prediction power (Q2 > 0.950 and SDEP < 2%) for both models. A network of effects associated with structural and chemical features of sesquiterpenic compounds such as shape, branching, symmetry, and presence of electronegative fragments, can modulate the hepatoprotective activity observed for these compounds. In conclusion, this study allowed the development of rapid and in-depth methods for the assessment of varietal volatile compounds that might have a positive impact on sensorial and health attributes related to Vitis vinifera L. These approaches can be extended to the analysis of other related food matrices, including grapes and musts, among others. In addition, the results of in vitro assays open a perspective for the promising use of the sesquiterpenic compounds, with similar chemical structures such as those studied in the present work, as antioxidants, hepatoprotective and antiproliferative agents, which meets the current challenges related to diseases of modern civilization.