2 resultados para ÁLGEBRAS DE LIE

em RUN (Repositório da Universidade Nova de Lisboa) - FCT (Faculdade de Cienecias e Technologia), Universidade Nova de Lisboa (UNL), Portugal


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The term res publica (literally “thing of the people”) was coined by the Romans to translate the Greek word politeia, which, as we know, referred to a political community organised in accordance with certain principles, amongst which the notion of the “good life” (as against exclusively private interests) was paramount. This ideal also came to be known as political virtue. To achieve it, it was necessary to combine the best of each “constitutional” type and avoid their worst aspects (tyranny, oligarchy and ochlocracy). Hence, the term acquired from the Greeks a sense of being a “mixed” and “balanced” system. Anyone that was entitled to citizenship could participate in the governance of the “public thing”. This implied the institutionalization of open debate and confrontation between interested parties as a way of achieving the consensus necessary to ensure that man the political animal, who fought with words and reason, prevailed over his “natural” counterpart. These premises lie at the heart of the project which is now being presented under the title of Res Publica: Citizenship and Political Representation in Portugal, 1820-1926. The fact that it is integrated into the centenary commemorations of the establishment of the Republic in Portugal is significant, as it was the idea of revolution – with its promise of rupture and change – that inspired it. However, it has also sought to explore events that could be considered the precursor of democratization in the history of Portugal, namely the vintista, setembrista and patuleia revolutions. It is true that the republican regime was opposed to the monarchic. However, although the thesis that monarchy would inevitably lead to tyranny had held sway for centuries, it had also been long believed that the monarchic system could be as “politically virtuous” as a republic (in the strict sense of the word) provided that power was not concentrated in the hands of a single individual. Moreover, various historical experiments had shown that republics could also degenerate into Caesarism and different kinds of despotism. Thus, when absolutism began to be overturned in continental Europe in the name of the natural rights of man and the new social pact theories, initiating the difficult process of (written) constitutionalization, the monarchic principle began to be qualified as a “monarchy hedged by republican institutions”, a situation in which not even the king was exempt from isonomy. This context justifies the time frame chosen here, as it captures the various changes and continuities that run through it. Having rejected the imperative mandate and the reinstatement of the model of corporative representation (which did not mean that, in new contexts, this might not be revived, or that the second chamber established by the Constitutional Charter of 1826 might not be given another lease of life), a new power base was convened: national sovereignty, a precept that would be shared by the monarchic constitutions of 1822 and 1838, and by the republican one of 1911. This followed the French example (manifested in the monarchic constitution of 1791 and in the Spanish constitution of 1812), as not even republicans entertained a tradition of republicanism based upon popular sovereignty. This enables us to better understand the rejection of direct democracy and universal suffrage, and also the long incapacitation (concerning voting and standing for office) of the vast body of “passive” citizens, justified by “enlightened”, property- and gender-based criteria. Although the republicans had promised in the propaganda phase to alter this situation, they ultimately failed to do so. Indeed, throughout the whole period under analysis, the realisation of the potential of national sovereignty was mediated above all by the individual citizen through his choice of representatives. However, this representation was indirect and took place at national level, in the hope that action would be motivated not by particular local interests but by the common good, as dictated by reason. This was considered the only way for the law to be virtuous, a requirement that was also manifested in the separation and balance of powers. As sovereignty was postulated as single and indivisible, so would be the nation that gave it soul and the State that embodied it. Although these characteristics were common to foreign paradigms of reference, in Portugal, the constitutionalization process also sought to nationalise the idea of Empire. Indeed, this had been the overriding purpose of the 1822 Constitution, and it persisted, even after the loss of Brazil, until decolonization. Then, the dream of a single nation stretching from the Minho to Timor finally came to an end.

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Neste trabalho propomos um novo tipo de modelo, que designamos por modelo com aninhamento em escada estruturado. Este modelo tem por base o modelo com aninhamento em escada e, tal como este, apresenta vantagens face ao aninhamento equilibrado. Permite grande economia no número de observações utilizadas e uma distribuição mais uniforme da informação pelos vários factores. Com este novo tipo de modelo podemos construir novos modelos, também em escada, mais complexos do que os existentes até agora. No aninhamento em escada a cada degrau do modelo corresponde um factor. Generalizamos a teoria destes modelos introduzindo a possibilidade de se desagregar cada um dos factores intervenientes, passando os degraus a terem submodelos com estrutura ortogonal. Para estudar o aninhamento em escada estruturado, propomos duas estruturas algébricas que, apesar de diferentes, possibilitam obter os mesmos estimadores dos parâmetros relevantes. Álgebras de Jordan comutativas são utilizadas para exprimir essas estruturas. Usando as matrizes da base principal, das álgebras a que se associam os modelos, a estimação vai ter por base a relação entre as componentes de variância canónicas e as usuais. Para além do aninhamento em escada estruturado, apresentamos também modelos obtidos cruzando vários desses aninhamentos.