Studies in non-Gaussian analysis

This thesis presents general methods in non-Gaussian analysis in infinite dimensional spaces. As main applications we study Poisson and compound Poisson spaces. Given a probability measure μ on a co-nuclear space, we develop an abstract theory based on the generalized Appell systems which are bi-orthogonal. We study its properties as well as the generated Gelfand triples. As an example we consider the important case of Poisson measures. The product and Wick calculus are developed on this context. We provide formulas for the change of the generalized Appell system under a transformation of the measure. The L² structure for the Poisson measure, compound Poisson and Gamma measures are elaborated. We exhibit the chaos decomposition using the Fock isomorphism. We obtain the representation of the creation, annihilation operators. We construct two types of differential geometry on the configuration space over a differentiable manifold. These two geometries are related through the Dirichlet forms for Poisson measures as well as for its perturbations. Finally, we construct the internal geometry on the compound configurations space. In particular, the intrinsic gradient, the divergence and the Laplace-Beltrami operator. As a result, we may define the Dirichlet forms which are associated to a diffusion process. Consequently, we obtain the representation of the Lie algebra of vector fields with compact support. All these results extends directly for the marked Poisson spaces.

Leadership of portuguese community schools in the East Coast of the United States and the public policies of education: a multiple case studies

The Portuguese community schools of the United States located in the areas of larger Portuguese population concentration are social organizations that come materializing throughout decades the designs of the educative policies of the Portuguese government in relation to the expansion and preservation of the language, the culture and the history of Portugal. These designs of the educative policies are enrolled in the Constitution of the Republic (1976), in the Basic Law of Educative System (1986) and, over all, in the successive legislative norms (Decree-laws and ordinances) of the successive governments. Portuguese community schools in the United States are structuralized in analogous way to schools of the Portuguese geographic space. For this qualitative study (multiple case), four directors of Portuguese schools of the East Coast of the United States were interviewed; two schools are in the state of Rhode Island and the other two are in the state of Massachusetts. Also, it was administered the questionnaire on practices of leadership “Leadership Practices Inventory” (LPI) of Kouzes and Posner (2002) to collect additional data about practices of leadership on the directors of the schools. The LPI evaluates practices of leadership classifying them in five domains: (a) Model the way; (b) Inspire a shared vision; (c) Challenge the process; (d) Enable others to act; and, (e) Encourage the heart. Results of this qualitative research indicate that the Portuguese Government has not had an educative policy stimulant, coherent and consistent of support, incentive, maintenance and diffusion of the Portuguese language and culture and the directors of the studied schools they have a proactive and serving leadership style in conducting the management of Portuguese community schools. The five practices of leadership are highly practiced by the directors of the studied schools above all the practices “Enable others to act” and “Encourage the heart”.