Aprendizagem matemática no ensino superior: a influência da plataforma M@T-educar com sucesso

Novas abordagens educacionais têm vindo a surgir como resultado de mudanças económicas, sociais e políticas, que levaram, a nível europeu ao desenvolvimento do Processo de Bolonha. As instituições de ensino superior enfrentam, assim, novos desafios e oportunidades, nomeadamente, o desenvolvimento de contextos educativos mais centrados nas aprendizagens dos alunos, promotores de cidadãos mais autónomos, mais ativos e mais provocadores, capazes de responderem às exigências da Sociedade do Conhecimento global. Diversos estudos apontam a importância de ambientes online na persecução desses objetivos, designadamente na área da Matemática. Neste contexto, desenvolveu-se a plataforma online – M@t-educar com Sucesso – que, a partir da informação teórica, permite a resolução de tarefas interativas, algumas delas contendo animações, das quais se fornece um feedback imediato, a qual carece de avaliação. Assim, este estudo tem como objetivo principal avaliar a influência da exploração prévia às aulas da referida plataforma no desenvolvimento de conhecimentos e capacidades matemáticas, da autonomia e do interesse por essa área em estudantes do ensino superior. O estudo ocorreu na unidade curricular de Cálculo Infinitesimal do Curso Superior de Gestão de uma instituição do ensino superior. Metodologicamente, optou-se por uma abordagem mista de investigação e pelo design de estudo de caso, tendo-se partido de uma análise macro, envolvendo todos os alunos de Cálculo Infinitesimal, seguida de uma análise meso, considerando os alunos da turma da professora/investigadora, que foi evoluindo para uma análise micro, estudando cinco casos da turma. Para tal, utilizaram-se diversas técnicas de recolha de dados – inquirição, observação e análise documental, suportadas por variados instrumentos. A análise estatística e de conteúdo a que os dados foram submetidos permite concluir que a exploração prévia dos conteúdos através desta plataforma contribui para o desenvolvimento, principalmente, de autonomia e da capacidade de aplicação de conhecimento produzido à resolução de tarefas de diversa natureza.

Multiplicity results for some classes of Schrödinger-Poisson systems

In this thesis, we study the existence and multiplicity of solutions of the following class of Schr odinger-Poisson systems: u + u + l(x) u = (x; u) in R3; = l(x)u2 in R3; where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity satis es the following three kinds of cases: (i) a subcritical exponent with (x; u) = k(x)jujp 2u + h(x)u (4 p < 2 ) under an inde nite case; (ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u; (iii) a critical growth exponent with (x; u) = k(x)juj2 2u + h(x)jujq 2u (2 q < 2 ). It is worth mentioning that the thesis contains three main innovations except overcoming several di culties, which are generated by the systems themselves. First, as an unknown referee said in his report, we are the rst authors concerning the existence of multiple positive solutions for Schr odinger- Poisson systems with an inde nite nonlinearity. Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3 that we do not need the condition R R3 k(x)ep 1dx < 0 with an inde nite noncoercive case, where e1 is the rst eigenfunction of +id in H1(R3) with weight function h. A similar condition has been shown to be a su cient and necessary condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity for a bounded domain (see e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be a su cient condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in this case can be applied to study other aspects of the Schr odinger-Poisson systems and it gives a way to study the Kirchho system and quasilinear Schr odinger system. Finally, to get sign changing solutions in Chapter 5, we follow the spirit of Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but the procedure is simpler than that they have proposed in their paper.

Metabolic signature of lung cancer: a metabolomic study of human tissues and biofluids

This thesis reports the application of metabolomics to human tissues and biofluids (blood plasma and urine) to unveil the metabolic signature of primary lung cancer. In Chapter 1, a brief introduction on lung cancer epidemiology and pathogenesis, together with a review of the main metabolic dysregulations known to be associated with cancer, is presented. The metabolomics approach is also described, addressing the analytical and statistical methods employed, as well as the current state of the art on its application to clinical lung cancer studies. Chapter 2 provides the experimental details of this work, in regard to the subjects enrolled, sample collection and analysis, and data processing. In Chapter 3, the metabolic characterization of intact lung tissues (from 56 patients) by proton High Resolution Magic Angle Spinning (HRMAS) Nuclear Magnetic Resonance (NMR) spectroscopy is described. After careful assessment of acquisition conditions and thorough spectral assignment (over 50 metabolites identified), the metabolic profiles of tumour and adjacent control tissues were compared through multivariate analysis. The two tissue classes could be discriminated with 97% accuracy, with 13 metabolites significantly accounting for this discrimination: glucose and acetate (depleted in tumours), together with lactate, alanine, glutamate, GSH, taurine, creatine, phosphocholine, glycerophosphocholine, phosphoethanolamine, uracil nucleotides and peptides (increased in tumours). Some of these variations corroborated typical features of cancer metabolism (e.g., upregulated glycolysis and glutaminolysis), while others suggested less known pathways (e.g., antioxidant protection, protein degradation) to play important roles. Another major and novel finding described in this chapter was the dependence of this metabolic signature on tumour histological subtype. While main alterations in adenocarcinomas (AdC) related to phospholipid and protein metabolisms, squamous cell carcinomas (SqCC) were found to have stronger glycolytic and glutaminolytic profiles, making it possible to build a valid classification model to discriminate these two subtypes. Chapter 4 reports the NMR metabolomic study of blood plasma from over 100 patients and near 100 healthy controls, the multivariate model built having afforded a classification rate of 87%. The two groups were found to differ significantly in the levels of lactate, pyruvate, acetoacetate, LDL+VLDL lipoproteins and glycoproteins (increased in patients), together with glutamine, histidine, valine, methanol, HDL lipoproteins and two unassigned compounds (decreased in patients). Interestingly, these variations were detected from initial disease stages and the magnitude of some of them depended on the histological type, although not allowing AdC vs. SqCC discrimination. Moreover, it is shown in this chapter that age mismatch between control and cancer groups could not be ruled out as a possible confounding factor, and exploratory external validation afforded a classification rate of 85%. The NMR profiling of urine from lung cancer patients and healthy controls is presented in Chapter 5. Compared to plasma, the classification model built with urinary profiles resulted in a superior classification rate (97%). After careful assessment of possible bias from gender, age and smoking habits, a set of 19 metabolites was proposed to be cancer-related (out of which 3 were unknowns and 6 were partially identified as N-acetylated metabolites). As for plasma, these variations were detected regardless of disease stage and showed some dependency on histological subtype, the AdC vs. SqCC model built showing modest predictive power. In addition, preliminary external validation of the urine-based classification model afforded 100% sensitivity and 90% specificity, which are exciting results in terms of potential for future clinical application. Chapter 6 describes the analysis of urine from a subset of patients by a different profiling technique, namely, Ultra-Performance Liquid Chromatography coupled to Mass Spectrometry (UPLC-MS). Although the identification of discriminant metabolites was very limited, multivariate models showed high classification rate and predictive power, thus reinforcing the value of urine in the context of lung cancer diagnosis. Finally, the main conclusions of this thesis are presented in Chapter 7, highlighting the potential of integrated metabolomics of tissues and biofluids to improve current understanding of lung cancer altered metabolism and to reveal new marker profiles with diagnostic value.