Um estudo sobre a relação entre matemática e religião na obra de Blaise Pascal

The aim of the present study is to investigate the way through which the relations between Mathematics and Religion emerge in the work of Blaise Pascal. This research is justified by the need to deepen these relations, so far little explored if compared to intersection points between Mathematics and other fields of knowledge. The choice for Pascal is given by the fact that he was one of the mathematicians who elaborated best one reflection in the religious field thus provoking contradictory reactions. As a methodology, it is a bibliographical and documental research with analytical-comparative reading of referential texts, among them the Oeuvres complètes de Pascal (1954), Le fonds pascalien à Clermont-Ferrand (2001), Mathematics in a postmodern age: a cristian perspective by Howell & Bradley (2001), Mathematics and the divine: a historical study by Koetsier & Bergmans (2005), the Anais dos Seminários Nacionais de História da Matemática and the Revista Brasileira de História da Matemática. The research involving Pascal's life as a mathematician and his religious experience was made. A wider background in which the subject matter emerges was also researched. Seven categories connected to the relation between mathematics and religion were identified from the reading of texts written by mathematicians and historians of mathematics. As a conclusion, the presence of four of these seven categories was verified in Pascal's work

Enumeração de espectro de distâncias de esquemas de modulação codificada em treliça empregando codificação turbo

In this work, a performance analysis of transmission schemes employing turbo trellis coded modulation. In general, the performance analysis of such schemes is guided by evaluating the error probability of these schemes. The exact evaluation of this probability is very complex and inefficient from the computational point of view, a widely used alternative is the use of union bound of error probability, because of its easy implementation and computational produce bounds that converge quickly. Since it is the union bound, it should use to expurge some elements of distance spectrum to obtain a tight bound. The main contribution of this work is that the listing proposal is carried out from the puncturing at the level of symbol rather than bit-level as in most works of literature. The main reason for using the symbol level puncturing lies in the fact that the enummerating function of the turbo scheme is obtained directly from complex sequences of signals through the trellis and not indirectly from the binary sequences that require further binary to complex mapping, as proposed by previous works. Thus, algorithms can be applied through matrix from the adjacency matrix, which is obtained by calculating the distances of the complex sequences of the trellis. This work also presents two matrix algorithms for state reduction and the evaluation of the transfer function of this. The results presented in comparisons of the bounds obtained using the proposed technique with some turbo codes of the literature corroborate the proposition of this paper that the expurgated bounds obtained are quite tight and matrix algorithms are easily implemented in any programming software language