Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

Estimativa de espessura crustal na Província Borborema (NE/Brasil) através de função do recpetor

Crustal thickness and VP/VS estimates are essential to the studies of subsurface geological structures and also to the understanding of the regional tectonic evolution of a given area. In this dissertation, we use the Langston´s (1979) Receiver Function Method using teleseismic events reaching the seismographic station with angles close to the vertical. In this method, the information of the geologic structures close to the station is isolated so that effects related to the instrument response and source mechanics are not present. The resulting time series obtained after the deconvolution between horizontal components contains the larger amplitude referring to the P arrival, followed by smaller arrival caused by the reverberation and conversion of the P-wave at the base of the crust. We also used the HK-Stacking after Zhu & Kanamori (2000) to obtain crustal thickness and Vp/VS estimates. This method works stacking receiver functions so that the best estimates of crustal thickness and Vp/VS are found when the direct P, the Ps wave and the first multiple are coherently stacked. We used five broadband seismographic stations distributed over the Borborema Province, NE Brazil. Crustal thickness and Vp/VS estimates are consistent with the crust-mantle interface obtained using gravity data. We also identified crutal thickening in the NW portion of the province, close to Sobral/CE. Towards the center-north portion of the province, there is an evident crustal thinning which coincides with a geological feature consisting of an alignment of sedimentary basins known as the Cariris-Potiguar trend. Towards the NE portion of the province, in Solânea/PB and Agrestina/PE regions, occurs a crustal thickening and a systematic increase in the VP/VS values which suggest the presence of mafic rocks in the lower crust also consistent with the hypothesis of underplating in the region