2 resultados para introductory calculus
em Biblioteca Digital da Produção Intelectual da Universidade de São Paulo (BDPI/USP)
Resumo:
To date, limited numbers of dental calculus samples have been analyzed by researchers in diverse parts of the world. The combined analyses of these have provided some general guidelines for the analysis of calculus that is non-destructive to archaeological teeth. There is still a need for a quantitative study of large numbers of calculus samples to establish protocols, assess the level of contamination, evaluate the quantity of microfossils in dental calculus, and to compare analysis results with the literature concerning the biology of calculus formation. We analyzed dental calculus from 53 teeth from four Brazilian sambaquis. Sambaquis are the shell-mounds that were established prehistorically along the Brazilian coast. The analysis of sambaqui dental calculi shows that there are relatively high concentrations of microfossils (phytoliths and starch), mineral fragments, and charcoal in dental calculus. Mineral fragments and charcoal are possibly contaminants. The largest dental calculi have the lowest concentrations of microfossils. Biologically, this is explained by individual variation in calculus formation between people. Importantly, starch is ubiquitous in dental calculus. The starch and phytoliths show that certainly Dioscorea (yam) and Araucaria angustifolia (Parana pine) were eaten by sambaqui people. Araceae (arum family), Ipomoea batatas (sweet potato) and Zea mays (maize) were probably in their diet. (C) 2009 Elsevier Ltd. All rights reserved.
Resumo:
Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.