Classical and quantum properties of a 2-sphere singularity

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.Comment: 10 pages, 1 figure, minor corrections, final versio

Mineral nutrition of cerrado species I: inorganic chemical composition of Byrsonima coccolobifolia (Sp) kunth, Kielmeyera coriacea (Sp) mart and "shurb" (Polypodiaceae)

The word "Cerrado" is used in Brazil in a broad sense. In the wide sense, it is a regional large-scale vegetation type that forms both a vegetational and a floristic province. This large-scale vegetational province posseses a distinctive flora with a few endemic genera and hundreds of endemic species. In the present work, the authors, run analysis of the differents parts of three species collected during one year, from a Regosol (Entisols), situated at the region of Cajuru, São Paulo, Brazil. In this paper, analysis of N, P, K, Ca, Mg, S, B, Cu, Fe, Mn, Mo, Zn and Al are presented. From the data the followings conclusions may be draw: 1 - The year seasons does not affected markedly the dry matter production of the species; 2 - The concentration on macro and micronutrients, with few exceptions, are similars to the cultivated plants; 3 - The lignotuber of "shrub" plant actually accumulate nutrients; 4 - All of the studied species are not aluminium accumulator plants.Com a finalidade de se determinar a concentração e extração dos macro e micronutrientes, assim como o teor de alumínio, em espécies que vegetam em condições de Cerrado, foram coletadas amostras de Byrsonima coccolobifolia (Sp) Kunth em um Regosolo nos meses de janeiro, agosto e novembro na região de Cajurú no Estado de São Paulo, Brasil. No mês de janeiro foram coletadas em igualdade de condições amostras de Kilmeyer coriacea (Sp) Mart, e "Samambaia". Os resultados mostram que: 1 - A estação climática do ano não tem influência marcante nas espécies; 2 - A concentração dos macro e micronutrientes, salvo algumas exceções, é semelhante a das plantas cultivadas; 3 - O xilopódio é órgão armazenador de nutrientes na espécie "samambaia"; 4 - As espécies não são acumuladoras de alumínio