Complex quadrics and spectral geometry

Some characterizations of complex quadrics in terms of the spectrum are given.     

Hyperfine interaction of Eu in Eu2TiO4

The hyperfine interaction of ¹⁵¹Eu in Eu₂TiO₄ has been measured using the Mössbauer Effect. Using the four-fold symmetry of the Eu²⁺ site, it has been found that the nuclear quadrupole moment ratio of the first-excited to the ground states of ¹⁵¹Eu is R = 1.34 ±0.03, and the quadrupole interaction energy is ρ²qQ_o = -(190 ± 7) MHZ. Below T_c = 7.8K, the magnetic hyperfine field H_hf points close to the direction of the four-fold axis. The zero-degree value of H_hf is estimated to be (305 ± 3) kOe.     

Effects of X-ray absorption in the analysis of thick target samples by XRF

The accuracy of the quantitative analysis of thick targets by XRF is impaired by effects due to the absorption of X-rays in the matrix associated with the non-uniformity of the X-ray beam and the lack of knowledge of the actual distribution of trace elements in the target. The uncertainty in the elemental mass associated to a definite number X-rays detected is discussed in the paper. A correction factor is derived to account specifically for the effect of the absorption of X-rays and the non-uniformity of the X-ray beam. Work partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico, Financiadora de Estudos e Projetos and International Atomic Energy Agency.     

Vinyllithiums from butyl-vinyl tellurides and bis-vinyl tellurides

Butyl vinyl tellurides and bis-vinyl tellurides furnish vinyllithiums with retention of configuration in good yields upon treatment with n-butyllithium at −78°C.     

Ferrimagnetic properties of Eu3Ti2O7

The Mossbauer spectrum of ¹⁵¹Eu₃Ti₂O₇ reveals a ferrimagnetic ordering below (8 ± 0.3) K with two inequivalent sites in ratio 2: 1, and with exchange constants nearly equal to those of EuTiO₃ and of Eu₂TiO₄. The sublattice magnetizations are explained in terms of these constants.     

A spectral characterization of the -torus by the first stability eigenvalue

Let be a compact hypersurface with constant mean curvature immersed into the unit Euclidean sphere . In this paper we derive a sharp upper bound for the first eigenvalue of the stability operator of in terms of the mean curvature and the length of the total umbilicity tensor of the hypersurface. Moreover, we prove that this bound is achieved only for the so-called -tori in , with . This extends to the case of constant mean curvature hypersurfaces previous results given by Wu (1993) and Perdomo (2002) for minimal hypersurfaces.

     

Thermal decomposition study of sewage sludge and of organicwaste used in the sorption of metals

The conventional treatments of effluents containing heavy metals produce significant quantities of byproducts with recalcitrant characteristics, making necessary looking after alternative techniques in order to avoid the production of new contaminated residues. Sorption process of chromium and zinc in vertical columns loaded with sewage sludge and organic solid waste has been studied in this work. The data from the TG curves of the two sorbents presented significant differences when they were submitted to the metal uptake, being noticed the displacement of the thermal events towards lower temperatures for both types of sorbents studied. As it was expected, for both sorbents, an increase in the mass of samples has been observed at the completion of the thermal tests upon metal uptake. Therefore, these facts demonstrate that during the biosorption process a physico-chemical interaction took place between sorbents and metals, as it was evidenced by the more than 100 K increase in the decomposition temperatures as well as the variation of the ΔH values of the samples.     

Synthesis of new chiral amines with a cyclic 1,2-diacetal skeleton derived from (2R, 3R)-(+)-tartaric acid

The syntheses of new chiral cyclic 1,2-diacetals from (2R, 3R)-( )-tartaric acid are described. C(2)-symmetrical diamines were prepared via direct amidation of the tartrate or from the corresponding bismesylate via reaction with sodium azide. For C1-symmetrical compounds, the Appel reaction was used to form the key intermediate, a monochlorocarbinol, from the diol. Some of the new chiral compounds, produced in good to high yields, may be potentially useful as asymmetric organocatalysts or as nitrogen and sulfur chelating ligands for asymmetric metal catalyzed reactions. Thus, a bis-N-methyl-methanamine derivative, used in substoichiometric amounts, was found to catalyze the enantioselective addition of cyclohexanone to (E)-beta-nitrostyrene with high diastereoselectivity (syn / anti = 92:8), albeit giving moderate optical purity (syn: 30 %).     

Estimate for index of hypersurfaces in spheres with null higher order mean curvature

In a recent paper (Barros, Sousa in: Kodai Math. J. 2009) the authors proved that closed oriented non-totally geodesic minimal hypersurfaces of the Euclidean unit sphere have index of stability greater than or equal to n + 3 with equality occurring at only Clifford tori provided their second fundamental forms A satisfy the pinching: |A|² ≥ n. The natural generalization for this pinching is ?(r + 2)S _r+2 ≥ (n ? r)S _r  > 0. Under this condition we shall extend such result for closed oriented hypersurface Σ ⁿ of the Euclidean unit sphere ${\mathbb{S}^{n+1}}$ with null S _r+1 mean curvature by showing that the index of r-stability, ${Ind_{\Sigma^n}^{r}}$ , also satisfies ${Ind_{\Sigma^n}^{r}\ge n+3}$ . Instead of the previous hypothesis if we consider ${\frac{S_{r+2}}{{S_r}}}$ constant we have the same conclusion. Moreover, we shall prove that, up to Clifford tori, closed oriented hypersurfaces ${\Sigma^{n}\subset \mathbb{S}^{n+1}}$ with S _r+1 = 0 and S _r+2 < 0 have index of r-stability greater than or equal to 2n + 5.