Lefschetz pencil structures for 2-calibrated manifolds

We prove that for closed 2-calibrated manifolds there always exist Lefschetz pencil structures. This generalizes similar results for symplectic and contact manifolds. To cite this article: A. Ibort, D. Marti´nez Torres, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

The Impact of the New Earth Gravity Models on the Measurement of the Lense–Thirring Effect

We examine how the new forthcoming Earth gravity models from the CHAMP and, especially, GRACE missions could improve the measurement of the general relativistic Lense–Thirring effect according to the various kinds of observables which could be adopted. In a very preliminary way, we use the first recently released EIGEN2 CHAMP–only and GGM01C GRACE–based Earth gravity models in order to assess the impact of the mismodelling in the even zonal harmonic coefficients of geopotential which represents one of the major sources of systematic errors in this kind of measurement. However, discretion is advised on evaluating the reliability of these results because the Earth gravity models used here, especially EIGEN2, are still very preliminary and more extensive calibration tests must be performed. According to the GGM01C model, the systematic error due to the unmodelled even zonal harmonics of geopotential amounts to 2% for the combination of the nodes of LAGEOS and LAGEOS II and the Perigee of LAGEOS II used up to now by Ciufolini and coworkers in the currently performed LAGEOS-LAGEOS II Lense-Thirring experiment, and to 14% for a combination explicitly presented here which involves the nodes only of LAGEOS and LAGEOS II.     

Reaction of halogenated hydrocarbon solvents with tertiary amines: Spectrophotometric and conductimetric study

Halogenated hydrocarbon solvents, SolvCl, (dichloromethane, chloroform, and 1,2‐dichloroethane) react with various types of tertiary amines, A, such as tri‐n‐buthylamine, tropane derivatives (tropine and atropine) and quinine generating a quaternary ammonium salt, N‐halogenalkylammonium chloride (SolvA⁺Cl^?). Some tertiary amines, as well as secondary and primary amines, cannot react with these solvents. This reaction has been detected and studied by both conductivity and visible spectrophotometry measures—the latter after adding a small quantity of a dye, such as bromocresol green (BCGH₂), bromophenol blue (BPBH₂), or tetrabromophenolphthaleinethyl ester (TBPEH). Both study methods permit the determination of the kinetic parameters, and they are in good agreement. The monoprotic TBPEH is the dye of the simplest mechanism, useful to study kinetics of amines of uncertain behavior as quinine, while BPBH₂ is the best dye for quantitative determinations. Kinetics for this reaction are of first order for both amine, A, and solvent, SolvCl; activation energy, E_a, and frequency factor are also determined. Rate constants increase with the amine basicity and with a reduction in the number of the halogen atoms present in the solvent. This reaction is slow but not negligible and must be considered a side reaction of these universally used solvents. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36:500–509, 2004     

Synthesis and properties of a new class of nitrogen-rich multinuclear[m.n] ferrocenophanes

The synthesis of the first tetraaza[3,3]ferrocenophane, from the previously unreported 1,1'-bis(triphenylphosphoranylidenamino)ferrocene and its conversion into a nitrogen-rich [2,2]bis[3,3]ferrocenophane is described. The electronic behaviour of these multinuclear ferrocenophanes indicates a strong electronic coupling between the iron centers.     

2,6-Bis[(o-hydroxy)phenyliminomethyl]-1-hydroxybenzene as a reagent for the selective spectrofluorimetric determination of aluminium

A spectrofluorimetric method for the determination of aluminium at ng/ml level has been developed. The method is based on the formation of a fluorescent 11 complex between Al(III) and 2,6-bis[(o-hydroxy)phenyliminomethyl]-1-hydroxybenzene at an apparent pH of 5.0 in an aqueous-ethanol medium (70% v/v ethanol). The influence of reaction variables is discussed. The range of concentration of the method is 1.0–10.0 ng/ml aluminium, the relative standard deviation 1.5% and the limit of detection 0.1 ng/ml. The advantages of the proposed method include high sensitivity and selectivity. The method has been applied to the determination of aluminium in natural waters.     

Extended partial geometries with minimal μ

Recently Fisher and Hobart extended the original work of Buekenhout and Hubaut on extended generalized quadrangles with a certain minimal value (minimal ) for the nonempty residue intersections. We show that there is another minimal which is sometimes better than the earlier one, and we extend all this to the case of extended partial geometries. We examine especially the triangular case, and find only a few new possibilities, which we are unable to settle, although some of these look extremely interesting.