51 research outputs found

    Gromov-Hausdorff-like distance function defined in the aspect of Riemannian submanifold theory

    Full text link
    In this paper, we discuss how a Gromov-Hausdorff-like distance function over the space of all isometric classes of compact CkC^k-Riemannian manifolds should be defined in the aspect of the Riemannan submanifold theory, where k≥1k\geq 1. The most important fact in this discussion is as follows. The Hausdorff distance function between two spheres of mutually distinct radii isometrically embedded into the hypebolic space of curvature cc converges to zero as c→−∞c\to-\infty. The key in the construction of the Gromov-Hausdorff-like distance function given in this paper is to define the distance of two Ck+1C^{k+1}-isometric embeddings of distinct compact CkC^k-Riemannian manifolds into a higher dimensional Riemannian manifold by using the Hausdorff distance function in the tangent bundle of order k+1k+1 equipped with the Sasaki metric. Furthermore, we show that the convergence of a sequence of compact Riemannian manifolds with respect to this distance function coincides with the convergence in the sense of R. S. Hamilton.Comment: 14 page

    The reaction of peroxy radicals with OH radicals

    No full text
    International audienc

    Rate Constants and Branching Ratios for the Self-Reaction of Acetyl Peroxy (CH3C(O)O2•) and Its Reaction with CH3O2

    No full text
    The self-reaction of acetylperoxy radicals (CH3C(O)O2•) (R1) as well as their reaction with methyl peroxy radicals (CH3O2•) (R2) have been studied using laser photolysis coupled to a selective time resolved detection of three different radicals by cw-CRDS in the near-infrared range: CH3C(O)O2• was detected in the Ã-X˜ electronic transition at 6497.94 cm−1, HO2• was detected in the 2ν1 vibrational overtone at 6638.2 cm−1, and CH3O2• radicals were detected in the Ã-X˜ electronic transition at 7489.16 cm−1. Pulsed photolysis of different precursors at different wavelengths, always in the presence of O2, was used to generate CH3C(O)O2• and CH3O2• radicals: acetaldehyde (CH3CHO/Cl2 mixture or biacetyle (CH3C(O)C(O)CH3) at 351 nm, and acetone (CH3C(O)CH3) or CH3C(O)C(O)CH3 at 248 nm. From photolysis experiments using CH3C(O)C(O)CH3 or CH3C(O)CH3 as precursor, the rate constant for the self-reaction was found with k1 = (1.3 ± 0.3) × 10−11 cm3s−1, in good agreement with current recommendations, while the rate constant for the cross reaction with CH3O2• was found to be k2 = (2.0 ± 0.4) × 10−11 cm3s−1, which is nearly two times faster than current recommendations. The branching ratio of (R2) towards the radical products was found at 0.67, compared with 0.9 for the currently recommended value. Using the reaction of Cl•-atoms with CH3CHO as precursor resulted in radical profiles that were not reproducible by the model: secondary chemistry possibly involving Cl• or Cl2 might occur, but could not be identified
    • …