A sharp Sobolev inequality on Riemannian manifoldsUne inégalité de Sobolev optimale sur les varietés riemanniennes

We outline our results in [11] concerning some sharp Sobolev inequalities on Riemannian manifolds. Our inequalities emphasize the role of scalar curvature in this context. To cite this article: Y.Y. Li, T. Ricciardi, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 519–524.     

A polymorph of tetrakis(acetonitrile‐κN)copper(I) tetrafluoridoborate

A P2₁2₁2₁ polymorph of the title compound, [Cu(CH₃CN)₄]BF₄, is reported. The crystal structure is very similar to the structure of the Pna2₁ polymorph reported by Jones & Crespo [Acta Cryst. (1998), C 54 , 18–20]. The anions and one of the three independent cations occupy similar positions in both polymorphs. Two of the four symmetry‐related positions of the other two cations are also identical in the two polymorphs, and the other two positions are related by mirror symmetry. The crystal used for the structure determination contained a volume fraction of 0.088 (7) of the Pna2₁ polymorph.     

Kinetic and electrochemical study of nitrile adducts of tetrachloro-bis (1,2-bis(diphenylphosphine)methane)dirhenium(II)

Summary The addition of two nitrile ligands to the complex Re₂Cl₄-(dppm)₂ (dppm= 1,2-bis(diphenylphosphine)methane)in CH₂Cl₂ solution has been investigated electrochemically. Upon addition of one equivalent of nitrile NCR (R = aromatic or aliphatic group) to the CH₂Cl₂/0.1m tetra-N-butylammonium hexafluorophosphate (TBAH) solution, Re₂Cl₄(dppm)₂(NCR) is formed immediately, without dissociation of chloride; electrochemical investigation indicates this nitrile addition is reversible upon oxidation of the dirhenium complex. On addition of two or more equivalents of nitrile, a slow ligand substitution takes place with addition of a second nitrile and concomitant loss of a chloride ion to form [Re₂Cl₃-(dppm)₂(NCR)₂]⁺. The rate of addition of nitrile to Re₂Cl₄(dppm)₂(NCR) appears to depend on the electrondonating or electron-withdrawing abilities of the ligand. The change from monoadduct to diadduct was followed with differential pulse voltammetry for various concentrations of added nitrile. The addition was found to be first order in nitrile.