Fluoroalkyl Radical Generation by Homolytic Bond Dissociation in Pentacarbonylmanganese Derivatives

Thermal decarbonylation of the acyl compounds [Mn(CO)₅(COR_F)] (R_F=CF₃, CHF₂, CH₂CF₃, CF₂CH₃) yielded the corresponding alkyl derivatives [Mn(CO)₅(R_F)], some of which have not been previously reported. The compounds were fully characterized by analytical and spectroscopic methods and by several single-crystal X-ray diffraction studies. The solution-phase IR characterization in the CO stretching region, with the assistance of DFT calculations, has allowed the assignment of several weak bands to vibrations of the [Mn(¹²CO)₄(eq-¹³CO)(R_F)] and [Mn(¹²CO)₄(ax-¹³CO)(R_F)] isotopomers and a ranking of the R_F donor power in the order CF₃<CHF₂<CH₂CF₃≈CF₂CH₃. The homolytic Mn−R_F bond cleavage in [Mn(CO)₅(R_F)] at various temperatures under saturation conditions with trapping of the generated R_F radicals by excess tris(trimethylsilyl)silane yielded activation parameters ΔH^≠ and ΔS^≠ that are believed to represent close estimates of the homolytic bond dissociation thermodynamic parameters. These values are in close agreement with those calculated in a recent DFT study (J. Organomet. Chem. 2018 , 864, 12–18). The ability of these complexes to undergo homolytic Mn−R_F bond cleavage was further demonstrated by the observation that [Mn(CO)₅(CF₃)] (the compound with the strongest Mn−R_F bond) initiated the radical polymerization of vinylidene fluoride (CH₂=CF₂) to produce poly(vinylidene fluoride) in good yields by either thermal (100 °C) or photochemical (UV or visible light) activation.     

Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.     

Fundamental groups of the complements of certain plane non-tame torus sextics

The moduli space of torus sextics with the configuration of singularities {A₂+A₅+2E₆} has two connected components. We compute the fundamental groups π₁(CP²−C) for sextics C in both components and study their differences.     

A counter-example to the characterization of the discontinuous value function of control problems with reflectionUn contre-exemple à la caractérisation de la fonction-valeur discontinue d'un problème de contrôle réfléchi

We consider a finite horizon deterministic optimal control problem with reflection. The final cost is assumed to be merely a locally bounded function which leads to a discontinuous value function. We address the question of the characterization of the value function as the unique solution of an Hamilton–Jacobi equation with Neumann boundary conditions. We follow the discontinuous approach developed by Barles and Perthame for problems set in the whole space. We prove that the minimal and maximal discontinuous viscosity solutions of the associated Hamilton–Jacobi can be written in terms of value functions of control problems with reflection. Nethertheless, we construct a counter-example showing that the value function is not the unique solution of the equation. To cite this article: O. Ley, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 469–473.     

Structures de Hodge mixtes et faisceaux réflexifs semistablesMixed Hodge structures and semistable reflexive sheaves

Let X be a smooth projective variety over an algebraically closed field of characteristic 0. We prove that the category of μ-semistable reflexive sheaves of slope μ equivariant for the action of some group on X is Abelian. The same claim for $\text{X=}\text{P}{}^2{}_{\mathrm{<mtext>C</mtext>}}$ and a stronger semistability condition gives us a geometric proof of the fact that the category of mixed Hodge structures is Abelian. To cite this article: O. Penacchio, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 475–480.     

Automorphismes des courbes modulaires X(n) en caractéristique p

 We prove that the group of automorphisms of the modular curve prime, in characteristic when the curve is ordinary is always when and a simple group when p = 2 or 3. In the non-ordinary cases we give informations about the ramification of and describe when q = 7,11 and 13 for all . Received: 12 October 2001 / Revised version: 29 April 2002     

On the non existence of monotone linear schema for some linear parabolic equations

In this Note, we present a result concerning the non existence of linear monotone schema with fixed stencil on regular meshes for some linear parabolic equation in two dimensions. The parabolic equations of interest arise from non isotropic diffusion modelling. A corollary is that no linear monotone 9 points-schemes can be designed for the one-dimensional heat equation emerged in the plane with an arbitrary direction of diffusion. Some applications of this result are provided: for the Fokker–Planck–Lorentz model for electrons in the context of plasma physics; all linear monotone scheme for the one-dimensional hyperbolic heat equation treated as a two-dimensional problem are not consistent in the diffusion limit for an arbitrary direction of propagation. We also examine the case of the Landau equation. To cite this article: C. Buet, S. Cordier, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Optimal mappings with minimum number of connected components in tree-to-tree comparison problems

In this paper we consider the problem of finding a minimum cost mapping between two unordered trees which induces a graph with a minimum number of connected components. The proposed algorithm is based on the generalization of an algorithm for computing an edit distance between trees, and it solves the stated problem in sequential time precisely in O(|T₁|×|T₂|×(degT₁+degT₂)×log₂(degT₁+degT₂)).