Crassiflorone, a new naphthoquinone from Diospyros crassiflora (Hien)

A new naphthoquinone, 11-hydroxy-1,9-dimethyl-6H-naphtho[2′,3′:4,5]furo[3,2-c]chromene-6,7,12-trione, named crassiflorone, was isolated from the stem bark of Diospyros crassiflora together with the known compounds plumbagin, cyclocanaliculatin, gerberinol, lupeol, lupenone and betulinic acid. The structures of the compounds were established on the basis of 1D and 2D NMR spectroscopic data, as well as co-TLC with authentic samples. Some of the above compounds exhibited significant antimicrobial activity against bacteria and yeasts.     

Different aspects of a random fragmentation model

This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random fragmentation processes.     

Quinone transfer radical polymerization (QTRP) of styrene: Catalysis by different metal complexes

Styrene has been polymerized by a Quinone Transfer Radical Polymerization (QTRP) based on the redox reaction of an ortho‐quinone and a metal catalyst. Several metal acetylacetonates have been tested in this work. The radical polymerization of styrene is largely controlled when phenanthrenequinone (PhQ) is used with catalytic amounts of Co(acac)₂, Ni(acac)₂, Mn(acac)_{2 or 3}, and Al(acac)₃. As a rule, in the presence of all these metallic complexes, the polystyrene molar mass increases with the monomer conversion, and polydispersity (M_w/M_n) is in the 1.3–1.6 range (at least until 40% monomer conversion). Styrene polymerization has also been resumed by polystyrene chains prepared by QTRP. In the specific case of manganese acetylacetonates, an amine or phosphine ligand has to be added for the control to be effective. Finally, two mechanistic hypotheses have been proposed, depending on whether the oxidation state of the metal can be easily changed or not. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2723‐2733, 2005     

Pathwidth of outerplanar graphs

We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected outerplanar graph is at most c plus the pathwidth of its dual. They also conjectured that this was actually true with c being one for every biconnected planar graph. Fomin [10] proved that the second conjecture is true for all planar triangulations. First, we construct for each p ≥ 1, a biconnected outerplanar graph of pathwidth 2p + 1 whose (geometric) dual has pathwidth p + 1, thereby disproving both conjectures. Next, we also disprove two other conjectures (one of Bodlaender and Fomin [3], implied by one of Fomin [10]. Finally we prove, in an algorithmic way, that the pathwidth of every biconnected outerplanar graph is at most twice the pathwidth of its (geometric) dual minus one. A tight interval for the studied relation is therefore obtained, and we show that all cases in the interval happen. © 2006 Wiley Periodicals, Inc. J Graph Theory 55: 27–41, 2007     

Boundary estimates for elliptic systems with L<Superscript>1</Superscript>–data

We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions and L ¹–data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div–curl and Hodge systems.