The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

Reversible polymerization of novel monomers bearing furan and plant oil moieties: a double click exploitation of renewable resources

Monomers based on plant oil derivatives bearing furan heterocycles appended through thiol-ene click chemistry were prepared and, subsequently, polymerized via a second type of click reaction, i. e. the Diels-Alder (DA) polycondensation between furan and maleimide complementary moieties. Two basic approaches were considered for these DA polymerizations, namely (i) the use of monomers with two terminal furan rings in conjunction with bismaleimides (AA + BB systems) and (ii) the use of a protected AB monomer incorporating both furan and maleimide end groups. This study clearly showed that both strategies were successful, albeit with different outcomes, in terms of the nature of the ensuing products. The application of the retro-DA reaction to these polymers confirmed their thermoreversible character, i. e. the clean-cut return to their respective starting monomers, opening the way to original macromolecular materials with interesting applications, like mendability and recyclability.