Postfunctionalization of poly(propargyl methacrylate) using copper catalyzed 1,3‐dipolar Huisgen cycloaddition: An easy route to electro‐optic materials

A one‐pot synthetic route based on copper‐catalyzed Huisgen reaction has been developed to functionalize a methacrylate propargylic polymer with azido‐substituted moieties. This procedure was used for the preparation of electro‐optic materials containing well‐known Disperse Red One (DR1) chromophores along with bulky adamantyl moieties (Adam). The postfunctionalization of the propargylic polymer was successfully achieved using different molar ratios of DR1/Adam. These novel polymers exhibit high glass transition temperature owing to the rigid structure of adamantyl units. Moreover, the second harmonic generation measurements demonstrated the effectiveness of adamantyl groups to act as insulating shield limiting thus the electrostatic interactions between chromophores. Indeed, higher optimal chromophore concentration (50 mol %) than in conventional DR1‐containing polymers (30 mol %) allowed us to increase the d₃₃ coefficient up to 92 pm/V. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5652–5660, 2009     

Enantioselective alkylidenecyclopropanation of norbornenes with terminal alkynes catalyzed by palladium–phosphinous acid complexes

Pd(II)-coordinated phosphinous acids catalyzed the formal enantioselective [2+1] cycloaddition of norbornene derivatives with terminal alkynes. The absolute configuration of (+)-3aa was assigned using VCD.     

Automorphy for some l-adic lifts of automorphic mod l Galois representations

We extend the methods of Wiles and of Taylor and Wiles from GL₂ to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL₂. Following Wiles’ method we show that this conjecture implies that our automorphy lifting theorem could be extended to cover lifts that are not minimally ramified.     

Entire vectors and time reversible Cauchy problems

Our major aim in this paper is to show the algebraic and topological equivalence between the set of all entire vectors ε(A) for a linear operatorA and the solution space of the corresponding abstract Cauchy problem, when—A is the generator of a strongly continuous holomorphic semigroup.     

A unique and highly remarkable boron Trifluoride catalyzed rearrangement Of 2,2-di-t-butyloxirane into 2,2,3,3,4,4-hexamethyltetrahydrofuran

-The boron trifluoride catalyzed rearrangement of 2,2-di-t-butyloxirane, involving competitive reactions of transient carbenium ions, could be selectively directed towards either 2,2,3,3,4,4- hexamethyltetrahydrofuran or 2-t-butyl-2,3-dimethyl-3-buten-1-ol. Hydride shift to afford 2,2-di-t-butylacetaldehyde was only observed to a minor extent.     

Weighted fusion graphs: Merging properties and watersheds

This paper deals with the mathematical properties of watersheds in weighted graphs linked to region merging methods, as used in image analysis.In a graph, a cleft (or a binary watershed) is a set of vertices that cannot be reduced, by point removal, without changing the number of regions (connected components) of its complement. To obtain a watershed adapted to morphological region merging, it has been shown that one has to use the topological thinnings introduced by M. Couprie and G. Bertrand. Unfortunately, topological thinnings do not always produce thin clefts.Therefore, we introduce a new transformation on vertex weighted graphs, called C-watershed, that always produces a cleft. We present the class of perfect fusion graphs, for which any two neighboring regions can be merged, while preserving all other regions, by removing from the cleft the points adjacent to both. An important theorem of this paper states that, on these graphs, the C-watersheds are topological thinnings and the corresponding divides are thin clefts. We propose a linear-time immersion-like algorithm to compute C-watersheds on perfect fusion graphs, whereas, in general, a linear-time topological thinning algorithm does not exist. Furthermore, we prove that this algorithm is monotone in the sense that the vertices are processed in increasing order of weight. Finally, we derive some characterizations of perfect fusion graphs based on the thinness properties of both C-watersheds and topological watersheds.