High-speed heck reactions in ionic liquid with controlled microwave heating

Palladium-catalyzed Heck arylations in the polar and robust ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate (bmimPF(6)), have for the first time been accomplished under microwave irradiation. The couplings were efficiently performed in sealed tubes within 5-45 min of heating. Without significant reductions in yield, a phosphine-free ionic catalyst phase could be recycled in five successive 20 min reactions at 180 degrees C. The product was easily removed from the reaction medium by distillation.     

Poly(ethylene-co-butylene) functionalized multi walled carbon nanotubes applied in polypropylene nanocomposites

A novel functionalized multi walled carbon nanotube (MWCNT) was prepared through grafting with α-azido-poly(ethylene-co-butylene) (PEB-N₃). The PEB-N₃ was prepared through a two step procedure and grafted onto an industrial grade multi walled carbon nanotube (MWCNT) through a highly efficient nitrene addition. This novel nano filler was melt mixed into polypropylene (PP) and the composite was characterized by FT-IR spectroscopy, Raman spectroscopy, Scanning Electron Microscopy (SEM), Rheology and Dielectric Relaxation Spectroscopy (DRS). The analyses showed that composites with the novel filler had a high degree of discharge from the surface and higher conductivity compared to the pristine filler, illustrating an efficient conductive network in the composites. The composites showed low percolation thresholds of 0.3 wt.% (0.15 vol.%) as well as improved stability at a range of temperatures from 25–135 °C.     

Photo-stability of photo-cured organic coatings: Part III—Photo-degradation of organic coatings photo-cured with alkoxyacetophenone and hydroxy alkylacetophenone photo-initiators

Photo-degradation studies of polystyrene (as model) and coating resins were made with three different photo-fragmenting initiators: 2,2-dimethoxy-2-phenylacetophenone, 1-[4-(2-propyl)-phenyl]-2-hydroxy-2-methyl-propanone-1 and 1-benzoyl-1-hydroxy-cyclohexane. Addition of the initiators to a benzene solution of polystyrene gave a rapid decrease in molecular weight when the solutions were uv irradiated. The degradation rate was increased by the presence of oxygen. Irradiation of polystyrene films, containing the same initiators, showed similar effects. In addition, the polymer became partially crosslinked. Addition of a free radical scavenger decreased the degradation rate. Both photo-oxidation rate and yellowing rate were affected by the concentration and the reactivity of the radicals. Photo-oxidation during photo-curing of a coating occurs in a thin surface layer. This is due to a combination of free radicals formed by the uv irradiation and the oxygen present. Oxidation during the photo-curing of a urethane resin corresponds to more than 50% of the total surface oxidation measured with ESCA.     

The number of pancyclic arcs in a k‐strong tournament

A tournament is a digraph, where there is precisely one arc between every pair of distinct vertices. An arc is pancyclic in a digraph D, if it belongs to a cycle of length l, for all 3 ≤ l ≤ |V (D) |. Let p(D) denote the number of pancyclic arcs in a digraph D and let h(D) denote the maximum number of pancyclic arcs belonging to the same Hamilton cycle of D. Note that p(D) ≥ h(D). Moon showed that h(T) ≥ 3 for all strong non‐trivial tournaments, T, and Havet showed that h(T) ≥ 5 for all 2‐strong tournaments T. We will show that if T is a k‐strong tournament, with k ≥ 2, then p(T) ≥ 1/2, nk and h(T) ≥ (k + 5)/2. This solves a conjecture by Havet, stating that there exists a constant α_k, such that p(T) ≥ α_k n, for all k‐strong tournaments, T, with k ≥ 2. Furthermore, the second results gives support for the conjecture h(T) ≥ 2k + 1, which was also stated by Havet. The previously best‐known bounds when k ≥ 2 were p(T) ≥ 2k + 3 and h(T) ≥ 5. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Finding cheapest cycles in vertex-weighted quasi-transitive and extended semicomplete digraphs

We consider the problem of finding a minimum cost cycle in a digraph with real-valued costs on the vertices. This problem generalizes the problem of finding a longest cycle and hence is NP-hard for general digraphs. We prove that the problem is solvable in polynomial time for extended semicomplete digraphs and for quasi-transitive digraphs, thereby generalizing a number of previous results on these classes. As a byproduct of our method we develop polynomial algorithms for the following problem: Given a quasi-transitive digraph D with real-valued vertex costs, find, for each j=1,2,…,|V(D)|, j disjoint paths P₁,P₂,…,P_j such that the total cost of these paths is minimum among all collections of j disjoint paths in D.     

Deformation of slow liquid and solid clusters upon deposition: A molecular-dynamics study of Al cluster impact on an Al surface

Using molecular-dynamics simulation, we investigate the self-deposition of Al_n clusters (n < 4000) on an Al substrate at velocities below the velocity of sound. Both cold crystalline and hot liquid clusters are studied. We examine the cluster deformation after impact on the surface, which we quantify by its height and base radius. At a given cluster velocity, the shape of deposited crystalline clusters is rather independent of the cluster size; only at small cluster sizes, n ? 40, the clusters are less strongly deformed. With increasing cluster size, liquid clusters are more strongly deformed than crystalline clusters. Faster projectiles become more strongly flattened by the deposition process. Even clusters depositing with vanishing velocity show a finite deformation, which is considerable for smaller clusters. At large cluster speed, clusters penetrate deeper into the (1 0 0) surface than into the (1 1 1) surface and also deform more strongly.     

When the greedy algorithm fails

We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in an independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection problem. The practical message of this paper is that the greedy algorithm should be used with great care, since for many optimization problems its usage seems impractical even for generating a starting solution (that will be improved by a local search or another heuristic).