Suzuki-Miyaura cross-coupling reaction catalyzed by Pd/MgLa mixed oxide

A new, reusable Pd/MgLa mixed oxide catalyst has been applied successfully in the Suzuki-Miyaura carbon-carbon cross-coupling reaction of aryl halides as well as benzylic bromide with boronic acids in ethanol. The catalyst is air stable, can be stored and handled under an ambient atmosphere and after the reaction it can be recovered by simple filtration and reused without significant loss of activity.     

On homomorphisms to acyclic local tournaments

A homomorphism of a digraph to another digraph is an edgepreserving vertex mapping. A local tournament is a digraph in which the inset as well as the outset of each vertex induces a tournament. Thus acyclic local tournaments generalize both directed paths and transitive tournaments. In both these cases there is a simple characterization of homomorphic preimages. Namely, if H is a directed path, or a transitive tournament, then G admits a homomorphism to H if and only if each oriented path which admits a homomorphism to G also admits a homomorphism to H. We prove that this result holds for all acyclic local tournaments. © 1995 John Wiley & Sons, Inc.     

Zur Erkennung terti?rer Alkohole

Ohne Zusammenfassung     

Numerical investigation of the elastic scattering of hydrogen (isotopes) and helium at graphite (0001) surfaces at beam energies of 1 to 4 eV using a split-step Fourier method

We report simulations of the elastic scattering of atomic hydrogen isotopes and helium beams from graphite (0001) surfaces in an energy range of 1–4 eV. To this aim, we numerically solve a time-dependent Schrödinger equation using a split-step Fourier method. The hydrogen- and helium-graphite potentials are derived from density functional theory calculations using a cluster model for the graphite surface. We observe that the elastic interaction of tritium and helium with graphite differs fundamentally. Whereas the wave packets in the helium beam are directed to the centers of the aromatic cycles constituting the hexagonal graphite lattice, they are directed toward the rings in case of the hydrogen beams. These observations emphasize the importance of swift chemical sputtering for the chemical erosion of graphite and provide a fundamental justification of the graphite peeling mechanism observed in molecular dynamics studies. Our investigations imply that wave packet studies, complementary to classical atomistic molecular dynamics simulations open another angle to the microscopic view on the physics underlying the sputtering of graphite exposed to hot plasma.     

A note on the star chromatic number

A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make some simple observations that lead to a purely combinatorial treatment. Our methods yield shorter proofs and offer further insight.