Upwind schemes and boundary conditions with applications to Euler equations in general geometries

A unified treatment of several upwind shock capturing algorithms is presented. Each algorithm has a Riemann initial value problem as its basis. The treatment of boundaries involves solving the associated Riemann initial-boundary value problem. The first author's algorithm, applied to multidimensional Euler equations in general geometries, is then presented. Its worth is verified by various calculations, which include Mach 8 supersonic flow past a circular cylinder.     

Nukleophile Additionen an Doppelbindungssysteme II. die Kinetik der Reaktion aromatischer Aldehyde mit Sulfit

The rate constants of the addition of sulfit to aromatic aldehydes have been measured directly atpH=7 using stopped flow and temperature jump methods.

Teil 1:Schreiber, B., Martinek, H., Wolschann, P., Schuster, P., J. Amer. Chem. Soc.101, 4708 (1979).     

Visibility in the plane

We find the size of the smallest subset of the set of integer lattice points, such that every element of a given rectangular grid is visible from our subset, which in particular answers a question of Paul Erd?s et al.     

Iterative Arylation of Amino Acids and Aliphatic Amines via δ‐C(sp3)−H Activation: Experimental and Computational Exploration

Directed C?H functionalization has been realized as a complementary tool to the traditional approaches for a straightforward access of non‐proteinogenic amino acids; albeit such a process is restricted mostly up to the γ‐position. In the present work, we demonstrate the diverse (hetero)arylation of amino acids and analogous aliphatic amines selectively at the remote δ‐position by tuning the reactivity controlled by ligands. An organopalladium δ‐C(sp³)?H activated intermediate has been isolated and crystallographically characterized. Mechanistic investigations carried out experimentally in conjunction with computational studies shed light on the difference in the mechanistic picture depending on the substrate structure.