Die Wirksamkeit der intramolekularen Neuverteilung der Schwingungsenergie in Modellsystemen: Chloracetylen

Ohne Zusammenfassung     

The Number of Hierarchical Orderings

An ordered set-partition (or preferential arrangement) of n labeled elements represents a single “hierarchy” these are enumerated by the ordered Bell numbers. In this note we determine the number of “hierarchical orderings” or “societies”, where the n elements are first partitioned into m ≤ n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the ordered Bell numbers are replaced by the composition numbers. If there is only a single hierarchy, we show that the average rank of an element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the unlabeled case. This revised version was published online in September 2006 with corrections to the Cover Date.     

New bounds on the number of unit spheres that can touch a unit sphere in n dimensions

New upper bounds are given for the maximum number, τ_n, of nonoverlapping unit spheres that can touch a unit sphere in n-dimensional Euclidean space, for n?24. In particular it is shown that τ₈ = 240 and τ₂₄ = 196560.     

Minimal-energy clusters of hard spheres

What is the tightest packing ofN equal nonoverlapping spheres, in the sense of having minimal energy, i.e., smallest second moment about the centroid? The putatively optimal arrangements are described forN≤32. A number of new and interesting polyhedra arise.     

Stereoretentive Reactions at the Anomeric Position: Synthesis of Selenoglycosides

Reported is the stereospecific cross‐coupling of anomeric stannanes with symmetrical diselenides, resulting in the synthesis of selenoglycosides with exclusive anomeric control. The reaction proceeds without the need for directing groups and is compatible with free hydroxy groups as demonstrated in the preparation of glycoconjugates derived from mono‐, di‐, and trisaccharides and peptides (35 examples). Given its generality and broad substrate scope, the glycosyl cross‐coupling method presented herein can find use in the synthesis of selenium‐containing glycomimetics and glycoconjugates.