An Asymptotic Independence Theorem for the Number of Matchings in Graphs

Let z(G) be the number of matchings (independent edge subsets) of a graph G. For a set M of edges and/or vertices, the ratio represents the probability that a randomly picked matching of G does not contain an edge or cover a vertex that is an element of M. We provide estimates for the quotient , depending on the sizes of the disjoint sets A and B, their distance and the maximum degree of the underlying graph G. It turns out that this ratio approaches 1 as the distance of A and B tends to ∞, provided that the size of A and B and the maximum degree are bounded, showing asymptotic independence. We also provide an application of this theorem to an asymptotic enumeration problem related to the dimer-monomer model from statistical physics. This material is based upon work supported by the German Research Foundation DFG under grant number 445 SUA-113/25/0-1 and the South African National Research Foundation under grant number 65972.     

Surface and contact properties of GaN produced from GaAs

Samples of some thickness and extent showed fine cracks on the brink already after oxidization in Ga₂O₃ which became more distinctive after nitriding into GaN. Current-voltage characteristics were recorded from different long nitrided samples with contacts of In, Sn, Sb, and Te. The long nitrided samples had a lower resistance. Some of the samples showed hysteresis effects with characteristics similar to varistors.     

Phosphonic systems. Part 15. Addition of diethyl prop-2-enylphosphonate to aldehydes: Fragmentation vs. isomerization of kinetic products

Lithiated diethyl prop-2-enylphosphonate adds to an aliphatic or an aromatic aldehyde, yielding a diastereomeric mixture of the kinetically controlled α-adduct. Upon warming, these adducts decompose back to starting materials to give finally the thermodynamically controlled γ-adducts, or undergo fragmentation to diethyl phosphate and (E) dienes. The distribution of the first product between these two pathways is a function of the aldehyde (aromatic vs. aliphatic) and of steric interactions operating within the two diastereomers of the adduct.     

Organische Chemie 2002

Die enantioselektive Synthese bleibt zentrales Thema in metallorganischen, metallfreien and bioorganischen Transformationen sowie in der industriellen organischen Chemie. Glanzpunkte zielmolekülorientierter Synthesechemie waren ein Zugang zu C₆₀, die Route zum Diazonamid A und die Totalsynthese von Vinblastin. Mit „Pyrrolysin”︁ wurde die 22. proteinogene Aminosäure entdeckt. Trotz der immer höheren Zahl an Testsubstanzen besteht in der medizinischen Chemie ein Engpass an klinisch erfolgreichen Wirkstoffen.