Einwirkung von Schwefel und Ammoniak auf Methyl-neopentylketon

Zusammenfassung Bei der Einwirkung von Schwefel und Ammoniak auf Methylneopentylketon in Pyridin bei Raumtemp. bilden sich die beiden theoretisch möglichen Thiazoline-³, das 2,4-Dimethyl-2-neopentyl-5-tert. butyl-thiazolin-³ und das 2-Methyl-2,4-di-neopentyl-thiazolin-³ (etwa im Verhältnis 793). Daneben entsteht 2-Methyl-2,4-dineopentyl-imidazolin-³. Die Darstellung und Charakterisierung der sich vom Methylneopentylketon ableitenden reinen isomeren -Brom- bzw. -Mercaptoketone sowie einiger daraus synthetisierter Thiazoline-³ bzw. Thiazole wird beschrieben.Für Korrespondenz ist diese Adresse zu verwenden.49. Mitt.:F. Asinger, W. Schäfer undA. Saus, Mh. Chem.96, 1278 (1965).Teil der DissertationF. Gentz, Techn. Univ. Dresden 1963.     

The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature

We investigate the limiting fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks with finitely many patterns at the critical temperature 1/β _c = 1. At the critical temperature, the measure-valued random variables given by the distribution of the appropriately scaled order parameter under the Gibbs measure converge weakly towards a random measure which is non-Gaussian in the sense that it is not given by a Dirac measure concentrated in a Gaussian distribution. This remains true in the case of β = β _N →β _c = 1 as N→∞ provided β _N converges to β _c = 1 fast enough, i.e., at speed ?(1/). The limiting distribution is explicitly given by its (random) density. Received: 12 May 1998 / Revised version: 14 October 1998     

Pathwise description of dynamic pitchfork bifurcations with additive noise

 The slow drift (with speed ɛ) of a parameter through a pitchfork bifurcation point, known as the dynamic pitchfork bifurcation, is characterized by a significant delay of the transition from the unstable to the stable state. We describe the effect of an additive noise, of intensity σ, by giving precise estimates on the behaviour of the individual paths. We show that until time after the bifurcation, the paths are concentrated in a region of size around the bifurcating equilibrium. With high probability, they leave a neighbourhood of this equilibrium during a time interval , after which they are likely to stay close to the corresponding deterministic solution. We derive exponentially small upper bounds for the probability of the sets of exceptional paths, with explicit values for the exponents. Received: 7 August 2000 / Revised version: 19 April 2001 / Published online: 20 December 2001     

Distributed data processing in NMR spectroscopy

The development and use of a communication system for the chemical laboratory is described. It provides local access to instruments, computers and personal work stations (PC) as well as connection to wide area networks via the X.25 standard protocol and respective gateways on the basis of the DFN services (Deutsches Forschungsnetz) dialog, remote job entry, file transfer and message handling (EAN X.400). The standardization of digital spectra is considered.     

Hunting French ducks in a noisy environment

We consider the effect of Gaussian white noise on fast–slow dynamical systems with one fast and two slow variables, containing a folded node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting of alternating large- and small-amplitude oscillations. We quantify the effect of noise and obtain critical noise intensities beyond which the small-amplitude oscillations become hidden by fluctuations. Furthermore we prove that the noise can cause sample paths to jump away from so-called canard solutions with high probability before deterministic orbits do. This early-jump mechanism can drastically influence the local and global dynamics of the system by changing the mixed-mode patterns.