Modeling the competitive dissociation of protonated 2,3-butanedione. The enthalpy of formation of methylhydroxycarbene

The enthalpy of formation of methylhydroxycarbene, CH(3)COH, has been determined from measurements of the threshold energy for collision-induced dissociation of protonated 2,3-butanedione in a flowing afterglow-triple quadrupole mass spectrometer and found to be 16 +/- 4 kcal/mol, 57 +/- 4 kcal/mol higher than that of acetaldehyde. From the measured enthalpy of formation, the difference between the first and second C-H BDEs in ethanol is found to be 17 kcal/mol, which implies a singlet-triplet splitting of 28 kcal/mol in the carbene. The activation energies for loss of ketene and carbon monoxide from protonated butanedione are found to be 60 +/- 4 and 50 +/- 4 kcal/mol, respectively. On the basis of experimental and computational results, the loss of carbon monoxide is proposed to proceed through a tight transition state. Although calculations also suggest a tight transition state for loss of ketene, the experimental data indicate that it occurs via a loose transition state, possibly forming by proton transfer along the direct dissociation pathway.     

Die Struktur des Paucins

Zusammenfassung Beim Abbau von Paucin wird Brenzcatechin, Kaffeesäure und Putrescin erhalten. Daraus und aus spektroskopischen Befunden ergibt sich für das Paucin die Strukturformel3.

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The structure of Paucine

Paucine can be degradated to catechol, caffeic acid and putrescine. This together with spectroscopic data allows us to deduce formula3 for paucine.

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Mit 6 Abbildungen

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Meinem Lehrer, Prof. Dr.H. Bretschneider, zum 65. Geburtstag gewidmet.     

Incipience of quantum chaos in the spin-boson model

The peculiar spectral properties of the spinboson model make it suitable for an investigation of quantum nonintegrability effects and level statistics from a new perspective. For fixed spin quantum numbers, its energy spectrum consists of 2s+1 sequences of levels with no upper bound. These sequences are identified and labelled consecutively by means of a quantum invariant calculated from the time average of a non-stationary operator. For integrable cases, level repulsion (on the energy axis) is limited to states within each sequence. From the observed spectral properties, we infer a series ofs-dependent level-spacing distributions. They converge towards a Poisson distribution fors. For nonintegrable cases, level repulsion becomes a universal phenomenon, but the amount of repulsion between two states decreases with increasing separation (in label) of the two sequences to which they belong. For smalls, the quantum nonintegrability effects are compelling but not at all chaotic. Nevertheless, they contain all the ingredients necessary to produce the symptoms commonly described as indicators of quantum chaos. In this model, we can observe quantum chaos in the making under very controllable conditions.     

Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

A characterization ofL n(K) as a permutation group

In 1972 M. O'Nan proved thatL _n (q),h 3; can be characterized as a doubly-transitive groupG on a finite set , whereG _a has an Abelian normal subgroup acting not semi-regularly on -a. In the Main Theorem we show that a similar statement holds if is infinite. Our result implies O'Nan's theorem.This paper is part of the author's Ph.D. thesis written under supervision of Prof. F. G. Timmesfeld.     

On the verification of Clark's example of a euclidean but not norm-euclidean number field

In the preceding paper [2], D. Clark proved—modulo a finite amount of computation—that the ring of integersR of admits explicit euclidean algorithms, although it is not euclidean for the norm: In fact, every completely multiplicative function ϕ:R→R _>-0 which sends the prime elements above 23 to a value larger than 25 and which agrees with the absolute norm at all other primes defines a euclidean algorithm forR. The referee had felt that an independent verification of the computer-assisted proofs of Lemmas 1 and 2 of [2] was desirable, and that it should be carried out separately from the refereeing process in the light of the public, conforming to C. Lam's eloquent suggestions [3]. F. Lemmermeyer and the present author succeeded in confirming Clark's result (independently of each other). This note gives some details of the methods employed in the verifications.