Representations of free lattice-ordered groups

We show for any uncountable cardinal that the free groupG of rank has a linear right ordering on which the natural action of the free lattice-ordered groupF of rank is faithful and pathologically 2-transitive. As a consequence, we obtain results on the root system of prime subgroups ofF . This generalizes previous results of McCleary which required the generalized continuum hypothesis and to be regular.     

A minimal proteinlike lattice model: an alpha-helix motif

A simple protein model of a four-helix bundle motif on a face-centered cubic lattice has been studied. Total energy of a conformation includes attractive interactions between hydrophobic residues, repulsive interactions between hydrophobic and polar residues, and a potential that favors helical turns. Using replica exchange Monte Carlo simulations we have estimated a set of parameters for which the native structure is a global minimum of conformational energy. Then we have shown that all the above types of interactions are necessary to guarantee the cooperativity of folding transition and to satisfy the thermodynamic hypothesis.     

Aldolkondensation von Isobutyraldehyd mit Aceton in der Gasphase

Zusammenfassung Am Beispiel der Gasphasenaldolkondensation von Isobutyraldehyd mit Aceton wird gezeigt, daß gekreuzte Aldolreaktionen in der Gasphase selektiver verlaufen können. Unter Verwendung eines erst seit kurzem bekannten Katalysatorsystems mit Zinn auf Kieselgel und Wasserstoff als Trägergas zur dauernden Regenerierung des Zinns wurden Isobutyraldehyd und Aceton in einem Strömungsreaktor zu den drei Isomeren, 5-Methyl-3-hexen-2-on, 5-Methyl-4-hexen-2-on und 5-Methyl-5-hexen-2-on, umgesetzt, die zu Methylisopentylketon hydriert werden können. Diese Gasphasen-aldolkondensation erwies sich bei Optimierungsversuchen mit dem obengenannten Katalysator als stark temperaturabhängige Gleichgewichtsreaktion. Bei 350 °C und Normaldruck ließ sich die Ausbeute an Methylhexenon deshalb nicht über 17 Molprozent des eingesetzten Acetons steigern. Bei Acetonumsätzen zwischen 10% und 30% lag die darauf bezogene Ausbeute bei 60 bzw. 48 Molprozent. Die Raum—Zeit-Ausbeute erreicht 54 g·l^–1·h^–1.

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Vapor-phase aldol condensation between isobutyraldehyde and acetone

Crossed vapor-phase aldol condensations are highly selective as the condensation between isobutyraldehyde and acetone shows. Following a publication describing a catalyst system with tin on silica and hydrogen as carrier gas to regenerate the tin continuously, isobutyraldehyde and acetone were reacted to the three isomeres 5-methyl-3-hexen-2-one, 5-methyl-4-hexen-2-one, and 5-methyl-5-hexen-2-one, which can be hydrogenated to methyl isopentyl ketone. Experiments carried out with the catalyst mentioned above in order to optimise this vapor-phase aldol condensation showed that this condensation is a strong temperature depending equilibrium reaction. At a temperature of 350 °C and atmospheric pressure it was not possible to get a yield more than 17 molepercent of the acetone used. Conversion of acetone between 10% and 30% gave rise to yields of 60 and 48 molepercent respectively of the isomeric methylhexenones. The space time yield was 54 g·l^–1·h^–1.

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Mit 5 Abbildungen

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Herrn Prof.F. Asinger zum 65. Geburtstag gewidmet.     

Bis-Anthracene Fused Porphyrin as an Efficient Photocatalyst: Facile Synthesis and Visible-Light-Driven Oxidative Coupling of Amines

Development of high-performance photocatalysts for the conversion of amines is of great importance, but has remained a challenging task. Here, a bis-anthracene fused porphyrin ( AFP ) was synthesized in a high yield by a facile synthetic protocol, which involves a Suzuki coupling for the conjugation of two anthracene groups with a porphyrin ring, followed by oxidative cyclodehydrogenation. When serving as a photocatalyst, AFP exhibits an outstanding photocatalytic performance for the visible-light-induced aerobic oxidation of amines to imines at ambient conditions. Density functional theory calculations revealed that the low energy band gap, caused by the large planar and π-extended porphyrin structure of AFP , contributed to its high photocatalytic performance.     

Chiral bands in odd-odd nuclei with rigid or soft cores

Properties of chiral bands in an odd-odd nucleus, which is treated as a system of an even-even core and a pair of particles in the πh _11/2 ⊗ υh _11/2 ^-1 configuration, are calculated in the frame of the Core-Particle-Hole Coupling (CPHC) model with either a rigid triaxial or a soft core. The results of calculations for the two different cores are compared. The properties of the nucleus with the rigid, maximally triaxial ( γ = 30^°and with the entirely soft core are qualitatively very similar.     

Absolute E3 and M2 transition probabilities for the electromagnetic decay of the \mathrm{\ensuremath I^{\pi}=K^{\pi}=8^{-}} isomeric state in 132Ce

The decay of the $\ensuremath I^{\pi}=K^{\pi}=8^{-}$ isomeric state at 2340keV in ¹³²Ce has been investigated in the ¹²⁰Sn(¹⁶O, 4n)¹³²Ce reaction. The measurements were carried out in e - $ \gamma$ and $ \gamma$ - $ \gamma$ coincidence modes using an electron spectrometer coupled to the OSIRIS II gamma-ray array at the Heavy Ion Laboratory of the University of Warsaw. Experimentally obtained internal conversion coefficients for the $\ensuremath 8^{-} \rightarrow 6^{+}$ and $\ensuremath 8^{-} \rightarrow 5^{+}$ transitions allowed the multipolarities, mixing ratios, reduced transition probabilities and hindrance factors to be determined.     

From Petri Nets to Automata with Concurrency

Automata with concurrency relations are labelled transition systems with a collection of state-dependent binary independence relations for the actions. We show how to associate with each Petri net (place/transition net) such an automaton having the same dynamic behaviour. We characterize the automata arising in this way, and with suitable notions of morphisms for Petri nets and for automata with concurrency relations we extend this correspondence to a coreflection between the associated categories. As a consequence, we derive that these categories have products and conditional coproducts.