5,6-Dimethoxy- und [4,5,6-Trimethoxy-benzo[b]-thienyl-(3)]-acylamine

Zusammenfassung Umsetzung von 5,6-Dimethoxy- und [4,5,6-Trimethoxy-benzo[b]thienyl-(3)]-essigsäure mit PCl₅ lieferte die methoxysubstituierten [Benzo[b]thienyl-(3)]-essigsäurechloride, die mit sekundären Aminen zu den entsprechenden Amiden reagierten.Die homologen Verbindungen mit einer C₃-Brücke wurden durchArndt-Eistert-Reaktion des Diazomethylketons in Gegenwart der entsprechenden sekundären Amine erhalten.

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Reaction of 5.6-dimethoxy- and [4.5.6-trimethoxybenzo[b]-thienyl-(3)]-acetic acid with PCl₅ gave the methoxy-substituted [benzo[b]thienyl-(3)]-acetic acid chlorides, which reacted with secondary amines to the corresponding amides.The homologous compounds with a C₃-bridge were synthesized viaArndt-Eistert reaction of the diazomethyl ketone in presence of the corresponding secondary amines.

     

Local products for relativistic quantum fields

A definition of local functions of generalized free fields is suggested. Their concrete form is determined in a fairly general setting by analysing realizations of locality. A huge class of new models of relativistic quantum fields results in this way.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Semiclassical Topological Flat Laguerre Planes Obtained by Pasting Along A Circle

A new rather large family of locally compact 2-dimensional topological Laguerre planes is introduced here. This family consists exactly of those Laguerre planes which can be obtained by pasting together two halves of the classical real Laguerre plane along a circle suitably. Isomorphism classes and automorphism groups of these planes are determined. Together with [9] this gives a complete classification of all semicalssical topological flat Lguerre planes.     

Quantum spin chains: Simple models with complex dynamics

The present study highlights some of the complexities observed in the dynamical properties of one-dimensional quantum spin systems. Exact results for zero-temperature dynamic correlation functions are presented for two contrasting situations:

1. a system with a fully ordered ferromagnetic ground state;
2. a system at aT _c=0 critical point.

For both situations it is found that the exact results are considerably more complex than has been anticipated on the basis of approximate approaches which are considered to be appropriate and reliable for such situations. A still higher degree of complexity is expected for the dynamics of quantum spin systems which are nonintegrable. The paper concludes with some observations concerning nonintegrability effects and quantum chaos in spin systems.     

Fast proton conductivity of polycrystalline titanoniobates

The proton conductivity of three layer-type compounds was studied: H₃OTi₂NbO₇. H₂O, HTiNbO₅ and HTiTaO₅. Measurements were made between 20 °C and 90°C on pellets pressed from crystalline powders and soaked with pure water. The hydrated compound had the highest conductivity, (20°C)-6.3–6.9·10^–4 (cm)^–1. Acid ions from the exchange process were quite firmly retained in its layer structure and contributed significantly to the measured conductivity. Consistent results were obtained after prolonged washing with water.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Cotangent functors of curve singularities

Let R be a complete analytic k-algebra of dimension one, where k is a field of characteristic 0. For a Noetherian normalization , the cotangent functors T_i(R/A, R) are of finite length. It is shown that if R is smoothable, then for all j, where denotes the complementary module. This result is used to give estimates for the length of the torsion of the module of differentials _R/k.