Zur Synthese von Derivaten des Pyrido[1,2-a]azepins

On the Synthesis of Derivatives of Pyrido[1,2-a]lazepine The conjugated pyridinium ylides of type 4 undergo 8π -electrocyclisation affording the heterobicyclic allenes 5 which, in the presence of H₂O and H₂O₂, are subsequently transformed into the substituted pyrido[1,2-a]-azepinones 6, a novel heterocyclic system. The chemical behaviour of 6a,b is dominated by cleavage of the lactam bond and subsequent reaction to pyridinc and isoquinoline derivatives, respectively; e.g. reaction of 6a, b with 4,5-dihydro-4-methyl-3H-1,2,4-triazole-3,5-dione affords the cycloadducts 11 and 12 almost quantitatively. The successful transformation of 6b into 15 is described, the latter being the first representative of the presently unknown, potentially antiaromatic pyrido[1,2-a]azepine ( 1 ).     

Synthesis and characterization of new oligosilane derivatives of iron and molybdenum

By use of salt elimination, the transition metal substituted oligosilanes (η⁵-C₅Me₄Et)Fe(CO)₂SiMe₂SiMe₂Cl 1, (η⁵-C₅Me₄Et)Mo(CO)₃SiMe₂SiMe₂Br 2, (η⁵-C₅Me₄Et)Fe(CO)₂(SiMe₂)₆(CO)₂Fe(η⁵-C₅Me₄Et) 3 and (η⁵-C₅Me₄Et)Fe(CO)₂(SiMe₂)₆Br 4 were prepared and characterized. Compound 1 is well crystallized from pentane and its structure has been determined by X-ray diffraction analysis.     

Toeplitz Operators with Uniformly Continuous Symbols

Let T _f be a Toeplitz operator on the Segal–Bargmann space or the standard weighted Bergman space over a bounded symmetric domain \({\Omega \subset {\bf C}^n}\) with possibly unbounded symbol f. Combining recent results in Bauer et al. (J. Funct. Anal. 259:57–78, 2010), Bauer et al. (J. reine angew. Math. doi: 10.1515/crelle-2015-0016), Issa (Integr. Equ. Oper. Theory 70:569–582, 2011) we show that in the case of uniformly continuous symbols f with respect to the Euclidean metric on C ⁿ and the Bergman metric on \({\Omega}\), respectively, the operator T _f is bounded if and only if f is bounded. Moreover, T _f is compact if and only if f vanishes at the boundary of \({\Omega.}\) This observation substantially extends a result in Coburn (Indiana Univ. Math. J. 23:433–439, 1973).     

Verified convex hull and distance computation for octree-encoded objects

This paper discusses algorithms for computing verified convex hull and distance enclosure for objects represented by axis-aligned or unaligned octrees. To find a convex enclosure of an octree, the concept of extreme vertices of boxes on its boundary has been used. The convex hull of all extreme vertices yields an enclosure of the object. Thus, distance algorithms for convex polyhedra to obtain lower bounds for the distance between two octrees can be applied. Since using convex hulls makes it possible to avoid the unwanted wrapping effect that results from repeated decompositions, it also opens a way to dynamic distance algorithms for moving objects.