Assignment of the 1H- and 13C-NMR spectra of congested helicenes using two-dimensional NMR methods: Phenanthro[3′,4′:3,4]phenanthro[2,1-b]thiophene

Phenanthro[3′,4′:3,4]phenanthro[2,1-b]thiophene has been prepared and its highly congested proton and carbon nmr spectra assigned. The nmr assignments required concerted utilization of two-dimensional nmr techniques which included: COSY, direct and long range optimized heteronuclear chemical shift correlation and heteronuclear relayed coherence transfer.     

Eine differentialgeometrische Kennzeichnung der allgemeinen Dupinschen Zykliden

Zusammenfassung Es werden die Flächen des projektiven dreidimensionalen Raumes bestimmt, die ein konjugiertes Netz aus Kegelschnitten, die zugleich Kegelschattengrenzen sind, tragen. Es kommen nur algebraische Flächen in Frage. Abgesehen von einem Sonderfall, handelt es sich um allgemeine Dupin'sche Zykliden. Die Untersuchung ist so angelegt, daß Fallunterscheidungen möglichst vermieden werden.

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Herrn Professor Dr. Dr. h.c.mult. Otto Haupt mit den besten Wünschen zum 100. Geburtstag gewidmet     

Complete characterization of almost Moore digraphs of degree three

It is well known that Moore digraphs do not exist except for trivial cases (degree 1 or diameter 1), but there are digraphs of diameter two and arbitrary degree which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. In this paper, we prove that digraphs of degree three and diameter k ≥ 3 which miss the Moore bound by one do not exist. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 112–126, 2005