The combinatorics of the bar resolution in group cohomology

We study a combinatorially defined double complex structure on the ordered chains of any simplicial complex. Its columns are related to the cell complex K_n whose face poset is isomorphic to the subword ordering on words without repetition from an alphabet of size n. This complex is shellable and as an application we give a representation theoretic interpretation for derangement numbers and a related symmetric function considered by Désarménien and Wachs [11].

We analyze the two spectral sequences arising from the double complex in the case of the bar resolution for a group. This spectral sequence converges to the cohomology of the group and provides a method for computing group cohomology in terms of the cohomology of subgroups. Its behavior is influenced by the complex of oriented chains of the simplicial complex of finite subsets of the group, and we examine the Ext class of this complex.     

Alkohole

Ohne Zusammenfassung     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

One cannot hear orbifold isotropy type

We show that the isotropy types of the singularities of Riemannian orbifolds are not determined by the Laplace spectrum. Indeed, we construct arbitrarily large families of mutually isospectral orbifolds with different isotropy types. Finally, we show that the corresponding singular strata of two isospectral orbifolds may not be homeomorphic. Received: 6 October 2005     

Dimethylzinc-mediated addition of alkenylzirconocenes to alpha-keto and alpha-imino esters

[reaction: see text] Hydrozirconation of alkynes followed by in situ transmetalation to dimethylzinc and 1,2-addition to activated ketones and N-diphenylphosphinoylimines leads to tertiary allylic alcohols and amines in high overall yield. With 8-phenylmenthol as the chiral auxiliary, si-face attack proceeds in good to excellent diastereoselectivities.     

A molecular modelling study of the interaction of noradrenaline with theβ 2-adrenergic receptor

Summary A model of the ₂-adrenergic receptor binding site is built from the primary structure of the receptor, experimental evidence for key binding residues and analogy with a homologous protein of partially determined structure. It is suggested that residues Trp-109, Thr-110 and Asp-113 are involved in ligand binding. Noradrenaline is successfully docked into this model, and the results of an INDO molecular orbital calculation on the complex indicate that a charge transfer interaction between Trp-109 and noradrenaline is possible.