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.     

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     

Mass spectra of transition metal π-complexes. VI—The metastable ion mass spectrum of (η1-Toluene)-tricarbonylchromium

First field free region metastable fragmentations of (η⁶-PhCH₃)Cr(CO)₃ have been examined by means of the linked scan technique. The molecular ion is shown to fragment exclusively by single and multiple CO loss. The ion [C₇H₈Cr(CO)₂]⁺? also fragments directly to [C₇H₈Cr]⁺?.     

Structure and protonation of some indolizine derivatives studied by ab initio MO calculations

Some gauge invariant atomic orbitals-coupled-perturbed Hartree-Fock (GIAO-CPHF) calculations were performed for seven indolizine derivatives and their monoprotonated forms. Chemical shift, molecular geometry, and charge distribution data are reported for each molecule. The calculations support the results of nuclear magnetic resonance (NMR) spectroscopy measurements showing that protonation occurs preferentially at N1. The good agreement between the calculated and observed ¹³C and ¹⁵N chemical shifts show that such calculations can be used for chemical shift assignment purposes. Cation structures and probable sites for electrophilic reaction or second protonation are also discussed.     

Conformations of 1,3,3,5,7,7-Hexamethyl-1,5-diazacyclooctane and Its Bis-BH(3) Adduct. Mono- and Bis-BH(3) Adducts of Di-Tertiary Amines

A variable-temperature (1)H- and (13)C-NMR study revealed a conformational equilibrium for 1,3,3,5,7,7-hexamethyl-1,5-diazacyclooctane (4) having DeltaG() = 8.8 +/- 0.6 kcal/mol at 184 K. This activation barrier connects a major and a minor form of 4. Molecular mechanics calculations on 4 led to the conclusion that the major form is a set of twist-chair-chairs interconverting rapidly via the chair-chair and that the minor form is most likely a set of twist-boat-boats interconverting rapidly via the boat-boat. The proximity of the two nitrogen lone pairs in the major form of 4 made plausible the expectation that 4, as well as a related diamine with apposed nitrogens, 3,7-dimethyl-3,7-diazabicyclo[3.3.1]nonane (3), might bind a Lewis acid, namely BH(3), using both lone pairs simultaneously and equally. This proved not to be the case: for 3 only the bis-BH(3) adduct was found and for 4 the mono-BH(3) adduct utilized only one nitrogen lone pair. The structure of the bis-BH(3) adduct of 4 (12) was determined by X-ray crystallography to be a twist-boat-boat with BH(3)s cis. Molecular mechanics calculations on 12 were consistent with the solid state conformation found.