Explicit Betti numbers for a family of nilpotent Lie algebras

Betti numbers for the Heisenberg Lie algebras were calculated by Santharoubane in his 1983 paper. However few other examples have appeared in the literature. In this note we give the Betti numbers for a family of -dimensional 2-step nilpotent extensions of by .

     

The rational LS-category of -trivial fibrations

We provide new upper and lower bounds for the rational LS-category of a rational fibration of simply connected spaces that depend on a measure of the triviality of which is strictly finer than the vanishing of the higher holonomy actions. In particular, we prove that if is -trivial for some and enjoys Poincaré duality, then

     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.     

Cyclophane bis(sulfoxides) a thermal analysis study

A thermogravimetry study of a series of cyclophane bis(sulfoxides) (1–6) has shown that thermal decomposition of these compounds occurs in two stages with a stepwise loss of the sulfoxide groups at well defined decomposition temperatures. The stepwise thermal cleavage has been rationalized in terms of the stereochemistry of the sulfoxide groups and the strain associated with the resultant elimination products.

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Zusammenfassung Eine thermogravimetrische Studie einer Reihe von Cyclophan-bis(sulphoxiden) (1–6) zeigte, dass die thermische Zersetzung dieser Verbindungen in zwei Stufen unter stufenweisem Verlust der Sulphoxidgruppen bei gut definierten Zersetzungstemperaturen vor sich geht. Die stufenweise thermische Spaltung wurde aufgrund der Stereochemie der Sulphoxidgruppen und der mit den resultierenden Eliminationsprodukten verbundenen Belastung erörtert.

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Résumé Une étude thermogravimétrique d'une série de bis (sulfoxydes) de cyclophane (1–6) a montré que la décomposition thermique de ces composés se déroule en deux étapes avec pertes graduelles des groupes sulfoxydes à des températures de décomposition bien définies. Le clivage thermique graduel est expliqué par la stéréochimie des groupes sulfoxydes et la contrainte associée aux produits éliminés.

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- , , , . , .

     

Nachweis und Bestimmung des Wismuts

Ohne Zusammenfassung