A Class of Periodic Continued Radicals

We compute the limits of a class of periodic continued radicals and we establish a connection between them and the fixed points of the Chebycheff polynomials

A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations

Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan, (-1,1)-, quasiassociative, quasialternative, right alternative and Malcev-admissible noncommutative Jordan algebras over the field of characteristic zero. Also, we describe all Leibniz-derivations of semisimple Jordan, right alternative and Malcev algebras

X-ray Structure Analysis and the Intervalent Electron Transfer in Organic Mixed-Valence Crystals with Bridged Aromatic Cation Radicals

X-ray crystallography identifies the aromatic donor group D = 2,5-dimethoxy-4-methylphenyl to be a suitable redox center for the construction of organic mixed-valence crystals owing to its large structural change attendant upon 1e oxidation to the cation−radical (D•+). The combination of cyclic voltammetry, dynamic ESR line broadening, and electronic (NIR) spectroscopy allows the intervalence electron transfer between the redox centers in the mixed-valence system D-br-D•+ [where br can be an aliphatic trimethylene or an aromatic (poly)phenylene bridge] to be probed quantitatively. Independent measures of the electronic coupling matrix element (H) for D/D•+ electron exchange via Mulliken−Hush theory accord with the X-ray crystallographic databoth sufficient to consistently identify the various D-br-D•+ according to the Robin−Day classification. Thus, the directly coupled biaryl D−D•+ is a completely delocalized cation in class III with the charge distributed equally over both redox centers. The trimethylene- and biphenylene-bridged cations D(CH2)3D•+ and D(ph)2D•+ with highly localized charge distributions are prototypical class II systems involving moderately coupled redox centers with H ≈ 400 cm-1. The borderline region between class II/III is occupied by the phenylene-bridged cation D(ph)D•+; and the X-ray, CV, and NIR analyses yield ambivalent H values (which we believe to be) largely a result of an unusually asymmetric (20/80) charge distribution that is polarized between the D/D•+ redox centers

A Troika of Agitators: Three Comintern Liaison Agents in Australia, 1920-22

Peter Simonoff, Consul-General in Australia for the Bolshevik regime from early 1918 to mid-1921, is known to have played an active role in the founding of the Communist Party of Australia in 1920, and in promoting the "Trades Hall" faction against the ASP faction when the new party divided. Paul Freeman and Alexander Zuzenko, both deported from Australia in 1919, made return visits to Australia from Moscow in 1921 and 1922 to carry the process further. Freeman, however, backed the ASP faction, while Zuzenko lent his support to "Trades Hall". This paper uses previously unknown reports to the Comintern's Executive Committee (ECCI) from Simonoff, Freeman and Zuzenko, as well as Australian sources, to study the relations between these men and their mutually contradictory actions