Involutions of RA Loops

Let L be an RA loop, that is, a loop whose loop ring over any coefficient ring R is an alternative, but not associative, ring. Let l bar right arrow l(theta) denote an involution on L and extend it linearly to the loop ring RL. An element alpha is an element of RL is symmetric if alpha(theta) = alpha and skew-symmetric if alpha(theta) = -alpha. In this paper, we show that there exists an involution making the symmetric elements of RL commute if and only if the characteristic of R is 2 or theta is the canonical involution on L, and an involution making the skew-symmetric elements of RL commute if and only if the characteristic of R is 2 or 4.

The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Supramolecular Approach to Gold Nanoparticle/Triruthenium Cluster Hybrid Materials and Interfaces

A systematic and comprehensive study of the interaction of citrate-stabilized gold nanoparticles with triruthenium cluster complexes of general formula [Ru(3)(CH(3)COO)(6)(L)](+) [L = 4-cyanopyridine (4-CNpy), 4,4`-bipyridine (4,4`-bpy) or 4,4`-bis(pyridyl)ethylene (bpe)] has been carried out. The cluster-nanoparticle interaction in solution and the construction of thin films of the hybrid materials were investigated in detail by electronic and surface plasmon resonance (SPR) spectroscopy, Raman scattering spectroscopy and scanning electron microscopy (SEM). Citrate-stabilized gold nanoparticles readily interacted with [Ru(3)O(CH(3)COO)(6)(L)(3)](+) complexes to generate functionalized nanoparticles that tend to aggregate according to rates and extents that depend on the bond strength defined by the characteristics of the cluster L ligands following the sequence bpe > 4,4`-bpy >> 4-CNpy. The formation of compact thin films of hybrid AuNP/[Ru(3)O(CH(3)COO)(6)(L)(3)](+) derivatives with L = bpe and 4,4`-bpy indicated that the stability/lability of AuNP-cluster bonds as well as their solubility are important parameters that influence the film contruction process. Fluorine-doped tin oxide electrodes modified with thin films of these nanomaterials exhibited similar electrocatalytic activity but much higher sensitivity than a conventional gold electrode in the oxidation of nitrite ion to nitrate depending on the bridging cluster complex, demonstrating the high potential for the development of amperometric sensors.

(1)H NMR spectroscopy as a tool to determine accurate photoisomerization quantum yields of stilbene-like ligands coordinated to rhenium(I) polypyridyl complexes

In this work, the use of proton nuclear magnetic resonance, (1)H NMR, was fully described as a powerful tool to follow a photoreaction and to determine accurate quantum yields, so called true quantum yields (Phi(true)), when a reactant and photoproduct absorption overlap. For this, Phi(true) for the trans-cis photoisomerization process were determined for rhenium(I) polypyridyl complexes, fac-[Re(CO)(3)(NN)(trans-L)](+) (NN = 1,10-phenanthroline, phen, or 4,7-diphenyl-1,10-phenanthroline, ph(2)phen, and L = 1,2-bis(4-pyridyl) ethylene, bpe, or 4-styrylpyridine, stpy). The true values determined at 365 nm irradiation (e. g. Phi(NMR) = 0.80 for fac-[Re(CO)(3)(phen)(trans-bpe)](+)) were much higher than those determined by absorption spectral changes (Phi(UV-Vis) = 0.39 for fac-[Re(CO)(3)(phen)(trans-bpe)](+)). Phi(NMR) are more accurate in these cases due to the distinct proton signals of trans and cis-isomers, which allow the actual determination of each component concentration under given irradiation time. Nevertheless when the photoproduct or reactant contribution at the probe wavelength is negligible, one can determine Phi(true) by regular absorption spectral changes. For instance, Phi(313) nm for free ligand photoisomerization determined both by absorption and (1)H NMR variation are equal within the experimental error (bpe: Phi(UV-Vis) = 0.27, Phi(NMR) = 0.26; stpy: Phi(UV-Vis) = 0.49, Phi(NMR) = 0.49). Moreover, (1)H NMR data combined with electronic spectra allowed molar absorptivity determination of difficult to isolate cis-complexes. (C) 2009 Elsevier B. V. All rights reserved.