Contrasting Photoelectrochemical Behaviour Of Two Isomeric Supramolecular Dyes Based On Meso-tetra(pyridyl)porphyrin Incorporating Four (μ3-oxo)- Triruthenium(iii) Clusters

A saddle shaped tetracluster porphyrin species containing four [Ru 3O(OAc)6(py)2]+ clusters coordinated to the N-pyridyl atoms of 5,10,15,20-tetra(3-pyridyl)porphyrin, H 2(3-TCPyP), has been investigated in comparison with the planar tetra(4-pyridyl)porphyrin analogue H2(4-TCPyP). The steric effects from the bulky peripheral complexes play a critical role in the H 2(3-TCPyP) species, determining a non-planar configuration around the porphyrin centre and precluding any significant π-electronic coupling, in contrast with the less hindered H2(4-TCPyP) species. Both systems exhibit a photoelectrochemical response in the presence of nanocrystalline TiO2 films, involving the porphyrin excitation around 450 nm. 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Classification of a family of non almost periodic free Araki-Woods factors

We obtain a complete classification of a large class of non almost periodic free Araki-Woods factors $\Gamma(\mu,m)"$ up to isomorphism. We do this by showing that free Araki-Woods factors $\Gamma(\mu, m)"$ arising from finite symmetric Borel measures $\mu$ on $\mathbf{R}$ whose atomic part $\mu_a$ is nonzero and not concentrated on $\{0\}$ have the joint measure class $\mathcal C(\bigvee_{k \geq 1} \mu^{\ast k})$ as an invariant. Our key technical result is a deformation/rigidity criterion for the unitary conjugacy of two faithful normal states. We use this to also deduce rigidity and classification theorems for free product von Neumann algebras.Comment: v2: minor changes, final version, to appear in Journal of the European Mathematical Societ

Additivity of Entangled Channel Capacity for Quantum Input States

An elementary introduction into algebraic approach to unified quantum information theory and operational approach to quantum entanglement as generalized encoding is given. After introducing compound quantum state and two types of informational divergences, namely, Araki-Umegaki (a-type) and of Belavkin-Staszewski (b-type) quantum relative entropic information, this paper treats two types of quantum mutual information via entanglement and defines two types of corresponding quantum channel capacities as the supremum via the generalized encodings. It proves the additivity property of quantum channel capacities via entanglement, which extends the earlier results of V. P. Belavkin to products of arbitrary quantum channels for quantum relative entropy of any type.Comment: 17 pages. See the related papers at http://www.maths.nott.ac.uk/personal/vpb/research/ent_com.htm