Hopf Algebras, Renormalization and Noncommutative Geometry

We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations. Received: 14 August 1998/ Accepted: 5 October 1998     

Synthesis and 1H, 19F NMR spectroscopic characterization of (pentafluorophenyl)3-n (pyrazol-1-yl-tetrafluorophenyl)n=1,2 porphyrins

Three new porphyrins bearing in the meso positions 4-(pyrazol-1-yl)-2,3,5,6-tetrafluorophenyl substituents have been prepared and characterized by nmr spectroscopy.     

Gelfand numbers of operators with values in a Hilbert space

In the paper we prove two inequalities involving Gelfand numbers of operators with values in a Hilbert space. The first inequality is a Rademacher version of the main result in [Pa-To-1] which relates the Gelfand numbers of an operator from a Banach spaceX intol ₂ ⁿ with a certain Rademacher average for the dual operator. The second inequality states that the Gelfand numbers of an operatoru froml ₁ ^N into a Hilbert space satisfy the inequality

Strong, low-energy two-photon absorption in extended amine-terminated cyano-substituted phenylenevinylene oligomers

Three quadrupolar oligophenylenevinylenes with five rings in the conjugated backbone, terminal donor groups, and various acceptors and/or donors along the backbone were synthesized and their two-photon spectroscopic properties investigated. These chromophores exhibit large two-photon absorption cross sections over a wide wavelength range and two distinct peaks, the strongest of which (deltamax > 3600 GM) is observed at 960-970 nm, a wavelength close to twice the value of the linear absorption maximum (2lambda(1)max). The findings on these chromophores are compared with those for analogous molecules with shorter conjugation length, for which the main two-photon band is at significantly shorter wavelength than 2lambda(1)max.     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.     

A straightforward preparation of amino–polystyrene resin from Merrifield resin

Azidomethyl–polystyrene, obtained by nucleophilic substitution of chloromethyl–polystyrene, undergoes a Schmidt rearrangement when treated with trifluoromethanesulfonic acid, affording amino–polystyrene. To assess its loading and reactivity the resin is used as a support for the preparation of triazene-linked amine.