Oscillator representations of the 2D-conformal algebra

We display irreducible representations of the Virasoro algebra (group of diffeomorphisms of the circle) for any value of the central chargec (central extension defined by a cocycle) and of the highest weight, where the Ka determinants do not vanish. The construction is done in terms of a simple bosonic free field. The unitarity of the representation is discussed, and it is realized with non-trivial hermiticity properties of the free field if<(c-1)/24. In the particular case of the central charge (c=1/2) corresponding to the Ising model, the three unitary irreducible representations (=0, 1/16, 1/2) are realized in terms of the anticommuting oscillators of the free fields of the Neveu-Schwarz-Ramond model.     

Characterization of porosity in a 19th century painting ground by synchrotron radiation X-ray tomography

The study of the early oeuvre of the Swiss painter Cuno Amiet (1868–1961) has revealed that, up to 1907, many of his grounds were hand applied and are mainly composed of chalk, bound in protein. These grounds are not only lean and absorbent, but also, as Synchrotron radiation X-ray microtomography has shown, porous. Our approach to the characterization of pore structure and quantity, their connectivity, and homogeneity is based on image segmentation and application of a clustering algorithm to high-resolution X-ray tomographic data. The issues associated with the segmentation of the different components of a ground sample based on X-ray imaging data are discussed. The approach applied to a sample taken from “Portrait of Max Leu” (1899) by Amiet revealed the presence of three sublayers within the ground with distinct porosity features, which had not been observed optically in cross-section. The upper and lower layers are highly porous with important connectivity and thus prone to water uptake/storage. The middle layer however shows low and nonconnected porosity at the resolution level of the X-ray tomography images, so that few direct water absorption paths through the entire sample exist. The potential of the method to characterize porosity and to understand moisture-related issues in paint layer degradation are discussed.     

Stereoselective Double Functionalization of Iron-Carbonyl Complexes of 5,6,7,8-Tetramethylidenebicyclo[2.2.2]oct-2-ene. Crystal Structure and Absolute Configuration of (–)-trans-μ-[(2S,5R,7S)-C,5,6,C-η:C,7,8,C-η-(6,7,8-trimethylidene-5-((Z)-2-oxopropylidene)-2-bicyclo[2.2.2]octyl acetate)]-bis(tricarbonyliron)

The Friedel-Crafts monoacylation of trans-η-[(1RS,2RS,4SR,5SR,6RS,7SR,8SR)-C,5,6,C-η:C,7,8,C-η-(5,6,7,8-tetramethylidene-2-bicyclo[2.2.2]octyl acetate)]-bis(tricarbonyliron) ((±)- 5 ) is highly stereoselective and yields trans-η-[(1RS,2RS,4RS,5SR,6RS,7RS,8SR)-C,6-η,oxo-σ:C,7,8,C-η-(6,7,8-trimethylidene-5-((Z)-2-oxopropylidene)-2-bicyclo[2.2.2]octyl acetate)]-bis(tricarbonyliron) ((±)- 8 ) which equilibrates with the trans-η-[(1RS,2RS,4RS,5SR,6RS,7RS,8SR)-C,5,6,C-η:C,7,8,C-η-(6,7,8-trimethylidene-5-((Z)-2-oxopropylidene)-2-bicyclo[2.2.2]octyl acetate)]-bis(tricarbonyliron) ((±)- 9 ) on heating. Optically pure (–)- 9 has been prepared from the corresponding optically pure alcohol (+)- 4 . The structure and absolute configuration of (–)- 9 was established by single-crystal X-ray diffraction.     

Metathetical reactions of carbonylate anions with dichlororuthenium complexes: Preparation and characterization of ruthenium—molybdenum and ruthenium—manganese complexes

The possibility of making metal—metal bonded heterobimetallic species by metathesis of ruthenium dichlorides with anionic carbonylates is demonstrated by the isolation of MoRu(μ-Cl)(μ-CO)(CO)₂(PPh₃)₂(η-C₅H₅) (1) and MnRuCl(μ-CO)₂(CO)₃(μ-dppm)₂ (2), obtained by action of [Mo(CO)₃(η-C₅H₅]^? on RuCl₂(PPh₃)₃ and of Mn(CO)₅^? on RuCl₂(dppm)₂, respectively. In contrast, reaction of Mn(CO)₅^? with RuCl₂(PMe₃)₄ yielded an ionic species 3 containing the diruthenium cation Ru₂Cl₃(PMe₃)₆⁺. More interestingly, the action of Mn(CO)₅^? on RuCl₂(PPh₃)₃ resulted in the formation of the unexpected complex MnRu(μ-PPh₂)(CO)₆(PPh₃)₂ (4) in which the phosphido group PPh₂ bridges the two metals; this process is shown to involve a hydride intermediate, and elimination of a molecule of benzene, both identified in the reaction mixture.     

Investigation of the interface in silica-encapsulated liposomes by combining solid state NMR and first principles calculations

In the context of nanomedicine, liposils (liposomes and silica) have a strong potential for drug storage and release schemes: such materials combine the intrinsic properties of liposome (encapsulation) and silica (increased rigidity, protective coating, pH degradability). In this work, an original approach combining solid state NMR, molecular dynamics, first principles geometry optimization, and NMR parameters calculation allows the building of a precise representation of the organic/inorganic interface in liposils. {(1)H-(29)Si}(1)H and {(1)H-(31)P}(1)H Double Cross-Polarization (CP) MAS NMR experiments were implemented in order to explore the proton chemical environments around the silica and the phospholipids, respectively. Using VASP (Vienna Ab Initio Simulation Package), DFT calculations including molecular dynamics, and geometry optimization lead to the determination of energetically favorable configurations of a DPPC (dipalmitoylphosphatidylcholine) headgroup adsorbed onto a hydroxylated silica surface that corresponds to a realistic model of an amorphous silica slab. These data combined with first principles NMR parameters calculations by GIPAW (Gauge Included Projected Augmented Wave) show that the phosphate moieties are not directly interacting with silanols. The stabilization of the interface is achieved through the presence of water molecules located in-between the head groups of the phospholipids and the silica surface forming an interfacial H-bonded water layer. A detailed study of the (31)P chemical shift anisotropy (CSA) parameters allows us to interpret the local dynamics of DPPC in liposils. Finally, the VASP/solid state NMR/GIPAW combined approach can be extended to a large variety of organic-inorganic hybrid interfaces.     

Activite optique de la methyl-3 cyclopentenanone; un calcul ab initio

Ab initio calculations for two conformers of 3-methyl cyclopentanone, with and without 3d orbitals, show that inclusion of d orbitals on the carbonyl group lower energies and is thus necessary, as follows from the variation principle; it also markedly affects rotatory strengths of the n→π^* and π→π^* transitions, but conformational equilibria of the cyclic skeleton and the methyl group are almost independent of the basis chosen. Internal rotation of the methyl group exerts a negligible influence on the rotatory strength of the n→π^* transition, so that this group can be considered as a sphere in this respect.     

Exploring the Molecular Structure of Imidazolium–Silica‐Based Nanoparticle Networks by Combining Solid‐State NMR Spectroscopy and First‐Principles Calculations

A DFT‐based molecular model for imidazolium–silica‐based nanoparticle networks (INNs) is presented. The INNs were synthesized and characterized by using small‐angle X‐ray scattering (SAXS), NMR spectroscopy, and theoretical ab initio calculations. ¹¹B and ³¹P HETCOR CP MAS experiments were recorded. Calculated ¹⁹F NMR spectroscopy results, combined with the calculated anion–imidazolium (IM) distances, predicted the IM chain density in the INN, which was also confirmed from thermogravimetric analysis/mass spectrometry results. The presence of water molecules trapped between the nanoparticles is also suggested. First considerations on possible π–π stacking between the IM rings are presented. The predicted electronic properties confirm the photoluminescence emissions in the correct spectral domain.     

Hidden Uq (sl(2)) Uq (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

In a previous paper, the quantum-group-covariant chiral vertex operators in the spin 1/2 representation were shown to act, by braiding with the other covariant primaries, as generators of the well known U_q(sl(2)) quantum group symmetry (for a single screening charge). Here, this structure is transformed to the Bloch wave/Coulomb gas operator basis, thereby establishing for the first time its quantum group symmetry properties. A U_q(sl(2)) U_q(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (Vermamodules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of the operator product. This hidden symmetry possesses a novel Hopf-like structure compatible with these conditions. At roots of unity it gives the right truncation. Its (non-linear) connection with the U_q(sl(2)) previously discussed is disentangled. Received: 25 April 1996/Accepted: 20 July 1996