On the Haar measure of the quantumSU(N) group

We prove that the Haar state associated to the compact matrix quantum groupSU (N) is faithful for ]–1,1[,0, and anyN2.     

A new route to trinuclear carbocyanines

Amides or vinylogous amides react with tosyl chloride-pyridine to form activated intermediates which condense with Fischer's base or their vinylogs to give carbocyanine structures. Under the same conditions formylated Fischer's base reacts with vinylogous Fischer's bases to give trinuclear carbocyanines in good yields. Their structure and the limitations of this route are discussed.     

Mécanisme de la réaction de cyclisation en milieu aqueux de carbanilates de propargyle en méthylène-4 oxazolidinones-2

The alkaline hydrolysis of propargyl 3-chlorocarbanilates was investigated kinetically using uv spectropotometry. The cyclization to 4-methoylene-2-oxazolisinones proceeds via the numcleophilic attack of the substrate anion concomitantly with that of the hydroxide ion on the triple bond. The nucleophilic attack leads directly to the heterocycle whereas the hydroxide ion attack gives rise to a ketocarbamate which is then cyclized to the oxazolidione.     

Novel [2 + 2] photocycloaddition-induced rearrangement of bichromophoric naphthalene-tethered resorcinol ethers

The first examples of sequential photocycloaddition-rearrangement reactions of naphthalene-tethered resorcinol ethers are described. Bichromophoric aromatic compounds with naphthalene and resorcinol ether moieties were irradiated in the presence/absence of a small amount of acid to give the corresponding cycloaddition-rearrangement products. From the determination of quantum yields, steady-state fluorescence spectral studies, and fluorescence lifetime measurements, the mechanism of this novel photoinduced multistep reaction was elucidated to involve the initial intramolecular exciplex formation, followed by the intramolecular [2 + 2] photocycloaddition between the two aromatic rings and the subsequent acid-catalyzed skeletal rearrangement of the resulting cyclobutane derivative leading to the final products.     

Supercapacitive admittance tomoscopy

A sensor for measuring adsorption on a substrate has been designed including a contactless detection scheme, called supercapacitive admittance tomoscopy (SCAT). The sensor comprises a thin dielectric layer with two parallel band electrodes on the one side and a chemically modified surface on the other onto which the adsorption of molecules occurs. Upon application of a high frequency ac voltage between the two electrodes, a capacitive coupling is established across the dielectric layer, and the admittance measured depends on the surface state of the chemically modified interface. On the basis of this principle, a flow sensor has been developed to measure sensorgrams to follow the dynamics of the adsorption and has been tested for the adsorption of IgG on the modified surface.     

Intrinsic folding of small peptide chains: spectroscopic evidence for the formation of beta-turns in the gas phase

Laser desorption of model peptides coupled to laser spectroscopic techniques enables the gas-phase observation of genuine secondary structures of biology. Spectroscopic evidence for the formation of beta-turns in gas-phase peptide chains containing glycine and phenylalanine residues establishes the intrinsic stability of these forms and their ability to compete with other stable structures. The precise characterization of local minima on the potential energy surface from IR spectroscopy constitutes an acute assessment for the state-of-the-art quantum mechanical calculations also presented. The observation of different types of beta-turns depending upon the residue order within the sequence is found to be consistent with the residue propensities in beta-turns of proteins, which suggests that the prevalence of glycine in type II and II' turns stems essentially from an energetic origin, already at play under isolated conditions.     

An exact homology sequences approach to the controllability of systems

Some results are given on the homology groups of the abstract simplicial complex associated to a multivariable control system, as an extension of the central result of J. Casti (J. Math. Anal. Appl.68 (1979), 347–370) to the multivariable case. The method used is “polyhedral dynamics” as termed by J. Casti, who introduced it. A given control system is mapped into a simplicial complex and then its homological structure is studied. These results, obtained in the multivariable case by the use of the Mayer-Vietoris homology sequence and of the relative homology sequence, present topological invariants for control systems thus creating the possibility of a new topological classification of multivariable systems. An example is given to clarify the approach.     

Unimolecular gas-phase reactions of the methyl acetoacetate radical cation. Oxygen atom permutation via ion-molecule complexes

The reactions of metastable decomposing methyl acetoacetate (a mixture of keto a ad enol tautomers) are reported and discussed. The unimolecular fragmentations of the tautomers are different. The metastable decomposing radical cation of the keto form displays four specific ions: [M –CO]⁺˙, [M – CH₂O]⁺˙, [M – CH₂CO]⁺˙ and m/z 43. The results derived from D-, ¹³C- and ¹⁸O-labelled precursors together with thermochemical data have been used to study the mechanisms. Experimental results indicate that an unexpected isomerization occurs before dissociation. It formally corresponds to oxygen atom permutation of the two carbonyl groups without participation of the carbon atoms. This remarkable process is interpreted in terms of a mechanism involving ion-molecule complexes.