The Schwinger cocycle on algebras with unbounded operators

In this article, we describe a class of algebras with unbounded operators on which the Schwinger cocycle extends. For this, we replace a space of bounded operators commonly used in the literature by some space of (maybe unbounded) tame operators, in particular by spaces of pseudo-differential operators, acting on the space of sections of a vector bundle E→M. We study some particular examples which we hope interesting or instructive. The case of classical and log-polyhomogeneous pseudo-differential operators is studied, because it carries other cocycles, defined with renormalized traces of pseudo-differential operators, that are some generalizations of the Khesin-Kravchenko-Radul cocycle. The present construction furnishes a simple proof of an expected result: The cohomology class of these cocycles are the same as cohomology class of the Schwinger cocycle. When M=S¹, we show that the Schwinger cocycle is non-trivial on many algebras of pseudo-differential operators (these operators need not to be classical or bounded). These two results complete the work and extend the results of a previous work [J.-P. Magnot, Renormalized traces and cocycles on the algebra of S¹-pseudo-differential operators, Lett. Math. Phys. 75 (2) (2006) 111-127]. When dim(M)>1, we furnish a new example of sign operator which could suggest that the framework of pseudo-differential operators is not adapted to all the cases. On this example, we have to work on some algebras of tame operators, in order to show that the Schwinger cocycle has a non-vanishing cohomology class.     

On the scalar modal analysis of optical waveguides using approximate methods

We have discussed the approximate methods which are used for obtaining scalar guided modes of optical waveguides. The methods include the perturbation method, the variational method including the Rayleigh-Ritz method, and the Galerkin and the collocation method. The main purpose of this paper is to discuss the inter-relationships and equivalences of these methods, and to bring out the fact that these relationships have, in fact, not been recognized in the guided wave optics literature, although in the numerical electromagnetics and applied mathematics literature some of these relationships are well known. We have also pointed out specific examples where, due to this lack of recognition of relationships, there are repetitions in the literature. In particular, we have noted that the Rayleigh-Ritz method and the Galerkin method have been used using the same set of basis functions for the same kind of waveguides without recognizing the existing literature. We have also reported for the first time an explicit relationship between the Galerkin method and the collocation method. This relationship also points out in which cases one method is more accurate and/or numerically efficient than the other. Another interesting relationship explored is that between the perturbation method and the variational method.     

The absolute configuration of an inherently chiral phosphonatocavitand and its use toward the enantioselective recognition of l-adrenaline

An inherently chiral ABii diphosphonato cavitand (±)-4 bearing a single quinoxaline bridging moiety was synthesized and resolved by chiral HPLC. Its chiroptical properties were investigated and VCD experiments allowed the determination of its absolute configuration. Distinguishable diastereomeric complexes in solution with l-adrenaline were observed by ¹H and ³¹P NMR together with a noticeable enantio-discrimination at 253 K (dr ～2:1) in favor of the dextrorotatory cavitand (+)-4.     

Electrochemical simulation of oxidation processes involving nucleic acids monitored with electrospray ionization–mass spectrometry

Oxidation is commonly involved in the alteration of nucleic acids giving rise to diverse effects including mutation, cell death, malignancy, and aging. We demonstrate that electrochemistry represents an efficient and fast method to mimic oxidative modification of nucleic acids occurring in biological systems. Oxidation reactions were performed in a thin-layer cell employing a conductive diamond electrode as the working electrode and were monitored with electrospray ionization–mass spectrometry. Mass voltammograms were acquired for guanosine, adenosine, cytidine, and uridine. The observed oxidation potentials increased in the order guanosine<<adenosine<cytidine<uridine. Oxidation products of guanosine were characterized using high-resolution (tandem) mass spectrometry performed with a quadrupole–quadrupole time-of-flight instrument. On the basis of these experiments, it was concluded that the initial electrode reaction involves a one-electron, one-proton step to give a free radical. The primary oxidation product represents the starting point for a number of follow-up reactions, including guanosine dimerization as well as further oxidation to 8-hydroxyguanosine. Similar results were obtained for guanosine monophosphate and the corresponding dinucleotide. Furthermore, the guanosine radical was identified as an important intermediate for the formation of a covalent adduct with acetaminophen. This observation sheds new light on the mechanism of adduct formation as it demonstrates that oxidative activation of both the nucleobase and the adduct-forming agent is necessary to observe a detectable amount of adduct species.     

Mono-Glycosylated 3-N-Alkylcatechols: Direct Synthesis from Glycosylacetates, 1H Nmr Analysis and Conformational Studies

ABSTRACT

The direct coupling of 3-n-alkyl catechols to the acetate or trichloroacetimidate derivatives of β-D- or α-D-glycosides (glucose, galactose, xylose, mannose and maltose) catalyzed by BF₃Ot₂ has been studied. β-Glycosides with an equatorial acetate group at position 2 formed exclusively β adducts with yields of 60–80%. α-Glycosides with an equatorial acetate group at position 2 formed β adducts, while β-glycosides with an axial acetate group formed α adducts when activated as trichloroacetimidates, with yields of 70–85%. This was applied to the coupling of 3-n-alkylcatechols of increasing chain length (up to C15) to sugar derivatives. The coupling position of glycosides on the catechol was determined either by differential NOE experiments and by the regioselective synthesis of 1-(O-β-D-glucopyranosyl)-3-pentadecylcatechol, a water soluble analogue of the poison ivy skin allergen. ¹H NMR of acetylated and deprotected compounds were investigated and the conformational preferences of the C₆ side chain determined using molecular modeling.     

Anthocyanin identification and composition of wild Vitis spp. accessions by using LC–MS and LC–NMR

The composition and concentration of anthocyanins of grape berry skins were analyzed in order to assess phenotypic variation between four grape wine varieties belonging to 4 different species: Vitis vinifera, Vitis amurensis, Vitis cinerea and Vitis X champinii. High-performance liquid chromatography coupled to mass spectrometry (LC–MS) and NMR spectroscopy (LC–NMR) were used to separate and identify the structure of anthocyanins present in these species. Combination of LC–MS and LC–NMR data resulted in the identification of 33 anthocyanins. In particular, newly reported cis isomers of p-coumaric-derivatives were identified (petunidin-, peonidin- and malvidin-3-(6-p-coumaroyl)-5-diglucoside). In V. cinerea and V. vinifera, anthocyanins were monoglucoside derivatives whereas in V. amurensis and V. X champinii, both mono- and diglucoside derivatives were identified. Malvidin-, delphinidin- and petunidin-derivatives were, respectively, the most abundant components in V. cinerea and V. vinifera, V. amurensis and V. X champinii.     

Number of terminal groups versus generation of the dendrimer, which criteria influence the catalytic properties?

We report the synthesis of a dense dendrimer ended by the PTA ligand (1,3,5-triaza-7-phosphaadamantane), and the use of the corresponding Rh and Ru complexes for catalysis. The catalytic properties of these dendrimers are compared with those of two other dendrimers: a dendrimer of the same generation but having half the number of ligands, and a dendrimer of the next generation, but having the same number of ligands. The positive influence of the density of catalytic sites on the surface of these dendrimers for alcohol isomerization in water has been evidenced.     

Characterization of Simultaneous Heat and Mass Transfer Phenomena for Water Vapour Condensation on a Solid Surface in an Abiotic Environment—Application to Bioprocesses

The phenomenon of heat and mass transfer by condensation of water vapour from humid air involves several key concepts in aerobic bioreactors. The high performance of bioreactors results from optimised interactions between biological processes and multiphase heat and mass transfer. Indeed in various processes such as submerged fermenters and solid-state fermenters, gas/liquid transfer need to be well controlled, as it is involved at the microorganism interface and for the control of the global process. For the theoretical prediction of such phenomena, mathematical models require heat and mass transfer coefficients. To date, very few data have been validated concerning mass transfer coefficients from humid air inflows relevant to those bioprocesses. Our study focussed on the condensation process of water vapour and developed an experimental set-up and protocol to study the velocity profiles and the mass flux on a small size horizontal flat plate in controlled environmental conditions. A closed circuit wind tunnel facility was used to control the temperature, hygrometry and hydrodynamics of the flow. The temperature of the active surface was controlled and kept isothermal below the dew point to induce condensation, by the use of thermoelectricity. The experiments were performed at ambient temperature for a relative humidity between 35?C65% and for a velocity of 1.0?ms^?1. The obtained data are analysed and compared to available theoretical calculations on condensation mass flux.     

Numerical study on the adhesion and reentrainment of nondeformable particles on surfaces: the role of surface roughness and electrostatic forces

In this paper, the reentrainment of nanosized and microsized particles from rough walls under various electrostatic conditions and various hydrodynamic conditions (either in air or aqueous media) is numerically investigated. This issue arises in the general context of particulate fouling in industrial applications, which involves (among other phenomena) particle deposition and particle reentrainment. The deposition phenomenon has been studied previously and, in the present work, we focus our attention on resuspension. Once particles are deposited on a surface, the balance between hydrodynamic forces (which tend to move particles away from the surface) and adhesion forces (which maintain particles on the surface) can lead to particle removal. Adhesion forces are generally described using van der Waals attractive forces, but the limit of these models is that any dependence of adhesion forces on electrostatic forces (due to variations in pH or ionic strength) cannot be reproduced numerically. For this purpose, we develop a model of adhesion forces that is based on the DLVO (Derjaguin and Landau, Verwey and Overbeek) theory and which includes also the effect of surface roughness through the use of hemispherical asperities on the surface. We first highlight the effect of the curvature radius on adhesion forces. Then some numerical predictions of adhesion forces or adhesion energies are compared to experimental data. Finally, the overall effects of surface roughness and electrostatic forces are demonstrated with some applications of the complete reentrainment model in some simple test cases.