Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, II. Geometry of the Level Sets of Symbols

In the first part [16] of this work, we described the commutative C*-algebras generated by Toeplitz operators on the unit ball whose symbols are invariant under the action of certain Abelian groups of biholomorphisms of . Now we study the geometric properties of these symbols. This allows us to prove that the behavior observed in the case of the unit disk (see [3]) admits a natural generalization to the unit ball . Furthermore we give a classification result for commutative Toeplitz operator C*-algebras in terms of geometric and “dynamic” properties of the level sets of generating symbols. This work was partially supported by CONACYT Projects 46936 and 44620, México.     

Initial stages of self-organization of silica-alumina gels in zeolite synthesis

We report the effect of aluminum on the formation and structure of silica nanoparticles formed in basic solutions of small organic and inorganic cations using a combination of small-angle X-ray scattering, conductivity, pH, and 27Al NMR spectroscopy methods. At low silica concentrations, our observations agree with previous reports and show the formation of small oligomers ((HO)4-nAl(OSi(OH)3)n)- that can be modeled qualitatively using a simple aqueous speciation model. We also find that aluminum drastically reduces the concentration of silica at which nanoparticles are formed. Using organic cations, the particles are smaller than the ones observed in pure silica systems (1.5 nm vs approximately 3 nm diameter), but in the case of sodium cations, larger particles are detected ( approximately 10 nm in diameter). The data suggests that sodium cations are incorporated within the inorganic silica/alumina core, as opposed to organic cations that appear to be excluded from such clusters. Important insights are gained by making analogies to the behavior of mixed surfactant systems using regular solution theory and noting that the formation of Si-O-Al bonds (as measured by the DeltaGdegrees(rxn) of condensation) is much more favorable than the formation of Si-O-Si bonds.     

Simple and efficient recyclable catalytic system for performing copper-catalysed S-arylation reactions in the presence of water

A novel protocol for the copper-catalysed S-arylation of thiophenol derivatives with aryl halides leading to diaryl sulfides is reported. The reactions were catalysed by a combination of a copper salt and a 1,2-diamine derivative (acting both as the ligand and as the base) using exclusively water as the solvent. The recovery and successful reutilisation of the aqueous medium containing the active catalyst is described. Furthermore, one example of a "one-pot" process involving Br/I exchange of an aryl bromide and further S-arylation is presented.     

Study of the interaction between progesterone and beta-cyclodextrin by electrochemical techniques and steered molecular dynamics

The interaction of progesterone with beta-cyclodextrin (beta-CD) was studied by differential pulse polarography. The aim of the present work was to study the effect of beta-CD on the electrochemical behavior of progesterone in aqueous solution and also to analyze the molecular interactions involved in formation of the inclusion complex. The complex with stoichiometry of 1:1 was thermodynamically characterized. In addition, steered molecular dynamics (SMD) was used to investigate the energetic properties of formation of the inclusion complex along four different pathways (reaction coordinates), considering two possible orientations. From multiple trajectories along these pathways, the potentials of mean force for formation of the beta-CD progesterone inclusion complex were calculated. The energy analysis was in good agreement with the experimental results. In the beta-CD progesterone inclusion complex, a large portion of the steroid skeleton is included in the beta-CD cavity. The lowest energy was found when the D-ring of the guest molecule is located near the secondary hydroxyls of the beta-CD cavity. In the most probable orientation, one intermolecular hydrogen bond is formed between the O of the C-20 keto group of the progesterone and a secondary hydroxyl of the beta-CD.     

The production of high polymer to surfactant microlatexes

Starved‐feed microemulsion polymerization of styrene was investigated. The influence of the type (SDS or Dowfax 2A1) and concentration of anionic surfactant on the final particle size of latex made by the polymerization of microemulsions of styrene was studied. In addition, the influence of 1‐pentanol and acrylic acid as cosurfactants was examined. Latexes with 20% solids content and polymer to surfactant ratio of 22 were produced, with a particle diameter of 42 nm and very low polydispersity indexes. Smaller particles are produced using SDS than Dowfax 2A1 for the same weight fraction of surfactant; however, similar particle sizes were obtained with the same molar concentrations of SDS and Dowfax 2A1. Further shot additions of monomer increased solids level as high as 40% and polymer to surfactant ratios greater than 40, with particles remaining monodisperse with average diameter smaller than 60 nm. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 48–54, 2010     

Comparative study of ZnO and CuSCN semiconducting nanowire electrodeposition on different substrates

In this study, we are reporting on the electrochemical deposition of two kinds of semiconducting nanowires (ZnO and CuSCN) on different substrates. ZnO and CuSCN are n- and p-type transparent semiconductors whose electrochemical preparation has some similarity, and it is a combination of two steps: an electrochemical reduction with consecutive chemical precipitation. Here, we show that despite the different physicochemical nature of the studied materials, when they are deposited electrochemically, their dimensions depend mainly on the surface state of the used substrate. Thus, depending on the substrate morphology, nanowires with diameters between 50 and 380 nm from both semiconductors could be grown. It is also shown that ZnO and CuSCN nanowires could be successfully grown on glass and plastic substrates as well as on a metallic one. The possibility of growing these transparent semiconductors on flexible substrates opens new perspectives for their use in “invisible” electronic devices.     

Synthesis of LeX and LeY Oligosaccharides with Azido-Type Spacer-Arms. Comparison of 3- and 4-Methoxybenzyl Groups as Key Temporary Protective Groups

Abstract

5-Azido-3-oxa-l-pentanol was prepared from 2-(2-chloroethoxy)ethanol and used as a spacer in the chemical synthesis of the trisaccharide β-D-Gal-(1→4)-[α-L-Fuc-(1→3)]-GlcNAc and the tetrasaccharide α-L-Fuc-α-(1→2)-β-D-Gal-(1→4)-[α-L-Fuc-(1→3)]-GlcNAc that represent the epitopes defining the human blood groups Le^x and Le^y. The classical 4-methoxybenzyl group and the remarably acid-stable 3-methoxybenzyl group were compared as temporary protective groups for position 3 at the glucosamine unit to circumvent the problems associated with the simultaneous presence of allyl and azido groups. The resulting oligosaccharides were coupled to proteins with high efficiency.

     

Two analyte calibrations from the transient response of a single potentiometric sensor employed with the SIA technique

Simultaneous quantification of Cd²⁺ and Pb²⁺ in solution has been correctly targeted using the kinetic information from a single non-specific potentiometric sensor. Dual quantification was accomplished from the complex information in the transient response of an electrode used in a Sequential Injection Analysis (SIA) system and recorded after step injection of sample. Data was firstly preprocessed with the Discrete Wavelet Transform (DWT) to extract significant features and then fed into an Artificial Neural Network (ANN) for building the calibration model. DWT stage was optimized regarding the wavelet function and decomposition level, while the ANN stage was optimized on its structure. To simultaneously corroborate the effectiveness of the approach, two different potentiometric sensors were used as study case, one using a glass selective to Cd²⁺ and another a PVC membrane selective to Pb²⁺.     

Numerical simulation of long laboratory sparks generated by positive switching impulses

A numerical methodology using two different leader channel criteria has been implemented. The methodology is based on Bondiou and Gallimberti's proposition [A. Bondiou, I. Gallimberti, Theoretical modelling of the development of the positive spark in long spark, J. Phys. D: Appl. Phys. 27 (1994) 1252–1266]. The leader channel criteria used are Rizk engineering criterion [Rizk, A model for switching impulse leader inception and breakdown of long air gaps, IEEE Trans. Power Deliv., 4(1) (1989)] and Local thermodynamic – L.T.E. – physical concept [I. Gallimberti, The mechanism of the long spark formation, Colloque C7, J. Phys. (supplement au nro 7, Tome 40) (July 1979) C7–193]. The methodology was tested in three different cases; a deterministic case, a statistical variation and a typical constant level test. Deterministic calculation considered corona inception using stabilization corona electric field criterion of Gallimberti [I. Gallimberti, The mechanism of the long spark formation, Colloque C7, J. Phys. (supplement au nro 7, Tome 40) (July 1979) C7–193] and the leader moving as segments. The statistical simulation has two different statistical delays, one at inception and the other due to the tortuous characteristics of the leader channel. The constant level test consists of 200 positive switching impulses with the same characteristics such as maximum applied voltage, time to crest and time to fall. Time to breakdown and breakdown voltage were found based on the results obtained from the constant level test characteristics. All the numerical results presented are based on experimental conditions reported in [Les Renardières Group, Research on long gap discharges at Les Renardières, Electra N 35 (1973)] from the world class research group namely Les Renardieres Group.