The self-dual point of the two-dimensional random-cluster model is critical for q?≥ 1

We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter q?≥?1 on the square lattice is equal to the self-dual point ${p_{sd}(q) = \sqrt{q} / (1+\sqrt{q})}$ . This gives a proof that the critical temperature of the q-state Potts model is equal to ${\log (1+\sqrt q)}$ for all q?≥ 2. We further prove that the transition is sharp, meaning that there is exponential decay of correlations in the sub-critical phase. The techniques of this paper are rigorous and valid for all q?≥ 1, in contrast to earlier methods valid only for certain given q. The proof extends to the triangular and the hexagonal lattices as well.     

Gold(I)-catalyzed intramolecular hydroamination of unactivated alkenes with carboxamides

N-Alkenyl carboxamides undergo gold-catalyzed intramolecular exo-hydroamination to form nitrogen heterocycles in excellent yield.     

ESR and electrochemical study of 5-nitroindazole derivatives with antiprotozoal activity

The electrochemistry of 3-alkoxy- and 3-hydroxy-1-[omega-(dialkylamino)alkyl]-5-nitroindazole derivatives were characterized using cyclic voltammetry in DMSO. The nitro reduction process was studied and this was affected by the acid moieties present in these compounds. A nitro anion self-protonation process was observed. This phenomenon was studied by cyclic voltammetry in presence of increasing amount of NaOH. The reactivity of the nitro anion radical of these derivatives with glutathione was also studied by cyclic voltammetry. The oxidizing effect of glutathione is supported by the parallel decrease of the anodic peak current and increase of the cathodic peak in the cyclic voltammograms, corresponding to the wave of the nitro anion radical from uncharged species with the addition of glutathione. Nitro anion radicals obtained by electrolytic reduction of these derivatives were measured and analyzed in DMSO using electron spin resonance spectroscopy.     

New lamellar structure formed by an adamantyl derivative of cholic acid

The self-aggregation of the sodium salt of a new adamantyl amide of the 3beta-amino derivative of cholic acid (Na-AdC) in aqueous solution has been investigated by surface tension, dynamic light scattering, fluorescence, small-angle X-ray scattering (SAXS), and transmission electron microscopy (TEM) measurements. These last two techniques suggest that a lamellar phase, consisting of charged bilayers of Na-AdC separated by solvent and periodically stacked, is formed in aqueous solution. The structure of the bilayer is inferred from the resolution of the crystal of the compound in its acid form. The adamantyl moieties, which are mutually interlocked, reside in the central region of the bilayer, and the carboxylic groups are directed toward the hydrophilic region. The structure is open enough to allow water molecules to interact with a fluorescence probe located at the central hydrophobic region.     

Zirconium-substituted isopolytungstates: structural models for zirconia-supported tungsten catalysts

The synthesis and characterization of a series of mixed W-Zr polynuclear Lindqvist-type complexes, deriving from hexatungstate [W6O19]2-, are described in this work. This family of compounds is built from {W5O18Zr}2- moieties as shown by the X-ray structures of the monomeric [W5O18Zr(H2O)(3-n)(DMSO)n]2- (n = 1 and 2) and dimeric [{W5O18Zr(mu-OH)}2]6- anions. A comprehensive spectroscopic study (183W NMR, FTIR, Raman, EXAFS, and EPR) of these compounds is presented. The goal of incorporating Zr(IV) cations into an oxotungstic core is to obtain spectroscopic models that could mimic the interactions that develop in supported catalysts between the active phase and the supporting oxide. This work tends to show that these molecular compounds can be regarded as soluble structural analogues of WOx/ZrO2 catalysts, which are interesting candidates for the skeletal isomerization of light n-alkanes.     

SiO2/Cr monolayers and formation of polyethylene films

1,3,5-tribenzylhexahydro-1,3,5-triazine-CrCl3 (TAC-CrCl3) was supported on monodisperse St?ber silica and on commercial silica particles. The monolayers of these catalyst particles were successfully prepared with Langmuir-Blodgett technique. The effect of TAC-CrCl3 molecules on the ordering and film-forming of the silica particles was investigated. The particles arrange in domains of hexagonal ordering, but the ordering of particles in the monolayer decreases with increasing Cr loading. These hybrid monolayers are active polymerization catalysts. After polymerization, a relatively rough layer of polyethylene molecules covers the catalyst monolayer and this layer is hydrophobic. The monolayers and the polymers coating films were characterized by IR, UV-vis-NIR, and SEM. The method provides a way to fabricate polyethylene films on silica monolayers.     

Controllability of the Ornstein-Uhlenbeck equation

^** Email: Leiva{at}ula.ve In this paper we study the controllability of the followingcontrolled Ornstein–Uhlenbeck equation [graphic: see PDF] then the system is approximately controllable on [0, t₁]. Moreover,the system can never be exactly controllable.     

Hydroxy-1-aminoindans and derivatives: preparation, stability, and reactivity

The chemical stability and reactivity of hydroxy-1-aminoindans and their N-propargyl derivatives are strongly affected by the position of the OH group and its orientation relative to that of the amino moiety. Thus, the 4- and 6-OH regioisomers were found to be stable, while the 5-OH analogues were found to be inherently unstable as the free bases. The latter, having a para orientation between the OH and the amino moieties, could be isolated only as their hydrochloride salts. 7-Hydroxy-1-aminoindans and 7-hydroxy-1-propargylaminoindans represent an intermediate case; while sufficiently stable even as free bases, they exhibit, under certain experimental conditions, unexpected reactivity. The instability of the 5- and 7-hydroxy-aminoindans is attributed to their facile conversion to the corresponding, reactive quinone methide (QM) intermediates. The o-QM obtained from 7-hydroxy-aminoindans was successfully trapped with ethyl vinyl ether via a Diels-Alder reaction to give tricyclic acetals 32a,b.