On Two Theorems about Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones). Dedicated to my friend J.-C. Cortet.     

Macrocyclic 14-Membered Ring Diketal Dilactams: Evaluation of their Divalent Cation Binding Properties

The binding abilities of a new class of 14-membered ring ligands bearing diketal dilactam functions were explored by UV-visible spectrophotometry. Their formation constants, determined in THF solution, showed appreciable complexation with divalent cations (stability order: Sr²⁺≥Ca²⁺>Zn²⁺≥Mg²⁺>Ba²⁺) whereas no association was observed with monovalent cations. The stoichiometry of the complexes formed was essentially 1:1 although sometimes a low percentage (<10%) of 1:2 (cation–ligand) species was detected. The corresponding formation constants determined by computation (STAR program) were in the range 1.5<log?β ¹¹<4.8 and 4.4<log?β ¹²<7.1. They depend significantly on the nature of the substituents. In addition, solvent extractions carried out in a water–chloroform system showed the highest constants (log K ^ex) for the most substituted macrocycles 7b and 7c (norephedrine series) with a lipophilic skeleton.     

Dynamical singlets and correlation-assisted Peierls transition in VO2

A theory of the metal-insulator transition in vanadium dioxide from the high- temperature rutile to the low- temperature monoclinic phase is proposed on the basis of cluster dynamical mean-field theory, in conjunction with the density functional scheme. The interplay of strong electronic Coulomb interactions and structural distortions, in particular, the dimerization of vanadium atoms in the low-temperature phase, plays a crucial role. We find that VO2 is not a conventional Mott insulator, but that the formation of dynamical V-V singlet pairs due to strong Coulomb correlations is necessary to trigger the opening of a Peierls gap.     

Has Bell's inequality a general meaning for hidden-variable theories?

We analyze the proof given by J. S. Bell of an inequality between mean values of measurement results which, according to him, would be characteristic of any local hidden-parameter theory. It is shown that Bell's proof is based upon a hypothesis already contained in von Neumann's famous theorem: It consists in the admission that hidden values of parameters must obey the same statistical laws as observed values. This hypothesis contradicts in advance well-known and certainly correct statistical relations in measurement results: One must therefore reject the type of theory considered by Bell, and his inequality has no general meaning.     

BaSnF4 fast ion conductor: Variations versus the method of preparation and anomalous temperature variation of the quadrupole splitting

A new method of preparation of high performance fluoride ion conductor, BaSnF₄, by water leaching of newly discovered barium tin(II) chloride fluorides, has been designed, and the materials have been studied and compared to the solid prepared by the usual dry method. The unit-cell parameters and crystallite dimensions were found to vary with the method of preparation. In addition, the crystallite dimensions were found to be highly anisotropic for the samples obtained by the wet method. The Mössbauer spectrum is made of a large tin(II) quadrupole doublet, and a broad tin(IV) oxide peak due to surface oxidation. The tin(II) spectrum is in agreement with covalently bonded tin(II) having a strongly stereoactive lone pair. An unusually high dependence of the quadrupole splitting at low temperatures was observed (5.8 times larger than for α-SnF₂).     

Understanding the importance of the viscosity contrast between the sample solvent plug and the mobile phase and its potential consequence in two-dimensional high-performance liquid chromatography

The effect of solvent viscosity mismatch on elution performance in reversed-phase HPLC was studied using moment analysis. Two conditions were tested: (1) the mobile phase viscosity was less than the injection plug viscosity, and (2) the mobile phase viscosity was greater than the injection plug viscosity. Under the first condition, retention time and elution performance decreased as the viscosity contrast between the mobile phase and injection plug increased. The effect on performance was more marked as the injection volume increased. A decrease in performance of 12% for compounds with retention factors up to 2.8 was apparent even when the viscosity contrast was only 0.165 cP. In the second set of conditions, elution performance was actually observed to increase, by as much as 25% for a 40 μL injection, as the viscosity contrast between the mobile phase and the solute plug increased. No change in the retention factor was observed. This behaviour was attributed to the shape of an injection plug as it enters into the column, whereby a low viscosity plug permeates away from the wall when the column contains a higher viscosity mobile phase, and vice a versa for a high viscosity plug entering a low viscosity mobile phase. At no stage was either a band splitting or shoulders observed with viscosity contrasts up to 1.283 cP, as could have been expected.     

High peak capacity separations of peptides in reversed-phase gradient elution liquid chromatography on columns packed with porous shell particles

The performance of 5 and 15 cm long columns packed with shell particles (Halo, AMT) is compared in gradient elution separations of the tryptic digests of myoglobin and bovine serum albumin. The influences of the temperature and the mobile phase flow rate on the column efficiency for two peptides are discussed. The influences of this flow rate, of the temperature, and of the gradient slopes on the peak capacities are also considered. Peak capacities in excess of 400 were achieved in 6h with the longer column. Peak capacities of 200 could be achieved in 30 min with the shorter column.