On the structure of weight modules

Given any simple Lie superalgebra , we investigate the structure of an arbitrary simple weight -module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuperalgebra. Then we classify the cuspidal Levi subsuperalgebras of all simple classical Lie superalgebras and of the Lie superalgebra W. Most of them are simply Levi subalgebras of , in which case the classification of all finite cuspidal representations has recently been carried out by one of us (Mathieu). Our results reduce the classification of the finite simple weight modules over all classical simple Lie superalgebras to classifying the finite cuspidal modules over certain Lie superalgebras which we list explicitly.

     

Ultrashort microwave pulses generated due to three magnon interactions

Density-functional theory is applied to the interaction site model to study gas-liquid nucleation in a partially immiscible binary system consisting of spherical Lennard-Jones atoms (monomers) and dumbbell molecules of two Lennard-Jones atoms (dimers). Increased interaction anisotropy between the dimer sites and monomers is shown to result in mutual enhancement of nucleation. Critical nuclei with a lamellar structure are observed at high dimer activities.     

Retardation effects in the rotating string model

A new method to study the retardation effects in mesons is presented. It is based on a generalized rotating string model, in which a nonzero value of the relative time between the quark and the antiquark is allowed. This approach leads to a retardation term in the Hamiltonian which behaves as a perturbation of the nonretarded Hamiltonian and preserves the Regge trajectories for light mesons. The straight-line ansatz is used to describe the string, and the relevance of this approximation is tested. It is shown that the string is actually curved because of retardation, but this bending does not bring a relevant contribution to the energy spectrum of the model.     

Magnetic anisotropy in icosahedral cobalt clusters

Magnetic anisotropy has been measured in multiply twinned, icosahedral cobalt clusters. It is found that the low-temperature magnetization of deposited cluster layers is well defined with the Stoner–Wohlfarth model by averaging over clusters with a range of anisotropy energy. Anisotropy energy calculation based on Néel's pair model shows that the icosahedral structure and the layer-by-layer growth of the clusters induce oscillations of the magnetic anisotropy as a function of the filling of the outer surface of the particle. The magnetization measurement at room temperature indicates a weakly correlated cluster glass, as deduced from the approach to saturation that is well described with 2D random anisotropy model.     

Electrochemical reduction of oxygen catalyzed by a wide range of bacteria including Gram-positive

Most bacteria known to be electrochemically active have been harvested in the anodic compartments of microbial fuel cells (MFCs) and are able to use electrodes as electron acceptors. The reverse phenomenon, i.e. using solid electrodes as electron donors, is not so widely studied. To our knowledge, most of the electrochemically active bacteria are Gram-negative. The present study implements a transitory electrochemical technique (cyclic voltammetry) to study the microbial catalysis of the electrochemical reduction of oxygen. It is demonstrated that a wide range of aerobic and facultative anaerobic bacteria are able to catalyze oxygen reduction. Among these electroactive bacteria, several were Gram-positive. The transfer of electrons was direct since no activity was obtained with the filtrate. These findings, showing a widespread property among bacteria including Gram-positive ones, open new and interesting routes in the field of electroactive bacteria research.     

Lithiation of 2-heterosubstituted pyridines with BuLi-LiDMAE: evidence for regiospecificity at C-6.

The determination of the initial deprotonation site of 2-chloro- and 2-methoxypyridine during reaction with BuLi-LiDMAE has been investigated. A series of experiments on deuterated regioisomers revealed a direct lithiation at C-6 excluding a potential first classical ortholithiation and lithium equilibration in the reaction medium. These results suggested that the formation of lithium aggregates at the neighboring of the pyridinic nitrogen atom favored BuLi delivery at C-6 as well as 6-lithio intermediate stabilization.     

osp(N, 2) AKNS equations

The osp(N, 2) extension of the AKNS scheme is reconsidered. It leads to a general class of integrable nonlinear evolution equations for 2+N(N–1)/2 commuting and 2N anticommuting fields. by reduction, various osp(N, 2) versions of the Korteweg-de Vries equation can be obtained. One of these is shown to be bi-Hamiltonian and its second Hamiltonian structure corresponds to the classical limit of the so(N) superconformal algebra. The nonlinear Schrödinger and modified Korteweg-de Vries reductions are also briefly discussed.Work supported by NSerc and FCAR.     

Thickness-dependent optical band gap in one-dimensional Ca3Co2O6 nanometric films

Recent studies on the physical properties of Ca₃Co₂O₆ nanometric samples have shown that their properties are significantly different from those of the bulk samples. The origin of this change is not trivial. We have carried out optical measurements on Ca₃Co₂O₆ thin films with different thicknesses in order to characterize their electronic structure using optical spectroscopy measurements. The absorption spectra show a dependence on the film thickness that is correlated to the grain size in the polycrystalline layers. We found that the optical band gap increases from 1.3 to 1.55 eV when the thickness changes from 35 to 100 nm. The change in the band gap evolution with the film thickness is discussed in terms of both the amorphous effect and the grain size in the Ca₃Co₂O₆ thin films. Finally, we show that these results are consistent with recent measurements concerning magnetic and electrical properties of Ca₃Co₂O₆ nanometric samples.     

Manifolds: Hausdorffness versus homogeneity

We analyze the relationship between Hausdorffness and homogeneity in the frame of manifolds not confined to be Hausdorff. We exhibit examples of homogeneous non-Hausdorff manifolds and prove that a Lindelöf homogeneous manifold is Hausdorff.