Anderson localization for one- and quasi-one-dimensional systems

We prove almost-sure exponential localization of all the eigenfunctions and nondegeneracy of the spectrum for random discrete Schrödinger operators on one- and quasi-one-dimensional lattices. This paper provides a much simpler proof of these results than previous approaches and extends to a much wider class of systems; we remark in particular that the singular continuous spectrum observed in some quasiperiodic systems disappears under arbitrarily small local perturbations of the potential. Our results allow us to prove that, e.g., for strong disorder, the smallest positive Lyapunov exponent of some products of random matrices does not vanish as the size of the matrices increases to infinity.     

A capacity constrained single-facility dynamic lot-size model

A computationally efficient algorithm for a multi-period single commodity production planning problem with capacity constraints is developed. The model differs from earlier well-known studies involving concave cost functions in the introduction of production capacity constraints which need not be equal in every period. The objective is to find an optimal production schedule that minimizes the total production and inventory costs. Backlogging is not allowed. The structure of the optimal solution is characterized and then used in an efficient algorithm.     

Acceleration by aggregation of successive approximation methods

Methods of successive approximation for solving linear systems or minimization problems are accelerated by aggregation-disaggregation processes. These processes, which modify the iterates being produced, are characterized by a two directional flow of information between the original higher dimensional problem and a lower dimensional aggregated version. This technique is characterized by means of Galerkin approximations, and this in turn permits analysis of the method. A deterministic as well as probabilistic analysis is given of a number of specific aggregation-disaggregation examples. Numerical experiments have been performed, and these confirm the analysis and demonstrate the acceleration.     

The covering problem of complete uniform hypergraphs

A result of Krichevskii [3] and Hansel [1], concerning coverings of complete bipartite graphs is extended to hypergraphs, thus providing a lower bound on the lengths of Boolean formulas of a certain type realizing the threshold functions.     

Absolute configuration of an iturinic acid as determined by CD spectrum of its DNP-p-methoxyanilide

Absolute configuration of the long chain β-amino acid obtained from the hydrolysate of iturin A has been determined to be R by application of Dnp-aromatic rule. This is the first assignment for the chirality of an iturinic acid.     

Etude d'impulsions lumineuses breves par interferometrie a deux ondes

We have studied the evolution of the light transmitted through matter in which an optical breakdown is taking place. With a two-waves interferometer made a birefringent plate between polarizers we get informations about the time correlation function of the fields. With an interferometer made of two identical harmonic generating plates separated by a dispersion medium, we learn about the correlation function of the square of the fields. Both systems act as spectral filters with a notch cosine-shaped centered at the incident frequency. We have also observed a transient angular spreading of the beam not previously emphasized which brings a further complication in the picture.     

A solid-phase approach to the phallotoxins: total synthesis of [Ala7]-phalloidin

Herein we report a solid-phase synthetic approach to [Ala7]-phalloidin (1). Prior syntheses of phallotoxins were carried out using solution-phase routes that required large scale and preclude library production. The route presented here consists of solution-phase preparation of key orthogonally protected amino acid building blocks, followed by a solid-phase peptide synthesis sequence, featuring two resin-bound macro-cyclization reactions. The final product mixture was composed of two atropisomeric compounds, one designated "natural" (1) and the other designated "non-natural" (1'). The structures of these species were modeled using restrained energy minimization with NMR-derived restraints.     

Acetate- and thiol-capped monodisperse ruthenium nanoparticles: XPS, XAS, and HRTEM studies

Monodisperse ruthenium nanoparticles were prepared by reduction of RuCl3 in 1,2-propanediol. The mean particle size was controlled by appropriate choice of the reduction temperature and the acetate ion concentration. Colloidal solutions in toluene were obtained by coating the metal particles with dodecanethiol. High-resolution transmission electron microscopy (HRTEM), X-ray photoelectron spectroscopy (XPS), and X-ray absorption spectroscopy (XANES and EXAFS for the Ru K-absorption edge) were performed on particles of two different diameters, 2 and 4 nm, and in different environments, polyol/acetate or thiol. For particles stored in polyol/acetate XPS studies revealed superficial oxidation limited to one monolayer and a surface coating containing mostly acetate ions. Analysis of the EXAFS spectra showed both oxygen and ruthenium atoms around the ruthenium atoms with a Ru-Ru coordination number N smaller than the bulk value, as expected for fine particles. In the case of 2 nm acetate-capped particles N is consistent with particles made up of a metallic core and an oxidized monolayer. For 2 nm thiol-coated particles, a Ru-S bond was evidenced by XPS and XAS. For the 4 nm particles XANES and XPS studies showed that most of the ruthenium atoms are in the zerovalent state. Nevertheless, in both cases, when capped with thiol, the Ru-Ru coordination number inferred from EXAFS is much smaller than for particles of the same size stored in polyol. This is attributed to a structural disorganization of the particles by thiol chemisorption. HRTEM studies confirm the marked dependence of the structural properties of the ruthenium particles on their chemical environment; they show the acetate-coated particles to be single crystals, whereas the thiol-coated particles appear to be polycrystalline.