Sequential stopping rules for the multistart algorithm in global optimisation

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.     

Composition of Lie transforms with rigorous estimates and applications to Hamiltonian perturbation theory

In this paper we exhibit a rigorous perturbation theory for nearly integrable Hamiltonian systems, based on the composition of Lie Transforms. Precisely, we first study the algorithm for the composition of Lie transforms, and provide rigorous estimates for the convergence radius and the truncation errors of the series; then we use our estimates for a particular model-example, namely a system of weakly coupled harmonic oscillators having Diophantine frequencies, and work out Nekhoroshev-like exponential estimates for the stability times.     

A fast solver for linear systems with displacement structure

We describe a fast solver for linear systems with reconstructible Cauchy-like structure, which requires O(rn ²) floating point operations and O(rn) memory locations, where n is the size of the matrix and r its displacement rank. The solver is based on the application of the generalized Schur algorithm to a suitable augmented matrix, under some assumptions on the knots of the Cauchy-like matrix. It includes various pivoting strategies, already discussed in the literature, and a new algorithm, which only requires reconstructibility. We have developed a software package, written in Matlab and C-MEX, which provides a robust implementation of the above method. Our package also includes solvers for Toeplitz(+Hankel)-like and Vandermonde-like linear systems, as these structures can be reduced to Cauchy-like by fast and stable transforms. Numerical experiments demonstrate the effectiveness of the software.     

A convenient preparation of 3-isopropyl-1-methylcyclopentylmethanol and 1-isopropyl-3-methylcyclopentylmethanol via Favorskii rearrangement

The Favorskii rearrangement of suitable α-chloro derivatives of commercially available (+)- and (−)-carvone, and (−)-menthone served efficiently to prepare the title compounds featuring delicious fruity, floral olfactory notes.     

A hyperbolic reaction–diffusion model for the hantavirus infection

A hyperbolic reaction–diffusion model for the hantavirus infection, generalizing the parabolic set of equations recently derived by Abramson and Kenkre, is proposed within the context of Extended Thermodynamics. The model, as in the parabolic case, captures some of the realistic features of the dynamics of hantavirus in mice population, while it avoids the unphysical features concerning the instantaneous diffusive effects typical of parabolic equations. Traveling wave solutions, related to the spread of the infection in the landscape, are investigated. Both analytical and numerical results obtained herein are discussed and validated from the behavior of the biological system. Copyright © 2007 John Wiley & Sons, Ltd.     

Pt dendrimer nanocomposites for oxygen reduction reaction in direct methanol fuel cells

Dendrimer-encapsulated Pt nanoparticles (G4OHPt) were prepared by chemical reduction at room temperature. The G4OHPt, with average diameters of ca. 2.7 nm, were characterized by X-ray diffraction, scanning electron microscopy, and thermogravimetric analysis. Electrocatalytic behavior for oxygen reduction reaction was investigated using a rotating disk electrode configuration in an acidic medium, with and without the presence of methanol (0.01, 0.1, and 1 M). Kinetic studies showed that electrodes based on Pt nanoparticles encapsulated inside the dendrimer display a higher selectivity for ORR in the presence of methanol than electrodes based on commercial Pt black catalysts. Also, the dendritic polymer confers a protective effect on the Pt in the presence of methanol, which allows its use as a cathode in a direct methanol fuel cell operating at different temperatures. Good performance was obtained at 90 °C and 2 bar of pressure with a low platinum loading on the electrode surface.