Stereoselective Peterson Olefinations from Bench‐Stable Reagents and N‐Phenyl Imines

The synthesis of bench‐stable α,α‐bis(trimethylsilyl)toluenes and tris(trimethylsilyl)methane is described and their use in stereoselective Peterson olefinations has been achieved with a wide substrate scope. Product stereoselectivity was poor with carbonyl electrophiles (E/Z ～1:1 to 4:1) though this was significantly improved by employing the corresponding substituted N‐benzylideneaniline (up to 99:1) as an alternative electrophile. The olefination byproduct was identified as N,N‐bis(trimethylsilyl)aniline and could be easily separated from product by aqueous acid extraction. Evidence for an autocatalytic cycle has been obtained.     

A general variable neighborhood search variants for the travelling salesman problem with draft limits

In this paper, we present two general variable neighborhood search (GVNS) based variants for solving the traveling salesman problem with draft limits (TSPDL), a recent extension of the traveling salesman problem. TSPDL arises in the context of maritime transportation. It consists of finding optimal Hamiltonian tour for a given ship which has to visit and deliver products to a set of ports while respecting the draft limit constraints. The proposed methods combine ideas in sequential variable neighborhood descent within GVNS. They are tested on a set of benchmarks from the literature as well as on a new one generated by us. Computational experiments show remarkable efficiency and effectiveness of our new approach. Moreover, new set of benchmarks instances is generated.     

Autoregressive functions estimation in nonlinear bifurcating autoregressive models

Bifurcating autoregressive processes, which can be seen as an adaptation of autoregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions and we use nonparametric techniques. We investigate both nonasymptotic and asymptotic behaviour of the Nadaraya–Watson type estimators of the autoregressive functions. We build our estimators observing the process on a finite subtree denoted by \(\mathbb {T}_n\), up to the depth n. Estimators achieve the classical rate \(|\mathbb {T}_n|^{-\beta /(2\beta +1)}\) in quadratic loss over Hölder classes of smoothness. We prove almost sure convergence, asymptotic normality giving the bias expression when choosing the optimal bandwidth. Finally, we address the question of asymmetry: we develop an asymptotic test for the equality of the two autoregressive functions which we implement both on simulated and real data.     

A Bistable Microelectromechanical System Actuated by Spin-Crossover Molecules

We report on a bistable MEMS device actuated by spin-crossover molecules. The device consists of a freestanding silicon microcantilever with an integrated piezoresistive detection system, which was coated with a 140 nm thick film of the [Fe(HB(tz)₃)₂] (tz=1,2,4-triazol-1-yl) molecular spin-crossover complex. Switching from the low-spin to the high-spin state of the ferrous ions at 338 K led to a reversible upward bending of the cantilever in agreement with the change in the lattice parameters of the complex. The strong mechanical coupling was also evidenced by the decrease of approximately 66 Hz in the resonance frequency in the high-spin state as well as by the drop in the quality factor around the spin transition.     

Well‐posedness and regularity results for a 2m‐th order parabolic equation in symmetric conical domains of ℝN+1

In this paper, we use the domain decomposition method to prove well‐posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high‐order parabolic equation set in conical time‐dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd.     

Analytical model for thermal resistance due to multiple moving circular contacts on a coated bodyModèle analytique pour la résistance thermique due à des contacts circulaires mobiles multiples à la surface d'un solide revêtu

The heat transfer at the interface of two solids in sliding/rolling contact depends on the constriction phenomenon which occurs at the vicinity of asperities. In order to study this problem, the micro-contacts are represented by multiple moving circular heat sources on the surface of a body. The studied body is constituted of a substrate and a surface coating. The thermal constriction resistance due to those contacts is determined analytically in this paper. The solution is developed by using the integral Fourier transforms, and it is valid regardless of the velocity and the relative contact size values. To cite this article: A. Baïri, C. R. Mecanique 331 (2003).     

Méthodes d'approximation et d'itération pour les opérateurs monotones

Sans résumé Mémoire présenté par J. L. Lions     

Evaluation of temperature gradients within combusting droplets in linear stream using two colors laser-induced fluorescence

The scope of this paper concerns the heating process of fuel droplets injected in a hot gaseous environment. The two colors laser-induced fluorescence technique allows measuring the temperature distribution within a droplet by scanning the droplet volume by a sufficiently small probe volume compared to the droplet volume itself. The temperature field is reconstructed using two approaches which have been compared. One is based on a geometrical optics model and the other is based on the 3D calculation of the internal excitation field within the droplet, using the generalized Lorenz-Mie theory. Experimental results have been obtained on a combusting monodisperse ethanol droplet stream (diameter around 200 m).     

Un nouveau préconditionneur pour les problèmes elliptiques à coefficients variablesA new preconditonner for general elleptic problems

In this Note we describe a preconditionner for iteratively solving the linear system arising from the discretization of a general nonseparable elliptic problem by spectral element method. This preconditionner is constructed from approximating the original problem with the closest (in some sense) separable elliptic problem. A direct method is then used to invert the preconditionner. To cite this article: M. Azaïez et al., C. R. Mecanique 331 (2003).