Variance of the virtual displacement

We show that the affine structure of the 3-dimensional space is deeply enmeshed with the static laws expression. The relevance of tensorial rules for calculus in mechanics is thus enhanced. The virtual work principle is stated precisely but a little twist is given to the usual statements: the tensorial nature of the so-called virtual displacement vector is asserted to be covariant. To cite this article: C. Vallée et al., C. R. Mecanique 332 (2004).

Résumé

Nous montrons que la structure affine de l'espace tridimensionnel est fortement imbriquée avec l'expression des lois de la statique. La pertinence de l'application des règles du calcul tensoriel à la mécanique est ainsi renforcée. Le principe des travaux virtuels est établi précisément avec une seule entorse aux exposés classiques : la nature tensorielle de l'habituel vecteur déplacement virtuel est affirmée covariante. Pour citer cet article : C. Vallée et al., C. R. Mecanique 332 (2004).     

Intramolecular Cyclization of 1-(ω-Phenylalkyl)-2-(nitromethylene)pyrrolidines in Triflic Acid

1-(ω-Phenylalkyl)-2-(nitromethylene)pyrrolidines in triflic acid undergo a C,O-diprotonation, followed by loss of water, to form conjugated iminium–hydroxynitrilium dications, which react with the tethered phenyl ring by electrophilic aromatic substitution to afford tricyclic iminium compounds as triflate salts. The scope and mechanism of this reaction are discussed.     

Non-invasive vibrational SFG spectroscopy reveals that bacterial adhesion can alter the conformation of grafted "brush" chains on SAM

Understanding bacterial adhesion on a surface is a crucial step to design new materials with improved properties or to control biofilm formation and eradication. Sum Frequency Generation (SFG) vibrational spectroscopy has been employed to study in situ the conformational response of a self-assembled monolayer (SAM) of octadecanethiol (ODT) on a gold film to the adhesion of hydrophilic and hydrophobic ovococcoid model bacteria. The present work highlights vibrational SFG spectroscopy as a powerful and unique non-invasive biophysical technique to probe and control bacteria interaction with ordered surfaces. Indeed, the SFG vibrational spectral changes reveal different ODT SAM conformations in air and upon exposure to aqueous solution or bacterial adhesion. Furthermore, this effect depends on the bacterial cell surface properties. The SFG spectral modeling demonstrates that hydrophobic bacteria flatten the ODT SAM alkyl chain terminal part, whereas the hydrophilic ones raise this ODT SAM terminal part. Microorganism-induced alteration of grafted chains can thus affect the desired interfacial functionality, a result that should be considered for the design of new reactive materials.     

On the elucidation of the mechanism of Vinca alkaloid fluorination in superacidic medium

Detailed investigations on one of the key steps of the superacidic fluorination of Vinca alkaloids that is the origin of C20' activation are reported. While two different pathways can be envisioned for the emergence of the transient secondary carbocationic intermediate, isotopic labeling experiments unambiguously revealed the involvement of a 1,2-hydride shift mechanism.     

Sharp asymptotics of the <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> approximation error for interpolation on block partitions

Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed and no exact formula for the optimal error of approximation can be given. Therefore, the next natural question would be to study the asymptotic behavior of the error and construct asymptotically optimal sequences of partitions. In this paper we provide sharp asymptotic estimates for the error of interpolation by splines on block partitions in \mathbbR^d{\mathbb{R}^d} . We consider various projection operators to define the interpolant and provide the analysis of the exact constant in the asymptotics as well as its explicit form in certain cases.     

Synthesis and foaming properties of new anionic surfactants based on a renewable building block: sodium dodecyl isosorbide sulfates

Two agro-based anionic surfactants containing an isosorbide moiety have been synthesized and their amphiphilic properties evaluated. Since isosorbide is now considered as an important platform chemical of the starch industry, these compounds could represent bio-sourced alternatives to the alkyl ether sulfates (notably lauryl ether sulfate, LES) that are based on petroleum-derived ethylene oxides. As isosorbide is an asymmetric diol, two isomers can be prepared (2-O-dodecyl isosorbide sulfate and 5-O-dodecyl isosorbide sulfate) that show significantly different aqueous properties as regards to their Krafft temperatures and critical micellar concentrations. 5-O-dodecyl isosorbide sulfate is the most soluble and the most efficient surfactant. It possesses a much lower critical micelle concentration (cmc) than sodium dodecyl sulfate, SDS, leading to comparable foaming properties with a three times lower concentration. Its behavior compares well with the one of pure diethoxylated dodecyl sulfate that has also been prepared and evaluated in this work.     

A comprehensive approach of planning and scheduling based on petri nets

The main results available on the use of black-and-white Petri nets for modelling, planning and scheduling manufacturing systems are presented. In the first part of the paper, the basics of Petri nets necessary to understand the subsequent presentation are introduced. Particular attention is paid to event graphs, a particular type of Petri nets used for modelling and evaluating ratio-driven systems. The second part of the paper is devoted to ratio-driven systems, their modelling and their scheduling. Job-shops, assembly systems, and KANBAN systems are used to illustrate this section. Finally, the general case is investigated of manufacturing systems subject to changing demands. An approach based on conflict-free Petri nets with input and output transitions is proposed for planning and scheduling this type of system.