A General Duality Scheme for Nonconvex Minimization Problems with a Strict Inequality Constraint

We establish a duality formula for the problem Minimize f(x)+g(x) for h(x)+k(x)<0 where g, k are extended-real-valued convex functions and f, h belong to the class of functions that can be written as the lower envelope of an arbitrary family of convex functions. Applications in d.c. and Lipschitzian optimization are given.     

Eléments finis stochastiques en élasticité linéaireA stochastic finite element method in linear mechanics

The stochastic finite element method presented in this Note consists in representing in a probabilistic form the response of a linear mechanical system whose material properties and loading are random. Each input random variable is expanded into a Hermite polynomial series in standard normal random variables. The response (e.g., the nodal displacement vector) is expanded onto the so-called polynomial chaos. The coefficients of the expansion are obtained by a Galerkin-type method in the space of probability. To cite this article: B. Sudret et al., C. R. Mecanique 332 (2004).     

DNS of premixed turbulent V-flame: coupling spectral and finite difference methods

To allow for a reliable examination of the interaction between velocity fluctuations, acoustics and combustion, a novel numerical procedure is discussed in which a spectral solution of the Navier–Stokes equations is directly associated to a high-order finite difference fully compressible DNS solver (sixth order PADE). Using this combination of high-order solvers with accurate boundary conditions, simulations have been performed where a turbulent premixed V-shape flame develops in grid turbulence. In the light of the DNS results, a sub-model for premixed turbulent combustion is analyzed. To cite this article: R. Hauguel et al., C. R. Mecanique 333 (2005).     

TMDS-Pd/C: a convenient system for the reduction of acetals to ethers

A simple and practical procedure for the reduction of acetals to ethers is described. It is based on the use of a 1,1,3,3-tetramethyldisiloxane (TMDS)-Pd/C system in the presence of a Brønsted acid as the co-catalyst. The reaction occurs under mild conditions and ethers are obtained in high yields.     

Copper-free click conjugation of methotrexate to a PAMAM dendrimer platform

The synthesis of a generation 5 (G5) poly(amidoamine) (PAMAM) dendrimer platform having cyclooctyne ligands that were subsequently be used for a copper-free Huisgen 1,3-dipolar cycloaddition (click reaction) with azido modified methotrexate is described. The G5 PAMAM dendrimer was first partially (70%) acetylated and then coupled with 20 cyclooctyne ligands through amide bonds. The remaining primary amine groups on the dendrimer surface were neutralized by acetylation. The platform was then ‘clicked’ with different numbers (5, 10, and 17) of γ-azido functionalized methotrexate. The copper-free click reactions were stoichiometric with excellent yields.     

Simultaneous fabrication of superhydrophobic and superhydrophilic polyimide surfaces with low hysteresis

Polyimide is of great interest in the field of MEMS and microtechnology. It is often used for its chemical, thermal, mechanical, and optical properties. In this paper, an original study is performed on controlled variation of polyimide film wettability. A two-step microtexturing method is developed to transform hydrophilic polyimide surfaces into a superhydrophobic surface with low magnitude of hysteresis (Δθ ≈ 0° and contact angle θ ≈ 158°). This method is based on the conception of a new kind of fakir surface with triangular cross-section micropillars, the use of a two-scale roughening, and a C(4)F(8) coating. We demonstrate that the absence of hysteresis is related to a combination of two scales of structuring and the pillar shape. The technology that has been developed results in the simultaneous fabrication of adjacent superhydrophobic and superhydrophilic small areas, which allows an effect of self-positioning of water droplets when deposited on such a checkerboard-like surface.     

Regioselective synthesis of novel substituted indazole-5,6-diamine derivatives

The synthesis of a series of novel indazole-5,6-diamine derivatives is described. This indazole ring system was incorporated in an octahydropyrrolo[3,4-b]phenazine scaffold and was diversely and regioselectively substituted on the nitrogen atoms at the 5- and 10-positions. Thus, the nitrogen atom at the 5-position was found to be more reactive toward electrophiles than the one at the 10-position. This difference of reactivity could be attributed to the electronic effect of the pyrazole moiety. Moreover, an unexpected tetrahydropyran protecting group migration was observed from the N-1 atom to the C-11 position of the octahydropyrrolo[3,4-b]phenazine scaffold.     

Solvent/base effects in the selective domino synthesis of phenanthridinones that involves high-valent palladium species: experimental and theoretical studies

The domino reaction of o-bromobenzamides 1a-m in the presence of K(2)CO(3) and the [PdCl(2)(PPh(3))(2)] catalyst granted a selective access to phenanthridinones 2 or to the new 1-carboxamide phenanthridinones 3 depending on the solvent, DMF or 1,4-dioxane, respectively. Investigations of the reaction parameters provided the first example of a direct correlation between the base dissociation and the solvent polarity on the selectivity observed. Moreover, mechanistic studies (NMR spectroscopy and ESI-MS monitoring) allowed us to characterize Pd(II) palladacycle 4 and biaryl species as common intermediates for these two domino processes. On that basis, C(sp(2))-C(sp(2)) bond formation is envisaged by generation of a Pd(IV) complex after oxidative addition of 1 into Pd(II) palladacycle 4, a rationale that is supported by DFT calculations. A general catalytic cycle is proposed to account for these observations.