Minimizing the number of machines for minimum length schedules

In this paper, we present a new objective function for scheduling on parallel machines: minimizing the number of machines for schedules of minimum length. We study its complexity and we prove the NP-completeness of this problem, even if there is no precedences or for unitary execution times. We propose several polynomial algorithms for various particular cases.     

Enzymatic resolution of a 1,2-cyclic sulphite glycerol derivative

cis-2-Oxo-5-hydroxymethyl-1,3,2-dioxathiolane 2a can be efficiently resolved by a lipase from Pseudomonas cepacia-catalysed acylation reaction with vinylbutyrate. Compound 2a was directly prepared from glycerol in one step. This first lipase-catalysed resolution of a cyclic sulphite derivative provides a potentially useful activated chiral synthon.     

An optimization-based numerical method for diffusion problems with sign-changing coefficients

A new optimization-based numerical method is proposed for the solution to diffusion problems with sign-changing conductivity coefficients. In contrast to existing approaches, our method does not rely on the discretization of a stabilized equation, and the convergence of the scheme can be proved without any symmetry assumption on the mesh near the interface where the conductivity sign changes.     

Lanthanide luminescence efficiency in eight- and nine-coordinate complexes: Role of the radiative lifetime

The photophysical parameters for the sensitization of metal-centred luminescence are analyzed in two series of complexes with tridentate and hexadentate ligands having N_xO_y chelating units. In particular, the radiative lifetime τ_rad is experimentally estimated for 29 nine-coordinate Eu^III complexes and 10 eight- and nine-coordinate Yb^III complexes. The known dependence of τ_rad on refractive index is substantiated by comparing data for solid-state samples and solutions. Moreover, a clear dependence of τ_rad with the coordination environment is evidenced and in the case of Eu^III, a comparison between τ_rad and the nephelauxetic effect generated by the ligands is attempted. Altogether, this extensive analysis points to the importance of having a handle on τ_rad when designing ligands for highly luminescent lanthanide-containing molecular edifices. This, in turn, should stimulate initiating theoretical considerations to unravel a reliable relationship between τ_rad and the electronic structure of the ligands.     

Iron-catalyzed selective reduction of nitro compounds to amines

An efficient reduction of the nitro group with a catalytic amount of Fe(acac)₃ and TMDS in THF at 60 °C affording the corresponding amine is described.     

Time-harmonic acoustic propagation in the presence of a shear flow

This work deals with the numerical simulation, by means of a finite element method, of the time-harmonic propagation of acoustic waves in a moving fluid, using the Galbrun equation instead of the classical linearized Euler equations. This work extends a previous study in the case of a uniform flow to the case of a shear flow. The additional difficulty comes from the interaction between the propagation of acoustic waves and the convection of vortices by the fluid. We have developed a numerical method based on the regularization of the equation which takes these two phenomena into account. Since it leads to a partially full matrix, we use an iterative algorithm to solve the linear system.     

Synthesis and metallation of 2-(pyridyl)benzoic acids and ethyl 2-(pyridyl)benzoates: a new route to azafluorenones

The ring deprotonation of 2-(2- and 4-pyridyl)benzoic acids using lithium dialkylamides in THF at rt, and the in situ cyclization afforded 4- and 2-azafluorenones, respectively. 1-Azafluorenone was obtained from ethyl 2-(3-pyridyl)benzoate using a similar protocol.     

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).     

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.