Equidistant hypersurfaces of the bidisk

The following are notes on the geometry of the bidisk, H ² × H ². In particular, we examine the properties of equidistant surfaces in the bidisk.     

Bis(diethoxyselenophosphinoyl) triselenide and bis(diisopropoxyselenophosphinoyl) diselenide

The title compounds, bis(diethoxyselenophosphinoyl) triselenide, [P(OEt)₂Se]Se₃[P(OEt)₂Se], and bis­(diisopropoxy­selenophosphinoyl) diselenide, [P(OⁱPr)₂Se]Se₂[P(OⁱPr)₂Se], comprise an Se₃ chain or an Se₂ chain bridging two (RO)₂PSe groups.     

An infinite horizon stochastic maximum principle for discounted control problem with Lipschitz coefficients

In the present work, a stochastic maximum principle for discounted control of a certain class of degenerate diffusion processes with global Lipschitz coefficient is investigated. The value function is given by a discounted performance functional, leading to a stochastic maximum principle of semi-couple forward–backward stochastic differential equation with non-smooth coefficients. The proof is based on the approximation of the Lipschitz coefficients by smooth ones and the approximation of the infinite horizon adjoint process.     

Diels-Alder cycloaddition of o-quinonedimethides and alkylidene-5H-furan-2-ones: new and rapid access to lambertellol cores and arthrinone derivatives

An efficient synthesis of deoxy-lambertellols was reported through a highly chemo- and diastereoselective intermolecular Diels-Alder cycloaddition between trans-1,2-disiloxybenzocyclobutenes and 2-methylprotoanemonine. Such transformation with δ-substituted γ-alkylidenebutenolides, to prepare new analogues of these tricyclic spirolactones, which would be very difficult to prepare by other ways, was also studied.     

Water soluble polymeric nanogels by xanthate-mediated radical crosslinking copolymerisation

Branched water-soluble copolymers were obtained by direct radical crosslinking copolymerisation of acrylic acid or acrylamide and N,N'-methylenebisacrylamide at high solid content in the presence of an O-ethylxanthate as a reversible chain transfer agent.     

Modélisation et simulation numérique du changement de phase liquide–vapeur en cavitéModeling and numerical simulation of liquid–vapor phase change in an enclosed cavity

A model for the simulation of boiling flow with phase change in a closed cavity is presented. A front-tracking method is used to deal with the liquid–vapor interface. The liquid phase is incompressible while the vapor phase is weakly compressible and obeys to the perfect gas law. This model can deal with large density ratio (${\rho }_l/{\rho }_v?1000$) flows while accounting for the saturation curve. Computations are performed on a 1D validation case, idealizing a pressure cooker. Results are compared with a low Mach number approximation. To cite this article: V. Daru et al., C. R. Mecanique 334 (2006).     

Comparison of two solid-phase microextraction methods for the quantitative analysis of VOCs in indoor air

Competitive adsorption on adsorptive solid-phase microextraction (SPME) fibres implies careful determination of operating conditions for reliable quantitative analysis of VOCs in indoor air. With this objective, two analytical approaches, involving non-equilibrium and equilibrium extraction, were compared. The average detection limit obtained for GC-MS analysis of nine VOCs by the equilibrium method is 0.2 μg m⁻³, compared with 1.9 μg m⁻³ with the non-equilibrium method. The effect of the relative humidity of the air on the calibration plots was studied, and shown to affect acetone adsorption only. Hence, the concentrations that can be accurately determined are up to 9 μmol m⁻³. The methods were then applied to indoor air containing different concentrations of VOCs. The non-equilibrium method, involving short extraction time, can be used for detection of pollution peaks whereas equilibrium extraction is preferable for measurement of sub-μg m⁻³ ground concentration levels.      

Dynamic kinetic resolution of α-chloro β-keto esters and phosphonates: hemisynthesis of Taxotere® through Ru-DIFLUORPHOS asymmetric hydrogenation

The dynamic kinetic resolution (DKR) of racemic α-chloro β-ketoesters and α-chloro β-ketophosphonates through ruthenium-mediated asymmetric hydrogenation is reported. The corresponding α-chloro β-hydroxyesters and α-chloro β-hydroxyphosphonates were obtained in good to high enantio- and diastereomeric excesses using, in particular, the atropisomeric ligand DIFLUORPHOS. This methodology allowed an efficient preparation of the anti phenylisoserine side chain of Taxotere® which has been used for the hemisynthesis of the cancer therapeutic agent itself. In addition, ¹³C NMR in chiral oriented solvents was used to investigate the DKR effect.