Unscaled spatial branging process with interaction: macrospic equation and local equilibrium

For some spatial branching processes with interaction considered as measure–valued processes, convergence to solutions of non–linear macroscopic equation and local equilibrium are proved, without scaling but providing each particle with a small mass ε and assuming convergence of the initial distribution when ε goes to 0     

Extendibility of bilinear forms on banach sequence spaces

We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c ₀ in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to any superspace.     

A statistical associating fluid theory for electrolyte solutions (SAFT-VRE)

A general theory for electrolyte solutions is examined within the framework of the statistical associating fluid theory for potentials of variable range (SAFT-VR). A first extension of the theory (SAFT-VRE) has already been used to describe the thermodynamics and phase equilibria of aqueous solutions of alkali-halide salts [GALINDO, A., GIL-VILLEGAS, A., JACKSON, G. and BURGESS, A. N., 1999, J. phys. Chem., 103, 10272]. The approach incorporates separate contributions describing the monomer, associating and ionic interactions. In the spirit of the SAFT-VR approach the monomer contribution is written as a high-temperature perturbation expansion up to second order; the separate effects of solvent-solvent, solvent-ion and ion-ion interactions on the phase equilibria are studied. Water is taken to be the solvent throughout the study, with the same four-site model and parameters as in the previous work. The association contribution is essential to account for the hydrogen bonding interactions present in water. The effects of ion pairing and solvent-ion association are also examined. For the ionic contribution several levels of approximation are discussed. The effect of the different molecular parameters on the phase behaviour of a model aqueous solution is examined for the different choices.     

In Situ Generation of ArCu from CuF2 Makes Coupling of Bulky Aryl Silanes Feasible and Highly Efficient

A bimetallic system of Pd/CuF₂, catalytic in Pd and stoichiometric in Cu, is very efficient and selective for the coupling of fairly hindered aryl silanes with aryl, anisyl, phenylaldehyde, p‐cyanophenyl, p‐nitrophenyl, or pyridyl iodides of conventional size. The reaction involves the activation of the silane by Cu^II, followed by disproportionation and transmetalation from the Cu^I(aryl) to Pd^II, upon which coupling takes place. Cu^III formed during disproportionation is reduced to Cu^I(aryl) by excess aryl silane, so that the CuF₂ system is fully converted into Cu^I(aryl) and used in the coupling. Moreover, no extra source of fluoride is needed. Interesting size selectivity towards coupling is found in competitive reactions of hindered aryl silanes. Easily accessible [PdCl₂(IDM)(AsPh₃)] (IDM = 1,3‐dimethylimidazol‐2‐ylidene) is by far the best catalyst, and the isolated products are essentially free from As or Pd (<1 ppm). The mechanistic aspects of the process have been experimentally examined and discussed.