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     

An Adjustable Cleft Based on an 8-Sulfonamide-2-Naphthoic Acid with Oxyanion Hole Geometry

Cleft type receptors showing the oxyanion hole motif have been prepared in a straightforward synthesis starting from the commercial 3,7-dihidroxy-2-naphthoic acid. The double H-bond donor pattern is achieved by the introduction of a sulfonamide group in the C-8 position of naphthalene and a carboxamide at the C-2 position. This cleft, for which the geometry resembles that of an oxyanion hole, is able to adjust to different guests, as shown by the analysis of the X-ray crystal structures of associates with methanol or acetic acid. Combination of hydrogen bonds and charge-transfer interactions led to further stabilization of the complexes, in which the electron-rich aromatic ring of the receptor was close in space to the electron-deficient dinitroaromatic guests. Modelling studies and bidimensional NMR experiments have been carried out to provide additional information.     

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.