Silica-supported l-proline organocatalysts for asymmetric aldolisation

New heterogenised silica-based organocatalysts have been prepared via the sol–gel process from two silylated derivatives of l-proline, featuring either a carbamate or an ether linker. Co-gelification with variable amounts of TEOS was performed with and without porogen to yield high surface area solids. These materials were evaluated as heterogeneous phase organocatalysts for the asymmetric aldol reaction of p-nitrobenzaldehyde with acetone.     

H-fields and their Liouville extensions

We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending , as well as the field of logarithmic-exponential series over are H-fields. We study Liouville extensions in the category of H-fields, as a step towards a model theory of H-fields. The main result is that an H-field has at most two Liouville closures. Received: 15 November 1999 / in final form: 19 December 2000 / Published online: 1 February 2002     

More on the analysis of local regularity through wavelets

In this paper we want to extend the results of pointwise analysis through wavelet transforms to the class of functions where the local fluctuation is bounded by any submultiplicative function. This generalizez the results obtained before in the well-known case of Hölder regularity.     

Asymmetric Spotty Patterns for the Gray–Scott Model in R2

In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray–Scott model in a bounded two-dimensional domain. We show that given any two positive integers   k ₁, k ₂  , there are asymmetric solutions with   k ₁  large spots (type A) and   k ₂  small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetric solutions are shown to be unstable. However, in a narrow range of parameters, asymmetric solutions may be stable.