Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Synthesis of profluorescent isoindoline nitroxides via palladium-catalysed Heck alkenylation

The synthesis of a new structural class of isoindoline nitroxides (aminoxyls), accessible via the palladium-catalysed Heck reaction, is presented. Reaction of the aryl bromoamine, 5-bromo-1,1,3,3-tetramethylisoindoline (4) or dibromoamine, 5,6-dibromo-1,1,3,3-tetramethylisoindoline (5) or the analogous bromonitroxides 6 and 7 with methyl acrylate gives the acrylate substituted tetramethylisoindoline amines 8 and 10 and nitroxides 12 and 14. Similarly, the reaction of the aryl bromides and dibromides 4–7 with methyl 4-vinylbenzoate gives the carboxystyryl substituted tetramethylisoindoline amines 9 and 11 and the analogous nitroxides 13 and 15. The carboxystyryl tetramethylisoindoline nitroxides demonstrate strongly suppressed fluorescence, which is revealed upon removal of the free radical by reduction or radical coupling.