An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

New dimeric supramolecular structure of mixed (phthalocyaninato)(porphyrinato)-europium(III) sandwiches : preparation and spectroscopic characteristics

The mixed double-decker Eu\[Pc(15C5)4](TPP) (1) was obtained by base-catalysed tetramerisation of 4,5-dicyanobenzo-15-crown-5 using the half-sandwich complex Eu(TPP)(acac) (acac = acetylacetonate), generated in situ, as the template. For comparative studies, the mixed triple-decker complexes Eu2\[Pc(15C5)4](TPP)2 (2) and Eu2\[Pc(15C5)4]2(TPP) (3) were also synthesised by the raise-by-one-story method. These mixed ring sandwich complexes were characterised by various spectroscopic methods. Up to four one-electron oxidations and two one-electron reductions were revealed by cyclic voltammetry (CV) and differential pulse voltammetry (DPV). As shown by electronic absorption and infrared spectroscopy, supramolecular dimers (SM1 and SM3) were formed from the corresponding double-decker 1 and triple-decker 3 in the presence of potassium ions in MeOH/CHCl3.