A new route to furanoeremophilane sesquiterpenoids. Synthesis of Senecio metabolites (+/-)-6-hydroxyeuryopsin, (+/-)-1,10-epoxy-6-hydroxyeuryopsin, (+/-)-toluccanolide A and (+/-)-toluccanolide C

A new strategy for the synthesis of sesquiterpenoids of the furanoeremophilane family was developed in which the tricyclic nucleus was assembled in an A + C -> A - C -> A - B - C sequence. The A - C connection was made via coupling of a cyclohexenylmethyl bromide with a stannylfuran under "ligandless" Stille conditions, and the key cyclization which closed ring B was accomplished with complete stereocontrol by intramolecular formylation of a 2-silylfuran in the presence of trimethylsilyl triflate. This route was used to complete the first total syntheses of the furanoeremophilane 6-hydroxyeuryopsin and the eremophilenolides toluccanolide A and toluccanolide C, as well as a formal synthesis of 1,10-epoxy-6-hydroxyeuryopsin.

On the recursive sequence Xn = axn-1+bxn-2/c+dxn-1xn-2

In this Paper, we study the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation x(n) = ax(n-1) + bx(n-2) / c + dx(n-1)x(n-2), n =1, 2, ..., where a greater than or equal to 0, b, c, d > 0. (C) 2004 Elsevier Inc. All rights reserved.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.