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.

High leverage interventions: three cases of defensive action and their lessons for OR/MS today.

This paper has two aims. First, to present cases in which scientists developed a defensive system for their homeland: Blackett and the air defense of Britain in WWII, Forrester and the SAGE system for North America in the Cold War, and Archimedes’ work defending Syracuse during the Second Punic War. In each case the historical context and the individual’s other achievements are outlined, and a description of the contribution’s relationship to OR/MS is given. The second aim is to consider some of the features the cases share and examine them in terms of contemporary OR/MS methodology. Particular reference is made to a recent analysis of the field’s strengths and weaknesses. This allows both a critical appraisal of the field and a set of potential responses for strengthening it. Although a mixed set of lessons arise, the overall conclusion is that the cases are examples to build on and that OR/MS retains the ability to do high stakes work.

‘Victory in a Nuclear War? A Comparison of NATO and WTO War Aims and Strategies’

Given the danger of the unbearable catastrophe of nuclear war, NATO in the mid-1950s abandoned any war aim of achieving victory in an all-out war with the Soviet Union or the Warsaw Treaty Organisation. Instead, it adopted the war aim of a cease-fire or war termination. By contrast, the WTO clung on to the war aim of victory - expressed even in terms of the survival of slightly more Soviet citizens than NATO citizens, after unprecedented losses of life in nuclear exchanges - until the mid-1980s when under Gorbachev the concept of victory in nuclear war was abandoned.

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.