Nothing Recedes Like Success - Risk Analysis and the Organizational Amplification of Risks

Professor Freudenburg believes that there is room for improvement in Risk analysis, particularly in drawing on systematic studies of human behavior in the calculation of real, empirical probabilities of failure. The need is argued to be especially acute where technological Risks are associated with low expected probabilities of failure and are managed by human organizations for extended periods of time. This permits complacency to set in

A Survey of Counterexamples to Hilbert's Fourteenth Problem

We survey counterexamples to Hilbert’s Fourteenth Problem, beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations. Historical framework and pertinent references are provided. We also include 8 important open questions

Non-rationality of some fibrations associated to Klein surfaces

We study the polynomial fibration induced by the equation of the Klein surfaces obtained as quotient of finite linear groups of automorphisms of the plane; this surfaces are of type A, D, E, corresponding to their singularities. The generic fibre of the polynomial fibration is a surface defined over the function field of the line. We proved that it is not rational in cases D, E, although it is obviously rational in the case A. The group of automorphisms of the Klein surfaces is also described, and is linear and of finite dimension in cases D, E; this result being obviously false in case A.Comment: 18 page