Lexicographic choice functions without archimedeanicity

We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld, Schervisch and Kadane (2010) but without imposing any Archimedean condition. We show that lexicographic probabilities are related to a particular type of sets of desirable gambles, and investigate the properties of the coherent choice function this induces via maximality. Finally, we show that the convexity axiom is necessary but not sufficient for a coherent choice function to be the infimum of a class of lexicographic ones

Gel spinning of porous poly(methyl methacrylate)) fibres

Solutions of poly(methyl methacrylate) in 1-butanol demix on cooling. By solution extrusion, fibres are produced which have an oriented porosity. The relation between this morphology, the phase diagram and the extrusion procedure is discussed

Infinite Exchangeability for Sets of Desirable Gambles

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study infinite exchangeability assessments for them, and give a counterpart of de Finetti's infinite representation theorem. We show how the infinite representation in terms of frequency vectors is tied up with multivariate Bernstein (basis) polynomials. We also lay bare the relationships between the representations of updated exchangeable models, and discuss conservative inference (natural extension) under exchangeability

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

Radiation chemistry of solid-state carbohydrates using EMR

We review our research of the past decade towards identification of radiation-induced radicals in solid state sugars and sugar phosphates. Detailed models of the radical structures are obtained by combining EPR and ENDOR experiments with DFT calculations of g and proton HF tensors, with agreement in their anisotropy serving as most important criterion. Symmetry-related and Schonland ambiguities, which may hamper such identification, are reviewed. Thermally induced transformations of initial radiation damage into more stable radicals can also be monitored in the EPR (and ENDOR) experiments and in principle provide information on stable radical formation mechanisms. Thermal annealing experi-ments reveal, however, that radical recombination and/or diamagnetic radiation damage is also quite important. Analysis strategies are illustrated with research on sucrose. Results on dipotassium glucose-1-phosphate and trehalose dihydrate, fructose and sorbose are also briefly discussed. Our study demonstrates that radiation damage is strongly regio-selective and that certain general principles govern the stable radical formation