Behaviour norms are considered for decision trees which allow both objective probabilities and uncertain states of the world with unknown probabilities. Terminal nodes have consequences in a given domain. Behaviour is required to be consistent in subtrees. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree. It implies that behaviour reveals a revealed preference ordering satisfying both the independence axiom and a novel form of sure-thing principle. Continuous consequentialist behaviour must be expected (...) utility maximizing. Other plausible assumptions then imply additive utilities, subjective probabilities, and Bayes' rule. (shrink)
Similarities and differences between the phenomena of kink banding in compressed layered structures and shear banding in compressed granular media are explored. Simple models are introduced for both, and the focus is directed onto how they can nucleate from the perfectly flat state. A convincing scenario is found for each in which a mode develops from an initial bifurcation into a periodic state, followed by rapid localization under falling load, while retaining decaying but wavy tails. At a certain lower critical (...) load, the tails lose their waviness, and the expected form of the kink or shear band appears. In each case, good numerical evidence is provided for the existence of this form of behaviour. A second potential instability for the layered case is also explored, linked to the appearance of a critical force dipole that overcomes bending stiffness locally at some point along the length. This mode, which should appear with non-wavy decaying tails at the lower of the two critical loads mentioned earlier, proves somewhat elusive. Evidence is found for its existence in the linearized approximation to the layered model, but the search for numerical solutions to the underlying nonlinear equation is hindered by a shortage of suitable boundary conditions. (shrink)
Introduction -- Structuring principles -- On right -- From interest and pleasure to the good in-itself -- Good in-itself and the rights of the ensouled person -- The good and friendship in the community of free souls -- The rehabilitation of politics through the recovery of its essence.
An ethical measure of income inequality corresponds to a social ordering of income distributions. Without interpersonal comparisons, the only possible social orderings are dictatorial, so there can be no ethical inequality measure. Interpersonal comparisons allow a very much richer set of possible social orderings, and the construction of ethical measures of inequality.
A regularized two-dimensional model for the buckling of force chains is presented, comprising identical rigid discs sitting initially in a conventional close-packed arrangement. As linear elastic constitutive laws are used throughout, the only nonlinearity in the system comes from large rotations as the resulting force chains are obliged to buckle under imposed end-shortening. The evolving deflected shapes are seen to develop and interact in a highly complex bifurcation structure. Analysis by the nonlinear continuation code Auto exposes at realistic load levels (...) an energy landscape rich in local minima. A number of such states are identified, amongst them families of solutions with the familiar appearance of shear bands over a finite number of discs. A well-known ?snakes and ladders? pattern is identified as the mechanism for the addition of extra discs to increase the width of the band. (shrink)
Iron bulk self-diffusion coefficients were measured in Fe2O3 single crystals using original methodology based on the utilization of 57Fe stable isotope as iron tracer and depth profiling by secondary ion-mass spectrometry (SIMS). The iron self-diffusion coefficients were measured along and perpendicular to the c-axis, between 900 and 1100°C, in an oxygen atmosphere. Along the c-axis, the coefficients can be described by D ? c (cm2/s)?=?5.2???106?exp[?510 (kJ/mol)/RT], and are close to reliable data, available in the literature, obtained by means of radioactive (...) techniques. Perpendicular to the c-axis, D ?c (cm2/s)?=? 83?exp[?430 (kJ/mol)/RT], and the coefficients are smaller than coefficients along the c-axis. The data are compared with previously results of cation bulk self-diffusion in Cr2O3 and Al2O3 single crystals. (shrink)