The shape of incomplete preferences

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.Comment: Published at http://dx.doi.org/10.1214/009053606000000740 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A behaviorally-based approach to measuring inequality

The measurement of inequality is often made using observed population-based distributions, such as the distribution of income or the distribution of members of different groups across neighborhoods. Unfortunately, such distributions confound the behavior of a given year with earlier events that influence the composition of the population. Here, we advocate measuring inequality using current behavioral measures and their compositional implications, and show how such measures may be obtained from frequently available data. The approach is then applied to trends in inequality between men and women in the distribution of ages at death. Observed death distributions indicate that, since 1970, mortality in 4 Western countries experienced increases in inequality that recently leveled off. In contrast, life table death distributions, which solely reflect the implications of a given year’s mortality rates, reveal a peak in inequality followed (in 3 of the 4 countries) by appreciable declines. The results are insensitive to whether inequality is measured by entropy, the Gini Index, or the Index of Dissimilarity. However, the type of distribution analyzed---whether observed or behaviorally derived---can make a significant difference in the results obtained. Because behaviorally derived distributions reflect the inequality implications of actual behavior, they are recommended for greater use in analyses of inequality.behaviorally-based, entropy, Gini Index, index of dissimilarity, inequality, measurement

Global Strong Solutions for a Class of Heterogeneous Catalysis Models

We consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a diffusion-advection system inside the bulk phase and a reaction-diffusion-sorption system modeling the processes on the catalytic wall and the exchange between bulk and surface. We assume Fickian diffusion with constant coefficients, sorption kinetics with linear growth bound and a network of chemical reactions which possesses a certain triangular structure. Our main result gives sufficient conditions for the existence of a unique global strong $L^2$-solution to this model, thereby extending by now classical results on reaction-diffusion systems to the more complicated case of heterogeneous catalysis.Comment: 30 page

Strain Limits for Concrete Filled Steel Tubes in AASHTO Seismic Provisions

INE/AUTC 13.1

NAVEX: A space shuttle experiment with atomic clocks

A navigation and time transfer experiment (NAVEX) to be flown within the payload of the first German Spacelab mission D-1 is discussed. The objectives of the experiment are to synchronize distant ground stations with an accuracy of better than 10 nsec and to demonstrate one way ranging with an accuracy of better than 30 m. Spread spectrum signals are used and the related technique is tested. On board a Cs and a Rb clock is used. The relativistic effect of these clocks is about -25 microsec per day. On the ground at least two receiving stations and one transmitting-receiving station will be installed. The synchronization of the ground clocks by shuttle signals is compared to those achieved with clock transportations and with GPS measurements. A system description of this experiment is given containing details on the technical concept, the hardware and the planned data evaluation. The present state of the preparatory work is briefly reviewed