Outer measure and utility

In most economics textbooks there is a gap between the non-existence of utility functions and the existence of continuous utility functions, although upper semi-continuity is sufficient for many purposes. Starting from a simple constructive approach for countable domains and combining this with basic measure theory, we obtain necessary and sufficient conditions for the existence of upper semi-continuous utility functions on a wide class of domains. Although links between utility theory and measure theory have been pointed out before, to the best of our knowledge this is the first time that the present route has been taken.preferences; utility theory; measure theory; outer measure

A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples

We enumerate all circulant good matrices with odd orders divisible by 3 up to order 70. As a consequence of this we find a previously overlooked set of good matrices of order 27 and a new set of good matrices of order 57. We also find that circulant good matrices do not exist in the orders 51, 63, and 69, thereby finding three new counterexamples to the conjecture that such matrices exist in all odd orders. Additionally, we prove a new relationship between the entries of good matrices and exploit this relationship in our enumeration algorithm. Our method applies the SAT+CAS paradigm of combining computer algebra functionality with modern SAT solvers to efficiently search large spaces which are specified by both algebraic and logical constraints

Ambient vibration re-testing and operational modal analysis of the Humber Bridge

An ambient vibration survey of the Humber Bridge was carried out in July 2008 by a combined team from the UK, Portugal and Hong Kong. The exercise had several purposes that included the evaluation of the current technology for instrumentation and system identification and the generation of an experimental dataset of modal properties to be used for validation and updating of finite element models for scenario simulation and structural health monitoring. The exercise was conducted as part of a project aimed at developing online diagnosis capabilities for three landmark European suspension bridges. Ten stand-alone tri-axial acceleration recorders were deployed at locations along all three spans and in all four pylons during five days of consecutive one-hour recordings. Time series segments from the recorders were merged, and several operational modal analysis techniques were used to analyse these data and assemble modal models representing the global behaviour of the bridge in all three dimensions for all components of the structure. The paper describes the equipment and procedures used for the exercise, compares the operational modal analysis (OMA) technology used for system identification and presents modal parameters for key vibration modes of the complete structure. The results obtained using three techniques, natural excitation technique/eigensystem realisation algorithm, stochastic subspace identification and poly-Least Squares Frequency Domain method, are compared among themselves and with those obtained from a 1985 test of the bridge, showing few significant modal parameter changes over 23 years in cases where direct comparison is possible. The measurement system and the much more sophisticated OMA technology used in the present test show clear advantages necessary due to the compressed timescales compared to the earlier exercise. Even so, the parameter estimates exhibit significant variability between different methods and variations of the same method, while also varying in time and having inherent variability. (C) 2010 Elsevier Ltd. All rights reserved