Composites of poly(ε‐caprolactone) and Mo6S3I6 Nanowires

Composites of poly(ε‐caprolactone) (PCL) and molybdenum sulfur iodine (MoSI) nanowires were prepared using twin‐screw extrusion. Extensive microscopic examination of the composites revealed the nanowires were well dispersed in the PCL matrix, although bundles of Mo₆S₃I₆ ropes were evident at higher loadings. Secondary electron imaging (SEI) showed the nanowires had formed an extensive network throughout the PCL matrix, resulting in increased electrical conductivity of PCL, by eight orders of magnitude, and an electrical percolation threshold of 6.5 × 10^?3 vol%. Thermal analysis (DSC), WAXD, and hot stage polarized optical microscopy (HSPOM) experiments revealed Mo₆S₃I₆ addition altered PCL crystallization kinetics, nucleation density, and crystalline content. A greater number of smaller spherulites were formed via heterogeneous nucleation. The onset of thermal decomposition (TGA) of PCL decreased by 70°C, a consequence of the thermal degradation of Mo₆S₃I₆ to MoO₃, which in turn accelerates the formation of volatile gases during the first stage of PCL decomposition. Copyright © 2010 John Wiley & Sons, Ltd.     

MATHEMATICS,LANGUAGE AND DERRIDA

Abstract

Derrida's revolutionary work in the study of language has seriously challenged the way in which we see words being attached to meanings. This paper makes tentative steps towards examining how his work might assist us in understanding the way in which our attempts to describe or capture our mathematical experiences modify the experience itself. In doing this we draw on the work of Jacques Derrida and John Mason in locating possible frameworks through which to conceptualise the relationship between language and mathematical cognition. It concludes that mathematical meaning never stabilises since it is caught between the individual's ongoing experience and society's ongoing renewal of its conventions. That is, mathematics, language and the human performing them are always evolving in relation to each other.     

A variant of Shelah's characterization of Strong Chang's Conjecture

Shelah considered a certain version of Strong Chang's Conjecture which we denote , and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an apparently weaker version, denoted , and prove an analogous characterization of it. In particular, is equivalent to the assertion that the the Friedman‐Krueger poset is semiproper. This strengthens and sharpens results by Cox and sheds some light on problems posed by Usuba, Torres‐Perez and Wu.     

A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature

Statistical estimation of the model parameters of component lifetime distribution based on system lifetime data with known system structure is discussed here. We propose the use of stochastic expectation-maximization (SEM) algorithm for obtaining the maximum likelihood estimates of model parameters based on complete and censored system lifetimes. Different ways of implementing the SEM algorithm are also studied. We have shown that the proposed methods are feasible and are easy to implement for various families of component lifetime distributions. The proposed methodologies are then illustrated with two popular lifetime models—the Weibull and Birnbaum-Saunders distributions. Monte Carlo simulation is then used to compare the performance of the proposed methods with the corresponding estimation by direct maximization. Finally, two illustrative examples are presented along with some concluding remarks.     

On the expectations of the mathematical knowledge of first-year undergraduates

In a recent survey Sutherland and Dewhurst itemized the extent to which various types of departments expected selected mathematical topics in the background of incoming undergraduates. Using the results of diagnostic tests it is possible to estimate the actual capability of students with given prior qualifications to provide a ‘probable preparedness’ in specific topics. This paper compares expectations with probable preparedness in a range of topics. It is found that while some departments have realistic expectations about the background of their incoming students, others seem over-optimistic about the mathematical knowledge of today's students. Sometimes, topics that the department actually requires must in fact be covered ab initio with the students that they recruit.