Asymptotic behaviour of random Markov chains with tridiagonal generators

Continuous-time discrete-state random Markov chains generated by a random linear differential equation with a random tridiagonal matrix are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors. The proof uses comparison theorems for Carath\'eodory random differential equations and the fact that the linear cocycle generated by the Markov chain is a uniformly contractive mapping of the positive cone into itself with respect to the the Hilbert projective metric. It does not involve probabilistic properties of the sample path and is thus equally valid in the nonautonomous deterministic context of Markov chains with, say, periodically varying transitions probabilities, in which case the attractor is a periodic path.Comment: 11 pages, 15 bibliography references, added bibliography, minor change

Revision of the African caecilian genus Schistometopum Parker (Amphibia: Gymnophiona: Caeciliidae)

http://deepblue.lib.umich.edu/bitstream/2027.42/56430/4/MP187.pd

Ex-nihilo: Obstacles Surrounding Teaching the Standard Model

The model of the Big Bang is an integral part of the national curriculum for England. Previous work (e.g. Baxter 1989) has shown that pupils often come into education with many and varied prior misconceptions emanating from both internal and external sources. Whilst virtually all of these misconceptions can be remedied, there will remain (by its very nature) the obstacle of ex-nihilo, as characterised by the question `how do you get something from nothing?' There are two origins of this obstacle: conceptual (i.e. knowledge-based) and cultural (e.g. deeply held religious viewpoints). The article shows how the citizenship section of the national curriculum, coming `online' in England from September 2002, presents a new opportunity for exploiting these.Comment: 6 pages. Accepted for publication in Physics E

Linguistic incompetence: giving an account of researching multilingually

This paper considers the place of linguistic competence and incompetence in the context of researching multilingually. It offers a critique of the concept of competence and explores the performative dimensions of multilingual research and its narration, through the philosophy of Judith Butler, and in particular her study Giving an account of oneself. It explores aspects of risk, justice, narrative limit and a morality of multilingualism in emergent multilingual research frameworks. These theoretical dimensions are explored through consideration of ‘linguistically incompetent’ ethnographic work with refugees and asylum seekers, in contexts of hospitality and in life long learning research in the Gaza Strip, and of early attempts to learn new languages. The paper offers a prospect of a relational approach to researching multilingually and affirms the vulnerability at the heart of linguistic hospitality