Characteristic Lie Algebra and Classification of Semi-Discrete Models

Characteristic Lie algebras of semi-discrete chains are studied. The attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.Comment: 33 pages, corrected typos, submitted to the Proceedings of the workshop "Nonlinear Physics: Theory and Experiment IV", Theoretical Mathematical Physic

An online Master's degree: Teaching and learning strategy vs. managerial constraints

This paper illustrates the work of a course team at Southampton Solent University to establish a delivery model for an online distance master’s degree. Working under the managerial constraint of ensuring that the course delivery is sustainably affordable, the focus was to develop a model that structures tutor to student engagement in such a way as to ensure the maintenance of a high standard of teaching and learning. This model is put forward as an approach that is applicable in a variety of contexts, and hence of value to course developers from other institutions investigating ways of effectively delivering online courses

On Some Algebraic Properties of Semi-Discrete Hyperbolic Type Equations

Nonlinear semi-discrete equations of the form t_x(n+1)=f(t(n), t(n+1), t_x(n)) are studied. An adequate algebraic formulation of the Darboux integrability is discussed and the attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.Comment: 18 page

Slow regions percolate near glass transition

A nano-second scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as it nears the glass transition. The scaling behaviour is in the same universality class as percolation. The exponents \gamma and \beta are found to be 1.7 \pm .1 and 0.41\pm 0.01 in agreement with the best percolation results in three dimensions.Comment: 7 pages, 3 figure