A new geometric setting for classical field theories

A new geometrical setting for classical field theories is introduced. This description is strongly inspired in the one due to Skinner and Rusk for singular lagrangians systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.Comment: 22 page

A potential library for primary MFL pedagogy: the case of Young Pathfinders

As readers of this journal will know very well, 2010 will see all KS2 (ages 7-11) pupils in England entitled to learn a modern foreign language in normal curriculum time. This development of the commitment to primary language learning should provide an excellent opportunity and experience for pupils, whilst at the same time requiring some radical changes for many teachers, schools and much of the wider language learning community. Recent research has indicated general trends suggesting an increase in primary languages already, in anticipation of this development and even beforehand. One of the most recent studies indicates that 43% of primary children currently learn a foreign language at KS2, either in class or as an extra-curricular activity, although the extent of this learning varies considerably (Driscoll, Jones and Macrory, 2004). It has also been suggested (Muijs et al, 2005) that there are certain aspects of the process that will be particularly demanding if the challenge of providing this entitlement are to be met

Comparing Mean Field and Euclidean Matching Problems

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d^2). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur

Singular lagrangian systems and variational constrained mechanics on Lie algebroids

The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangian systems and vakonomic mechanics (variational constrained mechanics). Several examples illustrate the interest of these developments.Comment: 42 pages, Section with examples improve

Contribution to the study of typhus group fevers in Rangoon

PART I: History of Typhus and Typhus-like Fevers in India, Burma and the Federated Malay States • Symptomatology • Serology • • PART II: Description of cases showing a positive Weil-Felix Reaction • • Commentary • Summary and conclusions • Tables • References