About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane

The relation of the noncommutative self-dual Chern-Simons (NCSDCS) system to the noncommutative generalizations of Toda and of affine Toda field theories is investigated more deeply. This paper continues the programme initiated in $JHEP {\bf 10} (2005) 071$, where it was presented how it is possible to define Toda field theories through second order differential equation systems starting from the NCSDCS system. Here we show that using the connection of the NCSDCS to the noncommutative chiral model, exact solutions of the Toda field theories can be also constructed by means of the noncommutative extension of the uniton method proposed in $JHEP {\bf 0408} (2004) 054$ by Ki-Myeong Lee. Particularly some specific solutions of the nc Liouville model are explicit constructed.Comment: 24 page

Torus n-Point Functions for R\mathbb{R}-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds

We consider genus one n-point functions for a vertex operator superalgebra with a real grading. We compute all n-point functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, we obtain all orbifold n-point functions for a twisted module associated with a continuous automorphism generated by a Heisenberg bosonic state. The modular properties of these orbifold n-point functions are given and we describe a generalization of Fay's trisecant identity for elliptic functions.Comment: 50 page

Is skilled technique characterized by high or low variability? An analysis of high bar giant circles

NOTICE: this is the author’s version of a work that was accepted for publication in Human Movement Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://dx.doi.org/10.1016/j.humov.2012.11.007There is conflicting evidence as to whether skilled performance is associated with lower or higher movement variability. The effect of skill level and task difficulty on movement variability during gymnastics swinging was investigated. Four male gymnasts ranging in skill from university standard through to international medallist performed 10 consecutive regular giant circles and 10 double straight somersault dismounts preceded by accelerated giant circles whilst kinematic data were recorded. Joint angle time histories of the hip and shoulder were calculated and the turning points between flexion and extension determined during each giant circle. Standard deviations of the time and magnitude of the angles at each turning point were calculated. The more elite gymnasts were found to have less variability in the mechanically important aspects of technique compared to the less elite gymnasts. The variability in the mechanically important aspects of technique was not statistically different between the two types of giant circles, whereas, the more elite gymnasts demonstrated more variability in some of the less mechanically important aspects