The dispersive self-dual Einstein equations and the Toda lattice

The Boyer-Finley equation, or $SU(\infty)$-Toda equation is both a reduction of the self-dual Einstein equations and the dispersionlesslimit of the $2d$-Toda lattice equation. This suggests that there should be a dispersive version of the self-dual Einstein equation which both contains the Toda lattice equation and whose dispersionless limit is the familiar self-dual Einstein equation. Such a system is studied in this paper. The results are achieved by using a deformation, based on an associative $\star$-product, of the algebra $sdiff(\Sigma^2)$ used in the study of the undeformed, or dispersionless, equations.Comment: 11 pages, LaTeX. To appear: J. Phys.

Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems

Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this prescription to the theory of the KP-hierarchy, I show that their integrability follows to the nature of their Wigner distribution. Furthermore the definition of the ``expectation value'' clarifies the relation between our approach and the Hamiltonian structure of the KP-hierarchy. A trial of the explicit construction of the Moyal bracket structure in the integrable system is also made.Comment: 19 pages, to appear in J. Phys. Soc. Jp

Realizations of the qq-Heisenberg and qq-Virasoro Algebras

We give field theoretic realizations of both the $q$-Heisenberg and the $q$-Virasoro algebra. In particular, we obtain the operator product expansions among the current and the energy momentum tensor obtained using the Sugawara construction.Comment: 9 page

The design specification for Syracuse : a multi-junction concentrator system computer model

This paper looks at the design specification for Syracus

Syracuse - a multi-junction concentrator system computer model

A multi-junction concentrator system computer model is presented, that aims to accurately model the power generated based on environmental data input, such as the irradiance, air temperature, humidity and pressure. The device model is discussed, illustrating the importance of statistical variation of module components when simulating a multi-cell module. This comprehensive concentrator computer model will be released for general use, aiming to become a useful resource for those designing and testing multi-junction based concentrator systems