Quantum Super-Integrable Systems as Exactly Solvable Models

We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are constructed through the action of the commuting operators. Finite dimensional representations of the quadratic algebras are thus constructed in a way analogous to that of the highest weight representations of Lie algebras.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Quantifying the effect of GST on inflation in eight Australian cities: an intervention analysis

This article examines the magnitude and duration of the effect of the Goods and Services Tax(GST) on inflation in Australia's eight capital cities using the Box and Tiao intervention analysis and quarterly data spanning from 1948:4 to 2003:l. We found that the GST had a significant but transitory impact on inflation only in the September quarter of 2000 when this new tax system was implemented. In this quarter inflation showed an additional increase of 2.6 per cent in Sydney (minimum effect) and 2.8 per cent in Australia as a whole, and the figure for Hobart was 3.3 per cent (maximum effect). Based on Wald test results, we also found some evidence that there is no significant (or substantial) difference in the average price changes among capital cities. We could not reject the null hypothesis that the GST increased the consumer price index by 2.8 per cent across the board in various cities. These results are also consistent with previous studies and surveys

Symplectic Maps from Cluster Algebras

We consider nonlinear recurrences generated from the iteration of maps that arise from cluster algebras. More precisely, starting from a skew-symmetric integer matrix, or its corresponding quiver, one can define a set of mutation operations, as well as a set of associated cluster mutations that are applied to a set of affine coordinates (the cluster variables). Fordy and Marsh recently provided a complete classification of all such quivers that have a certain periodicity property under sequences of mutations. This periodicity implies that a suitable sequence of cluster mutations is precisely equivalent to iteration of a nonlinear recurrence relation. Here we explain briefly how to introduce a symplectic structure in this setting, which is preserved by a corresponding birational map (possibly on a space of lower dimension). We give examples of both integrable and non-integrable maps that arise from this construction. We use algebraic entropy as an approach to classifying integrable cases. The degrees of the iterates satisfy a tropical version of the map

Experimental study of extrusion and surface treatment of organo clay with PET nano-composites

This article was submitted to and presented at the Polymer Process Engineering 2009 conference.Inclusion of organoclay in engineering polymers is increase annually and this trend will continue for the foreseeable future despite the economic downturn. This paper describes melt blending techniques using PET nanocomposites containing commercially available organoclays with different percentage of surfactant coatings. This paper will also evaluate the morphology and mechanical properties of the composites using a range of techniques like, scanning electron microscopy, melt rheology and thermal analysis. Comparisons will be made between properties of amorphous and semi crystalline films in terms of surfactant used and material properties. It will be demonstrated that the quantity of surfactant used with the organoclays can significantly affect dispersion and properties of composites produced