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

Amalgams of Inverse Semigroups and C*-algebras

An amalgam of inverse semigroups [S,T,U] is full if U contains all of the idempotents of S and T. We show that for a full amalgam [S,T,U], the C*-algebra of the inverse semigroup amaglam of S and T over U is the C*-algebraic amalgam of C*(S) and C*(T) over C*(U). Using this result, we describe certain amalgamated free products of C*-algebras, including finite-dimensional C*-algebras, the Toeplitz algebra, and the Toeplitz C*-algebras of graphs

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

Quantifying the Effect of GST on Inflation in Australia’s Capital Cities: An Intervention Analysis

This paper examines the magnitude and duration of the GST effect on inflation in Australia’s eight major capital cities using the Box and Tiao intervention analysis and quarterly data spanning from 1948:4 to 2003:1. We found that 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, the same figure for Hobart was 3.3 per cent (maximum effect). Based on the Wald test results, we have also found some evidence that there is no significant (or substantial) difference in the average price changes among major capital cities. We could not reject the null hypothesis that GST increased the CPI by 2.8 per cent across the board in various cities. These results are also consistent with previous studies/surveys.Intervention Analysis; State and Local Taxation; Australia.

WHAT IS A RECESSION?: A REPRISE.

This paper draws its title from a paper written over 30 years ago by Geoffrey H. Moore (1967). Why the need for a reprise? First, there would appear currently to be somewhat diverging views – particularly in Australia – as to what properly constitutes a recession. Second, largely as a result of this, in Australia and many other countries other than the US, there is no single widely-accepted business cycle chronology for the country in question. This paper will argue that in addition to an output dimension, there are other important dimensions to aggregate economic activity which need to be taken into account in determining the business cycle, viz., income, sales and employment. As such, our perspective would seem to be at odds with the apparent position taken by other recent Australian commentators on this issue who argue that GDP is all that is needed to represent Australia’s business cycle. We will also argue strongly against using the currently popular ‘two negative quarterly growth rate’ rule in dating the onset of a recession.