On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with $\gamma=0$. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as $s\to 1$. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with $\beta=0$.Comment: 38 pages, 5 figure

Alternative Co-operative Structures for the Agri-food Sector: An Exploratory Study

In a context of internationalisation and concentration, bio-foods co-operatives often face problems of capital access and governance. According to Spear (2001), limited access to capital, management structure, governance conflicts, and the local, regional or national focus of co-operatives limit their expansion. Recent events in Canada, such as Agricore going public and Dairyworld being absorbed by a corporation, have reinforced this perception (Thibault and Dupuis, 2003). In this evolving competitive environment, the traditional co-operative model cannot thrive and succeed if static. New hybrid co-operative models are emerging, and an analysis of these models should contribute to an understanding of the trade-off between co-operative values and other attributes necessary for survival in an increasingly competitive environment.Agribusiness, Marketing,