The Financial Accountability of Irish Credit Unions: an initial empirical study

Credit unions are member-owned, voluntary, self-help, democratic, not-for-profit institutions that provide financial services to their members. They have both economic and social goals. Over this last decade they have achieved remarkable growth levels and currently there are 600 such organisations in Ireland, with approximately 50 per cent of the adult population of Ireland belonging to a credit union. Accounting for credit unions is a much-neglected area and relatively little is known about the sector's accountability. This paper presents the results of an initial empirical study of the financial accountability of Irish credit unions. A series of interviews and a basic content analysis of 178 recent financial statements were used to identify the views of key stakeholders with respect to the discharge of financial accountability by credit unions and the current quality of financial reporting. Overall, the research points to a sector where financial accountability through the medium of the annual report is weak and possible adverse consequences of this are explored. On the basis of the interviews it is suggested that if changes in financial accountability are to be achieved then some more proactive engagement of parties external to the management of individual credit unions is needed.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.