Integrability of Dirac reduced bi-Hamiltonian equations

First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.Comment: 15 pages. Corrected some typos and added missing equations in Section 5 for g=sl_n, n>

The effects of tax deductibility on the mix of property taxes and use charges: an empirical analysis of the spanish case

This paper tests some hypothesis about the determinants of the local tax structure. In particular, we focus on the effects that the property tax deductibility in the national income tax has on the relative use of the property tax and user charges. We deal with the incentive effects that local governments face regarding the different sources of revenue by means of a model in which the local tax structure and the level of public expenditure arise as a result of the maximizing behaviour of local politicians subject to the economic effects of the tax system. We attempt to test the hypothesis developed with data corresponding to a set of Spanish municipalities during the period 1987-9l. We find that tax deductibility provides incentives to raise revenues from the property tax but does not introduce a biass against user charges or in favor of overall spending growth.local government finance, property tax, tax deductibility