Differential equations for generalized Jacobi polynomials

We look for spectral type differential equations satisfied by the generalized Jacobi polynomials, which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with two point masses at the endpoints of the interval of orthogonality. We show that such a differential equation is uniquely determined and we give explicit representations for the coefficients. In case of nonzero mass points the order of this differential equation is infinite, except for nonnegative integer values of (one of) the parameters. Otherwise, the finite order is explictly given in terms of the parameters.Comment: 33 pages, submitted for publicatio

On differential equations for Sobolev-type Laguerre polynomials

We obtain all spectral type differential equations satisfied by the Sobolev-type Laguerre polynomials. This generalizes the results found in 1990 by the first and second author in the case of the generalized Laguerre polynomials defined by T.H. Koornwinder in 1984.Comment: 45 page

Collective Strategies and Windfall Catches: Fisher Responses to Tsunami Relief Efforts in South India

To the surprise of both governments and NGOs, village-level caste organisations – or panchayats - played a significant role in the post-tsunami relief effort to fisher-men in Tamil Nadu, India. This paper discusses the pro-active role of caste pancha-yats in relief from the perspective of social resilience, a factor that is frequently ar-gued to be of importance for disaster management. It presents panchayat action as an expression of collective agency that has a long tradition in the fishing villages of the region. Finally, comparing the reactions of caste panchayats in the post-tsunami situation with their performance in other instances of collective need, it considers their future role in fields such as fisheries management

A difference operator of infinite order with Sobolev-type Charlier polynomials as eigenfunctions

AbstractPolynomials are considered which are orthogonal with respect to the inner product 〈f,g〉=∑x=0∞f(x)g(x)e−aaxx!+λf(0)g(0)+μΔf(0)Δg(0),a>0,λ≥0,μ≥0. A representation for these polynomials is presented. It is shown that in the case λ = 0 and μ > 0 these polynomials are eigenfunctions of a difference operator, which is shown to be of infinite order for all values of a > 0. The difference operator and the eigenvalues are linear perturbations of those in the Charlier case (λ = 0, μ = 0). A formula for the eigenvalues and a representation for the coefficients in the differential operator are presented

India: purse-seine fishing, growth blues

Coastal degradation, socioeconomic inequality and the rise of purse-seine fishing in India pose a set of problems that often end in a zero-sum game for fisher groups