Rational Convolution Roots of Isobaric Polynomials

In this paper, we exhibit two matrix representations of the rational roots of generalized Fibonacci polynomials (GFPs) under convolution product, in terms of determinants and permanents, respectively. The underlying root formulas for GFPs and for weighted isobaric polynomials (WIPs), which appeared in an earlier paper by MacHenry and Tudose, make use of two types of operators. These operators are derived from the generating functions for Stirling numbers of the first kind and second kind. Hence we call them Stirling operators. To construct matrix representations of the roots of GFPs, we use the Stirling operators of the first kind. We give explicit examples to show how the Stirling operators of the second kind appear in the low degree cases for the WIP-roots. As a consequence of the matrix construction, we have matrix representations of multiplicative arithmetic functions under the Dirichlet product into its divisible closure.Comment: 13 page

Topsl: a Domain-Specific Language for On-Line Surveys. Scheme Workshop

There are currently few choices for social scientists who want to employ web-based surveys in their studies. They can either use a special-purpose language whose notion of flow control may be too limiting to express advanced survey designs, or use a generalpurpose language that gives them the freedom to make complicated survey designs but makes them reimplement infrastructure code for saving questions to disk, generating HTML, and so on with each new survey. In this paper, we introduce Topsl, a domain-specific language embedded in PLT Scheme that takes the middle road, giving survey authors a way to reuse survey infrastructure for new surveys while also allowing them to express complicated survey designs easily.