Differential Equations for Classical and Non-Classical Polynomial Sets: A Survey †

Roland Hinnion ABOUT THE COEXISTENCE OF “CLASSICAL SETS” WITH “NON-CLASSICAL” ONES : A SURVEY

This is a survey of some possible extensions of ZF to a larger universe, closer to the “naive set theory” (the universes discussed here concern, roughly speaking : stratified sets, partial sets, positive sets, paradoxical sets and double sets). M athematics Subject Classification: 03B50, 03B30, 03B53, 03E35, 03E70.

Classical 2-orthogonal polynomials and differential equations

We construct the linear differential equations of third order satisfied by the classical 2orthogonal polynomials. We show that these differential equations have the following form: R4,n(x)P (3) n+3(x)+R3,n(x)P ′′ n+3(x)+R2,n(x)P ′ n+3(x)+R1,n(x)Pn+3(x)=0, where the coefficients {Rk,n(x)}k=1,4 are polynomials whose degrees are, respectively, less than or equal to 4, 3, 2, and 1. We also show tha...

Non-classical Metatheory for Non-classical Logics

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical meta-theory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena o...

A survey of non-classical polyandry.

We have identified a sample of 53 societies outside of the classical Himalayan and Marquesean area that permit polyandrous unions. Our goal is to broadly describe the demographic, social, marital, and economic characteristics of these societies and to evaluate some hypotheses of the causes of polyandry. We demonstrate that although polyandry is rare it is not as rare as commonly believed, is fo...

Differential and Difference Equations for Products of Classical Orthogonal Polynomials