Hierarchies of q-discrete Painleve equations
In this paper, we construct a new hierarchy based on the third q-discrete Painleve ́ equation (qPIII) and also study the hierarchy of the second q-discrete Painleve ́ equation (qPII). Both hierarchies are derived by using reductions of the general lattice modified Korteweg-de Vries equation. Our results include Lax pairs for both hierarchies and these turn out to be higher degree expansions of the non-resonant ones found by Joshi and Nakazono [29] for the second-order cases. We also obtain Ba ̈cklund transformations for these hierarchies. Special q-rational solutions of the hierarchies are constructed and corresponding q-gamma functions that solve the associated linear problems are derived.
In this paper, we construct a new hierarchy based on the third q-discrete Painleve ́ equation (qPIII) and also study the hierarchy of the second q-discrete Painleve ́ equation (qPII). Both…
We deal with a relational algebra model to define a refinement fuzzy ordering (demonic fuzzy inclusion) and also the associated fuzzy operations which are fuzzy demonic join, fuzzy demonic meet …