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For N ≥ 3 there are SN and DN actions on the space of solutions of the first nontrivial equation in the SL(N) MKdV hierarchy, generalizing the two Z2 actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painlevé equations. Given a solu...

In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develo...