Abstract There is a strange duality between the quadrangle isolated complete intersection singularities discovered by first author and Wall. We derive this from variation of Berglund–Hübsch transposition invertible polynomials introduced in our previous work about hypersurface using matrix factorizations size two.

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

We characterize those intersection-type theories which yield complete intersection-type assignment systems for λ-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics, the simple semantics and the F-semantics.

This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...