A twisted integrable hierarchy with D2\mathbb D_2 symmetry

A loop algebra approach to the Gerdjikov-Mikhailov-Valchev (GMV) equation is provided to exploit the associated twisted integrable structure and a new twisted integrable hierarchy is discovered. Using the twisted loop algebra structure, we obtain a transparent treatment of the associated scattering and inverse scattering theory and solve the initial value problem for the GMV equation

Interior and closure operators on bounded residuated lattice ordered monoids

summary:$GMV$-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior $GMV$-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on $DRl$-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on $GMV$-algebras