We consider classes of relation algebras expanded with new operations based on the formation of ordered pairs. Examples for such algebras are pairing (or projection) algebras of algebraic logic and fork algebras of computer science. It is proved in Sain{N emeti 36] that there is nòstrong' representation theorem for all abstract pairing algebras in most set theories including ZFC as well as most...

 In this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. In fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. Some examples are provided to verify the effectiveness and applicability of our results.

We prove a special case of the Dynamical André-Oort Conjecture formulated by Baker and DeMarco [3]. For any integer d ≥ 2, we show that for a rational plane curve C parametrized by (t, h(t)) for some non-constant polynomial h ∈ C[z], if there exist infinitely many points (a, b) ∈ C(C) such that both zd+a and zd+b are postcritically finite maps, then h(z) = ξz for a (d − 1)-st root of unity ξ. A...

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...