A relational structure X is said to be reversible iff every bijective endomorphism f : X → X is an automorphism. We define a sequence of non-zero cardinals 〈κi : i ∈ I〉 to be reversible iff each surjection f : I → I such that κj = ∑ i∈f[{j}] κi, for all j ∈ I , is a bijection, and characterize such sequences: either 〈κi : i ∈ I〉 is a finite-to-one sequence,… (More)

A relational structure is called reversible iff every bijective endomorphism of that structure is an automorphism. We give several equivalents of that property in the class of disconnected binary structures and some its subclasses. For example, roughly speaking and denoting the set of integers by Z, a structure having reversible components is reversible iff… (More)

We show that the diagonal dominance nonsingularity result of Shivakumar and Chew from 1974, and the diagonal dominance nonsingularity result of Farid from 1995, and the result of Huang on characterization of diagonally dominant H-matrices from 1995, all proven independently and in different contexts are, in fact, equivalent. We also offer the fourth and the… (More)