Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...

The structure function φ of a binary monotone system is assumed to be known and given in a disjunctive normal form, i.e. as the logical union of products of the indicator variables of the states of its subsystems. Based on this representation of φ, an improved Abraham algorithm is proposed for generating the disjoint sum form of φ. This form is the base for subsequent numerical reliability calc...

This paper investigates a consistent versions cwaS of sometimes inconsistent Reiter’s closed world assumption cwa, proving (theorem 4.3) that for every ∀-sentence φ and for every ∀-theory Σ, φ ∈ cwaS(Σ) iff Σ `min φ. A relativized version of this characterization (theorem 7.3) remains valid if not all relations are subject to minimization. Moreover, the paper relates cwaS to cwa and to Minker’s...

Abstract In this article, we show continuity of commutators Calderón-Zygmund operators [ b , T ] \left[b,T] with BMO functions in generalized Orlicz-Morrey spaces M Φ φ <...