We clarify the validity of a method that decouples a boundary value problem of biharmonic equation to two Poisson equations on polygonal domains. The method provides a way of computing deflections of simply supported polygonal plates by using Poisson solvers. We show that such decoupling is not valid if the polygonal domain is not convex. It may fail even when the right hand side function is in...

By the special polygonal curve we meana simple closed curve, that is a polygone and moreover has edges parallel to axes. We continue the formalization of the Takeuti-Nakamura proof [21] of the Jordan curve theorem. In the paper we prove that the complement of the special polygonal curve consists of at least two components. With the theorem which has at most two components we completed the theor...

The purpose of this paper is to construct perfect samplers for length-interacting Arak–Clifford–Surgailis polygonal Markov fields in the plane with nodes of order 2 (V-shaped nodes). This is achieved by providing for the polygonal fields a hard core marked point process representation with individual points carrying polygonal loops as their marks, so that the coupling from the past and clan of ...