In this paper we consider countably infinite partially ordered sets (posets) in which the order relations occur periodically. We show that the problem of determining the minimum number of chains (completely ordered subsets) needed to cover all of the elements may be solved efficiently as a finite network flow problem. A special case of the chain-cover problem for periodic posets is the problem ...

Consider a Hamiltonian system with Hamiltonian of the form H(x, t, p) where H is convex in p and periodic in x, and t and x ∈ R. It is well-known that its smooth invariant curves correspond to smooth Z-periodic solutions of the PDE ut +H(x, t, u)x = 0 . In this paper, we establish a connection between the Aubry-Mather theory of invariant sets of the Hamiltonian system and Z-periodic weak soluti...

Given two pseudo-Anosov homeomorphisms with distinct invariant measured foliations, some powers of their isotopy classes generate a rank two free subgroup of the mapping class group of the surface [6]. This construction gives an example of all pseudo-Anosov subgroup of the mapping class group. Whittlesey [13] gives a positive answer to the natural question of the existence of all pseudo-Anosov ...

in this article, multiple-product pvrp with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. a mathematical formulation was provided for this problem. each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. to solve the problem, two meta-heuristic methods...