We show that every plane graph admits a planar straight-line drawing in which all faces with more than three vertices are non-convex polygons.

We establish a semi-group solution concept for morphological differential equations, such as the mean curvature flow equation. The proposed method consists in generating flows from generalized minimizers of nonconvex energy functionals. We use relaxation and convexification to define generalized minimizers. The main part of this work consists in verification of the solution concept by comparing...

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lo...

This work investigates two aspects linked to the nature of feasible domain anisotropic laminates. In first part paper, proofs are given on non-convexity for full and membrane-orthotropic laminates, either in lamination parameters space or polar one. Then, adopting formalism, some particular cases studied, providing analytical expressions new narrower bounds, terms membrane stiffness tensor. For...