This paper contains a survey of different methods for generating knots and links based on geometric polyhedra, suitable for applications in chemistry, biology, architecture, sculpture (or jewelry). We describe several ways of obtaining 4-valent polyhedral graphs and their corresponding knots and links from geometrical polyhedra: midedge construction, cross-curve and double-line covering, and ed...

Metal-organic polyhedra (MOPs), are discrete metal-organic molecular assemblies. They are useful as host molecules that can provide tailorable internal volume in terms of metrics, functionality, and active metal sites. As a result, these materials are potentially useful for a variety of applications, such as highly selective guest inclusion and gas storage, and as nanoscale reaction vessels. Th...

In this paper, we address the issue of the formal verification of real-time systems in the context of a preemptive scheduling policy. We propose an algorithm which computes the state-space of the system, modeled as a time Petri net with stopwatches, exactly and efficiently, by the use of Difference Bounds Matrices (DBM) whenever possible and automatically switching to more time and memory consu...

The so-called ring spiral algorithm is a convenient means for generating and representing certain fullerenes and some other cubic poly-hedra. In 1993 Manolopoulos and Fowler presented a fullerene on 380 vertices without a spiral. No smaller unspirable fullerene is known. In the spring of 1997, using computer, Gunnar Brinkmann found the smallest cubic polyhedron without a spiral. It has only 18 ...

We propose a method for arbitrary 3D shape formation by folding chains of hinged polyhedra. This paper presents an incremental algorithm for finding a space filling curve, a Hamiltonian path, within a 3D solid. The algorithm is a bottom up approach that starts with minimal local paths connecting small clusters of neighboring constituent polyhedra and incrementally merges neighboring paths along...

The enumeration of points contained in an algebraically specified domain is one of the key algorithmic problems in the transformation of scientific programs. However, basic scanning algorithms accept only single convex polyhedra, requiring specialized techniques and causing run-time overhead if the set of points to enumerate is not convex. In this paper, we review the existing approaches to the...

We show that max-plus polyhedra are usable as a data structure in reachability analysis of timed automata. Drawing inspiration from the extensive work that has been done on difference bound matrices, as well as previous work on max-plus polyhedra in other areas, we develop the algorithms needed to perform forward and backward reachability analysis using maxplus polyhedra. To show that the appro...

Metal–Organic Polyhedra Surface modification of Ni-rich cathode is essential for advancing high energy density and long-term stability Li-ion batteries. Metal-organic polyhedra decorated with acyl groups (MOPAC) coated on the by spray method. The cathodes MOPAC offering selectivity facile electron transport exhibit enhanced structural gas suppression even at voltage. More details can be found i...