Convex isomorphisms of directed multilattices

Isomorphisms of Algebras Associated with Directed Graphs

Given countable directed graphs G and G, we show that the associated tensor algebras T+(G) and T+(G ) are isomorphic as Banach algebras if and only if the graphs G are G are isomorphic. For tensor algebras associated with graphs having no sinks or no sources, the graph forms an invariant for algebraic isomorphisms. We also show that given countable directed graphs G, G, the free semigroupoid al...

Isomorphisms and traversability of directed path graphs

The concept of a line digraph is generalized to that of a directed path graph. The directed path graph → Pk(D) of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k + 1 vertices or form a directed cycle on k vertices in D. In this introductory paper ...

Congruence Relations on Multilattices

Numerical Methods for Multilattices

Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices (Tadmor et al, 1999). Another existing numerical approach to modeling multilattices is homogenization. In the present paper we revie...

Probabilistic analysis of column-convex and directed diagonally-convex animals