The scaling laws of the vertical (Fwc) and longitudinal (Fuc) velocity-scalar cospectra within the inertial subrange are explored using dimensional arguments and a simplified cospectral budget in the canopy sublayer above three distinct forested ecosystems. The cospectral budget was shown to be consistent with plausible scaling laws originating from dimensional considerations. Using the analyti...

Given a graph G with its adjacency matrix A, the characteristic polynomial of G is defined as det(A − λI). Two graphs which have the same characteristic polynomial are called cospectral. It is known (see [2]) that there are non-isomorphic graphs which are co-spectral. In this note we consider the following generalization of the characteristic polynomial of a graph: For a graph G with adjacency ...

Let X be a graph on n vertices with adjacency matrix A and let H(t) denote the matrix-valued function exp(iAt). If u and v are distinct vertices in X, we say perfect state transfer from u to v occurs if there is a time τ such that |H(τ)u,v| = 1. The chief problem is to characterize the cases where perfect state transfer occurs. In this paper, it is shown that if perfect state transfer does occu...