Abstract: Many well-known interconnection networks, such as kary n-cubes, recursive circulant graphs, generalized recursive circulant graphs, circulant graphs and so on, are shown to belong to the family of cycle composition networks. Recently, various studies about mutually independent hamiltonian cycles, abbreviated as MIHC-s, on interconnection networks are published. In this paper, using an improved construction method, we obtain MIHC-s on cycle composition networks with a much weaker condition than the known result. In fact, we established the existence of MIHC-s in the cycle composition networks and the result is optimal in the sense that the number of MIHC-s we constructed is maximal.
Abstract: A mathematical model for the Dynamics of Economic
Profit is constructed by proposing a characteristic differential oneform
for this dynamics (analogous to the action in Hamiltonian
dynamics). After processing this form with exterior calculus, a pair of
characteristic differential equations is generated and solved for the
rate of change of profit P as a function of revenue R (t) and cost C (t).
By contracting the characteristic differential one-form with a vortex
vector, the Lagrangian is obtained for the Dynamics of Economic
Profit.
Abstract: The balanced Hamiltonian cycle problemis a quiet new topic of graph theorem. Given a graph G = (V, E), whose edge set can be partitioned into k dimensions, for positive integer k and a Hamiltonian cycle C on G. The set of all i-dimensional edge of C, which is a subset by E(C), is denoted as Ei(C).
Abstract: The position and momentum space information entropies
of hydrogen atom are exactly evaluated. Using isospectral
Hamiltonian approach, a family of isospectral potentials is constructed having same energy eigenvalues as that of the original potential. The information entropy content is obtained in position
space as well as in momentum space. It is shown that the information
entropy content in each level can be re-arranged as a function of deformation parameter.