It follows from a construction for independent sets in the powers of odd cycles given in the predecessor of this paper that the limit as k goes to infinity of k+ 1/2−Θ(C2k+1) is zero, where Θ(G) is the Shannon capacity of a graph G. This paper contains a shorter proof of this limit theorem that is based on an ‘expansion process’ introduced in an older paper of L. Baumert, R. McEliece, E. Rodemi...

We present a somewhat different way of looking on Shannon entropy. This leads to an axiomatisation of Shannon entropy that is essentially equivalent to that of Fadeev.

We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application, we have de...

In this work it is shown that the Shannon entropy an efficient dynamical indicator provides a direct measure of diffusion rate and thus time-scale for instabilities arising when dealing with chaos. Its computation just involves solution Hamiltonian flow, variational equations are not required. After review theory behind approach, two particular applications presented; 4D symplectic map exoplane...