The distribution of the number of points of the closed simple random walk, visited a given number of times (the -multiple point range) is analysed by a graph based approach. A general expression for the moments is derived. In this paper the joint generating function for dimension one is...

The problem of restricted random walks of fixed dimension and finite memory is considered using extension of methods discussed earlier. Inversion of recursion relations, derived in Ref. 1, is derived and recursion relations for restricted random walks of fixed dimension and four and six step...

In this article we present a framework describing the world foreign exchange market in terms of differential geometry on graphs, that is, in terms of vector lattice bundles on graphs and connections on these bundles. This framework is based on the concept of financial equivalence introduced by...

We show that it is decidable for any given ground term rewrite systems and if there is a ground term rewrite system such that . If the answer is yes, then we can effectively construct such a ground term rewrite system . In other words, for any given finitely generated congruences and over the...

A Hilbert module over a planar algebra is essentially a Hilbert module over a eanonieally defined algebra spanned by the annular tangles in It follows that any planar algebra containing is a module over and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar...