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...

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for...

In this paper, we shall study the eigenvalue problem of a singular quasilinear elliptic equation. We will show that many results about the eigenvalues and eigenfunctions in the non-singular case can be extended to the more general singular case, e.g., the first eigenvalue λ is associated to a...