Recent results for tree amplitudes for the N = 2 noncritical strings are presented and compared with the critical case. Arguments are given which indicate a certain discontinuity in passing from thê c < 1 model (in a Coulomb gas representation) to thê c = 1 critical case.

The valuation of American Options can often be reduced to the study of a free boundary value problem for a partial differential equation. This paper will discuss how the Method of Lines (MOL) can be used to study the numerical valuation of American Options and to determine the early exercise frontier. This method is flexible, accurate and computationally fast.

The NC-proximal average is a parametrized function used to continuously transform one proper, lsc, prox-bounded function into another. Until now it has been defined for two functions. The purpose of this article is to redefine it so that any finite number of functions may be used. The layout generally follows that of [11], extending those results to the more general case and in some instances g...

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is pr...

We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy momentum tensor also changes at the world-sheet boundary in such...