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...

Research demonstrates that police reduce crime. We study this question by using a natural experiment in which a private university increased the number of police patrols within an arbitrarily defined geographic boundary. Capitalizing on the discontinuity in patrols at the boundary, we estimate that the extra police decreased crime in adjacent city blocks by 43–73%. Our results are consistent wi...

a cytogenetic study was performed on m4 generation of gamma irradiated lines of shirpan cultivar of tetraploid cotton (gossypium hirsutum l.). a significant difference was observed in cytogenetical characteristics such as the number and type of quadrivalents as well as percentage of cells showing abnormality among the irradiated and non irradiated lines. cytomixis and post- pachytene diffuse st...

  The sporozoites of Theileria annulata invade bovine MHC II cells, where they differentiate into schizonts. The later can immortalize and induce fundamental changes in their host cells. Live attenuated vaccine is an important way of controlling T. annulata infection of cattle. Production is by prolonged cultivation of macroschizont-infected cells. The mechanisms underlying this transformation ...

Background: Downy mildew caused by Plasmopara halstedii is one of the most devastating diseases of sunflower worldwide. So far several dominant resistance genes designated as Pl have been identified and their molecular markers linked to these genes are available. However, no information on the resistance genes is available in Iranian lines. Objective: In this study, the presence of three map-b...