The Cartier-Perrin theorem, which was published in 1995 and is expressed in the language of nonstandard analysis, permits, for the first time perhaps, a clear-cut mathematical definition of the volatility of a financial asset. It yields as a byproduct a new understanding of the means of returns, of the beta coefficient, and of the Sharpe and Treynor ratios. New estimation techniques from automa...

This article outlines ways in which nonstandard methods can be applied to continuum theory in the plane. 1. Nonstandard Models Nonstandard analysis, first developed by Abraham Robinson in the early 1960’s [10], makes use of the fact that there are other models besides the usual ones that satisfy all the same mathematical statements that can be made in First Order Logic. The basic idea is to exp...

This paper presents analysis of data aggregated from three experiments, investigating whether there are social differences in the processing of sociolinguistic variation. Three self-paced reading experiments tested the processing of variable subject-verb agreement in English. Sentences appeared in one of three agreement conditions: standard [singular+doesn’t] or [plural+don’t], nonstandard [sin...