Periodic Functions On Non-Linear Temporal Models

By Alexia Puig

During this semester, while working with Dr. Devito, I plan to study the mathematical properties of functions of time.  According to Dr. Devito’s papers “A Non-Linear Model For Time” and “Time Scapes,” time is defined as a partially ordered set of instants.  Mathematically, the standard model of time is the number line and time is generally measured by periodic functions (ex. Lunar cycles).  The non-linear model gives an interesting new way to understand some of the properties of time.  Instants cannot be added.  There is, however, a translation function on the set of instants, defined in Devito’s paper, and by using this function one can formulate a definition of a periodic function of time.  I want to examine the properties of these functions.

I also want to study and interpret the integrals of functions defined on time tracks, which are totally ordered subsets of the set of instants.  The most natural integrals to apply in this connection are the Henstock-Stieltjes and the Reimann-Stieltjes Integrals.  I will try to formulate a definition of these integrals using two real-valued functions defined on the time axis.  I will study these integrals and try to find insights into the nature of time.