Proposal for Undergraduate Research Funding:
Periodic Functions and the Henstock-Stieltjes Integral
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 paper “A Non-Linear Model For Time,” time is defined as a partially ordered set of instants. Since time is generally measured by periodic functions (ex. Lunar cycles), I will begin by investigating periodic functions defined on certain subsets of the set of instants.
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 study these integrals and try to find insights into the nature of time.