Mentors: Nathan Dalaklis (UNT graduate), Dr. Kiko Kawamura
Title: The Partial Derivative of Okamoto's Functions
Abstract: The differentiability of the one parameter family of Okomoto's functions as functions of x has been analyzed extensively since their introduction in 2005. As an analogue to a similar investigation, in this paper, we consider the partial derivative of Okomoto's functions with respect to the parameter a. We place a significant focus on a=1/3 to describe the properties of a nowhere differentiable function K(x) for which the set of points of infinite derivative produces an example of a measure zero set with Hausdorff dimension 1.