ABSTRACT
Let I be an open real interval, / : I -* 1R, and r > 0 be an integer. In this paper, a point xq € I will be called a singularity of / of order r if the (r-l)-st derivative, is absolutely continuous in a neighborhood of x q , and is continuous in this neighborhood, except for a jump discontinuity at x q . In many applications, for example, image and data compression, prediction
of time series, and antenna technology, one needs to determine the location of the singularities of a function of various orders.
