  Part III of the reports consists of various unconventional distance function
wavelets (DFW). The dimension and the order of partial differential equation
(PDE) are first used as a substitute of the scale parameter in the DFW
transforms and series, especially with the space and time-space potential
problems. It is noted that the recursive multiple reciprocity formulation is
the DFW series. The Green second identity is used to avoid the singularity of
the zero-order fundamental solution in creating the DFW series. The fundamental
solutions of various composite PDEs are found very flexible and efficient to
handle a borad range of problems. We also discuss the underlying connections
between the crucial concepts of dimension, scale and the order of PDE through
the analysis of dissipative acoustic wave propagation. The shape parameter of
the potential problems is also employed as the "scale parameter" to create the
non-orthogonal DFW. This paper also briefly discusses and conjectures the DFW
correspondences of a variety of coordinate variable transforms and series.
Practically important, the anisotropic and inhomogeneous DFW's are developed by
using the geodesic distance variable. The DFW and the related basis functions
are also used in making the kernel distance sigmoidal functions, which are
potentially useful in the artificial neural network and machine learning. As or
even worse than the preceding two reports, this study scarifies mathematical
rigor and in turn unfetter imagination. Most results are intuitively obtained
without rigorous analysis. Follow-up research is still under way. The paper is
intended to inspire more research into this promising area.
