  Assume that there exists a hypersurface singularity which cannot be resolved
by iterated monoidal transformations in positive characteristic. We show that
in the set of defining functions of hypersurface singularities which cannot be
resolved, we can find a function satisfying very strong conditions. By these
conditions we may be able to deduce a contradiction under the above assumption.
Besides, we introduce fundamental concepts for the study of resolution of
singularities of germs such as space germs, iterated analytic monoidal
transforms with a normal crossing, Weierstrass representations, reduction
sequences, and so forth. This is a revised version of a part of contents of my
previous manuscript "Resolution of Singularities of Germs in Characteristic
Positive associated with Valuation Rings of Iterated Divisor Type" at
math.AG/9901048.
