[texhax] Three new symbols needed

[Swami Pallasena]

Hi:
I need the following three new symbols not available in the Comprehensice 
LaTeX Symbol List.

1. A  \frown symbol stacked over a  \smile symbol, with both the symbols 
thicker, and more bent (curved)

2.  An upper semicircle with the center dot but without the base diameter 
-- something like the upper half of the AMS symbol \odot

3.  A command like  \wave{x}  to insert a "wave" (sine like wave) over the 
character "x".

Any help will be appreciated.
P. Narayanaswami
(swami at math.mun.ca)