Common Notations

I have put a box around plain-text that should be in math mode.
sp     means that the word is misspelled.
?       means that I'm suggesting another word, but your word might be just as good. Try each and use your own judgment.
??     means that the word you've used is not appropriate for a scientific paper or for the explanation that you are trying to give, but I'm not certain that my word gets across the message that you wish to communicate. The suggested word/phrase is my best guess.
Ref or Ref #     means that you should cite the reference.
( ) around a word indicates that the word could (probably) be removed without disrupting the flow of your exposition. Scientific papers should strive for conciseness. Unless there is a reason to include the word, don't.
Uncertain antecedent       Means that your referance to 'it' or 'that' is ambiguous. Refer precisely to what you wish to refer to.

Preventative Maintenance

Spell check! From a command line inside your Paper directory type   ispell -t paper.tex
ispell -t abstract.tex
ispell -t biblio.tex
ispell -t appa.tex

Use emacs' Ctrl-s (search forward) to search for the following words:
    "it" "this" "that"     (1)
Justify each appearance. Can the words listed in (1) be replaced by precise words?
Note: Ctrl-r is a reverse search, searching for the last occurrence before your cursor.

In many cases, words ending in "-ing" are indicative of too informal a tone. Can the sentence or paragraph be rephrased?