Dear Werner, 
   I've found that if I use the mathematical symbols such as $\cdot$,
$\omega$ or anything alike in the *\section{}*, *\subsection{}* or
*subsubsection{}* commands, that is, they seem as follows:
*******************
[...]   
\usepackage{CJKutf8}
\usepackage{amsmath}
\usepackage[T1]{fontenc}
\usepackage[unicode]{hyperref}
[...] 
\section{blablabla$\omega$blablabla}
or
\subsection{blablabla$\omega$blablabla}
or  
\subsubsection{blablabla$\omega$blablabla}
*******************
   Then, when I compiled the tex source file, I will be warned that:
********************************************************
Package hyperref Warning: Token not allowed in a PDFDocEncoded string,
(hyperref)                removing `math shift' on input line 14.
*********************************************************
   As the result, the  corresponding mathematical symbols can be compiled
into the bookmarks correctly, but they appear in the article correctly!
  Why does this happen? How can I use mathematical symbols in my bookmarks?
  
  Best,
  Hongsheng.
  

P.S.
The CJKutf8.sty I used is the CVS version, that is, I can use it to generate
correct chinese bookmarks with UTF8 encoding, even the bookmarks including
some CJK-Ext B characters.

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