Some remarks on the Stanley's depth for multigraded modules
  We show that the Stanley's conjecture holds for any multigraded $S$-module $M$ with $\sdepth(M)=0$, where $S=K[x_1,...,x_n]$. Also, we give some bounds for the Stanley depth of the powers of the maximal irrelevant ideal in $S$. 
Mircea Cimpoeas