On a class of non-self-adjoint periodic eigenproblems with boundary and   interior singularities
  We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.SP/0702122] and John Weir [arXiv:0711.1371]. 
Lyonell Boulton, Michael Levitin and Marco Marletta