1. University of Alabama at Birmingham, Department of Mathematics, Birmingham, Alabama, 35294, USA
2. University of Siegen, Department of Electrical Engineering and Computer Science, Hölderlinstr. 3, 57068 Siegen, Germany
3. Meiji University, Department of Computer Science, 1-1-1 Higashimita, Tama-ku, Kawasaki, 214-8571, Japan