1. Department of Mathematics, Kindai University, Higashi–Osaka, Japan
2. Department of Mathematics and Informatics Faculty of Science, Chiba University, Chiba, Japan
3. Institute of Management and Information Technologies, Chiba University, Chiba, Japan
4. Donald Bren Distinguished Chair in Mathematics, Chapman University, Orange, CA, USA
5. Graduate School of Science and Engineering, Kindai University, Higashi–Osaka Japan