1. Professor Department of Mathematics, Bangalore University, Bangalore 560056, India e-mail:
2. Department of Mathematics, Bangalore University, Bangalore 560056, India e-mail:
3. Associate Professor Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan e-mail:
4. Professor Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan;
5. School of Civil Engineering and Architecture, Wuhan Polytechnic University, Wuhan 430023, China e-mail: