• East Asian mathematical journal
• /
• v.23 no.3
• /
• pp.371-380
• /
• 2007

It is well known that the solutions of the Diophantine equation $x^2+xy-y^2=1$ is related to the Fibonacci sequence. In this study, we generalize the above fact to the tribonacci sequence and its generalized from using the group structure of solutions of some Diophantine equations.

• Journal for History of Mathematics
• /
• v.21 no.3
• /
• pp.113-126
• /
• 2008

This work is devoted to study about the abc conjecture: how it works in the development of the proof of Fermat's last theorem and more generally in the diophantine equation theory. And it is also studied the application of the abc conjecture to the iteration of polynomials.

• Journal of Power System Engineering
• /
• v.9 no.4
• /
• pp.175-180
• /
• 2005

Incorrections between model and plant are parameter, system order uncertainties and modeling error due to disturbance like friction. Therefore to achieve a good tracking performance, adaptive discrete time sliding mode tracking controller is used under time-varying desired position. Based on the diophantine equation, a new discrete time sliding function is defined and utilized for the control law. Robustness is increased by using both a recursive least-square method and a sliding function-based nonlinear feedback. The effectiveness of the proposed control algorithm is proved by the results of simulation and experiment.