• East Asian mathematical journal
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• 제23권3호
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• pp.371-380
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• 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.

• 한국수학사학회지
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• 제21권3호
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• pp.113-126
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• 2008

abc추측의 역사적 발전 과정과 페르마정리와의 관계를 살펴보며, abc추측이 디오판토스방정식풀이와 이항다항식 f(x)=$x^n$-b 반복의 불변성연구에 응용되는 면을 연구한다.

• 동력기계공학회지
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• 제9권4호
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• pp.175-180
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• 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.