Thales of Miletus （640？-546 BC） is famous for his prediction of the total solar eclipse in 585 BC. In this paper, the author demonstrate how Thales may have used the same principle for prediction of solar eclipses ...Thales of Miletus （640？-546 BC） is famous for his prediction of the total solar eclipse in 585 BC. In this paper, the author demonstrate how Thales may have used the same principle for prediction of solar eclipses as that used on the Antikythera Mechanism. At the SEAC conference in Alexandria in 2009, the author presented the paper ＂Ten solar eclipses show that the Antikythera Mechanism was constructed for use on Sicily.＂ The best defined series of exeligmos cycles started in 243 BC during the lifetime of Archimedes （287-212 BC） from Syracuse. The inscriptions on the Antikythera Mechanism were made in 100-150 BC and the last useful exeligmos started in 134 BC. The theory for the motion of the moon was from Hipparchus （ca 190-125 BC）. A more complete investigation of the solar eclipses on the Antikythera Mechanism reveals that the first month in the first saros cycle started with the first new moon after the winter solstice in 542 BC. Four solar eclipses 537-528 BC, from the first saros cycle, and three one exeligmos cycle later, 487-478 BC, are preserved and may have been recorded in Croton by Pythagoras （ca 575-495 BC） and his school.展开更多
The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis method...The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.展开更多
文摘Thales of Miletus （640？-546 BC） is famous for his prediction of the total solar eclipse in 585 BC. In this paper, the author demonstrate how Thales may have used the same principle for prediction of solar eclipses as that used on the Antikythera Mechanism. At the SEAC conference in Alexandria in 2009, the author presented the paper ＂Ten solar eclipses show that the Antikythera Mechanism was constructed for use on Sicily.＂ The best defined series of exeligmos cycles started in 243 BC during the lifetime of Archimedes （287-212 BC） from Syracuse. The inscriptions on the Antikythera Mechanism were made in 100-150 BC and the last useful exeligmos started in 134 BC. The theory for the motion of the moon was from Hipparchus （ca 190-125 BC）. A more complete investigation of the solar eclipses on the Antikythera Mechanism reveals that the first month in the first saros cycle started with the first new moon after the winter solstice in 542 BC. Four solar eclipses 537-528 BC, from the first saros cycle, and three one exeligmos cycle later, 487-478 BC, are preserved and may have been recorded in Croton by Pythagoras （ca 575-495 BC） and his school.
基金supported by China Postdoctoral Science Foundation (Grant Nos. 20100470249, 20100470254)
文摘The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.
