We prove the Murphy and Cohen＇s conjecture that the maximum number of collisions of n ＋ 1 elastic particles moving freely on a line is n（n＋1）/2 if no interior particle has mass less than the arithmetic mean of th...We prove the Murphy and Cohen＇s conjecture that the maximum number of collisions of n ＋ 1 elastic particles moving freely on a line is n（n＋1）/2 if no interior particle has mass less than the arithmetic mean of the masses of its immediate neighbors. In fact, we prove the stronger result that, for the same conclusion, the condition that no interior particle has mass less than the geometric mean, rather than the arithmetic mean, of the masses of its immediate neighbors suffices.展开更多
基金the Special Funds for Chinese Major State Basic Research Projects "Nonlinear Science".
文摘We prove the Murphy and Cohen＇s conjecture that the maximum number of collisions of n ＋ 1 elastic particles moving freely on a line is n（n＋1）/2 if no interior particle has mass less than the arithmetic mean of the masses of its immediate neighbors. In fact, we prove the stronger result that, for the same conclusion, the condition that no interior particle has mass less than the geometric mean, rather than the arithmetic mean, of the masses of its immediate neighbors suffices.
