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| Proof of Murphy-Cohen Conjecture on One-Dimensional Hard Ball Systems |
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Citation： |
Lizhou CHEN.Proof of Murphy-Cohen Conjecture on One-Dimensional Hard Ball Systems[J].Chinese Annals of Mathematics B,2007,28(3):293~298 |
| Page view： 1189
Net amount： 958 |
Authors： |
Lizhou CHEN; |
Foundation： |
Project supported by the Special Funds for Chinese Major State Basic Research Projects “Nonlinear Science”. |
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| Abstract： |
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 \frac{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. |
Keywords： |
Hard ball, Elastic collision, Billiard, Reflection group, Numbers game |
Classification： |
70F99, 51F15, 20F55 |
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