Proof of Murphy-Cohen Conjecture on One-Dimensional Hard Ball Systems

O1; 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...

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Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 28; no. 3; pp. 293 - 298
Main Author Chen, Lizhou
Format Journal Article
LanguageEnglish
Published School of Mathematical Sciences,Fudan University,Shanghai 200433,China 01.06.2007
Subjects
Reflection group
Hard ball
Elastic collision
Numbers game
Billiard
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ISSN0252-9599
1860-6261
DOI10.1007/s11401-006-0135-2

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Summary:O1; 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.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-006-0135-2