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...
Saved in:
| Published in | Chinese annals of mathematics. Serie B Vol. 28; no. 3; pp. 293 - 298 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
School of Mathematical Sciences,Fudan University,Shanghai 200433,China
01.06.2007
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9599 1860-6261 |
| DOI | 10.1007/s11401-006-0135-2 |
Cover
| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Chen, Lizhou |
| AuthorAffiliation | School of Mathematical Sciences,Fudan University,Shanghai 200433,China |
| AuthorAffiliation_xml | – name: School of Mathematical Sciences,Fudan University,Shanghai 200433,China |
| Author_xml | – sequence: 1 givenname: Lizhou surname: Chen fullname: Chen, Lizhou |
| BookMark | eNp9kMFKAzEURYNUsK1-gLvZuYq-JDPJZKm1WqFSQV2HTPrGTp0mJZmi_Xun1JUL4cHb3HO5nBEZ-OCRkEsG1wxA3STGcmAUQFJgoqD8hAxZKYFKLtmADIEXnOpC6zMySmkNwHJVwJBMX2IIddbf8y5uV3s6CSv02ST4NbpuFzELPlt4pPfNBn1qgrdtNrNxmd3Zts1e96nDTTonp7VtE178_jF5f5i-TWZ0vnh8mtzOqeNKdVRx7TTWTqG1CuslCidzjarCclmBKCpdlyLXFec1E6oUgikpZQ4SrXCaWzEmV8feL-tr6z_MOuxivyiZ9O0_DfJeBQgA0SfVMeliSClibVzT2a7f30XbtIaBOXgzR2-m92YO3gzvSfaH3MZmY-P-H-YHhmtw7Q |
| CitedBy_id | crossref_primary_10_1088_0143_0807_38_1_015004 crossref_primary_10_1007_s10955_009_9846_6 |
| Cites_doi | 10.1016/S0166-8641(01)00133-X 10.1007/BF01049961 10.1007/978-3-662-04062-1_3 10.1103/PhysRevLett.13.743 |
| ClassificationCodes | O1 |
| ContentType | Journal Article |
| Copyright | Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| Copyright_xml | – notice: Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| DBID | AAYXX CITATION 2B. 4A8 92I 93N PSX TCJ |
| DOI | 10.1007/s11401-006-0135-2 |
| DatabaseName | CrossRef Wanfang Data Journals - Hong Kong WANFANG Data Centre Wanfang Data Journals 万方数据期刊 - 香港版 China Online Journals (COJ) China Online Journals (COJ) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1860-6261 |
| EndPage | 298 |
| ExternalDocumentID | sxnk_e200703003 10_1007_s11401_006_0135_2 |
| GrantInformation_xml | – fundername: 国家重点基础研究发展计划 funderid: (973计划) |
| GroupedDBID | -01 -0A -SA -S~ -Y2 .86 .VR 06D 0R~ 0VY 199 1N0 29B 2J2 2JN 2JY 2KG 2KM 2LR 2VQ 2~H 30V 4.4 406 408 40D 40E 5GY 5VR 5VS 5XA 5XB 6NX 78A 8TC 92E 92I 92M 95- 95. 95~ 96X 9D9 9DA AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYXX AAYZH ABAKF ABBBX ABBRH ABDBE ABDBF ABDZT ABECU ABFSG ABFTV ABHLI ABHQN ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACSTC ACUHS ACZOJ ADHHG ADHIR ADHKG ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AEZWR AFDZB AFGCZ AFHIU AFLOW AFOHR AFQWF AFUIB AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGQPQ AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMVHM AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AZFZN B-. B0M BA0 BAPOH BDATZ BGNMA BSONS CAG CAJEA CCEZO CCVFK CHBEP CITATION COF CS3 CSCUP CW9 DDRTE DNIVK DPUIP DU5 EAD EAP EBLON EBS EIOEI EJD EMK EPL ESBYG EST ESX FA0 FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 H13 HF~ HG6 HMJXF HRMNR HZ~ IHE IJ- IKXTQ ITM IWAJR I~X I~Z J-C JBSCW JUIAU JZLTJ KOV LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J P9R PF0 PT4 Q-- Q-0 QOS R-A R89 R9I REI ROL RPX RSV RT1 S.. S16 S1Z S27 S3B SAP SCL SCLPG SDD SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T8Q TCJ TGP TSG TUC TUS U1F U1G U2A U5A U5K UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 WSM YLTOR ZMTXR ZWQNP ~8M ~L9 2B. 4A8 93N PSX |
| ID | FETCH-LOGICAL-c277t-729c9efc7eaa7efde3c649e7be8db035b9f8349b22f13783317666406ea3c92a3 |
| ISSN | 0252-9599 |
| IngestDate | Thu May 29 03:54:51 EDT 2025 Thu Apr 24 22:51:49 EDT 2025 Tue Jul 01 03:12:53 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Reflection group Hard ball Elastic collision Numbers game Billiard |
| Language | English |
| License | http://www.springer.com/tdm |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c277t-729c9efc7eaa7efde3c649e7be8db035b9f8349b22f13783317666406ea3c92a3 |
| PageCount | 6 |
| ParticipantIDs | wanfang_journals_sxnk_e200703003 crossref_citationtrail_10_1007_s11401_006_0135_2 crossref_primary_10_1007_s11401_006_0135_2 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2007-06-00 |
| PublicationDateYYYYMMDD | 2007-06-01 |
| PublicationDate_xml | – month: 06 year: 2007 text: 2007-06-00 |
| PublicationDecade | 2000 |
| PublicationTitle | Chinese annals of mathematics. Serie B |
| PublicationTitle_FL | CHINESE ANNALS OF MATHEMATICS,SERIES B |
| PublicationYear | 2007 |
| Publisher | School of Mathematical Sciences,Fudan University,Shanghai 200433,China |
| Publisher_xml | – name: School of Mathematical Sciences,Fudan University,Shanghai 200433,China |
| References | Sinai (135_CR8) 1978; 33 135_CR5 Sandri (135_CR6) 1964; 13 Sevryuk (135_CR7) 1993; 96 135_CR1 Burago (135_CR2) 2002; 122 Murphy (135_CR4) 1993; 71 Thurston (135_CR9) 1964; 9 Gal'perin (135_CR3) 1983; 43 |
| References_xml | – volume: 96 start-page: 64 year: 1993 ident: 135_CR7 publication-title: Teoret. Mat. Fiz. – volume: 122 start-page: 87 year: 2002 ident: 135_CR2 publication-title: Topology Appl. doi: 10.1016/S0166-8641(01)00133-X – volume: 43 start-page: 142 year: 1983 ident: 135_CR3 publication-title: Trudy Moskov. Mat. Obshch. – volume: 71 start-page: 1063 year: 1993 ident: 135_CR4 publication-title: J. Statist. Phys. doi: 10.1007/BF01049961 – volume: 9 start-page: 386 year: 1964 ident: 135_CR9 publication-title: Bull. Amer. Phys. Soc. – ident: 135_CR5 doi: 10.1007/978-3-662-04062-1_3 – volume: 13 start-page: 743 year: 1964 ident: 135_CR6 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.13.743 – volume: 33 start-page: 229 year: 1978 ident: 135_CR8 publication-title: Uspehi Mat. Nauk. – ident: 135_CR1 |
| SSID | ssj0014750 |
| Score | 1.7083957 |
| Snippet | 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... |
| SourceID | wanfang crossref |
| SourceType | Aggregation Database Enrichment Source Index Database |
| StartPage | 293 |
| Title | Proof of Murphy-Cohen Conjecture on One-Dimensional Hard Ball Systems |
| URI | https://d.wanfangdata.com.cn/periodical/sxnk-e200703003 |
| Volume | 28 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Zi9swEBZhS6F9WHrS7YUfqpeCS6zDkh7jrMNS2m2hG9g3Y8sSu21xSpOwZX9Ef3NHR2InLb0gGKHISTzzZTwezXyD0IvaEKOYFmkmTZsyyZu0GWuVSmmZlbLlmc8mfHuan8zZ63N-Php9H2QtrVfNK339y7qS_9EqzIFeXZXsP2h2-6EwAWPQLxxBw3D8Kx2_B7fX-iQWL67U11q4Ir6PcWcAVPuuM-mxo_BfRiZhFzco_Ib0gKw8uqe4zLHiuBjjkuPJMZ7kblAoXDA3kBLLSYFLiYsSqwyXM1xM3SzMyAIXmT8_x1LgUmCp_FthzTbe8Oby-mKxdlQMpzsRB9FnRoWIY6AH9Rk6G2bZyFzSBds2W7dgnPrMEpj64MLfF_WlJ0p0QeTptj94tHaEk1Tx0C1pY5qJHECQDu1saKsYb9kkNLL-6W4wjtXR7iEyDaETymO15S7J9vJb96ky7mLB6Dny2BtEiMyliM7JZLsrxQQPMbv4Uze75L4Uc-9Ldvycm1d1Z0EAA9fl7A46jM8cySQA6C4ame4eut2LdXkflR5KCbyGUEp6KCWLLtmDUuKglDgoJRFKD9B8Vp5NT9LYYSPVcH0r18dYK2O1MHUtjG0N1TlTRjRGts2Y8kZZSZlqCLEZFZJSRyeagw9oaqoVqelDdNAtOvMIJYTI2ma8AXtOmSZW6roG57NtBGuZsewIjTfyqHSkn3ddUD5XPXG2E2HlEy1BhBU5Qi-3p3wJ3Cu_W5xEIVfxH7qs9rT6-M9LnqBbPeKfooPV17V5Bl7nqnnuofAD-r9zIg |
| linkProvider | Springer Nature |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Proof+of+Murphy-Cohen+Conjecture+on+One-Dimensional+Hard+Ball+Systems&rft.jtitle=%E6%95%B0%E5%AD%A6%E5%B9%B4%E5%88%8AB%E8%BE%91%EF%BC%88%E8%8B%B1%E6%96%87%E7%89%88%EF%BC%89&rft.au=Lizhou+CHEN&rft.date=2007-06-01&rft.pub=School+of+Mathematical+Sciences%2CFudan+University%2CShanghai+200433%2CChina&rft.issn=0252-9599&rft.volume=28&rft.issue=3&rft.spage=293&rft.epage=298&rft_id=info:doi/10.1007%2Fs11401-006-0135-2&rft.externalDocID=sxnk_e200703003 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fwww.wanfangdata.com.cn%2Fimages%2FPeriodicalImages%2Fsxnk-e%2Fsxnk-e.jpg |