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題名 Dimer-Monomer Model on the Sierpinski Gasket 作者 張書銓
Changa, Shu-Chiuan
陳隆奇
Lung-Chi Chen貢獻者 應數系 關鍵詞 Dimer-monomer model;Sierpinski gasket;Recursion relations;Asymptotic growth constant 日期 2008.03 上傳時間 13-Nov-2014 17:21:42 (UTC+8) 摘要 We present the numbers of dimer–monomers Md(n)Md(n) on the Sierpinski gasket SGd(n)SGd(n) at stage nn with dimension dd equal to two, three and four. The upper and lower bounds for the asymptotic growth constant, defined as zSGd=limv→∞lnMd(n)/vzSGd=limv→∞lnMd(n)/v where vv is the number of vertices on SGd(n)SGd(n), are derived in terms of the results at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of zSGdzSGd can be evaluated with more than a hundred significant figures accurate. From the results for d=2,3,4d=2,3,4, we conjecture the upper and lower bounds of zSGdzSGd for general dimension. The corresponding results on the generalized Sierpinski gasket SGd,b(n)SGd,b(n) with d=2d=2 and b=3,4b=3,4 are also obtained. 關聯 Physica A, 387(7), 1551-1566 資料類型 article dc.contributor 應數系 en_US dc.creator (作者) 張書銓 zh_TW dc.creator (作者) Changa, Shu-Chiuan en_US dc.creator (作者) 陳隆奇 zh_TW dc.creator (作者) Lung-Chi Chen en_US dc.date (日期) 2008.03 en_US dc.date.accessioned 13-Nov-2014 17:21:42 (UTC+8) - dc.date.available 13-Nov-2014 17:21:42 (UTC+8) - dc.date.issued (上傳時間) 13-Nov-2014 17:21:42 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/71413 - dc.description.abstract (摘要) We present the numbers of dimer–monomers Md(n)Md(n) on the Sierpinski gasket SGd(n)SGd(n) at stage nn with dimension dd equal to two, three and four. The upper and lower bounds for the asymptotic growth constant, defined as zSGd=limv→∞lnMd(n)/vzSGd=limv→∞lnMd(n)/v where vv is the number of vertices on SGd(n)SGd(n), are derived in terms of the results at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of zSGdzSGd can be evaluated with more than a hundred significant figures accurate. From the results for d=2,3,4d=2,3,4, we conjecture the upper and lower bounds of zSGdzSGd for general dimension. The corresponding results on the generalized Sierpinski gasket SGd,b(n)SGd,b(n) with d=2d=2 and b=3,4b=3,4 are also obtained. en_US dc.format.extent 915625 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.relation (關聯) Physica A, 387(7), 1551-1566 en_US dc.subject (關鍵詞) Dimer-monomer model;Sierpinski gasket;Recursion relations;Asymptotic growth constant en_US dc.title (題名) Dimer-Monomer Model on the Sierpinski Gasket en_US dc.type (資料類型) article en
