{"created":"2023-06-19T11:36:22.838820+00:00","id":3321,"links":{},"metadata":{"_buckets":{"deposit":"35733d61-d95a-4878-8d92-c7fb37722c91"},"_deposit":{"created_by":13,"id":"3321","owners":[13],"pid":{"revision_id":0,"type":"depid","value":"3321"},"status":"published"},"_oai":{"id":"oai:mie-u.repo.nii.ac.jp:00003321","sets":["143:144:262:267"]},"author_link":["5730","5731"],"item_4_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2009-03-31","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"14","bibliographicPageStart":"7","bibliographicVolumeNumber":"60","bibliographic_titles":[{"bibliographic_title":"三重大学教育学部研究紀要. 自然科学・人文科学・社会科学・教育科学"}]}]},"item_4_description_14":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_4_description_4":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"Sがコンパクト距離空間X上で定義された縮小写像の族のとき, Sの有限部分族Λに対して, 極限集合JΛ (アトラクターあるいはIFSフラクタルともよばれる)が定義できる. HD(JΛ) で極限集合のハウスドルフ次元を表すとき, ハウスドルフ次元の集合{HD(JΛ) : Λ ⊆ S}を次元集合とよぶことにする. 次元集合は, 閉区間[0, HD(Js)]の部分集合である. 極限集合の次元と測度については, MauldinとUrbańskiによる詳細な研究結果[5]があるが, 我々は, 次元集合が閉区間[0, HD(JS)] で稠密になるのはSがどのような条件をみたす場合か, あるいはどのような場合に疎になるか, という問題に興味を持っている. このような問題は, 文献[3]においてKesseböhmerとZhuによって初めて議論された. 特に「単純正則連分数に展開したとき, 指定された有限個の項だけを持つ無理数の集合のハウスドルフ次元は, 単位区間に稠密に存在する」という彼らの結果は非常に興味深い. 本稿では, Xが区間であり更にSがX上のアフィン変換(1次関数)族の場合に限って, この間題を議論する. 関数をアフィン変換に限ることで, この間題に対する明確な判定条件を与えることができた. 本稿の結果は, Xが区間でなくとも, d次元ユークリッド空間の連結なコンパクト集合であればそのまま成り立つと思われるが, その検証はこれからの研究課題である.","subitem_description_type":"Abstract"},{"subitem_description":"Let X be a non-empty compact connected subset of d-dimensional euclidean space and S a conformal iterated function system on X. For Λ ⊆ S, we denote the limit set with respect to Λ by JΛ and the Hausdorff dimension of it by HD(JΛ) . The dimensional and measure-theoretical properties for the limit set were studied in details by Mauldin and Urbański [5]. We are interested in the problem of deciding whether the dimension set {HD(JΛ) : Λ ⊆ S finite} is dense or nowhere dense in the interval [0, HD(JS)]. Such problem was studied by Kesseböhmer and Zhu [3] for the first time. In this paper we shall discuss the problem in the case where X is a closed interval and S a collection of affine transformations on X. Then the clear sufficient conditions of this problem will be obtained.","subitem_description_type":"Abstract"}]},"item_4_publisher_30":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"三重大学教育学部"}]},"item_4_source_id_7":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0389-9225","subitem_source_identifier_type":"PISSN"}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA12097333","subitem_source_identifier_type":"NCID"}]},"item_4_text_18":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"Dimension set of self-affine fractals on the real line"}]},"item_4_text_65":{"attribute_name":"資源タイプ（三重大）","attribute_value_mlt":[{"subitem_text_value":"Departmental Bulletin Paper / 紀要論文"}]},"item_4_version_type_15":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"玉城, 政和","creatorNameLang":"ja"},{"creatorName":"Tamashiro, Masakazu","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"服部, 恵美","creatorNameLang":"ja"},{"creatorName":"Hattori, Megumi","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-02-18"}],"displaytype":"detail","filename":"AA120973330600005.pdf","filesize":[{"value":"395.6 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"AA120973330600005.pdf","url":"https://mie-u.repo.nii.ac.jp/record/3321/files/AA120973330600005.pdf"},"version_id":"fffb812b-5547-4efc-987e-8bca1cb26725"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"実直線上の自己アフィンフラクタルと次元集合","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"実直線上の自己アフィンフラクタルと次元集合","subitem_title_language":"ja"}]},"item_type_id":"4","owner":"13","path":["267"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2010-03-31"},"publish_date":"2010-03-31","publish_status":"0","recid":"3321","relation_version_is_last":true,"title":["実直線上の自己アフィンフラクタルと次元集合"],"weko_creator_id":"13","weko_shared_id":-1},"updated":"2023-11-09T02:31:05.970588+00:00"}