{"created":"2021-03-01T05:58:36.994893+00:00","id":6184,"links":{},"metadata":{"_buckets":{"deposit":"ac06b786-acf8-441e-8a2b-c0de93da9c46"},"_deposit":{"id":"6184","owners":[],"pid":{"revision_id":0,"type":"depid","value":"6184"},"status":"published"},"_oai":{"id":"oai:kitami-it.repo.nii.ac.jp:00006184","sets":["7:15:21"]},"item_2_alternative_title_18":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"On Convergence of Infinite Continued Fractions"}]},"item_2_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1966-03","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"4","bibliographicPageEnd":"117","bibliographicPageStart":"109","bibliographicVolumeNumber":"1","bibliographic_titles":[{"bibliographic_title":"北見工業大学研究報告"}]}]},"item_2_description_14":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_2_description_4":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"Let {ν_k} be a sequence of natural numbers. The following form （1） of the sequence {ν_k} is called a infinite continued fraction. 1/(ν_1+1)/(ν_2+1)/(…) (1) From the sequence {ν_k} j the sequence ｛ξ_k｝is made as follows　(ξ_k=1)/(ν_1+1)/(…)/1/(ν_k-1+1)/(ν-1) (2)  and it is convergent sequence. In this paper, we give the following relationsξ_2＜ξ_4＜…＜<ξ_3＜ξ_1 (9) │ξ-ｋ-ξ-ｋ1│＜__-1/(k(k-1) (8) The conclusion drawn from these relations is the uniformity about convergence of infinite continued fractions. Namely, for any positive number s and sequence of natural numbers ε and sequence of natural numbers {ν_k}, there exists some natural number N such that N≦k, l implies │ξ-ｋ-ξ-1│＜εFurthermore, let S be the totality of all sequences of natural numbers and R be the totality of all irrational numbers in the open interval （0，I）. We define the metric function d in the space S as follows d(a, b)=1/(Min{k:ν_k≠μ_k} (S∋a, b, a={ν_k}, b={μ_k}). Ｔｈｅｓｐａｃｅ R is the subspace of the real line. In this paper, the relations between the spaces S and R are discussed.","subitem_description_type":"Abstract"}]},"item_2_full_name_3":{"attribute_name":"著者別名","attribute_value_mlt":[{"nameIdentifiers":[{"nameIdentifier":"31696","nameIdentifierScheme":"WEKO"}],"names":[{"name":"Kiro, lSOBE"}]}]},"item_2_publisher_32":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"北見工業大学"}]},"item_2_select_15":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_select_item":"publisher"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"礒部, 煕郎"}],"nameIdentifiers":[{"nameIdentifier":"31695","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-11-22"}],"displaytype":"detail","filename":"1-4-12.pdf","filesize":[{"value":"2.6 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"1-4-12.pdf","url":"https://kitami-it.repo.nii.ac.jp/record/6184/files/1-4-12.pdf"},"version_id":"f22f29ee-6238-49f1-8ae9-b231b2c2c9fa"}]},"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":"無限連分数の収束について","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"無限連分数の収束について"}]},"item_type_id":"2","owner":"1","path":["21"],"pubdate":{"attribute_name":"公開日","attribute_value":"2007-04-09"},"publish_date":"2007-04-09","publish_status":"0","recid":"6184","relation_version_is_last":true,"title":["無限連分数の収束について"],"weko_creator_id":"1","weko_shared_id":3},"updated":"2022-12-13T02:19:31.211815+00:00"}