{"created":"2023-06-19T11:42:33.824407+00:00","id":11807,"links":{},"metadata":{"_buckets":{"deposit":"37801881-0444-4833-971a-59bdd5fa649a"},"_deposit":{"created_by":13,"id":"11807","owners":[13],"pid":{"revision_id":0,"type":"depid","value":"11807"},"status":"published"},"_oai":{"id":"oai:mie-u.repo.nii.ac.jp:00011807","sets":["143:144:274:864"]},"author_link":["34269","34270","34271"],"item_4_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2018-01-04","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"21","bibliographicPageStart":"1","bibliographicVolumeNumber":"69","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・教育実践"},{"bibliographic_title":"BULLETIN OF THE FACULTY OF EDUCATION MIE UNIVERSITY. Natural Science,Humanities,Social Science,Education,Educational Practice","bibliographic_titleLang":"en"}]}]},"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":"本研究を進めるにあたり，「小林昭七著：曲線と曲面の微分幾何（改訂版）」（裳華房）と「梅原雅顕，山田光太郎著：曲線と曲面 -微分幾何的アプローチ-」（裳華房）を用いて曲線曲面論を学習した．その中で閉曲線と閉曲面の全曲率に注目した.閉曲線の全曲率は曲率を求めたのち，積分をすることで計算できる．しかし，閉曲線を複素数平面上に表示し，留数定理を用いることで容易に計算することができると考え，本研究に至った．その結果，複素数平面上の閉曲線γ(θ）の全曲率は，γ(θ）= 0の解の大きさによって定まる関係を見つけた．また，閉曲面は回転面に限定し，回転軸と回転させる曲線が交わることで全曲率がどのようになるのかを計算した．本論文について，竹内の論文「複素数を用いた平面曲線の全曲率の考察」と田中の論文「曲線の変形における全曲率の変化」を1つにまとめたものである．全5章の構成のうち，2章と3章は竹内の研究成果を，4章と5章は田中の研究成果をまとめた．1章では曲線と曲率の定義，そして閉曲線と全曲率の定義について触れ，さらに複素数を用いて計算するために留数定理を，本研究を進めるにあたっての準備として説明している．2章，3章では平面曲線の全曲率について，複素数を用いることの利便性と簡単な関数について定理を考え，さらにー般の閉曲線とその全曲率との関係を複素数を用いて説明した．4章では特異点をもつ平面曲線を特異点をもたない空間曲線として実現させることを考える．そして5章では平曲面を回転面に限定し，全曲率を計算している．通常では回転面は回転軸と回転させる曲線が交わらないように設定するが，本論文では回転軸と曲線が交わるような回転面も考えていく．","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":"1880-2419","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_31":{"attribute_name":"出版者（ヨミ）","attribute_value_mlt":[{"subitem_text_value":"ミエダイガクキョウイクガクブ"}]},"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":"竹内, 洋介","creatorNameLang":"ja"},{"creatorName":"タケウチ, ヨウスケ","creatorNameLang":"ja-Kana"},{"creatorName":"TAKEUCHI, Yosuke","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"田中, 健雄","creatorNameLang":"ja"},{"creatorName":"タナカ, タケオ","creatorNameLang":"ja-Kana"},{"creatorName":"TANAKA, Takeo","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"新田, 貴士","creatorNameLang":"ja"},{"creatorName":"ニッタ, タカシ","creatorNameLang":"ja-Kana"},{"creatorName":"NITTA, Takashi","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":"2018-01-18"}],"displaytype":"detail","filename":"20C18248.pdf","filesize":[{"value":"6.4 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"20C18248","url":"https://mie-u.repo.nii.ac.jp/record/11807/files/20C18248.pdf"},"version_id":"ee3b5130-a268-4c93-abb4-0e4c84533f45"}]},"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":"特異点が存在する曲線と曲面の全曲率について","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"特異点が存在する曲線と曲面の全曲率について","subitem_title_language":"ja"},{"subitem_title":"Some examples for total curvatures of curves and surfaces with singularities","subitem_title_language":"en"}]},"item_type_id":"4","owner":"13","path":["864"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2018-01-18"},"publish_date":"2018-01-18","publish_status":"0","recid":"11807","relation_version_is_last":true,"title":["特異点が存在する曲線と曲面の全曲率について"],"weko_creator_id":"13","weko_shared_id":-1},"updated":"2023-11-09T07:13:40.948531+00:00"}