{"created":"2023-05-15T15:29:16.068566+00:00","id":18914,"links":{},"metadata":{"_buckets":{"deposit":"37d4ade7-836e-42bb-b727-755eb4e5d5ac"},"_deposit":{"created_by":15,"id":"18914","owners":[15],"pid":{"revision_id":0,"type":"depid","value":"18914"},"status":"published"},"_oai":{"id":"oai:sucra.repo.nii.ac.jp:00018914","sets":["94:429:431:432:955"]},"author_link":[],"item_113_alternative_title_1":{"attribute_name":"タイトル（別言語）","attribute_value_mlt":[{"subitem_alternative_title":"分解されたMöbiusエネルギーに対する第二変分のL2表現とŁojasiewicz不等式"}]},"item_113_biblio_info_9":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2019","bibliographicIssueDateType":"Issued"}}]},"item_113_date_35":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2020-03-02","subitem_date_issued_type":"Created"}]},"item_113_date_granted_20":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2019-03-20"}]},"item_113_degree_grantor_22":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_name":"埼玉大学"}],"subitem_degreegrantor_identifier":[{"subitem_degreegrantor_identifier_name":"12401","subitem_degreegrantor_identifier_scheme":"kakenhi"}]}]},"item_113_degree_name_21":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士(理学)"}]},"item_113_description_13":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_description":"62 p.","subitem_description_type":"Other"}]},"item_113_description_23":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":" Knot energies, one of which is the Möbius energy, are constructed to measure the well-proportionedness of the knot. The best-proportioned knot in the given knot class may be determined by the gradient flow of the energy. Indeed, Blatt showed the global existence and convergence of the gradient flow of the Möbius energy near stationary points. The Łojasiewicz inequality played an important role in proving the results. The inequality can be proved by properties of L2-representation of the first and second variations. On the other hand, Ishizeki and Nagasawa showed that the Möbius energy can be decomposed into parts keeping the Möbius invariance and each part has the L2-representation of the first variation. In this thesis, we discuss the L2-representation of the second variation for each decomposed part of the Mobius energy, and derive it explicitly. As a consequence of it and Chill's theory, the Łojasiewicz inequality is derived from the representations.","subitem_description_type":"Abstract"}]},"item_113_description_25":{"attribute_name":"注記","attribute_value_mlt":[{"subitem_description":"指導教員 : 長澤壯之","subitem_description_type":"Other"}]},"item_113_description_33":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"text","subitem_description_type":"Other"}]},"item_113_description_34":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_113_dissertation_number_19":{"attribute_name":"学位授与番号","attribute_value_mlt":[{"subitem_dissertationnumber":"甲第1125号"}]},"item_113_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24561/00018883","subitem_identifier_reg_type":"JaLC"}]},"item_113_publisher_11":{"attribute_name":"出版者名","attribute_value_mlt":[{"subitem_publisher":"埼玉大学大学院理工学研究科"}]},"item_113_publisher_12":{"attribute_name":"出版者名（別言語）","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Science and Engineering, Saitama University"}]},"item_113_record_name_8":{"attribute_name":"書誌","attribute_value_mlt":[{"subitem_record_name":"博士論文（埼玉大学大学院理工学研究科（博士後期課程））"}]},"item_113_text_3":{"attribute_name":"著者 ローマ字","attribute_value_mlt":[{"subitem_text_value":"GUNJI, Katsunori"}]},"item_113_text_31":{"attribute_name":"版","attribute_value_mlt":[{"subitem_text_value":"[出版社版]"}]},"item_113_text_36":{"attribute_name":"アイテムID","attribute_value_mlt":[{"subitem_text_value":"GD0001096"}]},"item_113_text_4":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"埼玉大学大学院理工学研究科(博士後期課程)理工学専攻数理電子情報コース"}]},"item_113_text_5":{"attribute_name":"著者 所属（別言語）","attribute_value_mlt":[{"subitem_text_value":"Graduate School of Science and Engineering, Saitama University"}]},"item_113_version_type_32":{"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_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"郡司, 克徳","creatorNameLang":"ja"},{"creatorName":"グンジ, カツノリ","creatorNameLang":"ja-Kana"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2020-03-02"}],"displaytype":"detail","filename":"GD0001096.pdf","filesize":[{"value":"334.0 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"GD0001096.pdf","objectType":"fulltext","url":"https://sucra.repo.nii.ac.jp/record/18914/files/GD0001096.pdf"},"version_id":"e24a2ec6-7034-4f04-91b3-f797cd5b94b5"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"the Möbius energy","subitem_subject_scheme":"Other"},{"subitem_subject":"decomposed Möbius energies","subitem_subject_scheme":"Other"},{"subitem_subject":"the second variation","subitem_subject_scheme":"Other"},{"subitem_subject":"the Łojasiewicz inequality","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"doctoral thesis","resourceuri":"http://purl.org/coar/resource_type/c_db06"}]},"item_title":"The L2-representations of the Second Variations and the Łojasiewicz Inequalities for Decomposed Möbius Energies","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"The L2-representations of the Second Variations and the Łojasiewicz Inequalities for Decomposed Möbius Energies","subitem_title_language":"en"}]},"item_type_id":"113","owner":"15","path":["955"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2020-03-02"},"publish_date":"2020-03-02","publish_status":"0","recid":"18914","relation_version_is_last":true,"title":["The L2-representations of the Second Variations and the Łojasiewicz Inequalities for Decomposed Möbius Energies"],"weko_creator_id":"15","weko_shared_id":-1},"updated":"2023-06-23T02:08:23.930013+00:00"}