{"created":"2022-01-27T08:05:43.475186+00:00","id":2004456,"links":{},"metadata":{"_buckets":{"deposit":"43285e05-eb5a-4bf8-a1ee-e8480c1ef9ab"},"_deposit":{"id":"2004456","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2004456"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02004456","sets":["1642838403123","1642838403551:1642838405037"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_title":"離散幾何の総合的研究","subitem_title_language":"ja"},{"subitem_title":"Comprehensive Study on Discrete Geometry","subitem_title_language":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"前原, 濶","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"徳重, 典英","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"小関, 道夫","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"加納, 幹雄","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"榎本, 彦衛","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"伊藤, 栄明","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"Maehara, Hiroshi","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Tokushige, Norihide","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Ozeki, Michio","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Kano, Mikio","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Enomoto, Hikoe","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Itoh, Yoshiaki","creatorNameLang":"en"}]}]},"item_1617186476635":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_1617186609386":{"attribute_name":"Subject","attribute_value_mlt":[{"subitem_subject":"フレ-ムワ-ク","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"整数距離表現","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"球の接触パタ-ン","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"ランダム・ト-ナメント","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"破産問題","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"framework","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"integral distance representation","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Contact pattarn of spheres","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"random tournament","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"ruin problem","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"科研費番号: 08304019","subitem_description_type":"Other"},{"subitem_description":"平成8-9年度文部省科学研究費補助金(基盤研究(A)(1))研究成果報告書","subitem_description_type":"Other"},{"subitem_description":"研究概要 : 1.フレ-ムワ-クの剛性に関して:3次元空間内の変形しない等辺フレ-ムワ-クで三角形を含まないものを構成した.またmが3以上,nが5以上のとき, 平面上の2部フレ-ムワ-クK(m,n)が連続的に変形するための頂点の配置を特徴づけた.さらに,平面上の変形しないフレ-ムワ-クで,辺の長さとグラフの構造のデ-タだけからは作図できないような,頂点数が最少(6頂点)のフレ-ムワ-クを構成した.2.埋め込み等に関して:どんな有限グラフ Gについても,その頂点集合を平面上に配置して,2頂点が隣接するときに限り,2頂点の距離は整数になるようにすることができる(整数距離表現)こと,さらに,有限個の色による平面の任意の着色に対して,Gの整数距離表現で,頂点がすべて単色となるものが存在することを示した.有理数体上の内積の定義されたn次元のベクトル空間は,2n+1次元のユ-クリッド空間内に等長的に埋め込まれることを示した.球面の配置等について:平面上に置かれた球の接触パタ-ンとして得られるグラフ全体の族Fについて研究した.族Fと平面グラフ全体の族の間には包含関係がないこと,族Fは,いわゆるペテルセン.ファミリ-に属するグラフを一つも含まないこと,族Fに属するグラフの染色数の最大値は5か6であることを示した.ランダム・グラフ,確率分布等に関して:円周上のランダム点で生成されるドミナンス関係に含まれるレギュラ-・ト-ナメントの位数の最大値の確率分布を決定した.また,古典的な破産問題の 3人の場合への拡張を,格子上の乱歩に関するMcCrea & Whippleの結果を利用して解決した.","subitem_description_type":"Other"},{"subitem_description":"1.On the rigidity of frameworks : We presented a rigid unit-bar-framework in the 3-dimensional space that has no triangle, and a minimum rigid framework in the plane that cannot be constructed from the data of edge-lengths and graph structure. We proved that if a complete bipartite framework K (m, n) (m >= 3, n >= 5) in the plane admits a continuous deformation, then one of the partite-sets lies on a line L and the other partite-set lies on the line perpendicular to L.\\n2.On embeddings of structures : We proved that for any planar graph G = (V,E), there is an emebedding f : V * R^2 such that x, y * V are adijacent if and only if the distance between f (x) and f (y) is an integer. We also proved that every n dimensional inner product space over the rational field can be isometrically embedded into 2n + 1 dimensional Euclidean space.\\n3.On srrangements of spheres : A graph G is said to be representable by balls on the table, if we can place solid balls on a table, one ball for each vertex, so that two balls are tangent only when the corresponding vertices are adjacent. We proved that the family F of graphs representable by balls on a table is different from the family of planar graphs, and that F does not contain any member of the so-called Petersen family, and that the maximum value of the chromatic number of a graph in F is either 5 or 6.\\n4.On random graphs, probability : We determined the probability distribution of the order of the maximum regular tournament in a dominance relation generated by a randam n points on a circle. We extended the classical ruin problem to 3 persons' game, and calculated the probability that a fixed gambler A ruined first, and the probability that A is the sole survivor.","subitem_description_type":"Other"},{"subitem_description":"未公開：P.23～304（論文別刷のため）","subitem_description_type":"Other"},{"subitem_description":"研究報告書","subitem_description_type":"Other"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_publisher":"前原濶","subitem_publisher_language":"ja"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_1617186783814":{"attribute_name":"Identifier","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/20.500.12000/9348"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_source_identifier":"BA35621584","subitem_source_identifier_type":"NCID"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1998-03","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"none"}]},"item_1617258105262":{"attribute_name":"Resource Type","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_1617265215918":{"attribute_name":"Version Type","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_1617605131499":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","filename":"08304019.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004456/files/08304019.pdf"},"version_id":"ff1c7fe0-7ef4-4517-8453-fbcedc9ea51c"}]},"item_title":"離散幾何の総合的研究","item_type_id":"15","owner":"1","path":["1642838403123","1642838405037"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2009-03-23"},"publish_date":"2009-03-23","publish_status":"0","recid":"2004456","relation_version_is_last":true,"title":["離散幾何の総合的研究"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2024-11-19T07:05:35.898159+00:00"}