{"created":"2022-01-27T08:05:49.219773+00:00","id":2004459,"links":{},"metadata":{"_buckets":{"deposit":"2f6e9d4a-d639-4aa4-a15b-a557671c2f9c"},"_deposit":{"id":"2004459","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2004459"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02004459","sets":["1642838403123","1642838403551:1642838405037"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_1551255647225":"\u6709\u9650\u70b9\u96c6\u5408\u306e\u8ddd\u96e2\u3068\u914d\u7f6e\u306e\u7814\u7a76","subitem_1551255648112":"ja"},{"subitem_1551255647225":"Study on the distances and arrangement of finite-point-set","subitem_1551255648112":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"\u524d\u539f, \u6ff6","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"Maehara, 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1.\u53ef\u7b97\u500b\u306e\u9802\u70b9\u3092\u6301\u3064\u5b8c\u5168\u30b0\u30e9\u30d5\u304b\u30891\u8fba\u3092\u9664\u3044\u305f\u30b0\u30e9\u30d5\u306f\u3069\u3093\u306a\u6b21\u5143\u3067\u3082\u6574\u6570\u8ddd\u96e2\u30b0\u30e9\u30d5\u3068\u306a\u3089\u306a\u3044\u304c\u3001\u5e73\u9762\u4e0a\u306e\u6709\u7406\u6570\u8ddd\u96e2\u30b0\u30e9\u30d5\u3068\u306a\u308b\u3002\u307e\u305f\u3001K_n\u304c\u5e73\u9762\u4e0a\u306e\u6574\u6570\u8ddd\u96e2\u30b0\u30e9\u30d5\u3068\u3057\u3066\u3001\u3069\u306e3\u9802\u70b9\u3082\u540c\u4e00\u76f4\u7dda\u4e0a\u306b\u306a\u304f\u3001\u3069\u306e4\u9802\u70b9\u3082\u540c\u4e00\u5186\u5468\u4e0a\u306b\u306a\u3044\u3088\u3046\u306b\u5b9f\u73fe\u3067\u304d\u308b\u306a\u3089\u3001\u5b8c\u5168n\u90e8\u30b0\u30e9\u30d5 K(a_1,a_2,...,a_n)\u306f\u5e73\u9762\u4e0a\u306e\u6709\u7406\u6570\u8ddd\u96e2\u30b0\u30e9\u30d5\u3068\u306a\u308b\u3002\u3053\u3053\u3067\u3001a_k=(k-1 choose 2)+(k-1 choose 3)+1\u3067\u3042\u308b\u30022.\u5e73\u9762\u4e0a\u306e\u70b9\u96c6\u5408\u306e\u5834\u5408\u30011-\u30ce\u30eb\u30e0\u3068\u221e-\u30ce\u30eb\u30e0(max\u30ce\u30eb\u30e0)\u306b\u3064\u3044\u3066\u306f\u3001\u305d\u308c\u3089\u306e\u70b9\u3092\u7d50\u3076\u6700\u5c0f\u30b9\u30bf\u30fc\u306e\u4e2d\u5fc3\u304c\u5bb9\u6613\u306b\u6c42\u3081\u3089\u308c\u308b\u3002\u307e\u305f\u3001n(n\u22604,>2)\u3068k>1\u306b\u3064\u3044\u3066p-\u30ce\u30eb\u30e0(p=1,2,...,k)\u3067\u306e\u6700\u5c0f\u30b9\u30bf\u30fc\u306e\u4e2d\u5fc3\u304c\u3059\u3079\u3066\u7570\u306a\u308b\u3088\u3046\u306a\u5e73\u9762\u4e0a\u306e n\u70b9\u96c6\u5408\u304c\u5b58\u5728\u3059\u308b\u3002\u3068\u3053\u308d\u304c4\u70b9\u96c6\u5408\u306b\u3064\u3044\u3066\u306f\u3069\u3093\u306a\u30ce\u30eb\u30e0\u306b\u3064\u3044\u3066\u3082\u3001\u540c\u3058\u70b9\u304c\u6700\u5c0f\u30b9\u30bf\u30fc\u306e\u4e2d\u5fc3\u3068\u306a\u308b\u3002(\u5009\u6577\u82b8\u8853\u79d1\u5b66\u5927\u5b66\u306e\u6e21\u8fba\u5b88\u6c0f\u3068\u306e\u5171\u540c\u7814\u7a76)3. \u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u5185\u306em+2\u500b\u4ee5\u4e0a\u306e\u70b9\u306e\u96c6\u5408X\u306b\u5bfe\u3057\u3066\u3001X\u306e(m+1)-\u70b9\u96c6\u5408\u306b\u3001\u305d\u306e\u51f8\u5305\u306em\u6b21\u5143\u4f53\u7a4d\u3092\u5bfe\u5fdc\u3055\u305b\u308b\u5199\u50cf\u03bc\u306f\u3001\u6c4e\u8ddd\u96e2(hemi- metric)\u3067\u3001m\u6b21\u5143\u306e\u5358\u4f53\u4e0d\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u3002\u5404m\u306b\u3064\u3044\u3066\u3001\u3053\u306e\u4e0d\u7b49\u5f0f\u306e\u4f59\u88d5\u306e\u9650\u754c\u5024(super-bound)s(m)\u304c\u5b9a\u7fa9\u3067\u304d\u3001\u305d\u306e\u5024\u306f\u70b9\u96c6\u5408 X\u306e\u5f62\u72b6\u306b\u3042\u308b\u7a0b\u5ea6\u95a2\u4fc2\u304c\u3042\u308b\u3002\u5b9f\u969b\u3001|X|\u22675\u306e\u3068\u304d\u3001\u540c\u5024\u306a\u95a2\u4fc2\"s(1)=2\u21d4s(2)=3\u21d4[X\u306f\u6b63\u5247\u5358\u4f53\u306e\u9802\u70b9\u96c6\u5408]\"\u304c\u6210\u7acb\u3059\u308b\u30023\u6b21\u5143\u306e\u6b63\u591a\u9762\u4f53\u306e\u9802\u70b9\u96c6\u5408\u306b\u3064\u3044\u3066\u306fs(m)\u306e\u5024\u3092\u8a08\u7b97\u3057\u305f\u3002n\u6b21\u5143\u306e\u5341\u5b57\u591a\u9762\u4f53\u306e\u5834\u5408\u3001n\u2267m\u22673\u306a\u3089\u5e38\u306bs(m)=3\u3067\u3001n\u6b21\u5143\u7acb\u65b9\u4f53\u306e\u5834\u5408\u306fm>0\u306e\u3068\u304d\u3001s(m)\u21921(n\u2192\u221e)\u3068\u306a\u308b\u3002(M.Deza, M.Dutour\u3068\u306e\u5171\u540c\u7814\u7a76)","subitem_description_type":"Other"},{"subitem_description":"1.Let G be the graph obtained from a complete graph with countably many vertices by removing an edge. Then G is not an integral-distance graph in any dimension, but it is a rational distance graph in the plane. If a complete graph with n vertices can be realized as an integral distance graph in the plane in such a way that no three vertices lie on a line, and no four vertices lie on a circle, then the complete n-partite graph K(a_1,a_2,\u3010triple bond\u3011,a_n) is a rational distance graph in the plane, where a_k=(k-1 choose 2)+(k-1 choose 3)+1.2.For any n>4, and any k>1, there is an n-point-set such that the center of the minimal star of the n-point-set in p-norm (p=1,2,\u3010triple bond\u3011,k) are all distinct. But for any 4-point-set the center of the minimal star are the same point for any norm. (Joint work with M.Watanabe).3.Let X be a point-set with at least m+2 points. The map from the family of m+1 point-set of X to the nonnegative reals that assigns to each (m+1)-point-set, the m-dimensional volume of the convex hull of the (m+1)-point-set, is a hemimetric and satisfies the m-dimensional simplex inequality. For each m, we can define the \"bound\" s(m) of m-dimensional simplex inequality. This bound s(m) determines the \"configuration\" X to some extent. For example, if |X|>4, then the three statements s(2)=2,s(3)=3, and [X is the vertex-set of a regular simplex] are equivalent. We calculated s(m) for regular polyhedra in 3-space. Though s(m)=3 for the n-dimensional cross-polytope, n>m-1>1, the value s(m) for n-cube tends to 1 as n tends to infinity. (Joint work with M.Deza and M.Dutour).","subitem_description_type":"Other"},{"subitem_description":"\u672a\u516c\u958b\uff1aP.7\uff5e94\uff08\u8ad6\u6587\u5225\u5237\u306e\u305f\u3081\uff09","subitem_description_type":"Other"},{"subitem_description":"\u7814\u7a76\u5831\u544a\u66f8","subitem_description_type":"Other"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_1522300295150":"ja","subitem_1522300316516":"\u524d\u539f\u6ff6"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_1551255818386":"jpn"}]},"item_1617186783814":{"attribute_name":"Identifier","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/20.500.12000/9310"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_1522646500366":"NCID","subitem_1522646572813":"BA74599055"}]},"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_1522305645492":"VoR","subitem_1600292170262":"http://purl.org/coar/version/c_970fb48d4fbd8a85"}]},"item_1617605131499":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","filename":"15540131-2.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004459/files/15540131-2.pdf"},"version_id":"ca9778e0-c5be-4d75-b197-e551517b7fe8"},{"accessrole":"open_access","filename":"15540131-1.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004459/files/15540131-1.pdf"},"version_id":"086d7aa3-81af-45ae-8a97-03bad3a473c3"}]},"item_title":"\u6709\u9650\u70b9\u96c6\u5408\u306e\u8ddd\u96e2\u3068\u914d\u7f6e\u306e\u7814\u7a76","item_type_id":"15","owner":"1","path":["1642838403123","1642838405037"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2009-03-19"},"publish_date":"2009-03-19","publish_status":"0","recid":"2004459","relation_version_is_last":true,"title":["\u6709\u9650\u70b9\u96c6\u5408\u306e\u8ddd\u96e2\u3068\u914d\u7f6e\u306e\u7814\u7a76"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-02-15T04:44:56.310097+00:00"}