{"created":"2022-01-27T08:05:45.054439+00:00","id":2004457,"links":{},"metadata":{"_buckets":{"deposit":"bc24c6a6-23c7-4d37-aa27-ca3dedf41bf2"},"_deposit":{"id":"2004457","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2004457"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02004457","sets":["1642838403123","1642838403551:1642838405037"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_1551255647225":"3次元空間内の球の配置の研究","subitem_1551255648112":"ja"},{"subitem_1551255647225":"Study on arrangements of solid balls in 3-space","subitem_1551255648112":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"前原, 濶","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"加藤, 満生","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"松本, 修一","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"徳重, 典英","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"Maehara, Hiroshi","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Kato, Mitsuo","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Matsumoto, Shuichi","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Tokushige, Norihide","creatorNameLang":"en"}]}]},"item_1617186476635":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_1522299639480":"open access","subitem_1600958577026":"http://purl.org/coar/access_right/c_abf2"}]},"item_1617186609386":{"attribute_name":"Subject","attribute_value_mlt":[{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"arrangement of balls"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"knotted necklace"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"piercing balls"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"almost halving-plane"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"representation of a graph"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"科研費番号: 11640129","subitem_description_type":"Other"},{"subitem_description":"平成11年度～平成12年度科学研究費補助金(基盤研究(C)(2))研究成果報告書","subitem_description_type":"Other"},{"subitem_description":"研究概要 : 1.[結び目をなす球の配列について]単位球の巡回列で結び目を作るとき,15球あれば可能である.距離が2+√<2>離れた2枚の平行な平面の間にはさむことができる単位球の巡回列の場合は,結び目を作るのに16球以上必要で,三葉結び目の場合に限り,ちょうど16球で作れる.球の大きさがまちまちでよければ,12球で結び目を作ることができる.2.[球の配列によるグラフの実現について]3次元空間内で,グラフの各頂点を球で,各辺を,球と球を結ぶ球の列からなる鎖で実現する.ただし,球どうしはオーバーラップしないものとする.頂点数nの完全グラフの実現に必要な球の最小個数 b_nについてc_1n^3<b_n<c_2n^3lognなる評価を得た.すべてがテーブルの上に置かれている球の族でグラフを実現する場合も,必要な個数について類似の評価を得た.3.[球の族を刺す直線について]d-次元空間R^d内の互いに交わらないn個の球の族Fに対して, ある方向を選べば,その方向の直線ではO√<(1+logλ)nlogn>より多くの球を刺すことはできない.ただし,λ=(最大半径)/ (最小半径)である.一方,任意のn【greater than or equal】dについて,R^d内のn個の球からなるある族Fでは,どんな方向を指定しても,その方向のある直線でFの中のn-d+1個以上の球を刺すことができる.テーブルの上に置かれている球の族を,垂直な直線で刺す場合についても,刺す個数の平均の上限の評価を得た.4.[球の族の平面による分割について]R^3内の互いに交わらないn個の球の族については,logλ=ο((n/logn)^<1/3>)なら,どちら側にも約半数の無傷な球が残るように,その族を一枚の平面で切ることができる.","subitem_description_type":"Other"},{"subitem_description":"1. A cyclic sequence of nonoverlapping unit balls in R^3 in which each consecutive balls are tangent, is called a necklace of pearls. We show that to make a knotted necklace of pearls, 15 unit balls are sufficient. To make a knotted necklace that can be inscribed between a pair of parallel planes with distance 2+√<2> apart, 16 unit balls are necessary, and the trefoil is the unique knot that can be made by 16 unit balls. 2. A chain is a finite sequence of balls in which each consecutive pair of balls are tangent. Make a graph by representing vertices by balls, and edges by chains connecting two vertex-balls. Let b_n be the minimum number of balls necessary to make a complete graph of n vertices. Then we got the bound c_1n^3<b_n<c_2n^3 log n. A similar bound is also obtained when we use balls all sitting on a fixed table. 3. For a family F of balls in d-dimensional space R^d, let λ= λ(F)=(the max. radius) / (the min. radius). We proved that for any family of n balls in R^d, there is a direction such that any line with this direction intersects at most O (√<(1+logλ)n log n>) balls. On the otherhand, for n【greater than or equal】d, there is a family of nonoverlapping n balls in R^d such that for any direction, there is a line with this direction that intersects at least n-d+1 balls. For a family of balls sitting on a fixed table in R^3, we also got an upper bound of the average number of balls pierced by a vertical line meeting the table. 4. If a family of nonoverlapping balls in R^3 satisfies that logλ=o ((n/log n)^<1/3>), then there is a plane both sides of which contain n/2-o (n) intact balls.","subitem_description_type":"Other"},{"subitem_description":"未公開：P.7～120（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_1522300295150":"ja","subitem_1522300316516":"前原濶"}]},"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/20.500.12000/9347"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_1522646500366":"NCID","subitem_1522646572813":"BA64482732"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2001-03","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_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":"11640129.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004457/files/11640129.pdf"},"version_id":"ec3874ce-6e75-4cd7-868e-9de29383eb90"}]},"item_title":"3次元空間内の球の配置の研究","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":"2004457","relation_version_is_last":true,"title":["3次元空間内の球の配置の研究"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T01:58:05.940672+00:00"}