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"subitem_description_type": "Other"}, {"subitem_description": "1. For a graph G with N edges, put its vertices on the d-dimensional unit sphere. Let D denote the minimum spherical distance between a pair of points that correspond to a pair of adjacent vertices in G. Then, it was proved that the distribution of ND^d tends to exponential distribution with mean dB(1/2,d/2) as N tends to infinity, where B(p,q) denotes the beta function.2. Let F={C_1,C_2,\u2026,C_N} be a family of caps on the two dimensional unit sphere. A cap C_i is called extremal if the centers of those caps that intersect C_i are all contained in the same side of a great circle passing through the center of C_i. A cap that is smaller than a hemisphere is called proper. It was proved that if F has no extremal cap then the intersection graph G(F) of F is connected. If furthermore, all caps in F are proper then G(F) is 2-connected. For higher dimensional sphere, the similar result never holds. Applying this the following asymptotic result was proved. Now, let F denote a family of N random caps all of the same size (4\u03c0c/N)log N. If c\u003e1/2, then the probability that G(F) is 2-connected tends to 1 as N tends to infinity. If c\u003c1/4, then the probability that G(F) is connected tends to 0 as N tends to infinity.3. Let AOB be a triangle in the 3-space with angle \u2220AOB=\u03c9. When we look at this angle from a viewpoint P, this angle looks as though the angle of the orthogonal projection of AOB on a plane perpendicular to the line PO. And its size changes according to the location of the viewpoint P. If P is a random point on a unit sphere centered at O, then the \u0027visual\u0027 size of the angle \u2220AOB is called the random visual size and denoted by \u0398(\u03c9). By a joint study with Yoich Maeda (Tokai univ.), we proved that the expected value of \u0398(\u03c9) is equal to \u03c9, and derived a formula to calculate the variance of \u0398(\u03c9).", "subitem_description_type": "Other"}, {"subitem_description": "\u672a\u516c\u958b\uff1aP.7\uff5e71\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/20.500.12000/9309"}]}, "item_1617186920753": {"attribute_name": "Source Identifier", "attribute_value_mlt": [{"subitem_1522646500366": "NCID", "subitem_1522646572813": "BA64192299"}]}, "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", "download_preview_message": "", "file_order": 0, "filename": "13640126-2.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004460/files/13640126-2.pdf"}, "version_id": "f31f2177-682d-4c06-a91f-537796bb7c1e"}, {"accessrole": "open_access", "download_preview_message": "", "file_order": 1, "filename": "13640126-1.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004460/files/13640126-1.pdf"}, "version_id": "16aea07e-72f9-4b78-bdc4-79a32818e468"}]}, "item_title": "\u7403\u9762\u4e0a\u306e\u30e9\u30f3\u30c0\u30e0\u5e7e\u4f55\u3068\u305d\u306e\u5fdc\u7528", "item_type_id": "15", "owner": "1", "path": ["1642838403123", "1642838405037"], "permalink_uri": "http://hdl.handle.net/20.500.12000/9309", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2009-03-19"}, "publish_date": "2009-03-19", "publish_status": "0", "recid": "2004460", "relation": {}, "relation_version_is_last": true, "title": ["\u7403\u9762\u4e0a\u306e\u30e9\u30f3\u30c0\u30e0\u5e7e\u4f55\u3068\u305d\u306e\u5fdc\u7528"], "weko_shared_id": -1}