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We put R^\uff0b=\uff5b\uff58\uff1a\uff58\u2208R\uff0c\uff58\u22670\uff5d\u3000\u3000R^\uff0b is a semi-ordered set with the least element 0 and satisfies the following conditions:\u3000\u3000\u3000\u3000I.(1)for every a\uff0cb\u2208R^\uff0b we have a\uff0bb\u2208R^\uff0b\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(2)(a\uff0bb)\uff0bc=a\uff0b(b\uff0bc)\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(3)a\uff0bb=b\uff0b\uff41\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(4)a\uff0b0\uff1da\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(5)for every a\uff0cb\u2208R^\uff0b we have a\u2266a\uff0bb\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(6)a\uff0bc\uff1db\uff0bc implies a\uff1db\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(7)if a\u2266\uff42\uff0cthen we have uniquely determined \uff43\u2208R^\uff0b\u3000such that a\uff0bc\uff1db\uff0c\u3000\u3000\u3000\u3000II.(1)for any real number \u03b1\u2267O and a\u2208R^\uff0b we have\u03b1a\u2208R^\uff0b\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(2)\u03b1(\u03b2a)\uff1d(\u03b1\u03b2)a\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(3)\u03b1(a\uff0bb)\uff1d\u03b1a\uff0b\u03b1b\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(4)(\u03b1\uff0b\u03b2)a\uff1d\u03b1a\uff0b\u03b2a\uff0c\u3000\u3000\u3000\u3000\u3000\u3000(5)1a\uff1da\uff0c\u3000\u3000Generally let x be a semi-ordered set and we assume that x satisfies the previous conditions l. (1)-(7)and II.(1)-(5). In this paper\uff0csuch a semi-ordered set x is styled as \u201ca semi-ordered set with the least element and non-negative real domain of operators\". In this paper we discuss the existence of a semi-ordered vector space R which R^\uff0b\uff1dX and some properties of x.", "subitem_description_type": "Abstract"}]}, "item_2_full_name_3": {"attribute_name": "\u8457\u8005\u5225\u540d", "attribute_value_mlt": [{"nameIdentifiers": [{"nameIdentifier": "32234", "nameIdentifierScheme": "WEKO"}], "names": [{"name": "ISOBE, Kiro"}]}]}, "item_2_publisher_32": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "\u5317\u898b\u5de5\u696d\u5927\u5b66"}]}, "item_2_select_15": {"attribute_name": "\u8457\u8005\u7248\u30d5\u30e9\u30b0", "attribute_value_mlt": [{"subitem_select_item": "publisher"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "\u78ef\u90e8, \u7155\u90ce"}], "nameIdentifiers": [{"nameIdentifier": "32233", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2016-11-22"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "5-1-10.pdf", "filesize": [{"value": "1.6 MB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 1600000.0, "url": {"label": "5-1-10.pdf", "url": "https://kitami-it.repo.nii.ac.jp/record/6340/files/5-1-10.pdf"}, "version_id": "440b5100-2a3d-4643-98b7-ae14050467b0"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "jpn"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Semi-ordered Vector Space \u306ePositive Cone \u306b\u306a\u308b\u3088\u3046\u306aSemi-ordered Space \u306b\u3064\u3044\u3066", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Semi-ordered Vector Space \u306ePositive Cone \u306b\u306a\u308b\u3088\u3046\u306aSemi-ordered Space \u306b\u3064\u3044\u3066"}]}, "item_type_id": "2", "owner": "1", "path": ["7/15/27"], "permalink_uri": "https://kitami-it.repo.nii.ac.jp/records/6340", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_value": "2007-04-09"}, "publish_date": "2007-04-09", "publish_status": "0", "recid": "6340", "relation": {}, "relation_version_is_last": true, "title": ["Semi-ordered Vector Space \u306ePositive Cone \u306b\u306a\u308b\u3088\u3046\u306aSemi-ordered Space \u306b\u3064\u3044\u3066"], "weko_shared_id": 3}