{"id":898,"date":"2013-08-19T00:46:37","date_gmt":"2013-08-18T15:46:37","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=898"},"modified":"2021-10-20T14:22:22","modified_gmt":"2021-10-20T05:22:22","slug":"ykr201304","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201304\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2013\uff1a\u7b2c4\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(1\\) \u3064\u306e\u6574\u6570\u3092\u8868\u793a\u3059\u308b\u88c5\u7f6e\u304c\u3042\u308b.\r\n\u6700\u521d\u306b \\(2013\\) \u304c\u8868\u793a\u3055\u308c\u3066\u3044\u308b. \u3055\u3044\u3053\u308d\u3092 \\(1\\) \u56de\u6295\u3052\u308b\u305f\u3073\u306b\u6b21\u306e\u64cd\u4f5c\uff08\uff0a\uff09\u3092\u884c\u3046.<\/p>\r\n<ol>\r\n<li>\uff08\uff0a\uff09\u8868\u793a\u3055\u308c\u3066\u3044\u308b\u6574\u6570\u3092\u3055\u3044\u3053\u308d\u306e\u51fa\u305f\u76ee\u306e\u6570\u3067\u5272\u3063\u305f\u4f59\u308a \\(r\\) \u3092\u6c42\u3081, \u88c5\u7f6e\u306b \\(r\\) \u3092\u8868\u793a\u3055\u305b\u308b.<\/li>\r\n<\/ol>\r\n<p>\u3055\u3044\u3053\u308d\u3092 \\(n\\) \u56de\u6295\u3052\u305f\u3068\u304d, \u6700\u5f8c\u306b\u88c5\u7f6e\u306b\u8868\u793a\u3055\u308c\u3066\u3044\u308b\u6574\u6570 \\(0\\) \u3067\u3042\u308b\u78ba\u7387\u3092 \\(a _ n\\) , \\(1\\) \u3067\u3042\u308b\u78ba\u7387\u3092 \\(b _ n\\) , \\(3\\) \u3067\u3042\u308b\u78ba\u7387\u3092 \\(c _ n\\) \u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(a _ 1 , b _ 1 , c _ 1\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(a _ n , b _ n , c _ n\\) \u3092 \\(a _ {n-1} , b _ {n-1} , c _ {n-1}\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\\(a _ n , b _ n , c _ n\\) \u3092 \\(n\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u51fa\u305f\u76ee \\(m\\) \u3068\u8868\u793a\u3055\u308c\u308b\u6570 \\(r\\) \u306e\u95a2\u4fc2\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|cccccc} m & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline r & 0 & 1 & 0 & 1 & 3 & 3 \\end{array}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\na _ 1 = \\underline{\\dfrac{1}{3}} , \\ b _ 1 = \\underline{\\dfrac{1}{3}} , \\ c _ 1 = \\underline{\\dfrac{1}{3}} \\quad ... [1]\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(n \\geqq 2\\) \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u8003\u3048\u308b.<br \/>\r\n\u88c5\u7f6e\u306b \\(0 , 1 , 3\\) \u304c\u8868\u793a\u3055\u308c\u3066\u3044\u308b\u305d\u308c\u305e\u308c\u306e\u5834\u5408\u306b\u3064\u3044\u3066, <strong>(1)<\/strong> \u3068\u540c\u69d8\u306e\u8868\u3092\u66f8\u304f.<\/p>\r\n<ul>\r\n<li><p>\u8868\u793a\u304c \\(0\\) \u306e\u3068\u304d\r\n\\[\r\n\\begin{array}{c|cccccc} m & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline r & 0 & 0 & 0 & 0 & 0 & 0 \\end{array}\r\n\\]<\/li>\r\n<li><p>\u8868\u793a\u304c \\(1\\) \u306e\u3068\u304d\r\n\\[\r\n\\begin{array}{c|cccccc} m & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline r & 0 & 1 & 1 & 1 & 1 & 1 \\end{array}\r\n\\]<\/li>\r\n<li><p>\u8868\u793a\u304c \\(3\\) \u306e\u3068\u304d\r\n\\[\r\n\\begin{array}{c|cccccc} m & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline r & 0 & 1 & 0 & 3 & 3 & 3 \\end{array}\r\n\\]<\/li>\r\n<\/ul>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u305f\u5f8c\u306f, \u8868\u793a\u306f \\(0 , 1 , 3\\) \u306e\u3044\u305a\u308c\u304b\u3067\u3042\u308a, \u305d\u306e\u72b6\u614b\u9593\u306e\u9077\u79fb\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/yokokoku_r_2013_04_01.png\" alt=\"yokokoku_r_2013_04_01\" class=\"aligncenter size-full\" \/>\r\n<p>\u3088\u3063\u3066, \u6c42\u3081\u308b\u95a2\u4fc2\u5f0f\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} a _ n = a _ {n-1} +\\dfrac{1}{6} b _ {n-1} +\\dfrac{1}{3} c _ {n-1} & ... [2] \\\\ b _ n = \\dfrac{5}{6} b _ {n-1} +\\dfrac{1}{6} c _ {n-1} & ... [3] \\\\ c _ n = \\dfrac{1}{2} c _ {n-1} & ... [4] \\end{array} \\right.}\r\n\\]\r\n<p><strong>(3)<\/strong><\/p>\r\n[1] [4] \u3088\u308a, \u6570\u5217 \\(\\{ c _ n \\}\\) \u306f, \u521d\u9805 \\(c _ 1 = \\dfrac{1}{3}\\) , \u516c\u6bd4 \\(\\dfrac{1}{2}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\r\nc _ n = \\underline{\\dfrac{1}{3} \\left( \\dfrac{1}{2} \\right)^{n-1}}\r\n\\]\r\n\u3053\u308c\u3092, [3] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{gather}\r\nb _ n = \\dfrac{5}{6} b _ {n-1} +\\dfrac{1}{18} \\left( \\dfrac{1}{2} \\right)^{n-2} \\\\\r\n\\text{\u2234} \\quad b _ n +\\dfrac{1}{3} \\left( \\dfrac{1}{2} \\right)^{n} = \\dfrac{5}{6} \\left\\{ b _ {n-1} +\\dfrac{1}{3} \\left( \\dfrac{1}{2} \\right)^{n-1} \\right\\}\r\n\\end{gather}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\left\\{ b _ n +\\dfrac{1}{3} \\left( \\dfrac{1}{2} \\right)^{n} \\right\\}\\) \u306f, \u521d\u9805 \\(b _ 1 +\\dfrac{1}{3} \\cdot \\dfrac{1}{2} = \\dfrac{1}{2}\\) , \u516c\u6bd4 \\(\\dfrac{5}{6}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\\begin{gather}\r\nb _ n +\\dfrac{1}{3} \\left( \\dfrac{1}{2} \\right)^{n} = \\dfrac{1}{2} \\left( \\dfrac{5}{6} \\right)^{n-1} \\\\\r\n\\text{\u2234} \\quad b _ n = \\underline{\\dfrac{1}{2} \\left( \\dfrac{5}{6} \\right)^{n-1} -\\dfrac{1}{3} \\left( \\dfrac{1}{2} \\right)^{n}}\r\n\\end{gather}\\]\r\n<p><strong>(2)<\/strong> \u3067\u793a\u3057\u305f\u72b6\u614b\u9077\u79fb\u3088\u308a, \u81ea\u7136\u6570 \\(n\\) \u306b\u5bfe\u3057\u3066, \\(a _ n +b _ n +c _ n = 1\\) \u306a\u306e\u3067, \u4ee5\u4e0a\u306e\u7d50\u679c\u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\na _ n & = 1 -b _ n-c _ n \\\\\r\n& = \\underline{1 -\\dfrac{1}{2} \\left( \\dfrac{5}{6} \\right)^{n-1} -\\dfrac{1}{6} \\left( \\dfrac{1}{2} \\right)^{n-1}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(1\\) \u3064\u306e\u6574\u6570\u3092\u8868\u793a\u3059\u308b\u88c5\u7f6e\u304c\u3042\u308b. \u6700\u521d\u306b \\(2013\\) \u304c\u8868\u793a\u3055\u308c\u3066\u3044\u308b. \u3055\u3044\u3053\u308d\u3092 \\(1\\) \u56de\u6295\u3052\u308b\u305f\u3073\u306b\u6b21\u306e\u64cd\u4f5c\uff08\uff0a\uff09\u3092\u884c\u3046. \uff08\uff0a\uff09\u8868\u793a\u3055\u308c\u3066\u3044\u308b\u6574\u6570\u3092\u3055\u3044\u3053\u308d\u306e\u51fa\u305f\u76ee\u306e\u6570\u3067\u5272\u3063\u305f\u4f59\u308a \\(r\\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/ykr201304\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[104],"tags":[111,9],"class_list":["post-898","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2013","tag-111","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/898","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=898"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/898\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=898"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}