{"id":1390,"date":"2017-02-25T01:24:13","date_gmt":"2017-02-24T16:24:13","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1390"},"modified":"2021-03-18T16:17:04","modified_gmt":"2021-03-18T07:17:04","slug":"kyr201605","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201605\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2016\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(xy\\) \u5e73\u9762\u4e0a\u306e \\(6\\) \u500b\u306e\u70b9 \\(( 0, 0 ) , ( 0, 1 ) , ( 1, 0 ) , ( 1, 1 ) , ( 2, 0 ) , ( 2, 1 )\\) \u304c\u56f3\u306e\u3088\u3046\u306b\u9577\u3055 \\(1\\) \u306e\u7dda\u5206\u3067\u7d50\u3070\u308c\u3066\u3044\u308b. \u52d5\u70b9 X \u306f, \u3053\u308c\u3089\u306e\u70b9\u306e\u4e0a\u3092\u6b21\u306e\u898f\u5247\u306b\u5f93\u3063\u3066 \\(1\\) \u79d2\u3054\u3068\u306b\u79fb\u52d5\u3059\u308b.<\/p>\r\n<ol>\r\n<li>\u898f\u5247\uff1a\u3000\u52d5\u70b9 X \u306f, \u305d\u306e\u6642\u306b\u4f4d\u7f6e\u3059\u308b\u70b9\u304b\u3089\u51fa\u308b\u9577\u3055 \\(1\\) \u306e\u7dda\u5206\u306b\u3088\u3063\u3066\u7d50\u3070\u308c\u308b\u56f3\u306e\u70b9\u306e\u3044\u305a\u308c\u304b\u306b, \u7b49\u3057\u3044\u78ba\u7387\u3067\u79fb\u52d5\u3059\u308b.<\/li>\r\n<\/ol>\r\n<p>\u4f8b\u3048\u3070, X \u304c \\(( 2, 0 )\\) \u306b\u3044\u308b\u3068\u304d\u306f, \\(( 1, 0 ) , ( 2, 1 )\\) \u306e\u3044\u305a\u308c\u304b\u306b \\(\\dfrac{1}{2}\\) \u306e\u78ba\u7387\u3067\u79fb\u52d5\u3059\u308b. \u307e\u305f X \u304c \\(( 1, 1 )\\) \u306b\u3044\u308b\u3068\u304d\u306f, \\(( 0, 1 ) , ( 1, 0 ) , ( 2, 1 )\\) \u306e\u3044\u305a\u308c\u304b\u306b \\(\\dfrac{1}{3}\\) \u306e\u78ba\u7387\u3067\u79fb\u52d5\u3059\u308b.<br \/>\r\n\u3000\u6642\u523b \\(0\\) \u3067\u52d5\u70b9 X \u304c \\(\\text{O} = ( 0, 0 )\\) \u304b\u3089\u51fa\u767a\u3059\u308b\u3068\u304d, \\(n\\) \u79d2\u5f8c\u306b X \u306e \\(x\\) \u5ea7\u6a19\u304c \\(0\\) \u3067\u3042\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088. \u305f\u3060\u3057 \\(n\\) \u306f \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyr20160501.svg\" alt=\"\" class=\"aligncenter size-full\" \/>\r\n<hr\/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\\(n\\) \u79d2\u5f8c\u306b X \u306e \\(x\\) \u5ea7\u6a19\u304c \\(0 , 1 , 2\\) \u3067\u3042\u308b\u78ba\u7387\u3092\u305d\u308c\u305e\u308c \\(a _ n , b _ n , c _ n\\) \u3068\u304a\u304f.<br \/>\r\n\u6761\u4ef6\u3088\u308a\r\n\\[\r\na _ 0 = 1 , \\ b _ 0 = c _ 0 = 0\r\n\\]\r\n\u307e\u305f\r\n\\[\r\na _ n +b _ n +c _ n = 1\r\n\\]\r\n\u70b9\u306e\u79fb\u52d5\u898f\u5247\u304b\u3089, \\(n\\) \u79d2\u5f8c\u306e X \u306e\u4f4d\u7f6e\u304b\u3089 \\(n+1\\) \u79d2\u5f8c\u306e X \u306e\u4f4d\u7f6e\u3078\u306e\u79fb\u52d5\u306e\u78ba\u7387\u3092\u8003\u3048\u308b\u3068\r\n\\[\\begin{align}\r\na _ {n+1} & = \\dfrac{1}{2} a _ n +\\dfrac{1}{3} b _ n & ... [1] \\\\\r\nb _ {n+1} & = \\dfrac{1}{2} a _ n +\\dfrac{1}{3} b _ n +\\dfrac{1}{2} c _ n & ... [2] \\\\\r\nc _ {n+1} & = \\dfrac{1}{3} b _ n +\\dfrac{1}{2} c _ n & ... [3]\r\n\\end{align}\\]\r\n\\([1] -[3]\\) \u3088\u308a\r\n\\[\r\na _ {n+1} -c _ {n+1} = \\dfrac{1}{2} ( a _ n -c _ n )\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\{ a _ n -c _ n \\}\\) \u306f, \u521d\u9805 \\(a _ 0 -c _ 0 = 1\\) , \u516c\u6bd4 \\(\\dfrac{1}{2}\\) \u306e\u7b49\u6bd4\u6570\u5217\u3067\r\n\\[\r\na _ n -c _ n = \\left( \\dfrac{1}{2} \\right)^n \\quad ... [4]\r\n\\]\r\n\u307e\u305f, \\([2] +[4]\\) \u3088\u308a\r\n\\[\\begin{align}\r\na _ {n+1} +c _ {n+1} & = \\dfrac{1}{2} a _ n +\\dfrac{2}{3} ( 1 -a _ n -c _ n ) +\\dfrac{1}{2} c _ n \\\\\r\n& = \\dfrac{2}{3} -\\dfrac{1}{6} ( a _ n -c _ n )\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\na _ {n+1} +c _ {n+1} -\\dfrac{4}{7} = -\\dfrac{1}{6} \\left( a _ n +c _ n -\\dfrac{4}{7} \\right)\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\left\\{ a _ n +c _ n -\\dfrac{4}{7} \\right\\}\\) \u306f, \u521d\u9805 \\(a _ 0 +c _ 0 -\\dfrac{4}{7} = \\dfrac{3}{7}\\) , \u516c\u6bd4 \\(-\\dfrac{1}{6}\\) \u306e\u7b49\u6bd4\u6570\u5217\u3067\r\n\\[\\begin{align}\r\na _ n +c _ n -\\dfrac{4}{7} & = \\dfrac{3}{7} \\left( -\\dfrac{1}{6} \\right)^n \\\\\r\n\\text{\u2234} \\quad a _ n +c _ n & = \\dfrac{4}{7} +\\dfrac{3}{7} \\left( -\\dfrac{1}{6} \\right)^n \\quad ... [5]\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(( [4] +[5] ) \\div 2\\) \u3088\u308a, \u6c42\u3081\u308b\u78ba\u7387 \\(a _ n\\) \u306f\r\n\\[\r\na _ n = \\underline{\\dfrac{2}{7} +\\left( \\dfrac{1}{2} \\right)^{n+1} +\\dfrac{3}{14} \\left( -\\dfrac{1}{6} \\right)^n}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306e \\(6\\) \u500b\u306e\u70b9 \\(( 0, 0 ) , ( 0, 1 ) , ( 1, 0 ) , ( 1, 1 ) , ( 2, 0 ) , ( 2, 1 )\\) \u304c\u56f3\u306e\u3088\u3046\u306b\u9577\u3055 \\(1\\) \u306e\u7dda\u5206\u3067\u7d50 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201605\/\">\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":[151],"tags":[140,162],"class_list":["post-1390","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2016","tag-kyoto_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1390","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=1390"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1390\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1390"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1390"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}