{"id":1239,"date":"2015-08-19T11:00:38","date_gmt":"2015-08-19T02:00:38","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1239"},"modified":"2021-03-23T08:26:27","modified_gmt":"2021-03-22T23:26:27","slug":"kyr201506","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201506\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2015\uff1a\u7b2c6\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(2\\) \u3064\u306e\u95a2\u6570\u3092\r\n\\[\r\nf _ 0 (x) = \\dfrac{x}{2} , \\ f _ 1 (x) = \\dfrac{x+1}{2}\r\n\\]\r\n\u3068\u304a\u304f.\r\n\\(x _ 0 = \\dfrac{1}{2}\\) \u304b\u3089\u59cb\u3081, \u5404 \\(n = 1, 2, \\cdots\\) \u306b\u3064\u3044\u3066,\r\n\u305d\u308c\u305e\u308c\u78ba\u7387 \\(\\dfrac{1}{2}\\) \u3067 \\(x _ n = f _ 0 ( x _ {n-1} )\\) \u307e\u305f\u306f \\(x _ n = f _ 1 ( x _ {n-1} )\\) \u3068\u5b9a\u3081\u308b.\r\n\u3053\u306e\u3068\u304d, \\(x _ n \\lt \\dfrac{2}{3}\\) \u3068\u306a\u308b\u78ba\u7387 \\(P _ n\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u6761\u4ef6\u304b\u3089, \u5e30\u7d0d\u7684\u306b\u8003\u3048\u3066\r\n\\[\r\n0 \\leqq x _ n \\lt 1\r\n\\]\r\n\\(0 \\leqq x _ n \\lt \\dfrac{1}{3}\\) , \\(\\dfrac{1}{3} \\leqq x _ n \\lt \\dfrac{2}{3}\\) , \\(\\dfrac{2}{3} \\leqq x _ n \\lt 1\\) \u3068\u306a\u308b\u78ba\u7387\u3092\u305d\u308c\u305e\u308c \\(a _ n , b _ n , c _ n\\) \u3068\u304a\u304f\u3068, \u4e0b\u56f3\u306e\u30b0\u30e9\u30d5\u304b\u3089\u8003\u3048\u3066<\/p>\r\n<p><img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyr20150601.svg\" alt=\"kyr20150601\" class=\"aligncenter size-full\" \/>\r\n\\[\r\n\\left\\{ \\begin{array}{ll} a _ {n+1} = \\dfrac{a _ n +b _ n}{2} & ... [1] \\\\ b _ {n+1} = \\dfrac{a _ n +c _ n}{2} & ... [2] \\\\ c _ {n+1} = \\dfrac{b _ n +c _ n}{2} & ... [3] \\end{array} \\right.\r\n\\]\r\n\\(a _ 0 = c _ 0 = 0\\) \u304b\u3064 [1] [3] \u3088\u308a, \u5e30\u7d0d\u7684\u306b\r\n\\[\r\na _ n = c _ n \\quad ... [4]\r\n\\]\r\n\u307e\u305f, \\(a _ n +b _ n +c _ n = 1 \\ ... [5]\\) \u3067\u3042\u308b\u3053\u3068\u3092\u7528\u3044\u308c\u3070,[2] \u3088\u308a\r\n\\[\\begin{align}\r\nb _ {n+1} & = \\dfrac{1 -b _ n}{2} \\\\\r\nb _ {n+1} -\\dfrac{1}{3} & = -\\dfrac{1}{2} \\left( b _ n -\\dfrac{1}{3} \\right)\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\left\\{ b _ n -\\dfrac{1}{3} \\right\\}\\) \u306f\r\n\\[\r\n\\text{\u521d\u9805} : \\ b _ 0 -\\dfrac{1}{3} = \\dfrac{2}{3} , \\quad \\text{\u516c\u6bd4} : \\ -\\dfrac{1}{2}\r\n\\]\r\n\u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nb _ n -\\dfrac{1}{3} & = \\dfrac{2}{3} \\left( -\\dfrac{1}{2} \\right)^n \\\\\r\n\\text{\u2234} \\quad b _ n & = \\dfrac{1}{3} \\left\\{ 1 -\\left( -\\dfrac{1}{2} \\right)^{n-1} \\right\\}\r\n\\end{align}\\]\r\n[4] [5] \u3088\u308a\r\n\\[\r\na _ n = \\dfrac{1 -b _ n}{2}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\\begin{align}\r\nP _ n & = a _ n +b _ n = \\dfrac{1 +b _ n}{2} \\\\\r\n& = \\underline{\\dfrac{1}{3} \\left\\{ 2 +\\left( -\\dfrac{1}{2} \\right)^n \\right\\}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(2\\) \u3064\u306e\u95a2\u6570\u3092 \\[ f _ 0 (x) = \\dfrac{x}{2} , \\ f _ 1 (x) = \\dfrac{x+1}{2} \\] \u3068\u304a\u304f. \\(x _ 0 = \\dfrac{1}{2}\\) \u304b\u3089\u59cb\u3081,  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201506\/\">\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":[126],"tags":[140,137],"class_list":["post-1239","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2015","tag-kyoto_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1239","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=1239"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1239\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}