{"id":539,"date":"2012-12-27T21:32:52","date_gmt":"2012-12-27T12:32:52","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=539"},"modified":"2021-10-31T07:25:48","modified_gmt":"2021-10-30T22:25:48","slug":"tkb201003","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201003\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2010\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(2\\) \u3064\u306e\u7bb1 L \u3068 R , \\(30\\) \u500b\u306e\u30dc\u30fc\u30eb, \u30b3\u30a4\u30f3\u6295\u3052\u3067\u8868\u3068\u88cf\u304c\u7b49\u78ba\u7387 \\(\\dfrac{1}{2}\\) \u3067\u51fa\u308b\u30b3\u30a4\u30f3\u3092 \\(1\\) \u679a\u7528\u610f\u3059\u308b.\r\n\\(x\\) \u3092 \\(0\\) \u4ee5\u4e0a \\(30\\) \u4ee5\u4e0b\u306e\u6574\u6570\u3068\u3059\u308b. L \u306b \\(x\\) , R \u306b \\(30-x\\) \u500b\u306e\u30dc\u30fc\u30eb\u3092\u5165\u308c, \u6b21\u306e\u64cd\u4f5c <strong>(\uff03)<\/strong> \u3092\u7e70\u308a\u8fd4\u3059.<\/p>\r\n<ol>\r\n<li><strong>(\uff03)<\/strong>\u3000\u7bb1 L \u306b\u5165\u3063\u3066\u3044\u308b\u30dc\u30fc\u30eb\u306e\u500b\u6570\u3092 \\(z\\) \u3068\u3059\u308b.\r\n\u30b3\u30a4\u30f3\u3092\u6295\u3052, \u8868\u304c\u51fa\u308c\u3070\u7bb1 R \u304b\u3089\u7bb1 L \u306b, \u88cf\u304c\u51fa\u308c\u3070\u7bb1 L \u304b\u3089\u7bb1 R \u306b, \\(K(z)\\) \u500b\u306e\u30dc\u30fc\u30eb\u3092\u79fb\u3059.\r\n\u305f\u3060\u3057, \\(0 \\leqq z \\leqq 15\\) \u306e\u3068\u304d \\(K(z) = z\\) , \\(16 \\leqq z \\leqq 30\\) \u306e\u3068\u304d \\(K(z) = 30-z\\) \u3068\u3059\u308b.<\/li>\r\n<\/ol>\r\n<p>\\(m\\) \u56de\u306e\u64cd\u4f5c\u306e\u5f8c, \u7bb1 L \u306e\u30dc\u30fc\u30eb\u306e\u500b\u6570\u304c \\(30\\) \u3067\u3042\u308b\u78ba\u7387\u3092 \\(P _ m(x)\\) \u3068\u3059\u308b. \u305f\u3068\u3048\u3070 \\(P _ 1(15) = P _ 2(15) = \\dfrac{1}{2}\\) \u3068\u306a\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(m \\geqq 2\\) \u306e\u3068\u304d, \\(x\\) \u306b\u5bfe\u3057\u3066 \\(y\\) \u3092\u9078\u3073, \\(P _ m(x)\\) \u3092 \\(P _ {m-1}(y)\\) \u3067\u8868\u305b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(n\\) \u3092\u81ea\u7136\u6570\u3068\u3059\u308b\u3068\u304d, \\(P _ {2n}(10)\\) \u3092\u6c42\u3081\u3088.<\/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>L , R \u306e\u7bb1\u306b\u305d\u308c\u305e\u308c \\(z\\) \u500b, \\(30-z\\) \u500b\u30dc\u30fc\u30eb\u304c\u5165\u3063\u3066\u3044\u308b\u72b6\u614b\u3092 \\(( z , 30-z )\\) \u3068\u8868\u3059.<br \/>\r\n\\(1\\) \u56de\u76ee\u306e\u30b3\u30a4\u30f3\u6295\u3052\u306b\u3088\u308b\u72b6\u614b\u9077\u79fb\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(0 \\leqq x \\leqq 15\\) \u306e\u3068\u304d\r\n<ul>\r\n<li><p>\u8868\u304c\u51fa\u308b\uff1a\u3000\\(( x , 30-x ) \\ \\rightarrow \\ ( 2x , 30-2x )\\)<\/p><\/li>\r\n<li><p>\u88cf\u304c\u51fa\u308b\uff1a\u3000\\(( x , 30-x ) \\ \\rightarrow \\ ( 0 , 30 )\\)<\/p><\/li>\r\n<\/ul><\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(16 \\leqq x \\leqq 30\\) \u306e\u3068\u304d\r\n<ul>\r\n<li><p>\u8868\u304c\u51fa\u308b\uff1a\u3000\\(( x , 30-x ) \\ \\rightarrow \\ ( 30 , 0 )\\)<\/p><\/li>\r\n<li><p>\u88cf\u304c\u51fa\u308b\uff1a\u3000\\(( x , 30-x ) \\ \\rightarrow \\ ( 2x-30 , 60-2x )\\)<\/p><\/li>\r\n<\/ul><\/p><\/li>\r\n<\/ol>\r\n<p>\u7279\u306b, \\(K(0) = K(30) = 0\\) \u306a\u306e\u3067, \u4e00\u65e6 \\(( 0 , 30 )\\) \u307e\u305f\u306f \\(( 30 , 0 )\\) \u306b\u306a\u308b\u3068, \u4ee5\u5f8c\u306f\u30b3\u30a4\u30f3\u6295\u3052\u306e\u7d50\u679c\u306b\u3088\u3089\u305a\u72b6\u614b\u306f\u5909\u5316\u3057\u306a\u3044.<br \/>\r\n\u4ee5\u4e0a\u306e\u8003\u5bdf\u304b\u3089<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(0 \\leqq x \\leqq 15\\) \u306e\u3068\u304d\r\n\\[\r\nP _ m(x) = \\dfrac{1}{2} P _ {m-1}(2x) + \\dfrac{1}{2} \\cdot 0 = \\dfrac{1}{2} P _ {m-1}(2x)\r\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(16 \\leqq x \\leqq 30\\) \u306e\u3068\u304d\r\n\\[\r\nP _ m(x) = \\dfrac{1}{2} \\cdot 1 + \\dfrac{1}{2} P _ {m-1}(2x-30) = \\dfrac{1}{2} \\left\\{ P _ {m-1}(2x-30) +1 \\right\\}\r\n\\]<\/li>\r\n<\/ol>\r\n<p>\u3088\u3063\u3066\r\n\\[\r\n\\underline{ P _ m(x) = \\left\\{ \\begin{array}{ll} \\dfrac{1}{2} P _ {m-1}(2x) & ( \\ 0 \\leqq x \\leqq 15 \\text{\u306e\u3068\u304d} \\ ) \\\\ \\dfrac{1}{2} \\left\\{ P _ {m-1}(2x-30) +1 \\right\\} & ( \\ 16 \\leqq x \\leqq 30 \\text{\u306e\u3068\u304d} \\ ) \\end{array} \\right. }\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p><strong>(1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\r\nP _ {2n}(10) = \\dfrac{1}{2} P _ {2n-1}(20) = \\dfrac{1}{4} \\left\\{ P _ {2n-2}(10) +1 \\right\\} \\\\\r\n\\text{\u2234} \\quad P _ {2n}(10) -\\dfrac{1}{3} = \\dfrac{1}{4} \\left\\{ P _ {2(n-1)}(10) -\\dfrac{1}{3} \\right\\}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\left\\{ P _ {2n}(10) -\\dfrac{1}{3} \\right\\}\\) \u306f\u521d\u9805 \\(P _ 2(10) -\\dfrac{1}{3}\\) , \u516c\u6bd4 \\(\\dfrac{1}{4}\\) \u306e\u7b49\u6bd4\u6570\u5217\u3068\u306a\u308b.<br \/>\r\n\u3053\u3053\u3067\r\n\\[\r\nP _ 2(10) = \\dfrac{1}{2}P _ 1(20) = \\dfrac{1}{2} \\cdot \\dfrac{1}{2} = \\dfrac{1}{4}\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\r\nP _ {2n}(10) -\\dfrac{1}{3} = \\left\\{ \\dfrac{1}{4} \\right\\}^{n-1} \\left( \\dfrac{1}{4} -\\dfrac{1}{3} \\right) = -\\dfrac{1}{3} \\left( \\dfrac{1}{4} \\right)^n \\\\\r\n\\text{\u2234} \\quad P _ {2n}(10) = \\underline{ \\dfrac{1}{3} \\left\\{ 1 -\\left( \\dfrac{1}{4} \\right)^n \\right\\} }\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(2\\) \u3064\u306e\u7bb1 L \u3068 R , \\(30\\) \u500b\u306e\u30dc\u30fc\u30eb, \u30b3\u30a4\u30f3\u6295\u3052\u3067\u8868\u3068\u88cf\u304c\u7b49\u78ba\u7387 \\(\\dfrac{1}{2}\\) \u3067\u51fa\u308b\u30b3\u30a4\u30f3\u3092 \\(1\\) \u679a\u7528\u610f\u3059\u308b. \\(x\\) \u3092 \\(0\\) \u4ee5\u4e0a \\(30\\) \u4ee5\u4e0b &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkb201003\/\">\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":[80],"tags":[149,14],"class_list":["post-539","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2010","tag-tokyo_b","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/539","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=539"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/539\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=539"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=539"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}