{"id":662,"date":"2013-03-04T21:54:10","date_gmt":"2013-03-04T12:54:10","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=662"},"modified":"2021-09-14T16:05:42","modified_gmt":"2021-09-14T07:05:42","slug":"iks200702","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/iks200702\/","title":{"rendered":"\u533b\u79d1\u6b6f\u79d1\u59272007\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u52d5\u70b9 Q \u304c\u4ee5\u4e0b\u306e\u898f\u5247 (a) \uff5e (f) \u306b\u5f93\u3063\u3066 \\(1\\) \u79d2\u3054\u3068\u306b\u79fb\u52d5\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p>(a)\u3000\u539f\u70b9 \\((0,0)\\) \u3092\u51fa\u767a\u70b9\u3068\u3057, \u307e\u305a\u70b9 \\((1,0)\\) \u307e\u305f\u306f\u70b9 \\((0,1)\\) \u307e\u305f\u306f\u70b9 \\((0,-1)\\) \u306b, \u305d\u308c\u305e\u308c\u78ba\u7387 \\(\\dfrac{1}{3}\\) \u3067\u79fb\u52d5\u3059\u308b.<\/p><\/li>\r\n<li><p>(b)\u3000\u3042\u308b\u6642\u523b\u306b\u70b9 \\(( x-1 , y )\\) \u304b\u3089\u70b9 \\(( x , y )\\) \u306b\u79fb\u52d5\u3057\u305f\u306a\u3089\u3070, \u305d\u306e \\(1\\) \u79d2\u5f8c\u306b\u306f\u70b9 \\(( x+1 , y )\\) \u307e\u305f\u306f\u70b9 \\(( x , y+1 )\\) \u307e\u305f\u306f\u70b9 \\(( x , y-1 )\\) \u306b, \u305d\u308c\u305e\u308c\u78ba\u7387 \\(\\dfrac{1}{3}\\) \u3067\u79fb\u52d5\u3059\u308b.<\/p><\/li>\r\n<li><p>(c)\u3000\u3042\u308b\u6642\u523b\u306b\u70b9 \\(( x , 0 )\\) \u304b\u3089\u70b9 \\(( x , 1 )\\) \u306b\u79fb\u52d5\u3057\u305f\u306a\u3089\u3070, \u305d\u306e \\(1\\) \u79d2\u5f8c\u306b\u306f\u70b9 \\(( x , 2 )\\) \u307e\u305f\u306f\u70b9 \\(( x+1 , y )\\) \u306b, \u305d\u308c\u305e\u308c\u78ba\u7387 \\(\\dfrac{1}{2}\\) \u3067\u79fb\u52d5\u3059\u308b.<\/p><\/li>\r\n<li><p>(d)\u3000\u3042\u308b\u6642\u523b\u306b\u70b9 \\(( x , 0 )\\) \u304b\u3089\u70b9 \\(( x , -1 )\\) \u306b\u79fb\u52d5\u3057\u305f\u306a\u3089\u3070, \u305d\u306e \\(1\\) \u79d2\u5f8c\u306b\u306f\u70b9 \\(( x , -2 )\\) \u307e\u305f\u306f\u70b9 \\(( x+1 , -1 )\\) \u306b, \u305d\u308c\u305e\u308c\u78ba\u7387 \\(\\dfrac{1}{2}\\) \u3067\u79fb\u52d5\u3059\u308b.<\/p><\/li>\r\n<li><p>(e)\u3000\u3042\u308b\u6642\u523b\u306b\u70b9 \\(( x , 1 )\\) \u307e\u305f\u306f\u70b9 \\(( x , -1 )\\) \u304b\u3089\u70b9 \\(( x , 0 )\\) \u306b\u79fb\u52d5\u3057\u305f\u306a\u3089\u3070, \u305d\u306e \\(1\\) \u79d2\u5f8c\u306b\u306f\u70b9 \\(( x+1 , 0 )\\) \u306b\u79fb\u52d5\u3059\u308b.<\/p><\/li>\r\n<li><p>(f)\u3000\u76f4\u7dda \\(y = 2\\) \u4e0a\u306e\u70b9\u307e\u305f\u306f\u76f4\u7dda \\(y = -2\\) \u4e0a\u306e\u70b9\u306b\u9054\u3057\u305f\u5834\u5408\u306b\u306f\u505c\u6b62\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u3053\u306e\u3068\u304d\u4ee5\u4e0b\u306e\u5404\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(n\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b\u3068\u304d, Q \u304c\u3042\u308b\u6642\u523b\u306b\u70b9 \\(( n-1 , 0 )\\) \u306b\u4f4d\u7f6e\u3057, \u304b\u3064\u305d\u306e \\(1\\) \u79d2\u5f8c\u306b\u70b9 \\(( n , 0 )\\) \u306b\u79fb\u52d5\u3057\u3066\u3044\u308b\u78ba\u7387\u3092 \\(p _ n\\) \u3068\u3059\u308b.\r\n\u307e\u305f Q \u304c\u3042\u308b\u6642\u523b\u306b\u70b9 \\(( n-1 , 1 )\\) \u306b\u4f4d\u7f6e\u3057, \u304b\u3064\u305d\u306e \\(1\\) \u79d2\u5f8c\u306b\u70b9 \\(( n , 1 )\\) \u306b\u79fb\u52d5\u3057\u3066\u3044\u308b\u78ba\u7387\u3092 \\(p' _ n\\) \u3068\u3059\u308b. \\(p _ 1 , p _ 2 , p' _ 1 , p' _ 2\\) \u3092\u305d\u308c\u305e\u308c\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000Q \u304c\u76f4\u7dda \\(x=2\\) \u4e0a\u306e\u70b9\u306b\u9054\u3059\u308b\u78ba\u7387, \u304a\u3088\u3073\u76f4\u7dda \\(x=3\\) \u4e0a\u306e\u70b9\u306b\u9054\u3059\u308b\u78ba\u7387\u3092\u305d\u308c\u305e\u308c\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\\(m\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b\u3068\u304d, Q \u304c \\(( m , 0 )\\) \u306b\u9054\u3059\u308b\u78ba\u7387\u3092 \\(m\\) \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<ul>\r\n<li><p>\\(p _ 1\\) \u306b\u3064\u3044\u3066<br \/>\r\nQ \u304c, \u539f\u70b9\u304b\u3089\u300c\u2192\u300d\u306b\u52d5\u3044\u305f\u3068\u304d\u306a\u306e\u3067\r\n\\[\r\np _ 1 = \\underline{\\dfrac{1}{3}} \\ .\r\n\\]<\/li>\r\n<li><p>\\(p' _ 1\\) \u306b\u3064\u3044\u3066<br \/>\r\nQ \u304c, \u539f\u70b9\u304b\u3089\u300c\u2191\u2192\u300d\u306b\u52d5\u3044\u305f\u3068\u304d\u306a\u306e\u3067\r\n\\[\r\np' _ 1 = \\dfrac{1}{3} \\cdot \\dfrac{1}{2} = \\underline{\\dfrac{1}{6}} \\ .\r\n\\]<\/li>\r\n<li><p>\\(p _ 2\\) \u306b\u3064\u3044\u3066<br \/>\r\nQ \u304c, \u539f\u70b9\u304b\u3089\u300c\u2192\u2192\u300d\u300c\u2191\u2192\u2193\u2192\u300d\u300c\u2193\u2192\u2191\u2192\u300d\u306b\u52d5\u3044\u305f\u3068\u304d\u306a\u306e\u3067, \u898f\u5247\u306e \\(x\\) \u8ef8\u306b\u3064\u3044\u3066\u306e\u5bfe\u79f0\u6027\u304b\u3089\r\n\\[\r\np _ 2 = \\dfrac{1}{3} p _ 1 +2 \\cdot \\dfrac{1}{3} p' _ 1 = \\underline{\\dfrac{2}{9}} \\ .\r\n\\]<\/li>\r\n<li><p>\\(p' _ 2\\) \u306b\u3064\u3044\u3066<br \/>\r\nQ \u304c, \u539f\u70b9\u304b\u3089\u300c\u2191\u2192\u2192\u300d\u300c\u2192\u2191\u2192\u300d\u306b\u52d5\u3044\u305f\u3068\u304d\u306a\u306e\u3067\r\n\\[\r\np' _ 2 = \\dfrac{1}{3} p' _ 1 +\\dfrac{1}{3} \\cdot \\dfrac{1}{2} p _ 1 = \\underline{\\dfrac{1}{9}} \\ .\r\n\\]<\/li>\r\n<\/ul>\r\n<p><strong>(2)<\/strong><\/p>\r\n<ul>\r\n<li><p>\\(x = 2\\) \u306b\u9054\u3059\u308b\u5834\u5408<br \/>\r\n\u3053\u308c\u306f, Q \u304c\u70b9 \\((0, \\pm 2)\\) \u307e\u305f\u306f \\((1 , \\pm 2)\\) \u306b\u9054\u3059\u308b\u5834\u5408\u306e\u4f59\u4e8b\u8c61\u3067\u3042\u308b.<br \/>\r\n\u70b9 \\((0, \\pm 2)\\) \u306b\u9054\u3059\u308b\u78ba\u7387\u306f\r\n\\[\r\n2 \\cdot \\dfrac{1}{3} \\cdot \\dfrac{1}{2} = \\dfrac{1}{3} \\ .\r\n\\]\r\n\u70b9 \\((1, \\pm 2)\\) \u306b\u9054\u3059\u308b\u78ba\u7387\u306f\r\n\\[\r\n2 \\left( \\dfrac{1}{3} p' _ 1 +\\dfrac{1}{3} \\cdot \\dfrac{1}{2} p _ 1 \\right) = \\dfrac{1}{9} \\ .\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n1 -\\left( \\dfrac{1}{3} +\\dfrac{2}{9} \\right) = \\underline{\\dfrac{4}{9}} \\ .\r\n\\]<\/li>\r\n<li><p>\\(x=3\\) \u306b\u9054\u3059\u308b\u5834\u5408<br \/>\r\n\u3053\u308c\u306f, Q \u304c\u70b9 \\((k, \\pm 2)\\) \uff08 \\(k = 0, 1, 2\\) \uff09\u306b\u9054\u3059\u308b\u5834\u5408\u306e\u4f59\u4e8b\u8c61\u3067\u3042\u308b.<br \/>\r\n\u70b9 \\((2, \\pm 2)\\) \u306b\u9054\u3059\u308b\u78ba\u7387\u306f\r\n\\[\r\n2 \\left( \\dfrac{1}{3} p' _ 2 +\\dfrac{1}{3} \\cdot \\dfrac{1}{2} p _ 2 \\right) = \\dfrac{4}{27} \\ .\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n1 -\\left( \\dfrac{1}{3} +\\dfrac{2}{9} +\\dfrac{4}{27} \\right) =\\underline{\\dfrac{8}{27}} \\ .\r\n\\]<\/li>\r\n<\/ul>\r\n<p><strong>(3)<\/strong><\/p>\r\n<p>\u6c42\u3081\u308b\u78ba\u7387\u3092 \\(q _ m\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nq _ m & = p _ m +2 \\cdot \\dfrac{1}{3} p' _ m \\\\\r\n& = p _ m + \\dfrac{2}{3} p' _ m \\quad ... [1] \\ .\r\n\\end{align}\\]\r\n\u307e\u305f, <strong>(1)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u308b\u3068\r\n\\[\\begin{align}\r\np _ m & = \\dfrac{1}{3} p _ {m-1} +\\dfrac{2}{3} p' _ {m-1} \\quad ... [2] , \\\\\r\np' _ m & = \\dfrac{1}{6} p _ {m-1} +\\dfrac{1}{3} p' _ {m-1} \\quad ... [3] \\ .\r\n\\end{align}\\]\r\n\\([2] - [3] \\times 2\\) \u3088\u308a\r\n\\[\\begin{align}\r\np _ m -2p' _ m & = 0 \\\\\r\n\\text{\u2234} \\quad p _ m & = 2p' _ m \\quad ... [4] \\ .\r\n\\end{align}\\]\r\n[3] \u306b\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\r\np' _ m = \\dfrac{1}{6} \\cdot 2 p' _ {m-1} +\\dfrac{1}{3} p' _ {m-1} = \\dfrac{2}{3} p' _ {m-1} \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\{ p' _ m \\}\\) \u306f\u521d\u9805 \\(p' _ 1 = \\dfrac{1}{6}\\) , \u516c\u6bd4 \\(\\dfrac{2}{3}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\r\np' _ m = \\dfrac{1}{6} \\left( \\dfrac{2}{3} \\right)^{m-1} \\ .\r\n\\]\r\n[4] \u3088\u308a\r\n\\[\r\np _ m = \\dfrac{1}{3} \\left( \\dfrac{2}{3} \\right)^{m-1} \\ .\r\n\\]\r\n\u3053\u308c\u3089\u3092 [1] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\nq _ m & = \\dfrac{1}{3} \\left( \\dfrac{2}{3} \\right)^{m-1} +\\dfrac{2}{3} \\cdot \\dfrac{1}{6} \\left( \\dfrac{2}{3} \\right)^{m-1} \\\\\r\n& = \\underline{\\left( \\dfrac{2}{3} \\right)^{m+1}} \\ .\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u52d5\u70b9 Q \u304c\u4ee5\u4e0b\u306e\u898f\u5247 (a) \uff5e (f) \u306b\u5f93\u3063\u3066 \\(1\\) \u79d2\u3054\u3068\u306b\u79fb\u52d5\u3059\u308b. (a)\u3000\u539f\u70b9 \\((0,0)\\) \u3092\u51fa\u767a\u70b9\u3068\u3057, \u307e\u305a\u70b9 \\((1,0)\\) \u307e\u305f\u306f\u70b9 \\((0,1)\\) \u307e\u305f\u306f\u70b9 \\( &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/iks200702\/\">\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":[93],"tags":[145,109],"class_list":["post-662","post","type-post","status-publish","format-standard","hentry","category-ikashika_2007","tag-ikashika","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/662","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=662"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/662\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=662"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=662"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=662"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}