{"id":504,"date":"2012-12-05T21:12:47","date_gmt":"2012-12-05T12:12:47","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=504"},"modified":"2021-09-28T20:35:51","modified_gmt":"2021-09-28T11:35:51","slug":"thr200902","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200902\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2009\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(L\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570, \\(a\\) \u3092 \\(0 \\lt a \\lt 1\\) \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b.\r\n\u7e26 \\(1\\) cm , \u6a2a \\((L+1)\\) cm \u306e\u9577\u65b9\u5f62\u306e\u7d19\u3092\u7528\u3044\u3066, \u6b21\u306e\u3088\u3046\u306b\u9577\u65b9\u5f62 \\(A, B\\) \u3092\u4f5c\u308b.<\/p>\r\n

\u3000\u9577\u65b9\u5f62 \\(A\\) \u306e\u4f5c\u308a\u65b9. \\(L\\) \u679a\u306e\u7d19\u3092\u6a2a\u306b\u4e26\u3079\u3066, \u9806\u306b \\(1\\) \u8fba \\(1\\) cm \u306e\u6b63\u65b9\u5f62\u3092\u306e\u308a\u3057\u308d\u3068\u3057\u3066\uff08\u96a3\u308a\u5408\u3046\u7d19\u304c\u6a2a \\(1\\) cm \u91cd\u306a\u308b\u3088\u3046\u306b\uff09\u306f\u308a\u5408\u308f\u305b, \u7e26 \\(1\\) cm \u306e\u6a2a\u9577\u306e\u9577\u65b9\u5f62\u3092\u4f5c\u308b.<\/p>\r\n\"\"\r\n

\u3000\u9577\u65b9\u5f62 \\(B\\) \u306e\u4f5c\u308a\u65b9. \\(L\\) \u679a\u306e\u7d19\u3092\u7e26\u306b\u4e26\u3079\u3066, \u96a3\u308a\u5408\u3046\u7d19\u304c\u7e26 \\(a\\) cm \u91cd\u306a\u308b\u3088\u3046\u306b\u306f\u308a\u5408\u308f\u305b\u3066, \u6a2a \\((L+1)\\) cm \u306e\u9577\u65b9\u5f62\u3092\u4f5c\u308b.<\/p>\r\n\"\"\r\n

\u3000\u9577\u65b9\u5f62 \\(A, B\\) \u306e\u9762\u7a4d\u3092\u305d\u308c\u305e\u308c \\(S _ 1 \\ \\text{cm}^2\\) \u304a\u3088\u3073 \\(S _ 2 \\ \\text{cm}^2\\) \u3068\u304a\u304f\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(S _ 1\\) \u3068 \\(S _ 2\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(L=2\\) \u306e\u3068\u304d, \\(S _ 1 -1 \\lt S _ 2\\) \u3068\u306a\u308b \\(a\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(S _ 1 -1 \\lt S _ 2\\) \u3068\u306a\u308b \\(2\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570 \\(L\\) \u304c\u3042\u308b\u3088\u3046\u306a \\(a\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \\[\\begin{align}\r\nS _ 1 & = 1 \\cdot \\left\\{ L (L+1) -(L-1) \\right\\} \\\\\r\n& = \\underline{L^2+1} , \\\\\r\nS _ 2 & = (L+1) \\{ L-a(L-1) \\} \\\\\r\n& = \\underline{(1-a)L^2 +L+a}\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\(L=2\\) \u306e\u3068\u304d, \\(S _ 1-1 \\lt S _ 2\\) \u3092\u89e3\u304f\u3068\r\n\\[\\begin{align}\r\n4 & \\lt 4(1-a) +2+a \\\\\r\n\\text{\u2234} \\quad a & \\lt \\dfrac{2}{3}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(0 \\lt a<1\\) \u306a\u306e\u3067\r\n\\[\r\n\\underline{0 \\lt a \\lt \\dfrac{2}{3}}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    \\(S _ 1-1 \\lt S _ 2\\) \u3088\u308a\r\n\\[\\begin{align}\r\nL^2 \\lt (1-a)L^2 +L & +a \\\\\r\n(L^2-1) a -L & \\lt 0 \\quad ... [1]\r\n\\end{align}\\]\r\n\\(L \\geqq 2\\) \u306e\u3068\u304d\u306b\u3064\u3044\u3066, [1] \u3092 \\(a\\) \u306b\u3064\u3044\u3066\u89e3\u3051\u3070\u3088\u3044.
    \r\n\\(L^2-1 \\gt 0\\) \u306a\u306e\u3067, [1] \u3088\u308a\r\n\\[\r\na \\lt \\dfrac{L}{L^2-1}\r\n\\]\r\n\u4e21\u8fba\u9006\u6570\u3092\u3068\u3063\u3066\r\n\\[\r\n\\dfrac{1}{a} \\gt L -\\dfrac{1}{L}\r\n\\]\r\n\\(f(L) = L -\\dfrac{1}{L}\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nf'(L) = 1 +\\dfrac{1}{L^2} \\gt 0\r\n\\]\r\n\u306a\u306e\u3067, \\(f(L)\\) \u306f \\(L \\geqq 2\\) \u306b\u304a\u3044\u3066\u5358\u8abf\u5897\u52a0\u3059\u308b\u306e\u3067\r\n\\[\r\n\\dfrac{1}{a} \\gt f(L) \\geqq f(2) = \\dfrac{3}{2}\r\n\\]\r\n\u3088\u3063\u3066, \\(0 \\lt a \\lt 1\\) \u306a\u306e\u3067\r\n\\[\r\n\\underline{0 \\lt a \\lt \\dfrac{2}{3}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(L\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570, \\(a\\) \u3092 \\(0 \\lt a \\lt 1\\) \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b. \u7e26 \\(1\\) cm , \u6a2a \\((L+1)\\) cm \u306e\u9577\u65b9\u5f62\u306e\u7d19\u3092\u7528\u3044\u3066, \u6b21\u306e\u3088\u3046\u306b\u9577\u65b9\u5f62 \\( … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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":[75],"tags":[148,15],"class_list":["post-504","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2009","tag-tohoku_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/504","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=504"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/504\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}