\u8bbe\u5b57\u7b26\u4e32\\(s\\)\u53ef\u4ee5\u5206\u5272\u6210\\(\\{s_{12},s_3\\}\u00a0\u3001\\{s_1,s_{23}\\}\u00a0\u548c\\{s_1,s_2,s_3\\}\\)\u4e09\u79cd\u5f62\u5f0f\uff08\u5176\u4e2d\\(s_{12}\\)\u00a0\u7531\\(s_1\\)\u548c\\(s_2\\)\u62fc\u63a5\u800c\u6210\uff1b\\(s_{23}\\)\u7531\\(s_2\\)\u548c\\(s_3\\)\u62fc\u63a5\u800c\u6210\uff09\u3002\u8fd9\u4e9b\u5b57\u7b26\u4e32\\(\\{s,_1,s_2,s_3,s_{12},s_{23}\\}\\)\u5bf9\u5e94\u7684\u6982\u7387\\(\\{f,f_1,f_2,f_3,f_{12},f_{23}\\}\\)\u5747\u5b58\u5728\uff0c\u4e14\u5927\u4e8e0\u3002<\/p>\n\n\n\n
\u4e0b\u9762\u5148\u5206\u6790\u4e00\u4e0b\u5982\u4e0b\u4e24\u4e2a\u6570\u91cf\u7684\u5173\u7cfb\uff1a<\/p>\n\n\n\n
\\[\\gamma=\\frac {f}{3}(\\frac {1}{f_1} + \\frac {1}{f_2} +\\frac {1}{f_3})\\]<\/p>\n\n\n\n
\\[\\gamma^*=\\frac {f}{2}(\\frac {1}{f_1} + \\frac {1}{f_{23}})\\]<\/p>\n\n\n\n
\u8bbe\u5224\u522b\u5f0f\uff1a<\/p>\n\n\n\n
\\[\\Delta = \\gamma^* – \\gamma = \\frac {f}{2}(\\frac {1}{f_1} + \\frac {1}{f_{23}}) – \\frac {f}{3}(\\frac {1}{f_1} + \\frac {1}{f_2} +\\frac {1}{f_3}) \\\\ = f [ \\frac {1}{6} \\cdot \\frac {1}{f_1} + \\frac {1}{2} \\cdot \\frac {1}{f_{23}} – \\frac {1}{3}(\\frac {1}{f_2} + \\frac {1}{f_3})]\\]<\/p>\n\n\n\n
\u56e0\u4e3a\uff1a\\(\\gamma_{23} = \\frac {f_{23}}{2} (\\frac {1}{f_2} + \\frac {1}{f_3})\\),\u6240\u4ee5\uff1a\\(\\frac {1}{f_2} + \\frac {1}{f_3} = 2 \\cdot \\frac {\\gamma_{23}}{f_{23}}\\)\u3002<\/p>\n\n\n\n
\u5e26\u5165\u5176\u4e2d\u53ef\u5f97\uff1a<\/p>\n\n\n\n
\\[\\Delta = f [ \\frac {1}{6} \\cdot \\frac {1}{f_1} + \\frac {1}{2} \\cdot \\frac {1}{f_{23}} – \\frac {1}{3}(\\frac {1}{f_2} + \\frac {1}{f_3})] \\\\ = f[\\frac {1}{6} \\cdot \\frac {1}{f_1} + \\frac {1}{2} \\cdot \\frac {1}{f_{23}} – \\frac {1}{3} \\cdot 2 \\cdot \\frac {\\gamma_{23}}{f_{23}}] \\\\ = f[\\frac {1}{6} \\cdot \\frac {1}{f_1} + \\frac {1}{f_{23}}(\\frac {1}{2} – \\frac {2}{3} \\cdot \\gamma_{23})]\\]<\/p>\n\n\n\n
\u56e0\u4e3a\uff1a\\(0 \\le \\gamma_{23} \\le 1\\)\uff0c\u6240\u4ee5\uff1a\\(-\\frac {1}{6} \\le \\frac {1}{2} – \\frac {2}{3} \\cdot \\gamma_{23} \\le \\frac {1}{2}\\)\u3002<\/p>\n\n\n\n
\u5c06\u4e0d\u7b49\u5f0f\u5e26\u5165\uff0c\u53ef\u5f97\u5230\u5224\u522b\u5f0f\\(\\Delta\\)\u7684\u6570\u503c\u8303\u56f4\uff1a<\/p>\n\n\n\n
\\[\\frac {f}{6}(\\frac {1}{f_1} – \\frac {1}{f_{23}}) \\le \\Delta \\le \\frac {f}{6} (\\frac {1}{f_1} + 3 \\cdot \\frac {1}{f_{23}})\\]<\/p>\n\n\n\n
\u7531\u6b64\u4e0d\u7b49\u5f0f\u53ef\u4ee5\u5f97\u51fa\u4e00\u4e9b\u7ed3\u8bba\uff1a<\/p>\n\n\n\n
\uff081\uff09\u82e5\\(f_1 \\le f_{23}\\)\uff0c\u5219\uff1a<\/p>\n\n\n\n
\\(\\Delta \\ge \\frac {f}{6}(\\frac {1}{f_1}- \\frac {1}{f_{23}}) \\ge 0\\)\uff0c\u4e5f\u5373\uff1a\\(\\gamma^* \\ge \\gamma \\)\u3002<\/p>\n\n\n\n
\u5728\u8be5\u5047\u8bbe\u6761\u4ef6\u4e0b\uff0c\u53c8\u56e0\u4e3a\uff1a\\(f \\le f_1\\)\uff0c\\(f \\le f_{23}\\)\uff0c\u6240\u4ee5\uff1a<\/p>\n\n\n\n
\\[\\Delta \\le \\frac {f}{6} (\\frac {1}{f_1} + 3 \\cdot \\frac {1}{f_{23}}) \\le \\frac {1}{6}(1+3)=\\frac {2}{3}\\]<\/p>\n\n\n\n
\u5373\\(\\gamma^*\\)\u4e0e\\(\\gamma\\)\u4e4b\u95f4\u7684\u5dee\u503c\u4e0d\u4f1a\u5927\u4e8e\\(\\frac {2}{3}\\)\u3002<\/p>\n\n\n\n
\uff082\uff09\u4f9d\u636e\u5bf9\u79f0\u6027\uff0c\u540c\u6837\u53ef\u4ee5\u63a8\u51fa\uff1a<\/p>\n\n\n\n
\u5bf9\u4e8e\\(\\gamma^{**} = \\frac {f}{2}(\\frac {1}{f_{12}} + \\frac {1}{f_3})\\)\uff0c\u5f53\\(f_3 \\le f_{12}\\)\u65f6\uff0c\\(\\gamma^{**} \\ge \\gamma \\)\u3002<\/p>\n\n\n\n
\u4ee5\u4e0a\u4e24\u4e2a\u7ed3\u8bba\u5c31\u8bf4\u660e\u4e86\u6839\u636e\u5b57\u7b26\u4e32\u7684\u9891\u6b21\uff0c\u53ef\u4ee5\u786e\u5b9a\u8f83\u597d\u7684\u5b57\u7b26\u4e32\\(s\\)\u7ec4\u5408\u65b9\u5f0f\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u76f8\u5f53\u4e8e\u4e2d\u6587\u4e2d\u7684\u201c\u5206\u8bcd\u201d\u8fc7\u7a0b\u3002<\/p>\n\n\n\n
\uff083\uff09\\(\\gamma^*\\)\u00a0\u4e0e\u00a0\\(\\gamma^{**}\\)\u4e4b\u95f4\u7684\u5927\u5c0f\uff0c\u53ea\u80fd\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u8ba1\u7b97\u6bd4\u8f83\u6765\u786e\u5b9a\u3002<\/p>\n\n\n\n
\u8fd9\u4e5f\u662f\u8bcd\u6c47\u548c\u53e5\u5b50\u6709\u201c\u6b67\u4e49\u201d\u7684\u6570\u5b66\u63cf\u8ff0\u3002<\/p>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
\u8bbe\u5b57\u7b26\u4e32\u53ef\u4ee5\u5206\u5272\u6210\u4e09\u79cd\u5f62\u5f0f\uff08\u5176\u4e2d\u00a0\u7531\u548c\u62fc\u63a5\u800c\u6210\uff1b\u7531\u548c\u62fc\u63a5\u800c\u6210\uff09\u3002\u8fd9\u4e9b\u5b57\u7b26\u4e32\u5bf9\u5e94\u7684\u6982\u7387\u5747\u5b58\u5728\uff0c\u4e14\u5927\u4e8e0\u3002 \u4e0b\u9762\u5148 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":144,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1731","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1731"}],"collection":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/comments?post=1731"}],"version-history":[{"count":22,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1731\/revisions"}],"predecessor-version":[{"id":1769,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1731\/revisions\/1769"}],"up":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/144"}],"wp:attachment":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/media?parent=1731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}