{"id":8709,"date":"2016-10-27T01:00:00","date_gmt":"2016-10-26T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%swarma-paper%\/"},"modified":"2018-12-11T15:42:10","modified_gmt":"2018-12-11T07:42:10","slug":"%e7%94%9f%e5%91%bd%e4%b9%8b%e6%b5%81-%e8%bf%9e%e6%8e%a5%e4%b8%8a%e5%b8%9d%e7%9a%84%e7%ba%bd%e5%b8%a6-%e7%86%b5","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=8709","title":{"rendered":"\u751f\u547d\u4e4b\u6d41 | \u8fde\u63a5\u4e0a\u5e1d\u7684\u7ebd\u5e26\u2014\u2014\u71b5"},"content":{"rendered":"
\n
\n

\u751f\u547d\u4e4b\u6d41<\/strong>
<\/p>\n<\/section>\n

\n

\u300a\u751f\u547d\u4e4b\u6d41\u300b\u7cfb\u5f20\u6c5f\u8001\u5e082008\u5e74\u81f32009\u5e74\uff0c\u5229\u7528\u95f2\u6687\u65f6\u95f4\u6240\u6784\u601d\u7684\u4e00\u672c\u79d1\u666e\u96c6\u3002\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\uff1a\u4ece\u590d\u6742\u5230\u751f\u547d\u3001\u81ea\u4e3b\u751f\u547d\u4f53\u7b80\u53f2\u3001\u91cd\u65b0\u53d1\u73b0\u65f6\u95f4\u3001\u4ece\u6c38\u52a8\u673a\u5230\u4eba\u5de5\u667a\u80fd\u3001\u8fde\u63a5\u4e0a\u5e1d\u7684\u7ebd\u5e26\u2014\u2014\u71b5\u7b49\u7ae0\u8282\u3002\u73b0\u5c06\u5df2\u516c\u5f00\u90e8\u5206\u520a\u51fa\uff0c\u5e0c\u671b\u80fd\u591f\u548c\u5927\u5bb6\u5171\u540c\u5b66\u4e60\u3002
<\/span><\/p>\n<\/blockquote>\n

\n
\n
\n


<\/p>\n

\n
\u8fde\u63a5\u4e0a\u5e1d\u7684\u7ebd\u5e26\u2014\u2014\u71b5<\/span><\/section>\n<\/section>\n
<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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<\/span><\/p>\n

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\u7b2c\u4e00\u4e2a\u4f8b\u5b50\u770b\u4f3c\u4e0e\u70ed\u7269\u7406\u5e76\u4e0d\u76f8\u5173\uff0c\u4f46\u5b9e\u9645\u4e0a\u73bb\u5c14\u5179\u66fc\u7684\u601d\u60f3\u548c\u65b9\u6cd5\u5df2\u7ecf\u88ab\u5b8c\u5168\u5305\u542b\u5176\u4e2d\u4e86\u3002<\/span><\/p>\n

\u4f8b<\/strong>1  <\/strong>\u968f\u673a\u6570\u7a0b\u5e8f<\/strong><\/span><\/p>\n

\u8fd9\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u8ba1\u7b97\u673a\u7a0b\u5e8f\uff0c\u5b83\u5728\u6bcf\u4e00\u5468\u671f\u90fd\u968f\u673a\u4ea7\u751fN\u4e2a\u968f\u673a\u6570\uff0c\u5982x1<\/sub>,x2<\/sub>,\u2026,xN<\/sub>\uff0c\u5e76\u4e14\u6bcf\u4e2a\u6570\u7684\u503c\u90fd\u8981\u4e48\u662f0\u8981\u4e48\u662f1\u3002\u5047\u8bbe\u4f60\u770b\u4e0d\u5230\u8fd9\u4e2a\u7a0b\u5e8f\u5185\u90e8\u7684\u8fd0\u884c\u673a\u7406\uff0c\u4f46\u80fd\u591f\u770b\u5230\u6bcf\u4e00\u4e2a\u5468\u671f\u8fd9N\u4e2a\u6570\u7684\u548c\uff0c\u8bb0\u4e3aM=x1<\/sub>+x2<\/sub>+\u2026+xN<\/sub>\u3002\u6bcf\u4e00\u5468\u671f\u8fd0\u884c\u7684\u4f2a\u4ee3\u7801\u5982\u4e0b\uff1a<\/span><\/p>\n

RandomNum(Integer N){<\/span><\/p>\n

       Integer M=0;<\/span><\/p>\n

       For(i=1 to N){<\/span><\/p>\n

              R= Random(0,1);<\/span><\/p>\n

              M=M+R;<\/span><\/p>\n

     }<\/span><\/p>\n

       Return M;<\/span><\/p>\n

}<\/span><\/p>\n

\u53cd\u590d\u8fd0\u884c\u8be5\u7a0b\u5e8f\u4f60\u5c06\u770b\u5230\u4ec0\u4e48\u7ed3\u679c\uff1f\u7b54\u6848\u5f88\u7b80\u5355\uff0c\u4f60\u5c06\u7ecf\u5e38\u89c2\u5bdf\u5230N\/2\u8fd9\u4e2a\u6570\uff0c\u4e5f\u4f1a\u5076\u5c14\u89c2\u5bdf\u5230N\/2-1\u6216\u8005+1\u7b49\u9644\u8fd1\u7684\u6570\u3002\u6bd4\u5982\uff0c\u5f53N=6\uff0c\u90a3\u4e48\u4f60\u5c06\u5f88\u53ef\u80fd\u4f1a\u89c2\u5bdf\u52303\uff0c\u5076\u5c14\u4f1a\u770b\u52304\u30012\u7b49\uff0c\u800c\u4e0d\u592a\u53ef\u80fd\u89c2\u5bdf\u52300\u6216\u80056\u3002\u5f53N\u53d8\u5f97\u8d8a\u6765\u8d8a\u5927\u7684\u65f6\u5019\uff0c\u7ed3\u679cN\/2\u51fa\u73b0\u7684\u6b21\u6570\u4e5f\u4f1a\u53d8\u5927\u3002<\/span><\/p>\n

\u901a\u8fc7\u7b80\u5355\u8fd0\u7b97\uff0c\u5c31\u80fd\u5f97\u5230\u5047\u5982N=6\uff0c\u90a3\u4e48\u51fa\u73b0M=0\u5c31\u610f\u5473\u7740\u6240\u6709\u7684\u968f\u673a\u53d8\u91cfx1<\/sub>,x2<\/sub>,\u2026,x6<\/sub>=0\uff0c\u4e5f\u5c31\u662f\u8bf4\u8981\u5b9e\u73b0M=0\u8fd9\u4e2a\u7ed3\u679c\uff0c\u90a3\u4e9b\u968f\u673a\u53d8\u91cf\u5c31\u6709\u4e00\u79cd\u53ef\u80fd\u53d6\u503c\uff1a\u5b83\u4eec\u90fd\u7b49\u4e8e0\u3002<\/span><\/p>\n

\u5982\u679cx1<\/sub>~x6<\/sub>\u4e4b\u4e2d\u6709\u4e00\u4e2a\u51fa\u73b01\uff0c\u5176\u5b83\u90fd\u662f0\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8ba9M=1\uff0c\u8fd9\u6837\u8981\u5b9e\u73b0M=1\u8fd9\u4e2a\u7ed3\u679c\uff0c\u5c31\u53ef\u4ee5\u67096\u79cd\u53ef\u80fd\u6027\uff0c\u5373x1<\/sub>~x6<\/sub>\u5206\u522b\u53d6100000\u6216\u8005010000\u6216\u8005001000\uff0c\u2026\u2026\u7b49\u7b49\u3002<\/span><\/p>\n

\u5f53M=2\u7684\u65f6\u5019\uff0c\u53ea\u89816\u4e2a\u6570\u4e2d\u6709\u4e24\u4e2a\u53d61\uff0c\u5176\u5b83\u90fd\u662f0\u5c31\u53ef\u4ee5\u4e86\u3002\u5373\u5305\u62ec\uff1a110000, 101000, 100100, 100010, 100001, 011000, 010100, 010010, 010001, 001100, 001010, 001001, 000110, 000101, 000011\u8fd915\u79cd\u60c5\u51b5\u3002<\/span><\/p>\n

\u66f4\u4e00\u822c\u7684\uff0c\u4e00\u5171\u6709<\/span>\"\u96c6\u667a\"\u79cd\u8ba9M=k\u51fa\u73b0\u7684\u53ef\u80fd\u60c5\u51b5\uff0c\u6211\u4eec\u8bb0\u5b83\u4e3a\u03a9(k)\u3002<\/span><\/p>\n

\u5728\u8fd9\u4e2a\u7b80\u5355\u4f8b\u5b50\u4e2d\uff0c\u5bf9\u8fd9\u4e9b\u968f\u673a\u53d8\u91cfxi<\/sub>\u7684\u4e00\u6b21\u5168\u90e8\u8d4b\u503c\u79f0\u4e3a\u7cfb\u7edf\u7684\u4e00\u4e2a\u5fae\u89c2\u6001<\/strong>\u3002\u4f8b\u5982\uff0c100100\u3001000000\u3001101010\u5c31\u90fd\u662f\u7cfb\u7edf\u7684\u5fae\u89c2\u6001\u3002\u800c\u6211\u4eec\u79f0\u8fd9\u4e9b\u968f\u673a\u6570\u7684\u4e00\u79cd\u53ef\u80fd\u548c\u503cM\u53eb\u505a\u7cfb\u7edf\u7684\u4e00\u4e2a\u5b8f\u89c2\u6001<\/strong>\u3002\u4f8b\u5982M=0,2,6\u2026\u90fd\u662f\u53ef\u80fd\u7684\u5b8f\u89c2\u6001\u3002\u03a9(k)\u7684\u81ea\u7136\u5bf9\u6570\uff0c\u5373\u5f53\u5b8f\u89c2\u6001\u662fM=k\u7684\u65f6\u5019\u5bf9\u5e94\u7684ln\u03a9(k)\u5c31\u662f\u8be5\u7cfb\u7edf\u7684\u71b5\uff08\u6216\u8005\u53eb\u505a\u73bb\u5c14\u5179\u66fc\u71b5\uff09<\/strong>\uff0c\u5373\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"      \uff081\uff09                      <\/span><\/p>\n

\u4e3a\u4e86\u770b\u6e05\u695a\u8fd9\u51e0\u4e2a\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u53ef\u4ee5\u753b\u51fa\u4e0b\u9762\u7684\u793a\u610f\u56fe\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe5-1  \u968f\u673a\u6570\u5b9e\u4f8b\u4e2d\u5404\u79cd\u6982\u5ff5\u4e4b\u95f4\u7684\u5173\u7cfb<\/span><\/p>\n

\u4e00\u822c\u6765\u8bb2\uff0c\u7cfb\u7edf\u4ea7\u751f\u7684\u5b8f\u89c2\u7ed3\u679c\uff08\u5b8f\u89c2\u6001\uff09\u53ef\u80fd\u662f\u7531\u5f88\u591a\u79cd\u5fae\u89c2\u56e0\u7d20\u9020\u6210\u7684\u3002\u800c\u89c2\u5bdf\u8005\u5f80\u5f80\u770b\u4e0d\u5230\u90a3\u4e9b\u5fae\u89c2\u56e0\u7d20\uff0c\u4ec5\u4ec5\u80fd\u770b\u5230\u7cfb\u7edf\u7684\u5b8f\u89c2\u8868\u73b0\u3002\u8fd9\u5c31\u5bfc\u81f4\u4e86\u4e00\u79cd\u4ece\u5fae\u89c2\u72b6\u6001\u5230\u5b8f\u89c2\u72b6\u6001\u7684\u6620\u5c04\uff0c\u6240\u4ee5\u8be5\u4f8b\u5b50\u4e2d\u7684\u6c42\u548c\u8fc7\u7a0b\u5c31\u76f8\u5f53\u4e8e\u662f\u4e00\u79cd\u89c2\u5bdf\u5f15\u8d77\u7684\u538b\u7f29<\/strong>\u4f5c\u7528\uff0c\u5b83\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u4ece\u5b8f\u89c2\u72b6\u6001\u6765\u628a\u63e1\u7cfb\u7edf\uff0c\u4f46\u662f\u4e0d\u53ef\u907f\u514d\u5730\u5c31\u4f1a\u635f\u5931\u5bf9\u7cfb\u7edf\u7cbe\u786e\u63cf\u8ff0\u7684\u4fe1\u606f\uff0c\u8fd9\u5c31\u5bf9\u5e94\u4e86\u6bcf\u4e2a\u5b8f\u89c2\u6001\u5b9e\u9645\u4e0a\u201c\u538b\u7f29\u201d\u7684\u5fae\u89c2\u72b6\u6001\u6570\u76ee\uff0c\u5373\u03a9(k)\u3002\u7531\u4e8e\u03a9\u53ef\u80fd\u662f\u4e00\u4e2a\u5f88\u5927\u7684\u6570\uff0c\u6240\u4ee5\u53d6\u5bf9\u6570\u503c\u4e4b\u540e\u8ba1\u7b97\u71b5\u503c\u53ef\u4ee5\u7f29\u5c0f\u8fd9\u4e2a\u6570\u76ee\u800c\u65b9\u4fbf\u6bd4\u8f83\u548c\u64cd\u4f5c\uff0c\u4f46\u5374\u4e0d\u6539\u53d8\u51fd\u6570\u7684\u6027\u8d28\uff08\u4f8b\u5982\u5355\u8c03\u6027\uff0c\u6700\u5927\u503c\uff09\uff0c\u8fd9\u5c31\u662f\u71b5\u3002<\/span><\/p>\n

\u663e\u7136\u6211\u4eec\u53ef\u4ee5\u6269\u5c55\u8fd9\u4e2a\u4f8b\u5b50\uff0c\u4f8b\u5982\u628aM\u6539\u4e3a\u8ba1\u7b97x1<\/sub>x2<\/sub>\u2026xN<\/sub>\uff0c\u5373N\u4e2a\u6570\u7684\u4e58\u79ef\u3002\u8fd9\u6837\uff0c\u6211\u4eec\u5f97\u5230\u7684\u5b8f\u89c2\u6001\u5c31\u53ea\u67090\u548c1\u4e24\u79cd\u53ef\u80fd\u6027\u3002\u4f46\u662f\u6309\u7167\u540c\u6837\u7684\u65b9\u6cd5\uff0c\u4ecd\u7136\u53ef\u4ee5\u8ba1\u7b97\u8fd9\u4e24\u4e2a\u5b8f\u89c2\u72b6\u6001\u7684\u71b5\uff1aS(0)=ln(2N<\/sup>-1)\uff0cS(1)=ln1=0\u3002\u5f53\u7136\u6211\u4eec\u8fd8\u53ef\u4ee5\u7528\u5176\u5b83\u7684\u65b9\u6cd5\u8ba1\u7b97\u4ecex1<\/sub>,x2<\/sub>,\u2026,xN<\/sub>\u5230M\u7684\u51fd\u6570\uff0c\u6bcf\u79cd\u51fd\u6570\u539f\u5219\u4e0a\u90fd\u53ef\u4ee5\u5b9a\u4e49\u71b5\u3002\u8fd9\u4e2a\u4f8b\u5b50\u544a\u8bc9\u6211\u4eec\uff0c\u5176\u5b9e\u71b5\u7684\u8ba1\u7b97\u53ea\u4e0d\u8fc7\u662f\u4e00\u79cd\u8ba1\u6570\u65b9\u6cd5<\/strong>\u3002\u9488\u5bf9\u4e00\u4e2a\u7cfb\u7edf\uff0c\u53ea\u8981\u6211\u4eec\u80fd\u591f\u5b9a\u4e49\u5fae\u89c2\u6001\u3001\u5b8f\u89c2\u6001\uff0c\u6211\u4eec\u5c31\u80fd\u8ba1\u7b97\u51fa\u6bcf\u4e2a\u5b8f\u89c2\u91cf\u5bf9\u5e94\u591a\u5c11\u5fae\u89c2\u6001\uff0c\u4ece\u800c\u5c31\u53ef\u4ee5\u8ba1\u7b97\u71b5\u3002<\/span><\/p>\n

\u7136\u800c\uff0c\u8fd9\u6837\u4e00\u79cd\u62bd\u8c61\u7684\u4f8b\u5b50\u548c\u5b9e\u9645\u76f8\u5dee\u592a\u8fdc\uff0c\u8ba9\u6211\u4eec\u518d\u770b\u4e0b\u9762\u8fd9\u4e2a\u66f4\u63a5\u8fd1\u70ed\u529b\u5b66\u7cfb\u7edf\u7684\u4f8b\u5b50\u3002<\/span><\/p>\n

\u4f8b<\/strong>2<\/strong>\uff1a\u6c14\u4f53\u5206\u5b50\u6a21\u578b<\/strong><\/span><\/p>\n

\u8bbe\u6709N\u4e2a\u6c14\u4f53\u5206\u5b50\uff08\u4e00\u4e9b\u521a\u6027\u5c0f\u7403\uff09\u5206\u914d\u5230\u4e00\u4e2a\u5927\u7684\u5bb9\u5668\u91cc\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe5-2  6\u4e2a\u6c14\u4f53\u5206\u5b50\u5c0f\u7403\u5206\u914d\u5230\u4e00\u4e2a\u5bb9\u5668\u4e2d<\/span><\/p>\n

\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u5047\u8bbe\u6bcf\u4e2a\u5206\u5b50\u53ef\u4ee5\u968f\u673a\u5730\u5728\u6240\u6709\u5c0f\u65b9\u683c\u4e2d\u8df3\u6765\u8df3\u53bb\uff0c\u5e76\u4e14\u4e00\u4e2a\u5c0f\u683c\u53ef\u4ee5\u5bb9\u7eb3\u4efb\u610f\u591a\u4e2a\u5c0f\u7403\uff0c\u90a3\u4e48\u8fd9\u548c\u4f8b1\u5c31\u975e\u5e38\u76f8\u4f3c\u4e86\u3002\u540c\u6837\uff0c\u5bf9\u8fd9\u4e2a\u7cfb\u7edf\u7684\u63cf\u8ff0\u4e5f\u53ef\u4ee5\u4ece\u4e24\u79cd\u89c6\u89d2\u3002\u56e0\u4e3a\u6bcf\u4e2a\u5c0f\u7403\u5c31\u670916*8=128\uff08\u5c0f\u4e2a\u5b50\u7684\u4e2a\u6570\uff09\u79cd\u53ef\u80fd\u4f4d\u7f6e\uff0c\u90a3\u4e486\u4e2a\u5c0f\u7403\u5c31\u4e00\u5171\u53ef\u4ee5\u5305\u62ec1286<\/sup>\u79cd\u4e0d\u540c\u7684\u5fae\u89c2\u72b6\u6001<\/strong>\u3002\u4f8b\u5982\u4e0b\u5217\u5404\u56fe\u5c31\u8868\u793a\u4e86\u5404\u79cd\u4e0d\u540c\u7684\u7cfb\u7edf\u5fae\u89c2\u72b6\u6001\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe5-3  \u6c14\u4f53\u7cfb\u7edf\u53ef\u80fd\u5904\u7684\u5fae\u89c2\u72b6\u6001<\/span><\/p>\n

\u540c\u6837\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u7cfb\u7edf\u7684\u89c2\u5bdf\u8fd8\u5b58\u5728\u7740\u4e00\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u89c6\u89d2\uff1a\u5b8f\u89c2\u89c6\u89d2\u3002\u5047\u8bbe\u4e00\u4e2a\u89c2\u5bdf\u8005\u7ad9\u5728\u5f88\u8fdc\u7684\u5730\u65b9\u89c2\u5bdf\u8be5\u7cfb\u7edf\uff0c\u90a3\u4e48\u4ed6\u770b\u4e0d\u5230\u5177\u4f53\u7684\u4e00\u4e2a\u4e00\u4e2a\u5c0f\u683c\u5b50\uff0c\u800c\u53ea\u80fd\u770b\u5230\u9ed1\u8272\u8fb9\u6846\u5206\u5272\u7684\u5927\u683c\u5b50\uff08\u628a\u7cfb\u7edf\u5206\u6210\u4e86\u5de6\u3001\u53f3\u4e24\u4fa7\uff09\u3002\u8fd9\u4e2a\u89c2\u5bdf\u8005\u4e5f\u4e0d\u518d\u80fd\u591f\u5206\u8fa8\u51fa\u5177\u4f53\u7684\u5c0f\u7403\uff0c\u800c\u4ec5\u4ec5\u80fd\u770b\u5230\u4e00\u56e2\u4e1c\u897f\uff08\u591a\u4e2a\u5c0f\u7403\uff09\u5728\u5bb9\u5668\u7684\u5de6\u4fa7\uff0c\u53e6\u4e00\u56e2\u4e1c\u897f\u5728\u5bb9\u5668\u7684\u53f3\u4fa7\uff0c\u5e76\u4e14\u89c2\u5bdf\u8005\u80fd\u591f\u5224\u65ad\u51fa\u67d0\u4e00\u8fb9\u7684\u7403\u6570\u3002\u8fd9\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u56fe\u6765\u8868\u793a\u7cfb\u7edf\u7684\u5b8f\u89c2\u72b6\u6001<\/strong>\uff0c\u4f8b\u5982\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe5-4  \u4e0e\u56fe5-3\u5bf9\u5e94\u7684\u6c14\u4f53\u7cfb\u7edf\u5b8f\u89c2\u6001<\/span><\/p>\n

\uff08\u6570\u5b57\u8868\u793a\u5904\u4e8e\u8be5\u534a\u4e2a\u5bb9\u5668\u4e2d\u7684\u5206\u5b50\u6570\u76ee\uff09<\/span><\/p>\n

\u5f88\u663e\u7136\uff0c\u6bcf\u4e00\u4e2a\u5b8f\u89c2\u72b6\u6001\u5c31\u53ef\u80fd\u5bf9\u5e94\u4e86\u591a\u4e2a\u4e0d\u540c\u7684\u5fae\u89c2\u72b6\u6001\u3002\u56e0\u4e3a\u5bf9\u4e8e\u8fd9\u4e2a\u4ec5\u4ec5\u67096\u4e2a\u5206\u5b50\u7684\u6c14\u4f53\u7cfb\u7edf\u6765\u8bf4\uff0c\u6240\u6709\u53ef\u80fd\u7684\u5fae\u89c2\u6001\u6570\u76ee\u548c\u53ef\u80fd\u7684\u5b8f\u89c2\u6001\u6570\u76ee\u90fd\u662f\u6709\u9650\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa\u6bcf\u4e2a\u5b8f\u89c2\u6001\u5bf9\u5e94\u7684\u53ef\u80fd\u5fae\u89c2\u72b6\u6001\u6570\uff0c\u6211\u4eec\u7528\u4e0b\u56fe\u8868\u793a\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe5-5  \u6bcf\u4e2a\u5b8f\u89c2\u72b6\u6001\u53ef\u80fd\u5bf9\u5e94\u7684\u5fae\u89c2\u72b6\u6001\uff0c<\/span><\/p>\n

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\u8ba1\u7b97(8*8)6<\/sup>\u662f\u56e0\u4e3a\u6bcf\u4e2a\u5927\u65b9\u683c\u90fd\u5305\u542b\u4e868*8=64\u4e2a\u5c0f\u65b9\u683c\uff0c\u5e76\u4e14\u6bcf\u4e2a\u5c0f\u7403\u5f53\u88ab\u9650\u5b9a\u5728\u4e00\u4e2a\u5927\u65b9\u683c\u91cc\u9762\u7684\u65f6\u5019\uff0c\u5b83\u8fd8\u53ef\u4ee5\u5728\u8fd964\u4e2a\u5c0f\u65b9\u683c\u4e2d\u4efb\u610f\u9009\u62e9\u4e00\u4e2a\u3002CN<\/sub>k<\/sup>\u8868\u793a\u5c06\u8fd9N\u4e2a\u5206\u5b50\u5206\u5272\u6210\u4e00\u79cd\u5de6\u8fb9k\u4e2a\uff0c\u53f3\u8fb9N-k\u4e2a\u5b8f\u89c2\u6001\uff08\u5206\u6210\u5de6\u3001\u53f3\u4e24\u4fa7\uff09\u7684\u65b9\u6cd5\u6570\u3002\u6240\u4ee5\u66f4\u4e00\u822c\u7684\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u5b8f\u89c2\u6001\uff08k, N-k\uff09\uff0c\u5b83\u6240\u5bf9\u5e94\u7684\u5fae\u89c2\u72b6\u6001\u6570\u662f\uff1a<\/span>\"\u96c6\u667a\"\uff0c\u5176\u4e2dg\u4e3a\u4e00\u4e2a\u5927\u65b9\u683c\u5bf9\u5e94\u7684\u5c0f\u65b9\u683c\u6570\u76ee\u3002\u56e0\u4e3aN\u548cg\u90fd\u662f\u5e38\u6570\uff0c\u6240\u4ee5\u03a9\u7684\u6570\u503c\u4ec5\u4ec5\u53d6\u51b3\u4e8e\u7b2c\u4e00\u9879\uff0c\u6211\u4eec\u53ef\u4ee5\u753b\u51faCN<\/sub>k<\/sup>\u5728\u4e0d\u540c\u53c2\u6570N\u4e0b\u7684\u51fd\u6570\u66f2\u7ebf\u5982\u4e0b\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe5-6  \u03a9(k)\u5728\u4e0d\u540c\u53c2\u6570N\u4e0b\u7684\u51fd\u6570\u56fe<\/span><\/p>\n

\u89c2\u5bdf\u56fe5-6\uff0c\u53ef\u4ee5\u770b\u5230\u5f53k=N\/2\u7684\u65f6\u5019\uff0cCN<\/sub>k<\/sup>\u6700\u5927\u3002\u5e76\u4e14\uff0c\u5f53\u53c2\u6570N\u53d8\u5927\u7684\u65f6\u5019\u66f2\u7ebf\u7684\u5f62\u72b6\u4e5f\u53d8\u5f97\u8d8a\u6765\u8d8a\u9661\u3002\u5f53\u7136\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u63a8\u5e7f\uff0c\u5982\u5bf9\u7cfb\u7edf\u7684\u5212\u5206\u53ef\u4ee5\u6709h\u4e2a\u5927\u683c\u5b50\uff0c\u6bcf\u4e2a\u5927\u683c\u5b50\u5bf9\u5e94\u7684\u5c0f\u683c\u5b50\u6570\u662f\u4e0d\u4e00\u6837\u7684\u7b49\u60c5\u51b5\uff0c\u8fd9\u91cc\u5c31\u4e0d\u8ba8\u8bba\u4e86\u3002<\/span><\/p>\n

\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u7c7b\u4f3c\u5730\u5b9a\u4e49\u73bb\u5c14\u5179\u66fc\u71b5\uff0c\u5373\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"                         \uff081\uff09<\/span><\/p>\n

\u8fd9\u91cc\u73bb\u5c14\u5179\u66fc\u71b5S\u662f\u5173\u4e8e\u5b8f\u89c2\u72b6\u6001k\u7684\u51fd\u6570\uff0c\u5b83\u6b63\u6bd4\u4e8e\u8be5\u5b8f\u89c2\u72b6\u6001k\u6240\u5bf9\u5e94\u7684\u5fae\u89c2\u72b6\u6001\u6570\u03a9(k)\u7684\u5bf9\u6570\u503c\u3002\u5176\u4e2dkB<\/sub>\u4e3a\u73bb\u5c14\u5179\u66fc\u5e38\u6570\uff0c\u5b83\u7684\u6570\u503c\u662f\uff1a1.3806505(24) \u00d7 10\u2212<\/sup>23<\/sup> J\/K\uff0c\u5b83\u7684\u53d6\u503c\u662f\u4e3a\u4e86\u4e0e\u514b\u52b3\u4fee\u65af\u71b5\u4fdd\u6301\u4e00\u81f4\uff0c\u4ee5\u4fbf\u4e8e\u8fd9\u5957\u7edf\u8ba1\u65b9\u6cd5\u53ef\u4ee5\u8fd8\u539f\u6240\u6709\u7684\u70ed\u529b\u5b66\u89c4\u5f8b\u3002\uff08\u5728\u540e\u9762\u8ba8\u8bba\uff09\u3002<\/span><\/p>\n

\n
\n
\n
\u6a21\u62df\u8bd5\u9a8c<\/strong><\/span><\/section>\n<\/section>\n
<\/section>\n<\/section>\n<\/section>\n

    <\/span><\/p>\n

\u4e0b\u9762\uff0c\u6211\u4eec\u4e0d\u59a8\u8bbe\u8ba1\u4e00\u4e2a\u8ba1\u7b97\u673a\u6a21\u62df\u7a0b\u5e8f\uff0c\u53ef\u4ee5\u8ba9\u8fd9\u4e2a\u6c14\u4f53\u6a21\u62df\u7cfb\u7edf\u8dd1\u8d77\u6765\u3002\u5047\u5b9a\u7cfb\u7edf\u7684\u521d\u59cb\u72b6\u6001\u5982\u56fe5-7(a)\u6240\u793a\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe5-7  \u6c14\u4f53\u7cfb\u7edf\u6a21\u578b\u7684\u6f14\u5316<\/span><\/p>\n

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\u4e3a\u4e86\u907f\u514d\u8fd9\u4e9b\u7279\u6b8a\u60c5\u51b5\uff0c\u4f7f\u5f97\u7ed3\u8bba\u66f4\u5177\u666e\u904d\u6027\uff0c\u73bb\u5c14\u5179\u66fc\u5f53\u5e74\u505a\u51fa\u4e86\u4e00\u4e2a\u975e\u5e38\u806a\u660e\uff0c\u4f46\u4e5f\u662f\u5907\u53d7\u4e89\u8bae\u7684\u5404\u6001\u5386\u7ecf\u5047\u8bf4\uff0c\u6216\u79f0\u7b49\u6982\u7387\u5047\u8bf4<\/strong>\uff1a\u6bcf\u4e2a\u5206\u5b50\u5c0f\u7403\u5c06\u4f1a\u4ee5\u76f8\u540c\u7684\u6982\u7387\u5728\u6bcf\u4e2a\u5fae\u89c2\u72b6\u6001\u4e2d\u53d6\u503c<\/strong>\u3002\u5728\u8fd9\u4e2a\u5047\u8bf4\u524d\u63d0\u4e0b\uff0c\u4ed6\u5f97\u5230\u4e86\u786e\u5207\u7684\u7ed3\u8bba\uff1a\u6c14\u4f53\u5206\u5b50\u7cfb\u7edf\u5c06\u6700\u6709\u53ef\u80fd\u6f14\u5316\u5e76\u505c\u7559\u5230<\/strong>(N\/2,N\/2)<\/strong>\u8fd9\u6837\u7684\u5b8f\u89c2\u72b6\u6001\u4e0b<\/strong>\u3002\u6211\u4eec\u77e5\u9053\uff0c\u8fd9\u79cd(N\/2,N\/2)\u5bf9\u5e94\u7684\u5b8f\u89c2\u72b6\u6001\u6070\u6070\u5c31\u662f\u73bb\u5c14\u5179\u66fc\u71b5S\u6700\u5927\u7684\u72b6\u6001\uff08\u56e0\u4e3a\u5b8f\u89c2\u6001(N\/2,N\/2)\u5bf9\u5e94\u7684\u53ef\u80fd\u5fae\u89c2\u72b6\u6001\u6570\u6700\u591a\uff0c\u6240\u4ee5\u7cfb\u7edf\u5b9e\u73b0\u5e76\u505c\u7559\u5728\u8fd9\u4e2a\u72b6\u6001\u4e0b\u7684\u673a\u4f1a\u4e5f\u5c31\u6700\u591a\uff09\u3002\u6700\u540e\uff0c\u5c3d\u7ba1\u7cfb\u7edf\u4ece\u5fae\u89c2\u4e0a\u8bb2\u53ef\u80fd\u4ecd\u7136\u5904\u4e8e\u4e0d\u65ad\u53d8\u5316\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4f46\u5728\u5b8f\u89c2\u4e0a\uff0c\u7cfb\u7edf\u5c06\u4f1a\u4ee5\u6700\u5927\u7684\u6982\u7387\u505c\u7559\u5728\u71b5\u6700\u5927\u7684\u5b8f\u89c2\u72b6\u6001<\/strong>\u3002\u8fd9\u65f6\uff0c\u6211\u4eec\u5c06\u503e\u5411\u4e8e\u8bf4\u7cfb\u7edf\u5904\u4e8e\u4e86\u4e00\u79cd\u4e0d\u518d\u53d8\u5316\u7684\u5e73\u8861\u6001\uff0c\u5373\u70ed\u529b\u5b66\u5e73\u8861\u6001<\/strong>\u3002\u8fd9\u662f\u4e00\u79cd\u8868\u89c2\u7684\u5e73\u8861\uff0c\u4f46\u5b9e\u9645\u4e0a\u5185\u90e8\u5206\u5b50\u4ecd\u7136\u5728\u505a\u7740\u6fc0\u70c8\u7684\u8fd0\u52a8\u3002<\/span><\/p>\n

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\u6211\u4eec\u77e5\u9053\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u53ef\u4ee5\u770b\u4f5c\u662f\u5f3a\u52a0\u5728\u529b\u5b66\u5b9a\u5f8b\u4e4b\u4e0a\u7684\u4e00\u6761\u65b0\u7684\u5b9a\u5f8b\u3002\u73bb\u5c14\u5179\u66fc\u5f15\u5165\u8fd9\u5957\u7edf\u8ba1\u89e3\u91ca\u7684\u76ee\u7684\u662f\u4e3a\u4e86\u4ece\u5fae\u89c2\u725b\u987f\u529b\u5b66\u5bfc\u51fa\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u3002\u4f46\u662f\uff0c\u73bb\u5c14\u5179\u66fc\u867d\u7136\u90e8\u5206\u89e3\u91ca\u4e86\u71b5\u548c\u65f6\u95f4\u7bad\u5934\uff0c\u4f46\u4ed6\u4e5f\u540c\u65f6\u5f15\u5165\u4e86\u65b0\u7684\u5047\u8bbe\uff1a\u5404\u6001\u5386\u7ecf\uff08\u6216\u79f0\u7b49\u6982\u7387\uff09\u5047\u8bf4\u3002\u6240\u4ee5\uff0c\u73bb\u5c14\u5179\u66fc\u81ea\u5df1\u4e5f\u8ba4\u4e3a\uff0c\u4ed6\u5e76\u6ca1\u6709\u5b8c\u5168\u89e3\u7b54\u65f6\u95f4\u4e4b\u7bad\u7684\u95ee\u9898\u3002<\/span><\/p>\n

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 <\/span><\/span><\/p>\n

\n
\n
\n
\u8fd8\u539f\u70ed\u529b\u5b66<\/strong><\/span><\/section>\n<\/section>\n
<\/section>\n<\/section>\n<\/section>\n


<\/span><\/p>\n

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\u5728\u4e0a\u9762\u8ba8\u8bba\u7684\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u5b9e\u9645\u4e0a\u5e76\u6ca1\u6709\u8003\u8651\u6bcf\u4e2a\u7c92\u5b50\u7684\u901f\u5ea6\u95ee\u9898\u3002\u5728\u73b0\u5b9e\u7684\u6c14\u4f53\u7cfb\u7edf\u4e2d\uff0c\u6bcf\u4e2a\u5206\u5b50\u4e0d\u4ec5\u6709\u4f4d\u7f6e\uff0c\u800c\u4e14\u8fd8\u4f1a\u6709\u901f\u5ea6\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u9700\u8981\u628a\u4e0a\u9762\u6a21\u578b\u4e2d\u7684\u5e73\u9762\u7a7a\u95f4\u6269\u5145\u5230\u5305\u542b\u4e86\u901f\u5ea6\u4fe1\u606f\u7684\u72b6\u6001\u7a7a\u95f4\uff08\u6216\u79f0\u76f8\u7a7a\u95f4\u4e2d\uff0c\u89c1\u7b2c\u4e09\u7ae0\uff09\u3002\u8fd9\u6837\uff0c\u6bcf\u4e2a\u5c0f\u7403\u6240\u5904\u7684\u5bb9\u5668\u5c31\u4e0d\u518d\u662f\u4e00\u4e2a\u5e73\u9762\u7684\u5bb9\u5668\uff0c\u800c\u53ef\u80fd\u662f\u56db\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u7acb\u65b9\u533a\u57df\u3002\u90a3\u4e48\uff0c\u6309\u7167\u52a8\u529b\u7cfb\u7edf\u7684\u89c2\u70b9\uff0c\u6bcf\u4e2a\u5c0f\u7403\u7684\u8fd0\u52a8\u5c31\u662f\u4ece\u9ad8\u7ef4\u7684\u76f8\u7a7a\u95f4\u4e2d\u7684\u4e00\u70b9\u8df3\u5230\u53e6\u4e00\u70b9\u3002\u4f46\u662f\uff0c\u8fd9\u70b9\u6269\u5145\u5bf9\u4e8e\u6211\u4eec\u7684\u7edf\u8ba1\u6a21\u578b\u6ca1\u6709\u672c\u8d28\u5f71\u54cd\u3002\u56e0\u4e3a\u6211\u4eec\u7684\u6a21\u578b\u4e2d\u4ec5\u4ec5\u6d89\u53ca\u4e86\u5c0f\u683c\u5b50\u3001\u5927\u683c\u5b50\u8fd8\u6709\u5206\u5b50\u5c0f\u7403\uff0c\u800c\u81f3\u4e8e\u5c0f\u683c\u5b50\u3001\u5927\u683c\u5b50\u662f\u51e0\u7ef4\u7a7a\u95f4\u4e2d\u7684\u51e0\u4f55\u4f53\u5e76\u6ca1\u6709\u592a\u5927\u7684\u5173\u7cfb\u3002\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\u56fe5-3\u8868\u793a\u7684\u662f\u72b6\u6001\u7a7a\u95f4\uff0c\u5373\u6c34\u5e73\u65b9\u5411\u662f\u5c0f\u7403\u4f4d\u7f6e\uff0c\u7ad6\u76f4\u65b9\u5411\u662f\u5c0f\u7403\u7684\u4e0d\u540c\u901f\u5ea6\u3002\u6bcf\u4e2a\u5c0f\u65b9\u683c\u5c31\u662f\u5c0f\u7403\u7684\u4e00\u79cd\u53ef\u80fd\u72b6\u6001\uff08\u4f4d\u7f6e\u548c\u901f\u5ea6\u7684\u7ec4\u5408\uff09\uff0c\u5927\u65b9\u683c\u5c31\u662f\u5bf9\u8fd9\u4e9b\u5c0f\u72b6\u6001\u5f52\u5e76\u4e4b\u540e\u7684\u5b8f\u89c2\u72b6\u6001\uff0c\u7b49\u7b49\u3002\u4e0d\u8fc7\uff0c\u5728\u52a0\u5165\u4e86\u901f\u5ea6\u56e0\u7d20\u4e4b\u540e\uff0c\u80fd\u91cf\u3001\u6e29\u5ea6\u5c31\u4e0d\u4ec5\u4ec5\u662f\u5c0f\u7403\u548c\u5c0f\u7403\u5bc6\u5ea6\u4e86\u3002\uff08\u66f4\u52a0\u4e25\u683c\u7684\u6570\u5b66\u8ba8\u8bba\uff0c\u8bf7\u53c2\u8003\u76f8\u5173\u7684\u7edf\u8ba1\u7269\u7406\u7684\u6559\u79d1\u4e66\uff09\u3002<\/span><\/p>\n

 <\/span><\/span><\/p>\n

\n
\n
\n
\u4ece\u73bb\u5c14\u5179\u66fc\u5230\u5409\u5e03\u65af<\/strong><\/span><\/section>\n<\/section>\n
<\/section>\n<\/section>\n<\/section>\n


<\/span><\/p>\n

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<\/span><\/p>\n

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\"\u96c6\u667a\"<\/p>\n

\u56fe5-9  \u4e00\u4e2a\u6982\u7387\u5206\u5e03\u793a\u610f\u56fe<\/span><\/p>\n

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\u5728\u6bcf\u4e00\u4e2a\u5468\u671f\uff0c\u6211\u4eec\u90fd\u80fd\u5f97\u5230\u4e00\u4e2a\u8fd9\u6837\u7684\u6982\u7387\u5206\u5e03\u3002\u9488\u5bf9\u4e00\u79cd\u53ef\u80fd\u7684\u6982\u7387\u5206\u5e03\uff0c\u5409\u5e03\u65af\u53d1\u660e\u4e86\u4e00\u5957\u4e0d\u540c\u7684\u8ba1\u7b97\u71b5\u7684\u65b9\u6cd5\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"                         \uff082\uff09<\/span><\/p>\n

\u5176\u4e2dn\u8868\u793a\u6240\u6709\u7684\u65b9\u683c\u6570\uff0ci\u8868\u793a\u5176\u4e2d\u7684\u67d0\u4e00\u4e2a\u5c0f\u65b9\u683c\u3002pi<\/sub>\u8868\u793a\u8be5\u65b9\u683c\u88ab\u8bbf\u95ee\u7684\u6982\u7387\uff08\u5373\u989c\u8272\uff09\u3002SGibbs<\/sub>\u5c31\u662f\u5409\u5e03\u65af\u5b9a\u4e49\u7684\u71b5\uff0c\u5b83\u662f\u5173\u4e8e\u4e00\u7cfb\u5217\u6982\u7387\u5206\u5e03\uff08p1<\/sub>,p2<\/sub>,\u2026,pn<\/sub>\uff09\u7684\u51fd\u6570\u3002\u8fd9\u6837\uff0c\u786e\u5b9a\u4e86\u4e00\u7ec4\u6982\u7387\u5c31\u76f8\u5f53\u4e8e\u786e\u5b9a\u4e86\u7cfb\u7edf\u7684\u4e00\u4e2a\u72b6\u6001\uff0c\u90a3\u4e48\u4e0d\u540c\u7684\u72b6\u6001\u5c31\u5bf9\u5e94\u4e86\u4e0d\u540c\u7684\u71b5\u503c\u3002<\/span><\/p>\n

\u90a3\u4e48\uff0c\u5bf9\u5e94\u7684\u5e73\u8861\u6001\u7684\u6982\u7387\u5206\u5e03\u662f\u4ec0\u4e48\u6837\u5b50\u5462\uff1f\u8fd9\u5c06\u662f\u4e00\u4e2a\u6240\u6709\u7684\u683c\u5b50\u90fd\u5448\u73b0\u51fa\u76f8\u540c\u989c\u8272\u7684\u72b6\u6001\uff0c\u5373pi<\/sub>=1\/n\uff08\u5bf9\u6240\u6709\u7684i=1~n\uff09\u3002\u56e0\u4e3a\u6839\u636e\u73bb\u5c14\u5179\u66fc\u7684\u5404\u6001\u5386\u7ecf\u5047\u8bf4\uff0c\u6bcf\u4e2a\u5c0f\u7403\u5c06\u7b49\u53ef\u80fd\u5730\u8bbf\u95ee\u6bcf\u4e00\u4e2a\u5c0f\u65b9\u683c\uff0c\u6240\u4ee5\u5f53\u7cfb\u7edf\u5904\u4e8e\u5e73\u8861\u6001\uff0c\u6240\u6709\u65b9\u683c\u7684\u6982\u7387\u90fd\u76f8\u540c\uff0c\u8fd9\u6837\u5c31\u5f97\u5230\u4e86\u4e00\u4e2a\u5747\u5300\u989c\u8272\u7684\u5206\u5e03\u3002\u4ece\u6570\u5b66\u4e0a\u53ef\u4ee5\u8bc1\u660e\uff0c\u5f53pi<\/sub>=1\/n\uff08\u5bf9\u6240\u6709\u7684i=1~n\uff09\u7684\u65f6\u5019\uff0cSGibbs<\/sub>\u53d6\u6700\u5927\u503c\u3002\u6240\u4ee5\uff0c\u6c14\u4f53\u7cfb\u7edf\u7684\u5e73\u8861\u6001\u5c31\u662f\u71b5\u6700\u5927\u7684\u72b6\u6001\uff0c\u8fd9\u4e00\u70b9\u548c\u73bb\u5c14\u5179\u66fc\u71b5\u5f97\u5230\u7684\u7ed3\u679c\u662f\u5b8c\u5168\u4e00\u81f4\u7684\u3002<\/span><\/p>\n

\u8fdb\u4e00\u6b65\uff0c\u901a\u8fc7\u6570\u5b66\u4e0a\u7684\u63a8\u5bfc\u8fd8\u53ef\u4ee5\u770b\u5230\u73bb\u5c14\u5179\u66fc\u5b9a\u4e49\u7684\u71b5\uff081\uff09\u5f0f\u5b9e\u9645\u4e0a\u662f\u548c\uff082\uff09\u5f0f\u7b49\u4ef7\u7684\u3002\u5982\u679c\u6211\u4eec\u628a\u8fd9\u91cc\u7684\u6bcf\u4e2a\u5c0f\u65b9\u683c\u770b\u4f5c\u662f\u4f8b2\u4e2d\u7684\u5927\u65b9\u683c\uff0c\u5e76\u4e14\u628a\u6bcf\u4e2a\u5927\u65b9\u683c\u4e2d\u7684\u5206\u5b50\u6570\/\u603b\u5206\u5b50\u6570\u770b\u4f5c\u662f\u8bbf\u95ee\u8be5\u65b9\u683c\u7684\u6982\u7387\uff0c\u90a3\u4e48\u7ecf\u8fc7\u6570\u5b66\u4e0a\u7684\u63a8\u5bfc\uff0c\u6211\u4eec\u5b8c\u5168\u53ef\u4ee5\u4ece\uff081\uff09\u5f0f\u5f97\u5230\uff082\uff09\u5f0f\u3002<\/span><\/p>\n

\u5409\u5e03\u65af\u4e0d\u4ec5\u4ec5\u4ece\u53e6\u4e00\u4e2a\u89d2\u5ea6\u91cd\u65b0\u5b9a\u4e49\u4e86\u73bb\u5c14\u5179\u66fc\u71b5\uff0c\u800c\u4e14\u8fd8\u7ed9\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5d2d\u65b0\u7684\u601d\u8def\u6765\u7406\u89e3\u7cfb\u7edf\u3002\u56e0\u4e3a\u539f\u5219\u4e0a\u8bb2\uff0c\u7cfb\u7edf\u7684\u5fae\u89c2\u72b6\u6001\u662f\u6211\u4eec\u4e0d\u53ef\u89c2\u6d4b\u5230\u7684\uff0c\u6240\u4ee5\u8ba8\u8bba\u5b83\u4e5f\u53d8\u5f97\u6ca1\u6709\u610f\u4e49\u3002\u8fd9\u6837\uff0c\u6211\u4eec\u6240\u80fd\u89c2\u5bdf\u5230\u7684\u4ec5\u4ec5\u662f\u7cfb\u7edf\u7684\u4e00\u4e9b\u53ef\u89c2\u6d4b\u72b6\u6001<\/strong>\uff0c\u6700\u5927\u71b5\u72b6\u6001\u662f\u6240\u6709\u53ef\u89c2\u6d4b\u72b6\u6001\u4e2d\u6700\u53ef\u80fd\u88ab\u89c2\u6d4b\u5230\u7684\u90a3\u4e2a\u72b6\u6001<\/strong>\u3002<\/span><\/p>\n


<\/span><\/p>\n

\n
\n
\n
\u4ece\u7edf\u8ba1\u7269\u7406\u5230\u4fe1\u606f\u8bba<\/strong><\/span><\/section>\n<\/section>\n
<\/section>\n<\/section>\n<\/section>\n


<\/span><\/span><\/p>\n

\u5409\u5e03\u65af\u71b5\u7684\u53e6\u4e00\u4e2a\u597d\u5904\u662f\u5b83\u5728\u6570\u5b66\u5f62\u5f0f\u4e0a\u7684\u7b80\u6d01\u6027\u3002\u5f53\u6211\u4eec\u5fd8\u6389(2)\u4e2d\u6bcf\u4e00\u4e2ap<\/span>i<\/sub>\u7684\u5177\u4f53\u542b\u4e49\uff0c\u800c\u4ec5\u4ec5\u662f\u67d0\u79cd\u62bd\u8c61\u7684\u6982\u7387\u5206\u5e03\uff0c\u90a3\u4e48S<\/span>Gibbs<\/sub>\u4ecd\u7136\u662f\u4e00\u4e2a\u826f\u5b9a\u4e49\u7684\u91cf\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u8003\u8651\u629b\u63b7\u4e00\u679a\u786c\u5e01\uff0c\u90a3\u4e48\u8fd9\u679a\u786c\u5e01\u51fa\u73b0\u6b63\u9762\u548c\u53cd\u9762\u7684\u6982\u7387\u5c31\u90fd\u662f1\/2\u3002\u5bf9\u4e8e\u8fd9\u6837\u7b80\u5355\u7684\u6982\u7387\u5206\u5e03\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u8ba1\u7b97\u5409\u5e03\u65af\u71b5\uff1aS=-(1\/2 ln0.5+1\/2 ln0.5)=ln2\u3002<\/span>\u8fd9\u91cc\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u7cfb\u7edf\u53ef\u80fd\u5904\u4e8e\u7684\u6240\u6709\u72b6\u6001\u770b\u4f5c\u4e00\u4e2a\u5927\u7684\u5bb9\u5668\uff0c\u4e00\u6b21\u629b\u786c\u5e01\u4e8b\u4ef6\u5c31\u76f8\u5f53\u4e8e\u662f\u4e00\u4e2a\u5728\u8be5\u5bb9\u5668\u4e2d\u8fd0\u52a8\u7684\u5c0f\u7403\u3002\u8fd9\u6837\uff0c\u5c0f\u7403\u8bbf\u95ee\u5bb9\u5668\u7684\u6982\u7387\u5c31\u76f8\u5f53\u4e8e\u662f\u786c\u5e01\u7684\u4e00\u6b21\u6b63\u53cd\u9762\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u8ba1\u7b97\u71b5\u3002<\/span> \u4e00\u822c\u7684\uff0c\u5982\u679c\u4e00\u4e2a\u7cfb\u7edf\u53ef\u80fd\u5904\u5728n\u79cd\u72b6\u6001\uff0c\u5e76\u4e14\u6bcf\u79cd\u72b6\u6001\u7684\u6982\u7387\u5206\u522b\u662fp<\/span>1<\/sub>,p<\/span>2<\/sub>,\u2026,p<\/span>n<\/sub>\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7cfb\u7edf\u5c31\u6709\u7533\u519c\u4fe1\u606f\u71b5\uff1a<\/span><\/span><\/p>\n

\"\u96c6\u667a\"                      \uff083\uff09<\/span><\/p>\n

\u5176\u4e2dI\u53eb\u505a\u7cfb\u7edf\u6240\u5305\u542b\u7684\u4fe1\u606f\u91cf\uff0c\u5b83\u662f\u7533\u519c\u71b5\uff08Shannon Entropy\uff09\u7684\u76f8\u53cd\u6570\u3002\u7533\u519c\u71b5\u548c\u5409\u5e03\u65af\u71b5\u5177\u6709\u76f8\u540c\u7684\u5f62\u5f0f<\/strong>\uff0c\u4f46\u662f\uff0c\u5728\u8fd9\u4e24\u79cd\u63cf\u8ff0\u4e2d\uff0c\u7cfb\u7edf\u4ee5\u53cai\u7684\u542b\u4e49\u662f\u4e0d\u5b8c\u5168\u4e00\u6837\u7684\u3002\u5728\u524d\u9762\u5409\u5e03\u65af\u7684\u5b9a\u4e49\u4e2d\uff0c\u4e00\u4e2a\u7cfb\u7edf\u662f\u6307\u4e00\u4e2a\u5bb9\u5668\uff0c\u91cc\u9762\u6709\u591a\u4e2a\u5c0f\u7403\uff0c\u8fd9\u6837\u5c0f\u7403\u8bbf\u95ee\u5bb9\u5668\u7684\u4e0d\u540c\u90e8\u5206\u53ef\u4ee5\u5bfc\u81f4\u4e00\u4e2a\u5206\u5e03\u3002\u56e0\u6b64\uff0c\u7ed9\u5b9a\u4e00\u7cfb\u5217\u5bb9\u5668\u4e0d\u540c\u90e8\u5206\u7684\u6982\u7387\u5206\u5e03\uff0c\u5c31\u7ed9\u5b9a\u4e86\u8be5\u7cfb\u7edf\u7684\u72b6\u6001\uff0c\u56e0\u6b64\u4e5f\u5c31\u80fd\u591f\u5b9a\u4e49\u8be5\u7cfb\u7edf\u7684\u5409\u5e03\u65af\u71b5\uff08\u5373\u5409\u5e03\u65af\u71b5\u662f\u63cf\u8ff0\u7cfb\u7edf\u72b6\u6001\u7684\u91cf<\/strong>\uff09\u3002\u4f46\u662f\u5728\u7533\u519c\u71b5\u5b9a\u4e49\u4e2d\uff0c\u4e00\u4e2a\u7cfb\u7edf\u672c\u8eab\u7684\u72b6\u6001\uff0c\u4ee5\u53ca\u8fd9\u4e9b\u72b6\u6001\u4e0a\u7684\u6982\u7387\u5206\u5e03\u662f\u7cfb\u7edf\u672c\u8eab\u5df2\u7ecf\u51b3\u5b9a\u4e86\u7684\uff0c\u56e0\u6b64\u7533\u519c\u71b5<\/strong>\u4e5f\u51b3\u5b9a\u4e86\uff0c\u5b83\u662f\u63cf\u8ff0\u7cfb\u7edf\uff08\u800c\u4e0d\u662f\u72b6\u6001\uff09\u7684\u91cf<\/strong>\u3002<\/span><\/p>\n

\u4e3a\u770b\u6e05\u5409\u5e03\u65af\u71b5\u548c\u7533\u519c\u71b5\u7684\u533a\u522b\uff0c\u8ba9\u6211\u4eec\u518d\u6b21\u56de\u5fc6\u4f8b1\uff0c\u5373\u90a3\u4e2a\u4ea7\u751f0\u30011\u968f\u673a\u6570\u5e76\u6c42\u548c\u7684\u7a0b\u5e8f\u3002\u5982\u679c\u6211\u4eec\u628a\u8fd9\u4e2a\u7a0b\u5e8f\u770b\u4f5c\u4e00\u4e2a\u7cfb\u7edf\uff0c\u90a3\u4e48\u8be5\u7cfb\u7edf\u5c31\u67090,1,\u2026,N\u8fd9\u51e0\u79cd\u72b6\u6001\u3002\u5f53\u7a0b\u5e8f\u8fd0\u884c\u8d77\u6765\u4ee5\u540e\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u4e00\u4e2a\u5728\u5404\u4e2a\u72b6\u6001\u4e0a\u7684\u6982\u7387\u5206\u5e03p(k)=CN<\/sub>k<\/sup>\/2N<\/sup>\uff0c\u56e0\u6b64\u53ef\u4ee5\u7ed9\u8fd9\u4e2a\u7cfb\u7edf<\/strong>\u8ba1\u7b97\u7533\u519c\u71b5\uff1a<\/span>\"\u96c6\u667a\"\u3002<\/span><\/p>\n

\u6839\u636e\u4f8b1\u7684\u8ba8\u8bba\uff0c\u6211\u4eec\u53c8\u77e5\u9053\uff0c\u5b9e\u9645\u4e0a\u8fd9\u6bcf\u4e00\u4e2a\u72b6\u6001\u53c8\u662f\u4e00\u4e2a\u5b8f\u89c2\u6001\uff0c\u5b83\u53ef\u80fd\u5bf9\u5e94\u4e86\u591a\u79cd\u5fae\u89c2\u6001\u3002\u90a3\u4e48\uff0c\u4e5f\u5c31\u662f\u8bf4\u8be5\u7a0b\u5e8f\u7684\u6bcf\u4e00\u4e2a\u72b6\u6001<\/strong>\u53c8\u53ef\u4ee5\u8ba1\u7b97\u51fa\u4e00\u4e2a\u5409\u5e03\u65af\u71b5\u3002\u6bd4\u5982\u72b6\u6001k\uff0c\u4e5f\u5c31\u662f\u8bf4\u7a0b\u5e8f\u5f97\u5230\u7684\u548c\u6570\u662fk\u3002\u90a3\u4e48\u8fd9N\u4e2a\u968f\u673a\u6570\u5c31\u76f8\u5f53\u4e8e\u662f\u8981\u5360\u98860\u548c1\u4e24\u4e2a\u683c\u5b50\u7684\u7c92\u5b50\u3002\u8981\u5f97\u5230\u548c\u6570\u662fk\uff0c\u90a3\u4e48\u6211\u4eec\u77e5\u9053\u8fd9\u9700\u8981\u683c\u5b501\u88ab\u5360\u9886\u7684\u6982\u7387\u5e94\u8be5\u662fN\u4e2d\u7684k\u6b21\uff0c\u5373k\/N\uff0c\u800c\u5360\u98860\u7684\u6982\u7387\u5c31\u662f(N-k)\/N\u3002\u8fd9\u6837\uff0c\u72b6\u6001k\u7684\u5409\u5e03\u65af\u71b5\u662f:<\/span>\"\u96c6\u667a\"\u3002<\/span><\/p>\n

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\u201c\u4e3b\u89c2\u201d\u7edf\u8ba1\u7269\u7406<\/strong><\/span><\/section>\n<\/section>\n
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20\u4e16\u7eaa\u4e2d\u53f6\u7684\u7269\u7406\u5b66\u5bb6\u5409\u5c3c\u65af\uff08Jaynes\uff09\u5411\u6211\u4eec\u5c55\u793a\uff0c\u8fd9\u79cd\u5bf9\u7cfb\u7edf\u7684\u201c\u4e3b\u89c2\u201d\u8ba4\u8bc6\u53ef\u80fd\u66f4\u52a0\u672c\u8d28\u3001\u900f\u5f7b\u3002\u56e0\u4e3a\uff0c\u5b83\u4ece\u4fe1\u606f\u8bba\u51fa\u53d1\uff0c\u53ef\u4ee5\u53cd\u8fc7\u6765\u63a8\u5bfc\u51fa\u6574\u4e2a\u7edf\u8ba1\u7269\u7406<\/strong>\u3002\u800c\u4e14\uff0c\u8fd9\u79cd\u63a8\u5bfc\u65b9\u6cd5\u6bd4\u65e9\u5148\u7684\u7edf\u8ba1\u7269\u7406\u66f4\u52a0\u7b80\u5355\u3001\u660e\u4e86\uff08\u53c2\u89c1Jaynes\u7684\u6587\u7ae0\u300aInformation theory and statistical physics\u300b\uff09\u3002<\/span><\/p>\n

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\u603b\u7ed3\u6765\u770b\uff0c\u8fd9\u4e00\u7ae0\u7528\u4e00\u7cfb\u5217\u7b80\u5355\u7684\u4f8b\u5b50\u4ecb\u7ecd\u4e86\u4ece\u73bb\u5c14\u5179\u66fc\u71b5\u5230\u5409\u5e03\u65af\u71b5\u518d\u5230\u7533\u519c\u71b5\u7684\u8fc7\u7a0b\u3002\u71b5\u7a76\u7adf\u662f\u4ec0\u4e48\uff1f\u672c\u7ae0\u4ecb\u7ecd\u7684\u63a2\u7d22\u5386\u53f2\u672c\u8eab\u5c31\u662f\u4e00\u4e2a\u5bf9\u8fd9\u4e00\u6982\u5ff5\u7684\u9010\u6e10\u6df1\u5316\u8ba4\u8bc6\u8fc7\u7a0b\u3002\u5982\u679c\u975e\u8981\u7528\u4e00\u53e5\u8bdd\u6765\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u5b81\u613f\u8bf4\uff0c\u71b5\u5176\u5b9e\u5c31\u662f\u4e00\u6761\u8fde\u63a5\u7684\u7ebd\u5e26\u3002\u73bb\u5c14\u5179\u66fc\u71b5\u8fde\u63a5\u7684\u662f\u5b8f\u89c2\u4e0e\u5fae\u89c2\uff1b\u7533\u519c\u71b5\u8fde\u63a5\u7684\u662f\u4e3b\u89c2\u4e16\u754c\u4e0e\u5ba2\u89c2\u4e16\u754c\u3002\u5728\u8fd9\u6761\u7ebd\u5e26\u9762\u524d\uff0c\u88ab\u4f20\u7edf\u79d1\u5b66\u5272\u88c2\u5f97\u5f88\u6df1\u7684\u4e3b\u5ba2\u89c2\u5206\u79bb\u7684\u754c\u9650\u5df2\u7ecf\u53d8\u5f97\u9010\u6e10\u6a21\u7cca\u3002\u6b63\u662f\u57fa\u4e8e\u8fd9\u79cd\u4fe1\u5ff5\uff0c\u5409\u5c3c\u65af\u624d\u63d0\u51fa\u4e86\u4e00\u5957\u975e\u5e38\u4e0d\u540c\u7684\u201c\u4e3b\u89c2\u201d\u7edf\u8ba1\u7269\u7406\u5b66\u3002<\/span><\/p>\n

\u6211\u4eec\u5173\u5fc3\u7684\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u3001\u65f6\u95f4\u4e4b\u7bad\u7684\u95ee\u9898\u53c8\u600e\u6837\u5462\uff1f\u5c3d\u7ba1\u5386\u53f2\u4e0a\u5f88\u591a\u4f1f\u4eba\u90fd\u8bd5\u56fe\u4ece\u7ecf\u5178\u7269\u7406\u51fa\u53d1\u800c\u7ed9\u51fa\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u65b0\u7684\u89e3\u91ca\uff0c\u4f46\u662f\uff0c\u4ed6\u4eec\u5374\u6216\u591a\u6216\u5c11\u7684\u5f15\u5165\u4e86\u65b0\u7684\u5047\u8bbe\u3002\u4f8b\u5982\u73bb\u5c14\u5179\u66fc\u548c\u5409\u5e03\u65af\u7684\u7edf\u8ba1\u7269\u7406\u90fd\u9700\u8981\u5404\u6001\u5386\u7ecf\u5047\u8bbe\uff0c\u5409\u5c3c\u65af\u7684\u7edf\u8ba1\u7269\u7406\u9700\u8981\u5f15\u5165\u81ea\u52a8\u6700\u5927\u5316\u71b5\u7684\u5047\u8bbe\u3002\u6211\u4eec\u662f\u5426\u80fd\u591f\u6446\u8131\u8fd9\u4e9b\u5047\u8bbe\u800c\u5b8c\u5168\u7406\u89e3\u65f6\u95f4\u4e4b\u7bad\u4e4b\u8c1c\u5462\uff1f\u6211\u503e\u5411\u4e8e\u4e0d\u592a\u53ef\u80fd\uff0c\u8fd9\u6070\u6070\u662f\u590d\u6742\u7cfb\u7edf\u7684\u6d8c\u73b0\u6982\u5ff5\u6240\u523b\u753b\u7684\u3002\u5bf9\u4e8e\u7cfb\u7edf\u7684\u4e0d\u540c\u5c42\u6b21\u6211\u4eec\u9700\u8981\u4e0d\u540c\u7684\u63cf\u8ff0\u3002\u65f6\u95f4\u4e4b\u7bad\u5c31\u662f\u8fd9\u79cd\u4e0d\u53ef\u5316\u7ea6\u4e3a\u5fae\u89c2\u7269\u7406\u7684\u4e00\u79cd\u6d8c\u73b0\u5c5e\u6027\u3002\u5409\u5c3c\u65af\u7684\u7edf\u8ba1\u89e3\u91ca\u544a\u8bc9\u6211\u4eec\uff0c\u8fd9\u79cd\u4e0d\u53ef\u9006\u7684\u6d8c\u73b0\u6027\u8d28\u5176\u5b9e\u53ef\u4ee5\u89e3\u91ca\u4e3a\u6211\u4eec\u5bf9\u4e16\u754c\u7684\u4e00\u79cd\u4e3b\u89c2\u7684\u503e\u5411\uff0c\u5373\u6700\u5927\u5316\u4fe1\u606f\u71b5\u3002    <\/span><\/span><\/p>\n

                                                                                                    \u7f16\u8f91\uff1awangting<\/span> <\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\"\u96c6\u667a\"<\/span><\/p>\n
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\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n

\n
\"\u96c6\u667a\"
<\/section>\n<\/section>\n

\u957f\u6309\u8bc6\u522b\u4e8c\u7ef4\u7801\uff0c\u5173\u6ce8\u96c6\u667aClub\uff0c<\/span><\/p>\n

\u8ba9\u6211\u4eec\u79bb\u79d1\u5b66\u63a2\u7d22\u66f4\u8fd1\u4e00\u6b65\u3002<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\"\u96c6\u667a\"<\/span><\/span><\/section>\n


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\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff1a \u96c6\u667a\u4ff1\u4e50\u90e8 <\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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