{"id":43199,"date":"2023-06-15T19:20:20","date_gmt":"2023-06-15T11:20:20","guid":{"rendered":"https:\/\/swarma.org\/?p=43199"},"modified":"2023-06-15T19:20:20","modified_gmt":"2023-06-15T11:20:20","slug":"physics-reports-%e6%9c%80%e6%96%b0%e7%bb%bc%e8%bf%b0%ef%bc%9a%e6%ba%af%e6%ba%90%e5%9f%8e%e5%b8%82%e8%a7%84%e6%a8%a1%e6%b3%95%e5%88%99%e7%9a%84%e6%95%b0%e5%ad%a6%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=43199","title":{"rendered":"Physics Reports \u6700\u65b0\u7efc\u8ff0\uff1a\u6eaf\u6e90\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219\u7684\u6570\u5b66\u6a21\u578b"},"content":{"rendered":"
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\u8bba\u6587\u9898\u76ee\uff1a<\/span>Mathematical models to explain the origin of urban scaling laws<\/span><\/section>\n
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\u9996\u5148\uff0c\u4e0e\u793e\u4f1a\u7ecf\u6d4e\u6d3b\u52a8\u6709\u5173\u7684\u53d8\u91cf<\/span>\uff08\u5982GDP\u3001\u4e13\u5229\u3001\u827e\u6ecb\u75c5\u75c5\u4f8b\uff09<\/span>\u4e0e\u4eba\u53e3\u89c4\u6a21\u5448\u8d85\u7ebf\u6027\u5173\u7cfb\uff08\u03b2<\/em>>1\uff09\u3002\u6587\u5316\u548c\u7ecf\u6d4e\u4e0d\u540c\u7684\u56fd\u5bb6\u4ee5\u53ca\u4e0d\u540c\u7684\u57ce\u5e02\u6307\u6807\u7684\u7ecf\u9a8c\u8bc1\u636e\u8868\u660e\uff0c\u793e\u4f1a\u7ecf\u6d4e\u53d8\u91cf\u7684\u6807\u5ea6\u56e0\u5b50\u7ea6\u4e3a\u03b2<\/em>=1.15\u3002\u8fd9\u610f\u5473\u7740\u8fd9\u4e9b\u793e\u4f1a\u7ecf\u6d4e\u53d8\u91cf\u7684\u4eba\u5747\u6570\u91cf\u5f80\u5f80\u968f\u7740\u57ce\u5e02\u89c4\u6a21\u7684\u6269\u5927\u800c\u589e\u52a0\uff0c\u5373\u6240\u8c13\u7684\u89c4\u6a21\u6536\u76ca\u9012\u589e\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u4e00\u4e2a\u5927\u57ce\u5e02\u4ea7\u751f\u7684\u8d22\u5bcc\u6bd4\u4e24\u4e2a\u4e00\u534a\u5927\u5c0f\u7684\u57ce\u5e02\u52a0\u8d77\u6765\u8fd8\u8981\u591a\u3002\u56e0\u6b64\u53ef\u4ee5\u76f4\u89c2\u5730\u8bf4\uff0c\u57ce\u5e02\u8d8a\u5927\uff0c\u5b83\u4ea7\u751f\u7684\u8d22\u5bcc\u5c31\u8d8a\u591a\u3002<\/span><\/p>\n


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\u5176\u6b21\uff0c\u4e0e\u4e2a\u4eba\u57fa\u672c\u670d\u52a1\u76f8\u5173\u7684\u53d8\u91cf<\/span>\uff08\u5982\u623f\u5c4b\u6570\u91cf\u3001\u7528\u6c34\u91cf\uff09<\/span>\u4e0e\u57ce\u5e02\u4eba\u53e3\u5448\u7ebf\u6027\u5173\u7cfb\uff08\u03b2<\/em>=1\uff09\u3002\u800c\u4e0e\u57fa\u7840\u8bbe\u65bd\u76f8\u5173\u7684\u53d8\u91cf<\/span>\uff08\u5982\u5145\u7535\u6869\u3001\u52a0\u6cb9\u7ad9\u7684\u6570\u91cf\uff09<\/span>\u4e0e\u4eba\u53e3\u5448\u4e9a\u7ebf\u6027\u7684\u5173\u7cfb\uff08\u03b2<\/em><1\uff09\u3002\u7ecf\u9a8c\u8bc1\u636e\u8868\u660e\uff0c\u57fa\u7840\u8bbe\u65bd\u53d8\u91cf\u7684\u6807\u5ea6\u56e0\u5b50\u5728\u03b2<\/em>=0.85\u5de6\u53f3\u3002\u8fd9\u610f\u5473\u7740\u5927\u57ce\u5e02\u5bf9\u4eba\u5747\u57fa\u7840\u8bbe\u65bd\u7684\u9700\u6c42\u8f83\u5c11\uff0c\u53ef\u4ee5\u8bf4\u5927\u57ce\u5e02\u53ef\u4ee5\u7528\u66f4\u5c11\u7684\u94b1\u505a\u66f4\u591a\u7684\u4e8b\u3002\u4e5f\u6709\u8bc1\u636e\u8868\u660e\uff0c\u6807\u5ea6\u56e0\u5b50\u7684\u503c\u5b58\u5728\u67d0\u79cd\u7ea6\u675f\uff0c\u5982\u8fd9\u4e9b\u8d85\u7ebf\u6027\u548c\u4e9a\u7ebf\u6027\u6307\u6570\u52a0\u8d77\u6765\u7ea6\u7b49\u4e8e2\u3002<\/span><\/p>\n


<\/p>\n

\u4f46\u662f\uff0c\u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\uff1f\u672c\u6587\u8bd5\u56fe\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u5e76\u91cd\u70b9\u56de\u987e\u901a\u8fc7\u67d0\u79cd\u8d85\u8d8a\u7ecf\u9a8c\u7279\u5f81\u7684\u6570\u5b66\u6a21\u578b\u6765\u8bf4\u660e\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u51fa\u73b0\u76f8\u5173\u8bba\u6587\u3002\u8fd9\u91cc\u8ba8\u8bba\u7684\u8bb8\u591a<\/span>\uff08\u4f46\u4e0d\u662f\u5168\u90e8\uff09<\/span>\u6a21\u578b\u90fd\u662f\u5efa\u7acb\u5728\u793e\u4f1a\u7ecf\u6d4e\u6d3b\u52a8\u662f\u7531\u4eba\u53e3\u3001\u57ce\u5e02\u51e0\u4f55\u548c\u4eba\u4e0e\u4eba\u4e92\u52a8\u53ef\u80fd\u6027\u7684\u591a\u91cd\u7ec4\u5408\u7684\u7ed3\u679c\u8fd9\u4e00\u7406\u5ff5\u4e4b\u4e0a\u7684\u3002\u524d\u63d0\u662f\u4e92\u52a8\uff0c\u4ee5\u53ca\u968f\u4e4b\u800c\u6765\u7684\u77e5\u8bc6\u4ea4\u6d41\uff0c\u4ece\u800c\u4ea7\u751f\u521b\u65b0\u3001\u7ecf\u6d4e\u589e\u957f\u3001\u6536\u76ca\u9012\u589e\u548c\u89c4\u6a21\u7ecf\u6d4e\u3002\u5728\u4e00\u4e9b\u6a21\u578b\u4e2d\uff0c\u57ce\u5e02\u7684\u51e0\u4f55\u548c\u7f51\u7edc\u5c5e\u6027\u4e5f\u5728\u89e3\u91ca\u89c2\u5bdf\u5230\u7684\u89c4\u6a21\u6cd5\u5219<\/span>\u65b9\u9762\u53d1\u6325\u4e86\u91cd\u8981\u4f5c\u7528\uff0c\u56e0\u4e3a\u4eba\u7c7b\u7684\u4e92\u52a8\u5f3a\u70c8\u4f9d\u8d56\u4e8e\u57ce\u5e02\u7684\u7a7a\u95f4\u7ed3\u6784\u3002\u7531\u4e8e\u81ea\u7136\u56e0\u7d20\uff0c\u5982\u5d0e\u5c96\u7684\u5730\u5f62\u6216\u7269\u7406\u5c4f\u969c<\/span>\uff08\u5c71\u8109\u3001\u6cb3\u6d41\u3001\u6e56\u6cca\u7b49\uff09<\/span>\u7684\u5b58\u5728\uff0c\u5bfc\u81f4\u57ce\u5e02\u67d0\u4e9b\u90e8\u5206\u7684\u9694\u79bb\u3002\u6b64\u5916\uff0c\u4eba\u5de5\u56e0\u7d20\uff0c\u5982\u8857\u9053\u7f51\u7edc\u7684\u51e0\u4f55\u5f62\u72b6\u6216\u57ce\u5e02\u7684\u5f62\u72b6\uff0c\u4e5f\u4f1a\u5f71\u54cd\u4eba\u7c7b\u7684\u4e92\u52a8\u3002<\/span><\/p>\n


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

\u5728\u8fc7\u53bb\u7684\u51e0\u5e74\u91cc\uff0c\u5927\u91cf\u7684\u8bba\u6587\u81f4\u529b\u4e8e\u4ecb\u7ecd\u6709\u5173\u8fd9\u79cd\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u7ecf\u9a8c\u548c\u7406\u8bba\u8bc1\u636e\u3002\u4f46\u672c\u6587\u53ea\u9009\u62e9\u4ecb\u7ecd\u90a3\u4e9b\u89e3\u91ca\u6216\u63a8\u5bfc\u51fa\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u6a21\u578b\uff0c\u7279\u522b\u5173\u6ce8\u90a3\u4e9b\u4ece\u6570\u5b66\u4e0a\u63a8\u5bfc\u51fa\u7684\u6a21\u578b\u3002\u672c\u6587\u8fd8\u65e8\u5728\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u8fc7\u7a0b\u4e2d\uff0c\u89c2\u5bdf\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u76f8\u4e92\u8054\u7cfb\uff0c\u662f\u5426\u6709\u53ef\u80fd\u5728\u4e0d\u540c\u7684\u65b9\u6cd5\u4e2d\u770b\u5230\u4e00\u4e9b\u5171\u540c\u7684\u5c5e\u6027\uff0c\u4ee5\u53ca\u786e\u5b9a\u5b83\u4eec\u6709\u54ea\u4e9b\u5171\u540c\u7684\u5047\u8bbe\u548c\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u8fd9\u4e9b\u6a21\u578b\u8fdb\u884c\u4e86\u5206\u7c7b\uff0c\u8bc6\u522b\u51fa\u5177\u6709\u76f8\u540c\u57fa\u672c\u601d\u60f3\u7684\u6a21\u578b\u7ec4\uff0c\u5982\u56fe1\u548c\u88681\u6240\u793a\u3002<\/span><\/p>\n


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

\u672c\u6587\u4ecb\u7ecd\u7684\u6a21\u578b\u5206\u4e3a\u4e24\u7c7b\uff1a\u57ce\u5e02\u5185\u90e8\u6a21\u578b\u548c\u57ce\u5e02\u95f4\u6a21\u578b\u3002\u57ce\u5e02\u5185\u90e8\u6a21\u578b\u6307\u7684\u662f\u53ea\u8003\u8651\u57ce\u5e02\u5185\u90e8\u56e0\u7d20\u6765\u89e3\u91ca\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u6a21\u578b\u3002\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684\u4e92\u52a8\uff0c\u4ee5\u53ca\u57ce\u5e02\u51e0\u4f55\u548c\u7a7a\u95f4\u5206\u5e03\u5982\u4f55\u4ea7\u751f\u5f71\u54cd\uff0c\u662f\u89e3\u91ca\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u4e3b\u8981\u5185\u5bb9\u3002\u5728\u8fd9\u4e2a\u7c7b\u522b\u4e2d\uff0c\u6240\u6709\u7684\u5f15\u529b\u6a21\u578b\u90fd\u4ee3\u8868\u4e86\u4e00\u822c\u5f62\u5f0f\u5316\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/span><\/p>\n


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

\u7b2c\u4e8c\u7c7b\u662f\u5173\u4e8e\u57ce\u5e02\u95f4\u7684\u6a21\u578b\uff0c\u8fd9\u7c7b\u6a21\u578b\u8003\u8651\u5728\u57ce\u5e02\u4e4b\u95f4\u4ea4\u6362\u67d0\u79cd\u4fe1\u606f\u6765\u89e3\u91ca\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u51fa\u73b0\u3002\u5e76\u975e\u6240\u6709\u7684\u6a21\u578b\u90fd\u5bfc\u81f4\u4e86\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u51fa\u73b0\uff0c\u5b83\u4eec\u88ab\u5305\u62ec\u5728\u5185\u662f\u4e3a\u4e86\u66f4\u597d\u5730\u5c55\u793a\u57ce\u5e02\u95f4\u6a21\u578b\u8fd9\u4e2a\u4e0d\u592a\u6210\u719f\u7684\u7814\u7a76\u9886\u57df\u3002\u4e3a\u89e3\u91ca\u89c4\u6a21\u6cd5\u5219<\/span>\u800c\u63d0\u51fa\u7684\u4e3b\u8981\u673a\u5236\u6709\u9f50\u592b\u5b9a\u5f8b\u3001\u7b49\u7ea7\u7ec4\u7ec7\u548c\u4e0d\u540c\u57ce\u5e02\u7684\u4eba\u4eec\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002<\/span><\/p>\n


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

<\/p>\n

\u56fe1\uff1a\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219\u6a21\u578b\u7684\u5206\u7c7b<\/span><\/p>\n


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

<\/section>\n
\u56fe2\uff1a\u89e3\u91ca\u57fa\u672c\u5f02\u901f\u751f\u957f\u548c\u57fa\u7840\u8bbe\u65bd\u57ce\u5e02\u89c4\u6a21\u7684\u6a21\u578b\u5206\u7c7b<\/span><\/section>\n


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 <\/span><\/section>\n

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<\/section>\n

<\/section>\n
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<\/svg><\/section>\n<\/section>\n<\/section>\n
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\u4e8c\u3001\u57ce\u5e02\u5185\u90e8\u6a21\u578b<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u5728\u8fc7\u53bb\u7684\u51e0\u5e74\u91cc\u5927\u91cf\u7684\u5de5\u4f5c\u8ba4\u4e3a\u57ce\u5e02\u53d8\u91cf\u53d6\u51b3\u4e8e\u4eba\u53e3\u89c4\u6a21N<\/em>\uff0c\u800c\u6ca1\u6709\u5fc5\u8981\u7eb3\u5165\u5176\u4ed6\u53d8\u91cf\u6216\u751a\u81f3\u6765\u81ea\u90bb\u8fd1\u57ce\u5e02\u7684\u4fe1\u606f\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u80cc\u540e\u7684\u4e3b\u8981\u60f3\u6cd5\u662f\uff0c\u57ce\u5e02\u53d8\u91cf\u7684\u7ed3\u679c\u53ea\u662f\u57ce\u5e02\u5185\u90e8\u8fc7\u7a0b\u7684\u7ed3\u679c\u3002\u7136\u800c\uff0c\u57ce\u5e02\u4e4b\u95f4\u662f\u4e0d\u65ad\u4e92\u52a8\u7684\uff0c\u57ce\u5e02\u6307\u6807\u5bf9\u4eba\u53e3\u89c4\u6a21\u7684\u4f9d\u8d56\u53ef\u80fd\u4ec5\u4ec5\u662f\u4e00\u4e2a\u6210\u529f\u7684\u4e00\u9636\u8fd1\u4f3c\u8868\u73b0\u3002\u8fd9\u4e00\u8282\u4f7f\u7528\u57ce\u5e02\u7684\u5185\u751f\u56e0\u7d20\u4ecb\u7ecd\u4e86\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u8d77\u6e90\u7684\u6570\u5b66\u6a21\u578b\uff0c\u6b64\u5904\u5c06\u57ce\u5e02\u5185\u90e8\u7684\u6a21\u578b\u5206\u4e3a\u4e24\u7c7b\u3002\u7b2c\u4e00\u7c7b\u8003\u8651\u4e86\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684\u4e92\u52a8\uff0c\u4ee5\u89e3\u91ca\u975e\u7ebf\u6027\u7684\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u3002\u7b2c\u4e8c\u7c7b\u5219\u8ba4\u4e3a\u5f53\u57ce\u5e02\u4e2d\u5b58\u5728\u4e00\u4e9b\u5fc5\u8981\u7684\u8865\u5145\u56e0\u7d20\u65f6\uff0c\u5c31\u4f1a\u51fa\u73b0\u975e\u7ebf\u6027\u7684\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u3002<\/span><\/p>\n


<\/p>\n

\n
\n
\n

1 \u57fa\u4e8e\u4eba\u7c7b\u4e92\u52a8\u7684\u6a21\u578b<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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<\/p>\n<\/section>\n

1.1 \u57fa\u4e8e\u4eba\u9645\u4e92\u52a8\u7684\u6a21\u578b<\/span><\/strong><\/h3>\n


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

\u5927\u591a\u6570\u73b0\u6709\u7814\u7a76\u90fd\u8ba4\u4e3a\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684\u4e92\u52a8\u662f\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u51fa\u73b0\u7684\u4e3b\u8981\u673a\u5236\u3002\u5047\u8bbe\u57ce\u5e02\u662f\u7531\u5c45\u4f4f\u5728\u5efa\u6210\u533a\u57dfA= L2<\/sup><\/em>\u4e2d\u7684N<\/em>\u4e2a\u57ce\u5e02\u4eba\u53e3\u7ec4\u6210<\/span>\uff08\u5982\u56fe3\uff09<\/span>\u3002\u5f53\u4e24\u4e2a\u4eba\u5728\u57ce\u5e02\u76f8\u9047\u65f6\uff0c\u4ed6\u4eec\u4ea7\u751f\u7684\u60f3\u6cd5\u5bf9\u5e94\u4e8e\u793e\u4f1a\u7ecf\u6d4e\u6d3b\u52a8\u7684\u6570\u91cfg<\/em>\u3002\u4f8b\u5982\uff0cg<\/em>\u53ef\u4ee5\u4ee3\u8868\u4e13\u5229\u7684\u6570\u91cf\uff0c\u8d22\u5bcc\u7684\u6570\u91cf\u7b49\u7b49\u3002\u5982\u679c\u4e2a\u4f53i<\/em>\u4e0eki<\/sub><\/em>\u4e2a\u4f53\u4e92\u52a8\uff0c\u5219\u8fd9\u4e9b\u4ea4\u4e92\u4ea7\u751f\u8d22\u5bcc\u603b\u91cfgki<\/sub><\/em>\u3002\u5728\u4e0d\u4e27\u5931\u4e00\u822c\u6027\u7684\u60c5\u51b5\u4e0b\uff0cki<\/sub><\/em>\u53ef\u4ee5\u4ee3\u8868\u4e2a\u4f53\u8054\u7cfb\u4eba<\/span>\uff08\u670b\u53cb\u3001\u540c\u4e8b\u6216\u968f\u673a\u76f8\u9047\uff09<\/span>\u7684\u6570\u91cf\uff0c\u6216\u4ed6\/\u5979\u5728\u7279\u5b9a\u65f6\u671f\u7684\u4e92\u52a8\u6570\u91cf\uff0c\u751a\u81f3\u662f\u590d\u6742\u7f51\u7edc\u4e2d\u7684\u8282\u70b9\u5ea6\u3002<\/span><\/p>\n


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

<\/p>\n

\u56fe3\uff1a\u62c9\u592b\u62c9\u65af\u5e02\uff08Lavras\uff0c\u5df4\u897f\uff09\u53ca\u5176\u5468\u8fb9\u5730\u533aA<\/em>\uff0c\u7531\u4e00\u4e2a\u8fb9\u957f\u4e3aL<\/em>\u7684\u6b63\u65b9\u5f62\u5305\u56f4\u3002<\/span><\/p>\n


<\/p>\n

\u5982\u56fe3\u6240\u793a\uff0c\u4e00\u4e2a\u7279\u5b9a\u793e\u4f1a\u7ecf\u6d4e\u53d8\u91cf\u7684\u5168\u5e02\u603b\u91cfY<\/em>\u53ef\u4ee5\u7406\u89e3\u4e3a\u6240\u6709\u4e2a\u4f53\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fa\u7684\u603b\u548c\uff0c\u800c\u4e2a\u4eba\u7684\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fay<\/em>\u662f\u5355\u4e2a\u4eba\u4e92\u52a8\u4ea7\u751f\uff0c\u5373\u4ea4\u4e92\u4ea7\u751f\u7684\u6570\u91cf\u4e58\u4ee5\u603b\u7684\u4e92\u52a8\u6b21\u6570y<\/em>=gki<\/sub><\/em>\u3002\u73b0\u6709\u6587\u732e\u6a21\u578b\u7684\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\uff0c\u5b83\u4eec\u8ba1\u7b97\/\u786e\u5b9a\u4e2a\u4eba\u7684\u5e73\u5747\u4e92\u52a8\u6b21\u6570ki<\/sub><\/em>\uff0c\u4ee5\u53ca\u7531\u6b64\u4ea7\u751f\u7684\u793e\u4f1a\u7ecf\u6d4e\u8d22\u5bcc\u7684\u6570\u91cfg<\/em>\u3002<\/span><\/p>\n


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

\u4e0b\u9762\u4ecb\u7ecd\u7684\u6a21\u578b\u7684\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\uff0c\u5b83\u4eec\u662f\u5982\u4f55\u8ba1\u7b97\u4e2a\u4eba\u7684\u5e73\u5747\u63a5\u89e6\u5bc6\u5ea6\uff08nc<\/sub><\/em>\uff09\u7684\uff0c\u4ece\u800c\u8ba1\u7b97\u51fa\u8fd9\u4e9b\u63a5\u89e6\u4ea7\u751f\u7684\u793e\u4f1a\u7ecf\u6d4e\u8d22\u5bcc\u3002<\/strong>\u6240\u8003\u8651\u7684\u6a21\u578b\u57fa\u672c\u4e0a\u670d\u4ece\u4e8e\u4ee5\u4e0b\u63cf\u8ff0\uff0c\u7279\u5b9a\u793e\u4f1a\u7ecf\u6d4e\u53d8\u91cf\u7684\u603b\u7ed3\u679cY<\/em>\u53ef\u4ee5\u7406\u89e3\u4e3a\u8be5\u57ce\u5e02\u6240\u6709\u4e2a\u4f53\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fa\u7684\u603b\u548c\uff0c\u5373Y = Ny<\/em>\u3002\u53cd\u8fc7\u6765\uff0c\u4e2a\u4f53\u7684\u793e\u4f1a\u7ecf\u6d4e\u751f\u4ea7y<\/em>\u662f\u7531\u5355\u4e00\u4e92\u52a8\uff08g<\/em>\uff09\u4ea7\u751f\u7684\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fa\u4e58\u4ee5\u6bcf\u4e2a\u4e2a\u4f53\u7684\u4e92\u52a8\u603b\u6570\uff08ki<\/sub><\/em>\uff09\u7684\u7ed3\u679c\uff0c\u4ece\u800c\u4ea7\u751f\u4e86Y = gN ki<\/sub> = gN2<\/sup>nc<\/sub><\/em>\u7684\u5173\u7cfb\u3002<\/span><\/p>\n


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

<\/p>\n

\u56fe4\uff1a\u5c06\u57ce\u5e02\u6807\u5ea6\u89c6\u4e3a\u901a\u8fc7\u4eba\u7c7b\u4e92\u52a8\u8fdb\u884c\u77e5\u8bc6\u4ea4\u6362\u7684\u7ed3\u679c\u7684\u6a21\u578b\u3002<\/span><\/p>\n


<\/p>\n

\u53ef\u4ee5\u63a8\u5bfc\u51fa\uff0cnc<\/sub><\/em> <\/sub>\u2261ki<\/sub> \/N <\/em>\uff0c\u5f53\u6211\u4eec\u5047\u8bbe\u5355\u4e00\u4e92\u52a8\u4ea7\u51fag <\/em>\u4e0e\u4eba\u53e3\u89c4\u6a21\u65e0\u5173\u65f6\uff08a \u223c N0<\/sup><\/em>\uff09\uff0c\u5219Y \u223c N2<\/sup> nc<\/sub><\/em>\uff0c\u5bf9\u6bd4\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u7ecf\u9a8c\u516c\u5f0f<\/sub><\/span>\uff0c\u5176\u4e2d <\/sub><\/span><\/sub><\/em>\u2261 1.15<\/span>\uff08\u8fd1\u4f3c\uff09<\/span>\u4e3a\u793e\u4f1a\u7ecf\u6d4e\u6807\u5ea6\u56e0\u5b50\u7684\u7ecf\u9a8c\u503c\uff0c\u8868\u660e\u63a5\u89e6\u7684\u5e73\u5747\u5bc6\u5ea6\u5fc5\u987b\u670d\u4ece\u5e42\u5f8b<\/sub><\/span>\u3002\u6211\u4eec\u4e5f\u53ef\u4ee5\u7528<\/sub><\/span>\u22610.85\u6765\u8fd1\u4f3c\u8868\u793a\u57fa\u7840\u8bbe\u65bd\u6807\u5ea6\u56e0\u5b50\u7684\u7ecf\u9a8c\u503c\u3002\u8fd9\u4e24\u4e2a\u6807\u5ea6\u6307\u6570\u4e4b\u95f4\u5b58\u5728\u67d0\u79cd\u4e92\u8865\u5173\u7cfb\uff0c\u5373<\/sub><\/span>\u3002\u56e0\u6b64\uff0c<\/sub><\/span>\u3002<\/em>\u5f53\u7136\uff0c\u5230\u76ee\u524d\u4e3a\u6b62\u4ee5\u4e0a\u63a8\u5bfc\u90fd\u662f\u63a8\u6d4b\u6027\u8d28\u7684\uff0c\u4ee3\u8868\u4e86\u4e00\u79cd\u201c\u7ecf\u9a8c\u6cd5\u5219\u201d\uff0c\u5373\u57fa\u4e8e\u76f8\u4e92\u4f5c\u7528\u7684\u6a21\u578b\u5728\u5b9a\u91cf\u89e3\u91ca\u89c4\u6a21\u6cd5\u5219<\/span>\u65f6\u9700\u8981\u9075\u5b88\u7684\u5047\u8bbe\u3002\u4efb\u4f55\u57fa\u4e8e\u76f8\u4e92\u4f5c\u7528\u7684\u6a21\u578b\u7684\u63a5\u89e6\u5bc6\u5ea6\u548c\u7531\u6b64\u4ea7\u751f\u7684\u76f8\u4e92\u4f5c\u7528\u7684\u6982\u7387\u5fc5\u987b\u7b26\u5408\u4ee5\u4e0a\u516c\u5f0f\uff0c\u4ee5\u4fbf\u4e0e\u7ecf\u9a8c\u4e0a\u4fdd\u6301\u4e00\u81f4\u3002\u88681\u603b\u7ed3\u4e86\u63a5\u4e0b\u6765\u8981\u4ecb\u7ecd\u7684\u6a21\u578b\uff0c\u5e76\u5217\u51fa\u4e86\u7ec4\u7ec7\u5b83\u4eec\u7684\u4e3b\u8981\u673a\u5236\uff0c\u4ee5\u53ca\u5b83\u4eec\u6240\u9884\u6d4b\u7684\u6807\u5ea6\u56e0\u5b50\u3002\u5177\u4f53\u5230\u57fa\u4e8e\u4e92\u52a8\u7684\u6a21\u578b\uff0c\u5b83\u4eec\u90fd\u5305\u62ec\u8ba1\u7b97\u4eba\u4eec\u7684\u5e73\u5747\u63a5\u89e6\u6b21\u6570\uff0c\u800c\u8fd9\u4e2a\u6570\u91cf\u53c8\u53d6\u51b3\u4e8e\u6bcf\u4e2a\u6a21\u578b\u4e2d\u4f7f\u7528\u7684\u53c2\u6570\u3002<\/span><\/p>\n


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<\/p>\n

\u88681\uff1a\u89e3\u91ca\u57ce\u5e02\u975e\u7ebf\u6027\u89c4\u6a21\u6cd5\u5219\u7684\u6a21\u578b\u7684\u4e3b\u8981\u7279\u5f81<\/span><\/p>\n


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1.2 \u4eba\u7c7b\u4e92\u52a8\u7684\u6a2a\u622a\u9762\u6a21\u578b\uff08<\/span><\/strong>Bettencourt<\/span><\/strong>\uff09<\/span><\/strong><\/h3>\n


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

Bettencourt\u63d0\u51fa\u7684\u6a21\u578b\u53ef\u80fd\u662f\u6700\u6709\u5f71\u54cd\u529b\u7684\u7528\u4e8e\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219\u8d77\u6e90\u7684\u6a21\u578b\u3002\u8be5\u6a21\u578b\u4e0e\u7269\u7406\u5b66\u4e2d\u4f7f\u7528\u7684\u6a2a\u622a\u9762\u6982\u5ff5\u6709\u76f8\u4f3c\u4e4b\u5904<\/span>\uff08\u6ce8\uff1a\u7269\u7406\u5b66\u4e2d\u6d4b\u91cf\u7c92\u5b50\u78b0\u649e\u6982\u7387\u7684\u91cf\u662f\u6a2a\u622a\u9762\uff09<\/span>\u3002\u5b83\u8ba4\u4e3a\u6bcf\u4e2a\u4eba\u5728\u6574\u4e2a\u57ce\u5e02\u4e2d\u79fb\u52a8\uff0c\u89c4\u5b9a\u4e86\u4e00\u4e2a\u4e92\u52a8\u534a\u5f84\u4e3a<\/span>lo<\/sub><\/em>\uff0c\u957f\u5ea6\u4e3a<\/span>l<\/em>\u7684\u8f68\u8ff9\uff0c\u8fd9\u610f\u5473\u7740\u8fd9\u4e2a\u4eba\u5728\u4ed6\/\u5979\u7684\u8f68\u8ff9\u4e2d\u8fdb\u5165\u4e86\u57ce\u5e02\u7684\u4e00\u4e2a\u533a\u57df<\/span>a =lo<\/sub><\/em>\u00b7<\/span> l<\/em>\uff0c\u5219\u63a5\u89e6\u5bc6\u5ea6<\/span>nc <\/sub><\/em>\u5c31\u7b49\u4e8e\u4e2a\u4eba\u53ef\u8bbf\u95ee\u7684\u533a\u57df\u9664\u4ee5\u6574\u4e2a\u57ce\u5e02\u533a\u57df\uff0c\u5373<\/span>nc<\/sub> = a\/A<\/em>\u3002\u4e3a\u7b80\u5355\u8d77\u89c1\uff0c\u6b64\u65f6\u8003\u8651\u57ce\u5e02\u7684\u8fb9\u754c\u533a\u57dfA\uff0c\u5229\u7528\u7ecf\u9a8c\u516c\u5f0f<\/sub><\/span>\uff0c\u5e76\u8bb0\u4f4f\u53ef\u8fbe\u533a\u57df\u662f\u4e2a\u4f53\u7684\u56fa\u6709\u5c5e\u6027\uff0c\u56e0\u6b64\u662f\u65e0\u6807\u5ea6\u7684\uff08<\/span>a \u223c N0<\/sup><\/em>\uff09\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u4ee5\u4e0b\u5173\u7cfb<\/span>Y~N2<\/sup><\/em>\/A \u3002<\/em>\u4e3a\u4e86\u5f97\u5230\u66f4\u7cbe\u786e\u7684\u4f30\u8ba1\uff0cBettencourt \u4f7f\u7528\u4e86\u5efa\u6210\u533a\u57dfA<\/span>n<\/sub>\u6765\u4ee3\u66ff\u8fb9\u754c\u533a\u57dfA\uff0c\u5e76\u4e14\u5f15\u5165\u4e86\u4e2a\u4f53\u5e73\u5747\u8ddd\u79bb<\/span>\u03bb<\/em>\u548c\u4e2a\u4f53\u5bc6\u5ea6<\/span>\u03c1<\/em>\uff0c\u8fd9\u4e24\u4e2a\u53c2\u6570\u901a\u8fc7<\/span>\u03c1= N\/A = 1\/\u03bb2<\/sup><\/em>\u7684\u5173\u7cfb\u8054\u7cfb\u8d77\u6765\u3002\u901a\u8fc7\u4f30\u8ba1\u5f97\u5230<\/span><\/sub><\/span><\/em>\uff0c\u8fd9\u8868\u660e\u4e2a\u4f53\u95f4\u7684\u5e73\u5747\u8ddd\u79bb\u968f\u7740\u57ce\u5e02\u89c4\u6a21\u7684\u589e\u5927\u800c\u51cf\u5c0f\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6b63\u5982\u5b9e\u8bc1\u7814\u7a76\u8868\u660e\u7684\u90a3\u6837\uff0c\u5927\u57ce\u5e02\u7684\u4eba\u53e3\u5bc6\u5ea6\u6bd4\u5c0f\u57ce\u5e02\u8981\u5927\u3002\u4e8e\u662f\uff0c\u53ef\u4ee5\u4f30\u8ba1\u51fa<\/span><\/span>\u03b2super<\/sub><\/span><\/span><\/em>=7\/6<\/span>\uff0c\u03b2sup<\/sub><\/span><\/span><\/em>=5\/6<\/span>\uff0c\u4e0e\u7ecf\u9a8c\u503c\u76f8\u8fd1\u3002<\/span><\/p>\n


<\/p>\n

\u603b\u4e4b\uff0cBettencourt\u7684\u6a21\u578b\u5b9a\u91cf\u5730\u9884\u6d4b\u4e86\u7ecf\u9a8c\u7684\u6807\u5ea6\u56e0\u5b50\u3002\u8fd9\u662f\u975e\u5e38\u4e86\u4e0d\u8d77\u7684\uff0c\u56e0\u4e3a\u8be5\u6a21\u578b\u662f\u57fa\u4e8e\u76f8\u5f53\u5177\u4f53\u7684\u5047\u8bbe\u7684\u3002\u4f8b\u5982\uff0c\u8be5\u6a21\u578b\u5c06\u8fb9\u754c\u533a\u57df\u4f5c\u4e3a\u57fa\u7840\u8bbe\u65bd\u7684\u66ff\u4ee3\u53d8\u91cf\uff0c\u800c\u6ca1\u6709\u8003\u8651\u57fa\u7840\u8bbe\u65bd\u7684\u6570\u91cf\u3002\u4f46\u662f\uff0c\u8be5\u6a21\u578b\u6ca1\u6709\u8003\u8651\u5efa\u7b51\u7269\uff0c\u5982\u679c\u8003\u8651\u8fd9\u4e2a\u56e0\u7d20\u5c06\u4f7f\u4e92\u52a8\u8303\u56f4\u4ece\u4e8c\u7ef4\u6269\u5c55\u5230\u4e09\u7ef4\u3002\u56e0\u6b64\u4e0b\u9762\u7684\u6a21\u578b\u4f1a\u5bf9\u8fd9\u4e00\u95ee\u9898\u4f5c\u8fdb\u4e00\u6b65\u8ba8\u8bba\u3002<\/span><\/p>\n


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

1.3 \u57fa\u4e8e\u76f8\u4e92\u534f\u4f5c\u6a21\u578b\uff08<\/span><\/strong>Yang\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/h3>\n


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

Yang\u7b49\u4eba\u5c06\u8d85\u7ebf\u6027\u6807\u5ea6\u89e3\u91ca\u4e3a\u5728\u57ce\u5e02\u4e2d\u627e\u5230\u6240\u9700\u5408\u4f5c\u53ef\u80fd\u6027\u7684\u7ed3\u679c\uff0c\u8fd9\u662f\u4e00\u9879\u4e8b\u4e1a\u7684\u5fc5\u8981\u6761\u4ef6\u3002\u8003\u8651\u5230\u67d0\u4e00\u4ea7\u54c1\u7684\u5f00\u53d1\u9700\u8981 q+1 <\/em>\u540d\u4e13\u5bb6\uff0cq=0<\/em>\u65f6\u60c5\u51b5\u610f\u5473\u7740\u4e00\u4e2a\u4eba\u53ef\u4ee5\u5b8c\u6210\u8fd9\u79cd\u6d3b\u52a8\u7684\u6240\u6709\u5fc5\u8981\u8fc7\u7a0b\u3002\u672c\u6587\u4ecb\u7ecd\u7684\u5176\u4ed6\u6570\u5b66\u6a21\u578b\u4e2d\uff0c\u5982Bettencourt\u6a21\u578b\u548c\u4e0b\u4e00\u8282\u4ecb\u7ecd\u7684\u5f15\u529b\u6a21\u578b\uff0c\u6d3b\u52a8\u548c\u751f\u4ea7\u529b<\/span>\uff08\u6211\u4eec\u79f0\u4e4b\u4e3ag\uff09<\/span>\u9700\u8981\u4e24\u4e2a\u4eba\uff0c\u4e5f\u5c31\u662fq=1<\/em>\u3002\u4f5c\u8005\u5c06pq<\/sub>(ki<\/sub>)<\/em>\u4ecb\u7ecd\u4e3a\u4e00\u4e2a\u4ebai<\/em>\u5728ki<\/sub><\/em>\u63a5\u89e6\u4e2d\u627e\u5230\u6240\u6709q<\/em>\u4e2a\u5408\u4f5c\u8005\u7684\u6982\u7387\u3002\u90a3\u4e48\uff0c\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fa\u53ef\u4ee5\u5b9a\u4e49\u4e3aY<\/em> \u223c N pq<\/sub>(<\/em><ki<\/sub>>)<\/em>, \u5176\u4e2dki<\/sub><\/em>\u662f\u5c45\u4f4f\u5728\u8be5\u57ce\u5e02\u7684\u4e00\u4e2a\u4eba\u7684\u5e73\u5747\u552f\u4e00\u8054\u7cfb\u4eba\u6570\u91cf\uff0c\u8868\u660epq<\/sub>(<ki<\/sub>>) \u223c <\/em><ki<\/sub>>q<\/sup><\/em>\u3002\u4e8e\u662f\u53ef\u4ee5\u63a8\u5bfc\u5f97\u51fa\uff1a<\/span><\/p>\n


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<\/p>\n


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\u4ece\u8fd9\u4e2a\u7ed3\u679c\u53ef\u4ee5\u63a8\u65ad\u51fa\u4e00\u4e9b\u542b\u4e49\u3002\u9996\u5148\uff0c\u8d85\u7ebf\u6027\u89c4\u6a21\u6cd5\u5219<\/span>\u51fa\u73b0\u7684\u4e00\u4e2a\u5fc5\u8981\u6761\u4ef6\u662f\uff0c\u5728\u8f83\u5927\u7684\u57ce\u5e02\uff0c\u63a5\u89e6\u7684\u4eba\u6570\u66f4\u591a\u3002\u5176\u6b21\uff0c\u5b58\u5728\u9700\u8981\u67091\u4e2a\u4eba\u4ee5\u4e0a\uff08\u5373q>0\uff09\u5408\u4f5c\u624d\u80fd\u5b8c\u6210\u7684\u4e8b\u4e1a\u3002\u867d\u7136\u5b58\u5728\u4e00\u4e2a\u53ef\u4ee5\u5355\u72ec\u5b8c\u6210\u7684\u4e8b\u4e1a\uff08q = 0\uff09\uff0c\u4f46\u4f1a\u4ea7\u751f\u4e00\u4e2a\u7ebf\u6027\u6807\u5ea6\u56e0\u5b50\u03b2super<\/sub><\/span><\/span><\/em>=<\/span>1\uff0c\u610f\u5473\u7740\u5982\u679c\u4e00\u4e2a\u4eba\u4e0d\u9700\u8981\u5408\u4f5c\u6765\u5b8c\u6210\u67d0\u4ef6\u4e8b\u60c5\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6d3b\u52a8\u7684\u603b\u91cf\u5c31\u4f1a\u5f88\u5feb\u6269\u5927\uff0c\u800c\u4e0d\u4f1a\u51fa\u73b0\u89c4\u6a21\u6536\u76ca\u7684\u589e\u52a0\u3002\u5728\u8fd9\u4e2a\u610f\u4e49\u4e0a\uff0c\u89c4\u6a21\u6536\u76ca\u9012\u589e\u5f52\u56e0\u4e8eq>0\u7684\u4e8b\u4e1a\u3002\u56e0\u6b64\uff0c\u9700\u8981\u66f4\u591a\u5408\u4f5c\u8005\u7684\u57ce\u5e02\u4ea7\u51fa\u53d8\u91cf\u4f1a\u51fa\u73b0\u66f4\u660e\u663e\u7684\u8d85\u7ebf\u6027\u6807\u5ea6\u3002<\/span><\/p>\n


<\/p>\n

1.4 \u5f15\u529b\u6a21\u578b<\/span><\/strong><\/h3>\n


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

\u5f15\u529b\u6a21\u578b\u662f\u5229\u4e2a\u4f53\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u8ddd\u79bb\u8870\u51cf\u6548\u5e94\u6765\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\uff0c\u7c7b\u4f3c\u4e8e\u4e24\u4e2a\u5927\u8d28\u91cf\u7269\u4f53\u7684\u725b\u987f\u5f15\u529b\u3002\u5f15\u529b\u6a21\u578b\u6709\u5f88\u591a\u79cd\u5b9a\u4e49\u65b9\u5f0f\uff0c\u4f46\u5b83\u4eec\u5b58\u5728\u901a\u7528\u7684\u6982\u5ff5\u3002\u672c\u6587\u628adN(r)<\/em>\u8868\u793a\u4e3a\u5d4c\u5165D\u7ef4\u7a7a\u95f4\u7684\u8d85\u4f53\u79ef\u5143\u7d20<\/span>\uff08hyper-volume element\uff09<\/span>dr<\/em>\u5185\u4e2a\u4f53\u7684\u6570\u91cf\u3002\u4f8b\u5982\uff0c\u5f53D=2\uff0c\u8fd9\u4e2a\u8d85\u4f53\u79ef\u5143\u7d20\u5c31\u662f\u4e00\u4e2a\u4e8c\u7ef4\u5e73\u9762\uff1b\u5982\u679cD=3\uff0c\u5c31\u662f\u4e00\u4e2a\u4e09\u7ef4\u4f53\u79ef\u3002\u6b64\u5916\uff0c r<\/em>\u662f\u4ece\u4e2a\u4f53i<\/em>\u6307\u5411\u8d85\u4f53\u79efdr<\/em>\u4e2d\u7684\u4e2a\u4f53\u7684\u4e00\u4e2a\u77e2\u91cf\u3002\u8fd9\u4e2a\u77e2\u91cf\u53ef\u4ee5\u7528\u4e24\u79cd\u65b9\u5f0f\u6765\u89e3\u91ca\uff0c\uff08i\uff09\u4f5c\u4e3aD\u7ef4\u4e2d\u7684\u4f4d\u7f6e\u77e2\u91cf\uff0c\u56e0\u6b64\u5b83\u7684\u6a21\u662f\u6b27\u6c0f\u8ddd\u79bbr<\/em><\/span>\uff08\u5982\u56fe5\uff09<\/span>\uff1b\u6216\u8005\uff08ii\uff09\u4f5c\u4e3a\u5728\u590d\u6742\u7f51\u7edc\u5185\u5206\u9694\u4efb\u4f55\u4e24\u4e2a\u4e2a\u4f53\u7684\u975e\u6b27\u6c0f\u8ddd\u79bb\u3002\u6709\u4e86\u8fd9\u4e9b\u91cf\u7684\u5b9a\u4e49\uff0c\u5c31\u53ef\u4ee5\u8ba1\u7b97\u51fa\u57ce\u5e02\u4e2d\u7684\u4e2a\u4f53\u603b\u6570\u4e3a<\/sub><\/span>\uff0c\u548cr<\/em>\u5904\u7684\u4e2a\u4f53\u5bc6\u5ea6\u4e3a\u03c1(r)=dN(r)\/dr<\/em>\uff0c\u8fd9\u8868\u5f81\u4e86\u4eba\u53e3\u5728\u7a7a\u95f4\u4e2d\u7684\u6392\u5217\u65b9\u5f0f\u3002<\/span><\/p>\n


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

\u5f53\u6211\u4eec\u8003\u8651\u7b2ci<\/em>\u4e2a\u4e2a\u4f53\u4e0er<\/em>\u5904\u7684\u4eba\u4e92\u52a8\u7684\u6982\u7387\u65f6\uff0c\u5c31\u5f15\u5165\u4e86\u5f15\u529b\u601d\u60f3\uff0c\u90a3\u4e48\u57ce\u5e02\u4e2d\u7684\u793e\u4f1a\u7ecf\u6d4e\u603b\u4ea7\u51fa<\/sub><\/span>\u3002\u5176\u4e2d\uff0c<\/span><\/sub><\/span>\u4ee3\u8868\u4e2a\u4f53\u5728r<\/em>\u5904\u7684<\/span>\uff08\u5e73\u5747\uff09<\/span>\u4e92\u52a8\u6b21\u6570\uff0cg(r)<\/span>\u8868\u793a\u4e2a\u4f53i<\/em>\u4e0e\u4f4d\u4e8er<\/em>\u5904\u7684\u53e6\u4e00\u4e2a\u4eba\u4e92\u52a8\u6240\u4ea7\u751f\u7684\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fa\u3002\u4ee5\u4e0a\u5c31\u662f\u5f15\u529b\u6a21\u578b\u7684\u4e00\u822c\u8868\u8ff0\uff0c\u4e0d\u540c\u5f15\u529b\u6a21\u578b\u7684\u4e3b\u8981\u533a\u522b\u5728\u4e8e\u77e2\u91cfr<\/em>\u3001\u76f8\u4e92\u4f5c\u7528\u7684\u6982\u7387<\/sub><\/span>\u3001\u7528\u03c1(r)<\/em>\u8868\u793a\u4eba\u53e3\u7684\u7a7a\u95f4\u5206\u5e03\u7279\u5f81\u4ee5\u53ca\u5355\u6b21\u4ea7\u51fag(r)\u8fd9\u51e0\u4e2a\u53c2\u6570\u7684\u5b9a\u4e49\u3002<\/span><\/p>\n


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

<\/p>\n

\u56fe5\uff1a\u77e2\u91cfr<\/em>\u8868\u793a\u4e2a\u4f53i<\/em>\u548c\u8d85\u4f53\u79ef\u5143\u7d20dr<\/em>\u4e4b\u95f4\u7684\u6b27\u6c0f\u8ddd\u79bb\u3002<\/span><\/p>\n


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

\uff081\uff09\u7b80\u5355\u5f15\u529b\u6a21\u578b\uff08<\/span><\/strong>F.Ribeiro\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/h3>\n


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

Ribeiro\u7b49\u4eba\u7684\u6a21\u578b\u8ba4\u4e3a\uff0c\u4e24\u4e2a\u4e2a\u4f53\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u7684\u6982\u7387\u968f\u7740\u5b83\u4eec\u4e4b\u95f4\u7684\u6b27\u6c0f\u8ddd\u79bbr<\/em>\u7684\u5e42\u5f8b\u800c\u8870\u51cf\uff0c\u5c06\u4e92\u52a8\u6982\u7387\u5b9a\u4e49\u4e3a<\/sub><\/span>\uff0c\u5176\u4e2d\u8870\u51cf\u6307\u6570\u03b3\u662f\u6a21\u578b\u7684\u4e00\u4e2a\u53c2\u6570\uff0c\u7528\u4e8e\u6d4b\u91cf\u76f8\u4e92\u4f5c\u7528\u8303\u56f4\u3002\u8be5\u6a21\u578b\u8fd8\u8ba4\u4e3a\uff0c\u4eba\u53e3\u7a7a\u95f4\u5206\u5e03\u5f62\u6210\u4e86\u4e00\u4e2a\u5206\u5f62\u7ed3\u6784\uff0c\u5176\u5206\u5f62\u7ef4\u5ea6\u4e3aDp<\/sub><\/em>\uff0c\u5d4c\u5165\u5230\u4e00\u4e2a\u5177\u6709\u6b27\u6c0f\u7ef4\u5ea6D\u7684\u8d85\u4f53\u79ef\u4e2d\uff08\u4fdd\u6301Dp<\/sub><\/em>\u2264D\uff09\uff0c\u56e0\u6b64\u53ef\u4ee5\u5c06\u03c1(r)<\/em>\u5199\u4e3a\uff1a<\/span><\/p>\n


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

<\/p>\n


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

\u6700\u540e\uff0c\u8be5\u6a21\u578b\u8fd8\u5047\u8bbe\u6240\u6709\u7684\u4e92\u52a8\u90fd\u5177\u6709\u76f8\u540c\u7684\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fa\uff0c\u5373g(r)\u4e3a\u4e00\u4e2a\u5e38\u6570\uff0c\u6700\u7ec8\u63a8\u5bfc\u51fa<\/sub><\/span>\u3002\u8fd9\u610f\u5473\u7740\u6807\u5ea6\u56e0\u5b50\u662f\u7531\u8870\u51cf\u6307\u6570\u548c\u7fa4\u4f53\u5206\u5f62\u7ef4\u5ea6\u7684\u6bd4\u7387\u6765\u51b3\u5b9a\u7684\u3002\u6700\u8fd1\u7684\u4e00\u4e9b\u7814\u7a76\u91c7\u7528\u76f8\u540c\u65b9\u6cd5\u7814\u7a76\u80bf\u7624\u7684\u751f\u957f\uff0c\u5f97\u51fa\u4e86\u7c7b\u4f3c\u7684\u7ed3\u679c\uff0c\u8fd9\u4e2a\u6a21\u578b\u5728\u57ce\u5e02\u7cfb\u7edf\u548c\u764c\u7ec6\u80de\u7684\u4e92\u52a8\u4e4b\u95f4\u8fdb\u884c\u67d0\u79cd\u7c7b\u6bd4\u3002<\/span><\/p>\n


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

\u6839\u636e\u8fd9\u4e00\u6a21\u578b\uff0c\u793e\u4f1a\u7ecf\u6d4e\u53d8\u91cf\u7684\u8d85\u7ebf\u6027\u662f\u5b8c\u6574\u6027\u7684\u5fc5\u7136\u7ed3\u679c\u3002\u5426\u5219\uff0c\u5982\u679c\u57ce\u5e02\u662f\u7531\u5b64\u7acb\u7684\u533a\u57df\u7ec4\u6210\u7684\uff0c\u4e92\u52a8\u7684\u6570\u91cf\u4ee5\u53ca\u7531\u6b64\u4ea7\u751f\u7684\u793e\u4f1a\u7ecf\u6d4e\u6307\u6807\u5c06\u7ebf\u6027\u5730\u53d6\u51b3\u4e8e\u4eba\u53e3\u89c4\u6a21\uff0c\u800c\u4e0d\u4f1a\u589e\u52a0\u89c4\u6a21\u6536\u76ca\u3002\u6709\u8da3\u7684\u662f\uff0c\u8fd9\u4e00\u7ed3\u679c\u4e0eBettencourt\u4f7f\u7528\u7684\u8bba\u70b9\u76f8\u4e00\u81f4\uff0c\u5373\u4eba\u5747\u793e\u4f1a\u7ecf\u6d4e\u751f\u4ea7\u5fc5\u987b\u8db3\u4ee5\u652f\u4ed8\u8fd0\u8f93\u6210\u672c\uff0c\u4ee5\u786e\u4fdd\u57ce\u5e02\u7684\u5730\u57df\u7edf\u4e00\u6027\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4e24\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\u4f7f\u7528\u76f8\u540c\u7684\u8bba\u70b9\u6765\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\uff0c\u5373\u6784\u6210\u57ce\u5e02\u7684\u5404\u4e2a\u90e8\u5206\u4e4b\u95f4\u7684\u76f8\u4e92\u8054\u7cfb\u3002\u8870\u51cf\u6307\u6570\u03b3\u4ee3\u8868\u4e86\u8ddd\u79bb\u5f71\u54cd\u7684\u4e00\u4e2a\u590d\u5408\u503c\uff0c\u968f\u7740\u4e92\u8054\u7f51\u7edc\u548c\u89c6\u9891\u4f1a\u8bae\u7684\u666e\u53ca\uff0c\u7ebf\u4e0b\u4ea4\u4e92\u53ef\u80fd\u53d8\u5f97\u4e0d\u90a3\u4e48\u91cd\u8981\uff0c\u8fd9\u53ef\u80fd\u4f1a\u964d\u4f4e\u8ddd\u79bb\u7684\u5f71\u54cd\u3002\u7136\u800c\uff0c\u03b3\u7684\u65f6\u95f4\u6f14\u5316\u8fd8\u6709\u5f85\u7ecf\u9a8c\u8bc1\u660e\u3002<\/span><\/p>\n


<\/p>\n

\uff082\uff09\u4e2a\u4f53\u5438\u5f15\u529b\u6a21\u578b\uff08<\/span><\/strong>Yakubo\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/h3>\n


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

Yakubo\u7b49\u4eba\u8003\u8651\u4e86\u4e00\u4e2a\u989d\u5916\u7684\u56e0\u7d20\uff0c\u5373\u4eba\u4eec\u5bf9\u5f7c\u6b64\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u5438\u5f15\u529b\uff0c\u53d6\u51b3\u4e8e\u4e2a\u4eba\u7684\u5f71\u54cd\u529b\u5982\u4f55\u3002\u6700\u540e\u4f5c\u8005\u63a8\u5bfc\u51fa\u7684\u6a21\u578b\u516c\u5f0f\u4e3a\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5176\u4e2d\uff0c\u03b1<\/em>\u3001m<\/em>\u548c<\/span>\u03b7<\/span><\/em>\u662f\u6a21\u578b\u53c2\u6570\uff0c\u670d\u4ece<\/sub><\/span>\u3002\u6839\u636e\u8be5\u6a21\u578b\uff0c\u5373\u4f7f\u5728\u4e92\u52a8\u4ea7\u751f\u7684\u751f\u4ea7\u529b\u4e0e\u8ddd\u79bb\u65e0\u5173\u7684\u60c5\u51b5\u4e0b\uff08\u5373\u03b7=0\u65f6\uff09\uff0c\u793e\u4f1a\u7ecf\u6d4e\u6807\u5ea6\u56e0\u5b50\u7684\u8d85\u7ebf\u6027\u4e5f\u4f1a\u51fa\u73b0\u3002\u4e8b\u5b9e\u4e0a\uff0c\u63a7\u5236\u8fd9\u79cd\u8d85\u7ebf\u6027\u7684\u4e3b\u8981\u56e0\u7d20\u662f\u4e92\u52a8\u8303\u56f4\uff08\u7528\u03b3= m(\u03b1<\/em>-1)<\/em>\u8868\u793a\uff09\u548c\u57ce\u5e02\u7684\u5206\u5f62\u7ef4\u5ea6\uff08Dp<\/sub>\uff09\u4e4b\u95f4\u7684\u6bd4\u7387\u3002\u5f53\u03b7=0<\/em>\u548c\u03b1<\/em>=2<\/em>\u65f6\uff0cYakubo\u7b49\u4eba\u7684\u6a21\u578b\u548cRibeiro\u7b49\u4eba\u7814\u7a76\u7684\u5f15\u529b\u6a21\u578b\u662f\u7b49\u6548\u7684\u3002\u6b64\u5916\uff0c\u03b3= m(\u03b1<\/em>-1)<\/em>\u5bf9\u53c2\u6570\u03b3\u7ed9\u51fa\u4e86\u66f4\u57fa\u672c\u7684\u89e3\u91ca\uff0c\u8868\u660e\u8fd9\u4e2a\u63a7\u5236\u76f8\u4e92\u4f5c\u7528\u8303\u56f4\u7684\u53c2\u6570\u4e0d\u4ec5\u53d6\u51b3\u4e8e\u51e0\u4f55\u7279\u6027\uff08\u7531\u53c2\u6570m\u8868\u793a\uff09\uff0c\u800c\u4e14\u8fd8\u53d6\u51b3\u4e8e\u7ec4\u6210\u57ce\u5e02\u7684\u4eba\u7684\u5f71\u54cd\u7a0b\u5ea6\/\u5438\u5f15\u529b\uff08\u7531\u53c2\u6570\u03b1<\/em>\u8868\u793a\uff09\u3002\u603b\u800c\u8a00\u4e4b\uff0c\u4e3a\u4e86\u6539\u5584\u57ce\u5e02\u7684\u793e\u4f1a\u7ecf\u6d4e\u6307\u6807\uff08\u66f4\u5927\u7684<\/sub><\/span>\uff09\uff0c\u4e0d\u4ec5\u8981\u4e3a\u57ce\u5e02\u7684\u5176\u4ed6\u90e8\u5206\u63d0\u4f9b\u826f\u597d\u7684\u901a\u9053\uff0c\u800c\u4e14\u8981\u5728\u4eba\u53e3\u4e2d\u62e5\u6709\u80fd\u591f\u5728\u57ce\u5e02\u7684\u9065\u8fdc\u90e8\u5206\u4e4b\u95f4\u5efa\u7acb\u4e92\u52a8\u7684\u5f71\u54cd\u8005\u3002<\/span><\/p>\n


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

\uff083\uff09\u6811\u5f62\u793e\u4f1a\u7f51\u7edc\u6a21\u578b\uff08<\/span><\/strong>Arbesman\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/h3>\n


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

\u76ee\u524d\u4e3a\u6b62\u4ecb\u7ecd\u7684\u6a21\u578b\u662f\u57fa\u4e8e\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684\u4e92\u52a8\u9700\u8981\u514b\u670d\u5730\u7406\u8ddd\u79bb\u7684\u60f3\u6cd5\u3002\u7136\u800c\uff0cAbersman\u7b49\u4eba\u7684\u5de5\u4f5c\u8868\u660e\uff0c\u5f53\u8003\u8651\u5230\u4e00\u4e2a\u5206\u5c42\u7684\u793e\u4f1a\u7f51\u7edc\u65f6\uff0c\u57ce\u5e02\u53d8\u91cf\u8d85\u7ebf\u6027\u6807\u5ea6\u4e5f\u4f1a\u51fa\u73b0\u3002\u4f5c\u8005\u63d0\u51fa\uff0c\u4eba\u53e3\u88ab\u7ec4\u7ec7\u5728\u4e00\u4e2a\u6811\u5f62\u7684\u793e\u4f1a\u7f51\u7edc\u4e2d<\/span>\uff08\u5982\u56fe6\uff09<\/span>\uff0c\u4eba\u53e3\u4e2d\u7684N\u4e2a\u4e2a\u4f53\u5728\u8fd9\u68f5\u6811\u7684N\u4e2a\u53f6\u5b50\u91cc\uff0c\u8fd9\u4e2a\u7b49\u7ea7\u7f51\u7edc\u4e2d\u7684\u6bcf\u4e2a\u5206\u652f\u90fd\u4f1a\u5206\u88c2\u6210b\u4e2a\u65b0\u7684\u5206\u652f\u3002\u4e24\u4e2a\u4e2a\u4f53\u4e4b\u95f4\u7684\u793e\u4f1a\u8ddd\u79bbd\u88ab\u5b9a\u4e49\u4e3a\u4ed6\u4eec\u6700\u4f4e\u5171\u540c\u7956\u5148\u7684\u9ad8\u5ea6\u3002\u4e0e\u672c\u8282\u5f00\u5934\u4ecb\u7ecd\u7684\u4e00\u822c\u5f15\u529b\u6846\u67b6\u76f8\u6bd4\uff0c\u8ddd\u79bb\u5411\u91cf\u6210\u4e3a\u4e00\u4e2a\u6807\u91cf\uff0c\u5373r\u2192d\uff0c\u5b83\u4e0d\u4ee3\u8868\u7269\u7406\u8ddd\u79bb\uff0c\u800c\u662f\u793e\u4f1a\u8ddd\u79bb\u3002<\/span><\/p>\n


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

\u7ed3\u679c\u8868\u660e\uff0c\u5f53\u793e\u4f1a\u8ddd\u79bb\u8f83\u8fdc\u7684\u4eba\u7fa4\u76f8\u4e92\u4f5c\u7528\u65f6\uff0c\u793e\u4f1a\u7ecf\u6d4e\u6807\u5ea6\u56e0\u5b50\u66f4\u5927\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5f53\u793e\u4f1a\u4e0d\u540c\u4eba\u7fa4\u4e4b\u95f4\u7684\u4e92\u52a8\u4ee5\u7c7b\u4f3c\u4e8e\u4e4b\u524d\u8ba8\u8bba\u7684\u5730\u7406\u8ddd\u79bb\u7684\u65b9\u5f0f\u6210\u4e3a\u53ef\u80fd\u65f6\uff0c\u57ce\u5e02\u7684\u793e\u4f1a\u7ecf\u6d4e\u5c31\u4f1a\u5f97\u5230\u6539\u5584\u3002\u6b63\u5982\u7814\u7a76\u6240\u6307\u51fa\u7684\u90a3\u6837\uff0c\u793e\u533a\u4e4b\u95f4\u7684\u7d27\u5bc6\u8054\u7cfb\u521b\u9020\u4e86\u66f4\u597d\u7684\u57ce\u5e02\uff0c\u8fd9\u610f\u5473\u7740\u793e\u4f1a\u8fdc\u8ddd\u79bb\u7684\u4e92\u52a8\u53ef\u4ee5\u6210\u4e3a\u4e00\u79cd\u793e\u4f1a\u7ecf\u6d4e\u529b\u91cf\u3002<\/span><\/p>\n


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

<\/p>\n

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

\uff084\uff09\u6b27\u6c0f\u8ddd\u79bb\u4e0e\u793e\u4f1a\u8ddd\u79bb\u7684\u5173\u7cfb<\/span><\/strong><\/h3>\n


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

\u4ee5\u4e0a\u4e09\u4e2a\u5f15\u529b\u6a21\u578b\u5206\u522b\u8003\u8651\u4e86\u7269\u7406\u8ddd\u79bb\u548c\u793e\u4f1a\u8ddd\u79bb\u3002\u7136\u800c\uff0c\u672c\u6587\u60f3\u8bc1\u660e\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e24\u4e2a\u7248\u672c\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u662f\u7b49\u4ef7\u7684\u3002\u8fd9\u6837\u7684\u731c\u60f3\u662f\u5408\u7406\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u751f\u6d3b\u5728\u6211\u4eec\u8ba4\u8bc6\u7684\u4eba\u8eab\u8fb9\u3002\u6b64\u5916\uff0c\u901a\u8fc7\u516c\u5f0f\u63a8\u5bfc\u53d1\u73b0\uff0c\u4eba\u53e3\u90e8\u5206\u5730\u4ee5\u5206\u5f62\u65b9\u5f0f\u5206\u5e03\uff0c\u540c\u65f6\u5b83\u9075\u5faa\u4e00\u4e2a\u5206\u5c42\u7684\u793e\u4f1a\u7f51\u7edc\uff0c\u8870\u51cf\u6307\u6570\u03b3\u4e5f\u4e0e\u793e\u4f1a\u5173\u7cfb\u6709\u5173\u3002\u8fd9\u610f\u5473\u7740\uff0c\u4e0d\u540c\u7684\u4f5c\u8005\u91c7\u7528\u4e0d\u540c\u7684\u60f3\u6cd5\u548c\u65b9\u6cd5\u72ec\u7acb\u5f00\u53d1\u4e86\u4ed6\u4eec\u7684\u6a21\u578b\uff0c\u5374\u5f97\u5230\u4e86\u7b49\u4ef7\u7684\u7ed3\u679c<\/span>\uff08\u5177\u4f53\u63a8\u5bfc\u8fc7\u7a0b\u53ef\u67e5\u770b\u539f\u6587\uff09<\/span>\u3002<\/span><\/p>\n


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

\uff085\uff09\u4e9a\u7ebf\u6027\u6807\u5ea6\u6a21\u578b\uff08<\/span><\/strong>F.Ribeiro\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/h3>\n


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

\u57fa\u7840\u8bbe\u65bd\u7684\u6807\u5ea6\u56e0\u5b50\u03b2sup<\/sub><\/span><\/em>\u4e5f\u53ef\u4ee5\u7528\u5f15\u529b\u6a21\u578b\u63a8\u5bfc\u51fa\u6765\u3002\u7136\u800c\uff0c\u4e0eBettencourt\u6a21\u578b\u4e0d\u540c\u7684\u662f\uff0cRibeiro\u7b49\u4eba\u5173\u6ce8\u7684\u662f\u57ce\u5e02\u4e2d\u6ee1\u8db3\u4eba\u4eec\u9700\u6c42\u6240\u9700\u7684\u8bbe\u65bd\u6570\u91cf\u3002\u4ed6\u4eec\u5229\u7528\u4eba\u4eec\u503e\u5411\u4e8e\u9009\u62e9\u9760\u8fd1\u7684\u5730\u65b9\u6d88\u8d39\u7684\u60f3\u6cd5\uff0c\u89c4\u5b9a\u4e86\u8bbe\u65bd\u6570\u91cf\uff0c\u4f5c\u4e3a\u4eba\u53e3\u89c4\u6a21\u51fd\u6570\u7684\u7f29\u653e\u7279\u6027\uff0c\u5e76\u63a8\u5bfc\u51fa<\/sub><\/span>\u3002<\/span><\/p>\n


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

\u8fd9\u4e2a\u6a21\u578b\u8868\u660e\uff0c\u53ea\u6709\u5728\u03b3<Dp<\/sub>\u7684\u60c5\u51b5\u4e0b\uff0c\u624d\u4f1a\u51fa\u73b0\u57fa\u7840\u8bbe\u65bd\u7684\u4e9a\u7ebf\u6027\u6807\u5ea6\u56e0\u5b50\u3002\u8fd9\u4e2a\u03b3\u8303\u56f4\u5b9e\u9645\u4e0a\u8868\u5f81\u4e86\u8fdc\u8ddd\u79bb\u76f8\u4e92\u4f5c\u7528\u533a\u57df\uff0c\u8fd9\u662f\u57ce\u5e02\u4f5c\u4e3a\u6574\u4e2a\u8026\u5408\u7cfb\u7edf\u7684\u7ed3\u679c\u3002\u6b63\u5982\u524d\u9762\u63d0\u5230\u7684\u5f15\u529b\u6a21\u578b\u548c\u4e0eBettencout\u6a21\u578b\u7684\u6bd4\u8f83\uff0c\u4e92\u52a8\u8303\u56f4\u8d8a\u5927\uff0c\u89c4\u6a21\u7ecf\u6d4e\u5c31\u8d8a\u5927\uff0c\u56e0\u6b64\u57fa\u7840\u8bbe\u65bd\u6210\u672c\u5c31\u8d8a\u4f4e\u3002<\/span><\/p>\n


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

\uff086\uff09\u5f15\u529b\u6a21\u578b\u7684\u53d1\u73b0\u4e0e\u7ed3\u8bba<\/span><\/strong><\/h3>\n


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

\u6211\u4eec\u53d1\u73b0\uff0c\u4ee5\u4e0a\u51e0\u7ec4\u4f5c\u8005\u72ec\u7acb\u5730\u91c7\u7528\u4e86\u5f15\u529b\u601d\u60f3\u6765\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\uff0c\u5374\u4ea7\u751f\u4e86\u4e00\u81f4\u7684\u7ed3\u679c\u3002\u8fd9\u4e00\u89c2\u5bdf\u5f3a\u8c03\u4e86\u5f15\u529b\u65b9\u6cd5\u5bf9\u4e8e\u7406\u89e3\u57ce\u5e02\u73b0\u8c61\u7684\u91cd\u8981\u6027\uff0c\u56e0\u4e3a\u6258\u5e03\u52d2\u5df2\u7ecf\u4ece\u5b9a\u6027\u4e0a\u63d0\u51fa\u4e86\u4ed6\u7684\u5730\u7406\u5b66\u7b2c\u4e00\u5b9a\u5f8b\u3002\u672c\u5de5\u4f5c\u7684\u4e00\u4e2a\u521b\u65b0\u4e4b\u5904\u5728\u4e8e\u5c06\u8fd9\u4e9b\u60f3\u6cd5\u7ec4\u7ec7\u5728\u4e00\u4e2a\u5355\u4e00\u7684\u3001\u4e00\u822c\u7684\u6846\u67b6\u4e2d\uff0c\u4ece\u800c\u53ef\u4ee5\u786e\u5b9a\u76f8\u4f3c\u6027\u548c\u5171\u540c\u7684\u7ed3\u679c\u3002\u5404\u79cd\u5f15\u529b\u6a21\u578b\u5728\u7279\u6b8a\u60c5\u51b5\u4e0b\u662f\u7b49\u4ef7\u7684\uff0c\u5b83\u4eec\u4ee3\u8868\u4e86\u5404\u79cd\u53d8\u4f53\u3002\u901a\u8fc7\u6574\u5408\u8fd9\u4e9b\u6a21\u578b\uff0c\u6211\u4eec\u5f97\u51fa\u7ed3\u8bba\uff0c\u57ce\u5e02\u89c4\u6a21\u7684\u6269\u5927\u57fa\u672c\u4e0a\u662f\u7531\u5206\u5f62\u51e0\u4f55\u548c\u52a0\u5f3a\u6216\u51cf\u5c11\u4e92\u52a8\u7684\u793e\u4f1a\u5173\u7cfb\u6240\u9020\u6210\u7684\u7a7a\u95f4\u5206\u5e03\u7684\u7ed3\u679c\u3002\u5177\u4f53\u800c\u8a00\uff0c\u57ce\u5e02\u6807\u5ea6\u5f8b\u7684\u51fa\u73b0\u9700\u8981\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/span><\/p>\n


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

    \n
  • \n

    \u53ef\u4ee5\u65b9\u4fbf\u5730\u5230\u8fbe\u57ce\u5e02\u7684\u5404\u4e2a\u5730\u65b9\u3002\u589e\u52a0\u89c4\u6a21\u56de\u62a5\u9700\u8981\u4e00\u4e2a\u5730\u7406\u4e0a\u8fde\u63a5\u826f\u597d\u7684\u57ce\u5e02\uff0c\u5141\u8bb8\u6574\u4e2a\u57ce\u5e02\u5185\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u5e76\u5141\u8bb8\u57ce\u5e02\u7684\u5b8c\u6574\u6027\u3002\u5728\u5b9e\u8df5\u4e2d\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u9ad8\u6548\u7684\u4ea4\u901a\u7cfb\u7edf\u6765\u5b9e\u73b0\u3002<\/span><\/p>\n<\/li>\n

  • \n

    \u6709\u5230\u8fbe\u57ce\u5e02\u504f\u8fdc\u5730\u533a\u7684\u4eba\u7269\u3002\u4f18\u79c0\u7684\u6709\u5f71\u54cd\u529b\u4eba\u7269\u7684\u5b58\u5728\u53ef\u4ee5\u6574\u5408\u57ce\u5e02\u7684\u9065\u8fdc\u5730\u533a\uff0c\u4fc3\u8fdb\u4e92\u8054\u4e92\u901a\uff0c\u4ece\u800c\u4ea7\u751f\u66f4\u663e\u8457\u7684\u57ce\u5e02\u89c4\u6a21\u6548\u5e94\u3002<\/span><\/p>\n<\/li>\n

  • \n

    \u793e\u4ea4\u8ddd\u79bb\u8f83\u8fdc\u7684\u4eba\u4e4b\u95f4\u7684\u4e92\u52a8\u3002\u5f53\u793e\u4f1a\u8ddd\u79bb\u9065\u8fdc\u7684\u4eba\u80fd\u591f\u66f4\u597d\u5730\u4e92\u52a8\u65f6\uff0c\u793e\u4f1a\u7ecf\u6d4e\u6807\u5ea6\u56e0\u5b50\u5c31\u66f4\u5927\u3002\u672c\u6587\u5df2\u7ecf\u8bc1\u660e\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u793e\u4f1a\u8ddd\u79bb\u548c\u5730\u7406\u8ddd\u79bb\u662f\u76f8\u5173\u7684\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


    <\/span><\/h3>\n

    1.5 \u57fa\u7840\u8bbe\u65bd\u51e0\u4f55\u6a21\u578b\uff08<\/span><\/strong>Molinero \u548c Thurner<\/span><\/strong>\uff09<\/span><\/strong><\/h3>\n


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

    \u4e0e\u4e0a\u4e00\u8282\u4ecb\u7ecd\u7684\u4e00\u4e9b\u6a21\u578b\u4e00\u6837\uff0cMolinero\u548cThurner\u63d0\u51fa\u7684\u6a21\u578b\u4e5f\u5c06\u5206\u5f62\u51e0\u4f55\u4f5c\u4e3a\u57ce\u5e02\u6807\u5ea6\u7684\u4e3b\u8981\u56e0\u7d20\u3002\u4f5c\u8005\u5728\u8ba8\u8bba\u4e2d\u5f15\u5165\u4e86\u65b0\u7684\u6210\u5206\uff0c\u5982\u57ce\u5e02\u5782\u76f4\u5316\u548c\u4eba\u53e3\u7684\u5206\u5f62\u7ef4\u5ea6\uff08Dp<\/sub><\/em>\uff09\u4e0e\u57fa\u7840\u8bbe\u65bd\u7684\u5206\u5f62\u7ef4\u5ea6\uff08Dinfra<\/sub><\/em>\uff09<\/span>\uff08\u5373\u8857\u9053\u7f51\u7edc\uff09<\/span>\u4e4b\u95f4\u7684\u533a\u522b\u3002\u7531\u4e8e\u8857\u9053\u7f51\u7edc\u4f4d\u4e8e\u4e8c\u7ef4\u5730\u7403\u8868\u9762\uff0c\u5176\u7ef4\u5ea6\u53d7\u5230Dinfra<\/sub><\/em>\u22642\u7684\u9650\u5236\u3002Molinero\u548cThurner\u8ba4\u4e3a\uff0c\u4eba\u53e3\u548c\u57fa\u7840\u8bbe\u65bd\u5206\u5f62\u7ef4\u5ea6\u7684\u533a\u5206\u5bf9\u4e8e\u5728\u57ce\u5e02\u95f4\u89c2\u5bdf\u5230\u7684\u89c4\u6a21\u6cd5\u5219<\/span>\u81f3\u5173\u91cd\u8981\u3002<\/span><\/p>\n


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

    \u4f5c\u8005\u8ba4\u4e3a\uff0c\u4eba\u53e3\u4f4d\u4e8e\u6cbf\u8857\u7684\u623f\u5c4b\u548c\u5efa\u7b51\u7269\u4e2d\uff0c\u5982\u679c\u6211\u4eec\u5ffd\u7565\u4e86\u5782\u76f4\u8303\u56f4\uff0c\u90a3\u4e48\u4eba\u53e3\u7684\u5206\u5f62\u7ef4\u5ea6\u5c06\u4e0e\u8857\u9053\u7ed3\u6784\u7684\u5206\u5f62\u7ef4\u5ea6\u975e\u5e38\u76f8\u4f3c\u3002\u8fd9\u4e0e\u4e4b\u524d\u7684\u6a21\u578b\u6240\u8003\u8651\u7684\u76f8\u4f3c\uff0c\u5373Dinfra<\/sub><\/em>= Dp<\/sub><\/em>\u3002\u7136\u800c\uff0c\u6b63\u5982Molenero\u548cThurner\u6240\u8ba4\u4e3a\u7684\uff0c\u57ce\u5e02\u6709\u4e00\u4e2a\u4e0d\u80fd\u5ffd\u7565\u7684\u5782\u76f4\u90e8\u5206\uff0c\u8fd9\u5c31\u628aDp<\/sub><\/em>\u9650\u5236\u5728Dinfra<\/sub><\/em>\u2264Dp<\/sub><\/em>\u2264Dinfra<\/sub><\/em>+Dh<\/sub><\/em>\u7684\u533a\u95f4\u5185\uff0c\u5176\u4e2dDh<\/sub><\/em>\u662f\u4e0e\u57ce\u5e02\u5efa\u7b51\u9ad8\u5ea6\u6709\u5173\u7684\u7ef4\u5ea6\u3002<\/span><\/p>\n


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

    \u4f5c\u8005\u6700\u540e\u63a8\u5bfc\u51fa\u03b2sup<\/sub><\/span><\/em>=Dinfra<\/sub><\/em>\/Dp<\/sub><\/em>\uff0c\u63ed\u793a\u4e86\u5206\u5f62\u7ed3\u6784<\/span>\uff08\u4eba\u53e3\u548c\u8857\u9053\u7f51\u7edc\uff09<\/span>\u5728\u57ce\u5e02\u6807\u5ea6\u4e2d\u7684\u4f5c\u7528\uff0c\u5373\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u51fa\u73b0\u662f\u7531\u4e8e\u4eba\u4eec\u5c45\u4f4f\u7684\u5730\u65b9\u548c\u4ed6\u4eec\u79fb\u52a8\u7684\u7ed3\u6784\u4e0d\u5e73\u8861\u7684\u7ed3\u679c\u3002\u540c\u6837\u9700\u8981\u5f3a\u8c03\u7684\u662f\uff0c\u6b63\u5982\u4f5c\u8005\u6240\u8bc1\u660e\u7684\u90a3\u6837\uff0c\u867d\u7136\u4eba\u53e3\u548c\u57fa\u7840\u8bbe\u65bd\u5206\u7ef4(Dp<\/sub><\/em>\u548cDinfra<\/sub><\/em>)\u5728\u4e2a\u522b\u57ce\u5e02\u4e2d\u5dee\u5f02\u5f88\u5927\uff0c\u4f46Dinfra<\/sub><\/em>\/Dp<\/sub><\/em>\u7684\u7ecf\u9a8c\u6bd4\u7387<\/span>\uff08\u5bf9\u6570\u5343\u4e2a\u57ce\u5e02\u800c\u8a00\uff09<\/span>\u975e\u5e38\u7a33\u5065\uff0c\u4e14Dinfra<\/sub><\/em>\/Dp<\/sub><\/em>\u7684\u503c\u7ea6\u4e3a0.86\u3002\u8fd9\u4e2a\u503c\u4e0e\u57fa\u7840\u8bbe\u65bd\u6807\u5ea6\u56e0\u5b50\uff08\u03b2sup<\/sub><\/span><\/em>=0.85\uff09\u7684\u7ecf\u9a8c\u503c\u8f83\u4e3a\u8fd1\uff0c\u4f7f\u5f97\u8fd9\u4e2a\u7406\u8bba\u6210\u4e3a\u5728\u57fa\u7840\u8bbe\u65bd\u80cc\u666f\u4e0b\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u6700\u6210\u529f\u7684\u7406\u8bba\u4e4b\u4e00\u3002<\/span><\/p>\n


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

    \u540c\u65f6\uff0c\u53ef\u4ee5\u53d1\u73b0\u516c\u5f0f<\/sub><\/span>\u4e0eF.Ribeiro\u7b49\u4eba\u7ed9\u51fa\u7684\u516c\u5f0f<\/sub><\/span>\u5b58\u5728\u4e00\u5b9a\u7684\u76f8\u4f3c\u6027\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6bd4\u8f83\u8fd9\u4e24\u4e2a\u72ec\u7acb\u7684\u7ed3\u679c\u4e3a\u5f15\u529b\u6307\u6570\u03b3\u63d0\u4f9b\u4e86\u4e00\u4e2a\u989d\u5916\u7684\u89e3\u91ca\uff0c\u5e76\u6697\u793a\u4e86\u5bf9Molinero\u548cThurner\u7ed3\u679c\u7684\u4e00\u4e2a\u66f4\u6839\u672c\u7684\u89e3\u91ca\u3002\u6211\u4eec\u53ef\u4ee5\u7528Dinfra<\/sub><\/em>\u4ee3\u66ff\u03b3\uff0c\u5f97\u51fa<\/sub><\/span>\u3002\u8fd9\u4e2a\u7ed3\u679c\u8868\u660e\u4e86\u7a7a\u95f4\u6216\u8005\u8bf4\u8857\u9053\u7f51\u7edc\u7ed3\u6784\uff08\u8fd9\u91cc\u7528\u5206\u5f62\u7ef4\u5ea6Dinfra<\/sub><\/em>\u8868\u793a\uff09\u662f\u5982\u4f55\u5f71\u54cd\u4eba\u4eec\u4e4b\u95f4\u4e92\u52a8\u7684\u3002\u5982\u679c\u4ee5\u4e0a\u516c\u5f0f\u6210\u7acb\uff0c\u90a3\u4e48\u8857\u9053\u7f51\u7edc\u8d8a\u7d27\u51d1\uff08Dinfra<\/sub><\/em>\u8d8a\u5927\uff09\uff0c\u4e92\u52a8\u8303\u56f4\u5c31\u8d8a\u5c0f\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u968f\u7740\u5bc6\u5ea6\u7684\u589e\u52a0\uff0c\u4e2a\u4eba\u53ef\u4ee5\u8fdb\u5165\u57ce\u5e02\u7684\u90e8\u5206\u8d8a\u6765\u8d8a\u5c11\u3002\u5728\u8fd9\u4e2a\u610f\u4e49\u4e0a\uff0c\u4ee5\u4e0a\u63d0\u51fa\u4e86\u4e00\u79cd\u91cf\u5316\u7684\u65b9\u6cd5\u6765\u7406\u89e3\u8857\u9053\u7684\u7ed3\u6784\u662f\u5982\u4f55\u5f71\u54cd\u4eba\u4eec\u7684\u4e92\u52a8\u7684\uff0c\u4ee5\u53ca\u56e0\u6b64\u5982\u4f55\u5728\u57ce\u5e02\u53d1\u5c55\u4e0a\u4ea7\u751f\u5f71\u54cd\u3002<\/span><\/p>\n


    <\/p>\n

    \n
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    2 \u57fa\u4e8e\u57ce\u5e02\u5fc5\u8981\u56e0\u7d20\u7684\u6a21\u578b<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

    \n


    <\/p>\n<\/section>\n

    Gomez-Lievano\u7b49\u4eba\u57282016\u5e74\u7684\u63d0\u51fa\u5fc5\u8981\u56e0\u7d20\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u5c5e\u4e8e\u57ce\u5e02\u5185\u6a21\u578b\u8303\u7574\uff0c\u4f46\u4e0e\u4e4b\u524d\u4ecb\u7ecd\u7684\u5176\u4ed6\u6a21\u578b\u4e0d\u540c\u3002\u5176\u4ed6\u57ce\u5e02\u5185\u6a21\u578b\u662f\u57fa\u4e8e\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684\u4e92\u52a8\u4e3a\u524d\u63d0 \uff0c\u800c\u8fd9\u4e2a\u6a21\u578b\u5219\u662f\u57fa\u4e8e\u57ce\u5e02\u5185\u7684\u5fc5\u8981\u56e0\u7d20\u3002\u56e0\u6b64\uff0c\u4e0a\u8282\u4e2d\u4ecb\u7ecd\u7684\u4e00\u822c\u6846\u67b6\u5728\u8fd9\u91cc\u5e76\u4e0d\u9002\u7528\u3002\u8be5\u6a21\u578b\u91c7\u7528\u4e86\u7ecf\u6d4e\u590d\u6742\u6027\u548c\u6587\u5316\u6f14\u53d8\u7684\u6982\u5ff5\u6765\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u7684\u8d77\u6e90\u3002\u4e3b\u8981\u89c2\u70b9\u662f\uff0c\u5f53\u57ce\u5e02\u4e2d\u5b58\u5728\u4e00\u4e9b\u5fc5\u8981\u7684\u4e92\u8865\u56e0\u7d20\u65f6\uff0c\u5c31\u4f1a\u51fa\u73b0\u57ce\u5e02\u793e\u4f1a\u7ecf\u6d4e\u73b0\u8c61\u3002<\/span><\/p>\n


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

    \u628aM<\/em>\u770b\u4f5c\u662f\u67d0\u9879\u793e\u4f1a\u7ecf\u6d4e\u6d3b\u52a8\u6240\u9700\u7684\u53ef\u80fd\u56e0\u7d20\u7684\u6570\u91cf\u3002\u4f8b\u5982\uff0c\u5982\u679cY<\/em>\u662f\u4e00\u4e2a\u57ce\u5e02\u7684\u4e13\u5229\u603b\u6570\uff0cM<\/em>\u53ef\u4ee5\u662f\u4e00\u4e2a\u4eba\u5f00\u53d1\u4e13\u5229\u6240\u9700\u7684\u4e0d\u540c\u6280\u80fd\u7684\u6570\u91cf\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cM<\/em>\u662f\u5bf9\u6709\u5173\u73b0\u8c61\u7684 \u201c\u590d\u6742\u6027\u201d<\/span>\uff08\u590d\u6742\u5ea6\u3001\u96be\u5ea6\u7b49\uff09<\/span>\u7684\u4e00\u79cd\u5ea6\u91cf\u3002\u5047\u8bbe\u8fd9\u4e9b\u56e0\u7d20\u4e2d\u7684\u6bcf\u4e00\u4e2a\u90fd\u662f\u7531\u76f8\u5e94\u7684\u57ce\u5e02\u63d0\u4f9b\u7684\uff0c\u6982\u7387\u4e3az<\/em>\u3002\u90a3\u4e48\uff0c\u5982\u679c\u8fd9\u4e9b\u56e0\u7d20\u662f\u72ec\u7acb\u7684\uff0c\u57ce\u5e02\u63d0\u4f9b\u8fd9M<\/em>\u4e2a\u56e0\u7d20\u4e2d\u7684m<\/em>\u4e2a\u7684\u6982\u7387\uff0c\u5373p(m)<\/em>\uff0c\u5c06\u9075\u5faa\u4e8c\u9879\u5f0f\u5206\u5e03\uff1a<\/span><\/p>\n


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

    <\/p>\n


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

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    <\/p>\n

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    3 \u6781\u7aef\u503c\u6a21\u578b<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

    \n


    <\/p>\n<\/section>\n

    Gomez-Lievano\u7b49\u4eba\u57282021\u5e74\u7684\u4e00\u7bc7\u6587\u7ae0\u4e2d\u5206\u6790\u8ba4\u4e3a\uff0c\u8d85\u7ebf\u6027\u6807\u5ea6\u56e0\u5b50\u53ef\u80fd\u4e0d\u662f\u901a\u5e38\u6240\u5047\u8bbe\u7684\u89c4\u6a21\u6536\u76ca\u9012\u589e\u7684\u7ed3\u679c\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u4f5c\u8005\u5047\u8bbe\u5373\u4f7f\u6ca1\u6709\u4e2a\u4f53\u4e4b\u95f4\u7684\u4e92\u52a8\u8fc7\u7a0b\uff0c\u57ce\u5e02\u6807\u5ea6\u7684\u975e\u7ebf\u6027\u4e5f\u4f1a\u51fa\u73b0\u3002\u4ed6\u4eec\u8868\u660e\uff0c\u975e\u7ebf\u6027\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u4f5c\u7528\u4e8e\u72ec\u7acb\u968f\u673a\u53d8\u91cf\u7684\u9009\u62e9\u8fc7\u7a0b\u51fa\u73b0\u3002\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bf4\uff0c\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u53cd\u800c\u4ee3\u8868\u4e86\u4e00\u4e2a\u4f2a\u547d\u9898\u3002\u4e3a\u4e86\u8bc1\u660e\u8fd9\u4e00\u8bba\u70b9\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4ee5\u4e0b\u6a21\u578b\u3002\u5047\u8bbe\u67d0\u4e2a\u4eba\u7684\u751f\u4ea7\u7387w<\/em>\uff0c\u662f\u4e00\u4e2a\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\uff0c\u56e0\u6b64\uff0c\u5b83\u4e0d\u53d6\u51b3\u4e8e\u4ed6\/\u5979\u6240\u5c45\u4f4f\u7684\u57ce\u5e02\u7684\u5927\u5c0f\u3002\u6b64\u5916\uff0c\u8fd9\u4e2a\u751f\u4ea7\u529b\u662f\u5bf9\u6570\u6b63\u6001\u5206\u5e03\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/span><\/p>\n

    <\/p>\n


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    \u5176\u4e2dw0<\/sub><\/em>\u548c\u03c3<\/em>\u662f\u6b63\u53c2\u6570\uff0c ln w0<\/sub> = <ln w><\/em>\u662fln w<\/em>\u7684\u671f\u671b\u503c\uff0c\u03c3<\/em>2<\/sup><\/span>= VAR[ln w]<\/em>\u662f\u65b9\u5dee\uff0c\u751f\u4ea7\u529b\u671f\u671b\u503c\u7531<\/sub><\/span><\/em>\u7ed9\u51fa\u3002\u5bf9\u6570\u6b63\u6001\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08pdf\uff09\u7684\u9009\u62e9\u662f\u7531\u4e00\u4e9b\u7ecf\u9a8c\u7814\u7a76\u8bc1\u660e\u7684\uff0c\u8fd9\u4e9b\u8bc1\u636e\u8868\u660e\uff0c\u7531\u5de5\u8d44\u95f4\u63a5\u8861\u91cf\u7684\u5de5\u4eba\u7684\u751f\u4ea7\u7387\u9075\u5faa\u8fd9\u79cd\u5206\u5e03\u3002\u4f5c\u8005\u6700\u7ec8\u63a8\u5bfc\u51fa<\/sub><\/span>\uff0c\u5f53\u51fa\u73b0\u6781\u7aef\u503c<\/span>N<\/span><\/em> << \u03c3<\/em>\u624d<\/span>\u4f1a\u51fa\u73b0\u8d85\u7ebf\u6027\u6807\u5ea6\u56e0\u5b50\uff0c\u5426\u5219<\/span>\u03b2<\/span><\/em>=1<\/em>\u3002\u8fd9\u4e2a\u6a21\u578b\u7684\u7ed3\u679c\u81f3\u5c11\u6709\u4e24\u4e2a\u542f\u793a\u3002\u9996\u5148\uff0c\u4e0d\u65ad\u589e\u52a0\u7684\u8d85\u7ebf\u6027\u6807\u5ea6\u548c\u89c4\u6a21\u6536\u76ca\u7387\uff0c\u53ef\u80fd\u53ea\u662f\u4e00\u4e2a\u4f2a\u547d\u9898\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u4ece\u72ec\u7acb\u968f\u673a\u53d8\u91cf\u7684\u9009\u62e9\u8fc7\u7a0b\u4e2d\u53d1\u751f\u3002\u5176\u6b21\uff0c\u5b83\u5141\u8bb8\u7ebf\u6027\u548c\u8d85\u7ebf\u6027\u4e0d\u540c\u7ed3\u679c\u7684\u51fa\u73b0\uff0c\u53d6\u51b3\u4e8e\u57ce\u5e02\u7684\u89c4\u6a21\u548c\u5de5\u4eba\u751f\u4ea7\u529b\u5206\u5e03\u7684\u65b9\u5dee\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u5c0f\u57ce\u5e02\uff08N<\/span><\/em> << \u03c3<\/em><\/span>\uff09\u5c06\u8868\u73b0\u51fa\u8d85\u7ebf\u6027\u6807\u5ea6\u56e0\u5b50\uff0c\u800c\u5927\u57ce\u5e02\uff08N<\/span><\/em> >> \u03c3<\/em><\/span>\uff09\u5219\u51fa\u73b0\u7ebf\u6027\u7279\u5f81\u3002<\/span><\/p>\n


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

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    \u4e09\u3001\u57ce\u5e02\u95f4\u6a21\u578b<\/strong><\/strong><\/p>\n<\/section>\n

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    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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    \u4ee5\u4e0a\u4ecb\u7ecd\u7684\u90fd\u662f\u57ce\u5e02\u5185\u90e8\u7684\u6a21\u578b\u3002\u7136\u800c\uff0c\u57ce\u5e02\u5e76\u4e0d\u662f\u5c01\u95ed\u7684\u6216\u5b64\u7acb\u7684\u5bf9\u8c61\u3002\u5b9e\u9645\u4e0a\uff0c\u57ce\u5e02\u4e4b\u95f4\u5b58\u5728\u7740\u4e0d\u65ad\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u65e0\u8bba\u662f\u4e0d\u540c\u57ce\u5e02\u7684\u4e2a\u4eba\u6216\u4f01\u4e1a\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u8fd8\u662f\u57ce\u5e02\u4e4b\u95f4\u7684\u4eba\u53e3\u6d41\u52a8\uff0c\u5747\u662f\u5982\u6b64\u3002\u56e0\u6b64\uff0c\u57ce\u5e02\u4e4b\u95f4\u53d1\u751f\u4e92\u52a8\u7684\u8fc7\u7a0b\u4e00\u5b9a\u4f1a\u4ee5\u67d0\u79cd\u65b9\u5f0f\u5e72\u6270\u751f\u4ea7\u529b\u548c\u57fa\u7840\u8bbe\u65bd\u7684\u4f7f\u7528\uff0c\u9700\u8981\u9610\u91ca\u57ce\u5e02\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u662f\u5982\u4f55\u89e3\u91ca\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u6216\u5f71\u54cd\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\uff0c\u5373\u4f7f\u53ea\u662f\u5728\u4e8c\u9636\u8fd1\u4f3c\u7684\u60c5\u51b5\u4e0b\u3002\u672c\u8282\u5c06\u89e3\u91ca\u57ce\u5e02\u95f4\u6a21\u578b\uff0c\u4f46\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u4e0d\u592a\u6210\u719f\uff0c\u56e0\u6b64\u6a21\u578b\u7684\u6570\u91cf\u8f83\u5c11\uff0c\u6982\u5ff5\u7684\u8303\u56f4\u8f83\u5e7f\uff0c\u5176\u4e2d\u8fd8\u5305\u62ec\u4e00\u4e9b\u5b9a\u6027\u7684\u65b9\u6cd5\u3002<\/span><\/p>\n


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    1 \u6280\u672f\u6269\u6563\u6a21\u578b\uff08Pumain\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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

    Pumain\u7b49\u4eba\u8ba4\u4e3a\uff0c\u975e\u7ebf\u6027\u662f\u7531\u4e8e\u57ce\u5e02\u7cfb\u7edf\u5185\u7684\u76f8\u4e92\u4f5c\u7528\u9020\u6210\u7684\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u4ed6\u4eec\u63d0\u51fa\uff0c\u975e\u7ebf\u6027\u662f\u901a\u8fc7\u4ece\u6700\u5927\u7684\u57ce\u5e02\u5230\u8f83\u5c0f\u7684\u57ce\u5e02\u7684\u5206\u5c42\u521b\u65b0\u8fc7\u7a0b\u51fa\u73b0\u7684\u3002\u6839\u636e\u8fd9\u4e00\u4e3b\u5f20\uff0c\u521b\u65b0\u8fc7\u7a0b\u5728\u5927\u57ce\u5e02\u4e2d\u4e0d\u6210\u6bd4\u4f8b\u5730\u9ad8\u3002\u7ecf\u6d4e\u6307\u6807\u7684\u8d85\u7ebf\u6027\u6807\u5ea6\u56e0\u5b50\u4ee3\u8868\u4e86\u65b0\u6280\u672f\u7684\u51fa\u73b0\u9636\u6bb5\uff0c\u8fd9\u53d1\u751f\u5728\u8f83\u5927\u7684\u57ce\u5e02\uff1b\u7ebf\u6027\u6807\u5ea6\u56e0\u5b50\u4ee3\u8868\u4e86\u7cfb\u7edf\u4e2d\u4ece\u5927\u57ce\u5e02\u5230\u57ce\u9547\u548c\u5c0f\u57ce\u5e02\u7684\u6269\u6563\u9636\u6bb5\uff0c\u800c\u4e9a\u7ebf\u6027\u5219\u4ee3\u8868\u4e86\u6280\u672f\u7684\u6210\u719f\u9636\u6bb5\uff0c\u4e5f\u4ee5\u8870\u843d\u6216\u66ff\u4ee3\u8fc7\u7a0b\u4e3a\u7279\u5f81\u3002\u8fd9\u4e2a\u7406\u8bba\u7684\u4f18\u70b9\u662f\u5b83\u628a\u57ce\u5e02\u4e4b\u95f4\u7684\u76f8\u4e92\u8054\u7cfb\u5e26\u5230\u4e86\u524d\u53f0\uff0c\u4f8b\u5982\uff0c\u9f50\u592b\u5b9a\u5f8b\u63ed\u793a\u4e86\u57ce\u5e02\u7cfb\u7edf\u4e2d\u7684\u67d0\u79cd\u7b49\u7ea7\u7ed3\u6784\u3002<\/span><\/p>\n


    <\/p>\n

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    2 \u9f50\u592b\u5b9a\u5f8b\uff08Gomez-Lievano\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

    \n


    <\/p>\n<\/section>\n

    Gomez-Lievano\u7b49\u4eba\u63d0\u51fa\u4e86\u4e00\u4e2a\u7edf\u8ba1\u6846\u67b6\u6765\u63cf\u8ff0\u57ce\u5e02\u89c4\u6a21\u5927\u5c0f\u5206\u5e03\u7684\u7279\u70b9\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u4ed6\u4eec\u63a8\u5bfc\u51fa\u57ce\u5e02\u4eba\u53e3\u89c4\u6a21N<\/em>\u9075\u5faa\u9f50\u592b\u5b9a\u5f8b\u7684\u60c5\u51b5\uff0c\u5373\u5e42\u5f8b\u5206\u5e03P(N) ~N–<\/sup><\/span><\/em><\/em><\/em><\/span>\u03b1<\/sup><\/em><\/em><\/em><\/span><\/em><\/em><\/span>\uff0c\u5e76\u63a8\u5bfc\u51fa<\/sub><\/span>\uff0c\u5176\u4e2d\u57ce\u5e02\u6307\u6807Y<\/em>\u670d\u4eceP(Y)~Y–<\/sup><\/span><\/em><\/em><\/em><\/span>\u03b1<\/sup><\/em><\/em><\/em><\/span>Y<\/sup><\/span><\/em><\/em>\uff0c<\/em>\u8fd9\u610f\u5473\u7740\u6807\u5ea6\u56e0\u5b50\u4e0e\u9f50\u592b\u6307\u6570\u76f4\u63a5\u76f8\u5173\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u6700\u8fd1\uff0c\u4eba\u4eec\u63d0\u51fa\u4e86\u5404\u79cd\u89e3\u91ca\uff0c\u91cd\u65b0\u4ece\u5b9a\u91cf\u4e0a\u548c\u5b9a\u6027\u4e0a\u89e3\u91ca\u9f50\u592b\u5f8b\u548c\u6807\u5ea6\u56e0\u5b50\u4e4b\u95f4\u7684\u8054\u7cfb\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u57ce\u5e02\u6807\u5ea6\u5c06\u9f50\u592b\u5206\u5e03\uff08\u03b1<\/em>\u22481\uff09\u8f6c\u53d8\u4e3a\u53e6\u4e00\u4e2a\u5e42\u5f8b\u5206\u5e03\uff0c\u5176\u6307\u6570\u03b1<\/span><\/em>Y<\/em>\u5728<\/span>\u03b2<\/span><\/em>\u4e0d\u7b49\u4e8e1\u7684\u60c5\u51b5\u4e0b\u4e0e\u03b1<\/span><\/em>\u4e0d\u540c\u3002<\/span><\/p>\n


    <\/p>\n

    \u4f46\u662fRibeiro\u7b49\u4eba\u8ba4\u4e3a<\/sub><\/span>\u4ec5\u4ee3\u8868\u4e0a\u9650\u3002\u901a\u8fc7\u5bf9\u4e0d\u540c\u57ce\u5e02\u7684N<\/em>\u548cY<\/em>\u7684\u503c\u8fdb\u884c\u7f6e\u6362\uff0c\u516c\u5f0f\u4e0d\u6210\u7acb\uff0c\u4ece\u800c\u4f7f\u76f8\u5173\u6027\u6d88\u5931\uff08\u03b2<\/span><\/em>\u22480\uff09\uff0c\u4f46\u5206\u5e03\u548c\u6307\u6570\u03b1<\/em>\u3001\u03b1<\/em>Y<\/em>\u4ecd\u7136\u4e0d\u53d7\u5f71\u54cd\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u8fd9\u4e2a\u601d\u60f3\u5b9e\u9a8c\u610f\u5473\u7740P(N) ~N–<\/sup><\/span><\/em><\/em><\/em><\/span>\u03b1<\/sup><\/em><\/em><\/em><\/span><\/em><\/em><\/em>\u548cY<\/em>\u223cN<\/em>\u03b2<\/em><\/sup><\/span><\/em>\u53ef\u4ee5<\/span>\u63a8\u5bfc\u51faP(Y)~Y–<\/sup><\/span><\/em><\/em><\/em><\/span>\u03b1<\/sup><\/em><\/em><\/em><\/span>Y<\/sup><\/span><\/em><\/em><\/em><\/span><\/em>\uff0c\u4f46P(N) ~N–<\/sup><\/span><\/em><\/em><\/em><\/span>\u03b1<\/sup><\/em><\/em><\/em><\/span><\/em><\/em><\/em><\/em>\u548cP(Y)~Y–<\/sup><\/span><\/em><\/em><\/em>\u03b1<\/sup><\/em><\/em><\/em><\/span>Y<\/sup><\/span><\/em><\/em><\/em><\/em><\/em>\u5374\u5e76\u4e0d\u80fd\u63a8\u51faY<\/em>\u223cN<\/em>\u03b2<\/em><\/sup><\/span><\/em>\u3002<\/span><\/p>\n


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    3 \u56fd\u5bb6\u6807\u5ea6\u6a21\u578b\uff08H.Ribeiro\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

    \n


    <\/p>\n<\/section>\n

    Ribeiro\u7b49\u4eba\u6839\u636e\u7ecf\u9a8c\u5c06\u57ce\u5e02\u9f50\u592b\u5f8b\u4e0e\u548c\u57ce\u5e02\u6807\u5ea6\u8054\u7cfb\u8d77\u6765\u3002\u57fa\u4e8e\u8bb8\u591a\u56fd\u5bb6\u7684\u6570\u636e\uff0c\u4ed6\u4eec\u53d1\u73b0\u4e86GDP\u7684\u9f50\u592b\u6307\u6570\u03b1<\/em>\u548c\u57ce\u5e02\u6807\u5ea6\u6307\u6570\u03b2<\/em>\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u3002\u4e3a\u4e86\u89e3\u91ca\u8fd9\u4e9b\u76f8\u5173\u6027\uff0c\u4f5c\u8005\u8ba4\u4e3a\uff0c\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u57ce\u5e02\u603b\u4eba\u53e3\uff0c\u5168\u56fd\u8303\u56f4\u5185\u7684\u57ce\u5e02GDP\u662f\u56fa\u5b9a\u7684\uff0c\u4e0d\u540c\u7684\u03b1<\/em>\u503c\u9700\u8981\u5bf9\u03b2<\/em>\u8fdb\u884c\u8c03\u6574\uff0c\u4ee5\u4fdd\u6301\u5168\u56fd\u8303\u56f4\u5185\u7684\u603b\u91cf\u3002\u53cd\u4e4b\u4ea6\u7136\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f5c\u8005\u6ca1\u6709\u5bf9\u53ef\u80fd\u7684\u56e0\u679c\u5173\u7cfb\u7684\u65b9\u5411\u4f5c\u51fa\u8bf4\u660e\u3002\u4f5c\u8005\u63a8\u5bfc\u51fa\u4e0d\u540c\u7684\u03b2<\/em>\u503c\u4e0e\u03b1<\/em>\u5b58\u5728\u4ee5\u4e0b\u5173\u7cfb<\/span>\uff0c\u5176\u4e2d\u03b4\u3001\u03b8\u548c\u03b3\u4e3a<\/span>\u5e38\u6570\u3002<\/span><\/p>\n


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    <\/p>\n


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

    \u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u03b1<\/em>\u548c\u03b2<\/em>\u662f\u8de8\u57ce\u5e02\u7684\u6307\u6570\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u56fd\u5bb6\/\u5730\u533a\uff0c\u5b83\u4eec\u5404\u6709\u4e00\u4e2a\u503c\u3002\u5176\u4ed6\u6307\u6570\u03b4\u3001\u03b8\u548c\u03b3<\/span><\/span>\u662f\u5404\u56fd\u7684\u6807\u5ea6\u56e0\u5b50\u3002\u8fd9\u610f\u5473\u7740\uff0c\u8003\u8651\u4e00\u4e2a\u56fd\u5bb6\u6216\u4e00\u4e2a\u7c7b\u4f3c\u7684\u533a\u57df\uff0c\u56fd\u5bb6\u6807\u5ea6\u56e0\u5b50\u662f\u5e38\u6570\u3002\u4f46\u662f\u4f5c\u8005\u63a8\u5bfc\u51fa\u7684\u56fd\u5bb6\u6807\u5ea6\u56e0\u5b50\u53ea\u662f\u5e73\u5747\u800c\u8a00\u7684\uff0c\u56e0\u6b64\u8fd8\u9700\u8981\u66f4\u7ec6\u81f4\u7684\u89e3\u91ca\u3002<\/span><\/p>\n


    <\/h2>\n
    \n
    \n
    \n

    4 \u5438\u5f15\u529b\u6807\u7b7e\u6a21\u578b\uff08Altmann\u7b49\u4eba<\/span><\/strong>\uff09<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

    \n


    <\/p>\n<\/section>\n

    D. Altmann\u7b49\u4eba\u7684\u5438\u5f15\u529b\u6807\u7b7e\u6a21\u578b<\/span>\uff08attractiveness token\uff09<\/span>\u662f\u5728\u6700\u521d\u7531Leit\u00e3o\u7b49\u4eba\u63d0\u51fa\u7684\u65b9\u6cd5\u57fa\u7840\u4e0a\u5f00\u53d1\u7684\u3002\u8fd9\u4e2a\u6a21\u578b\u4e0e\u5176\u4ed6\u6a21\u578b\u4e0d\u540c\uff0c\u56e0\u4e3a\u5b83\u4e0d\u4f1a\u5bfc\u81f4\u6807\u5ea6\u56e0\u5b50\u6210\u4e3a\u4e00\u79cd\u6d8c\u73b0\u7684\u73b0\u8c61\u3002\u7136\u800c\uff0c\u6709\u5fc5\u8981\u63d0\u5230\u5b83\uff0c\u662f\u56e0\u4e3a\u8be5\u6a21\u578b\u5efa\u7acb\u5728\u4e0d\u540c\u57ce\u5e02\u7684\u4e2a\u4f53\u4e4b\u95f4\u7684\u4e92\u52a8\u4e0a\uff0c\u5f15\u5165\u4e86\u5173\u4e8e\u6574\u5408\u57ce\u5e02\u5185\u90e8\u548c\u57ce\u5e02\u4e4b\u95f4\u6a21\u578b\u7684\u60f3\u6cd5\u3002\u6b64\u5916\uff0c\u8fd9\u4e2a\u6a21\u578b\u8fd8\u63d0\u51fa\u4e86\u7eb3\u5165\u57ce\u5e02\u5185\u90e8\u6a21\u5f0f\u7684\u60f3\u6cd5\uff0c\u4ee5\u4fbf\u6269\u5c55\u57ce\u5e02\u95f4\u6a21\u578b\u3002<\/span><\/p>\n


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

    \u8be5\u6a21\u578b\u8003\u8651\u4e86\u4e00\u4e2a\u7531Ncit<\/sub><\/em>\u4e2a\u57ce\u5e02\u7ec4\u6210\u7684\u57ce\u5e02\u7cfb\u7edf\uff0c\u5176\u4e2dNc<\/sub><\/em>\u662f\u7b2cc-th<\/em>\u4e2a\u57ce\u5e02\u7684\u4eba\u53e3\uff0c\u4ee5\u8fd9\u79cd\u65b9\u5f0f\uff0c\u57ce\u5e02\u7cfb\u7edf\u7684\u603b\u4eba\u53e3\u4e3aN*<\/em>\u3002\u5c06\u6807\u7b7eY*<\/em>\u968f\u673a\u5206\u914d\u7ed9\u7cfb\u7edf\u7684\u4eba\uff0c\u8fd9\u79cd\u6807\u5fd7\u53ef\u4ee5\u662f\u4e00\u9879\u4e13\u5229\u6216\u4e00\u9879\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u51fa\u3002\u7528p(i)<\/em>\u8868\u793a\u5728N*<\/em>\u4e2a\u4eba\u4e2d\uff0c\u4e00\u4e2a\u6807\u7b7e\u88ab\u5f52\u4e8e\u4e2a\u4ebai<\/em>\u7684\u6982\u7387\u3002Altmann\u63d0\u51fa\uff0c\u8fd9\u4e2a\u6807\u7b7e\u5206\u914d\u662f\u8be5\u4e2a\u4f53\u7684\u5438\u5f15\u529bxi<\/sub><\/em>\u7684\u51fd\u6570\u3002\u5438\u5f15\u529b\u5c06\u4e0e\u4e2a\u4eba\u83b7\u5f97\u6807\u7b7e\u7684\u80fd\u529b\u6709\u5173\uff0c\u4f8b\u5982\uff0c\u9b45\u529b\u3001\u9886\u5bfc\u529b\u6216\u4e13\u4e1a\u57f9\u8bad\u7b49\u3002\u8fd9\u4e2a\u6570\u91cf\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u8fd9\u4e2a\u4eba\u548c\u6240\u6709\u5176\u4ed6\u4eba\u4e4b\u95f4\u4e92\u52a8\u7684\u7ed3\u679c\uff0c\u5176\u516c\u5f0f\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/span><\/p>\n


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

    <\/p>\n


    <\/p>\n

    \u5176\u4e2dpint<\/sub>(rij<\/sub>)<\/em>\u662f\u8861\u91cfi<\/em>\u548cj<\/em>\u8fd9\u4e24\u4e2a\u4e2a\u4f53\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u5b83\u4eec\u4e4b\u95f4\u7684\u8ddd\u79bb\u662frij<\/sub><\/em>\u3002\u5176\u4e2d\uff0ci<\/em>\u548cj<\/em>\u53ef\u4ee5\u5c5e\u4e8e\u540c\u4e00\u4e2a\u57ce\u5e02\uff0c\u4e5f\u53ef\u4ee5\u5c5e\u4e8e\u4e0d\u540c\u7684\u57ce\u5e02\u3002<\/span><\/p>\n


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

    \u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5438\u5f15\u529bxi<\/sub><\/em>\u4e5f\u51fa\u73b0\u5728Yakubo\u7b49\u4eba\u7684\u6a21\u578b\u4e2d\uff0c\u800cpint<\/sub>(rij<\/sub>)<\/em>\u662f\u5f15\u529b\u6a21\u578b\u4e2d\u7684\u4e92\u52a8\u6982\u7387\u3002\u5f53pint<\/sub>(rij<\/sub>)<\/em>=0\u65f6\uff0ci<\/em>\u548cj<\/em>\u5c45\u4f4f\u5728\u4e0d\u540c\u7684\u57ce\u5e02\u3002Yakubo\u7b49\u4eba\u6240\u8003\u8651\u7684\u5438\u5f15\u529b\u4e0eAltmann\u6240\u8003\u8651\u7684\u5438\u5f15\u529b\u4e4b\u95f4\u6709\u4e00\u4e2a\u5fae\u5999\u4f46\u91cd\u8981\u7684\u533a\u522b\u3002\u5728\u524d\u8005\u5438\u5f15\u529b\u610f\u5473\u7740\u4e92\u52a8\u7684\u6982\u7387\uff0c\u800c\u5728\u540e\u8005\u5438\u5f15\u529b\u662f\u4e92\u52a8\u6982\u7387\u7684\u7ed3\u679c\uff0c\u8be6\u7ec6\u63a8\u5bfc\u8fc7\u7a0b\u53ef\u67e5\u770b\u539f\u6587\u3002<\/span><\/p>\n


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

    Altmann\u8ba4\u4e3a\uff0c\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u51fa\u73b0\u662f\u4e2a\u4eba\u6548\u7387\u7684\u975e\u7ebf\u6027\u7684\u7ed3\u679c\uff0c\u5b83\u53d6\u51b3\u4e8e\u4ed6\u4eec\u6240\u5c45\u4f4f\u7684\u57ce\u5e02\u7684\u5927\u5c0f\uff0c\u901a\u8fc7\u6539\u53d8\u53c2\u6570\u53ef\u4ee5\u6a21\u62df\u4e0d\u540c\u4e2a\u4f53\u4e92\u52a8\u7684\u8303\u56f4<\/span>\uff08\u57ce\u5e02\u5185\u90e8\u6216\u57ce\u5e02\u95f4\uff09<\/span>\u3002\u56e0\u6b64\uff0c\u5728\u672a\u6765\u7684\u5de5\u4f5c\u4e2d\uff0c\u5c06\u4ee5\u524d\u63d0\u51fa\u7684\u6a21\u578b\u4e2d\u7684\u4e00\u4e9b\u60f3\u6cd5\u7eb3\u5165\u8fd9\u4e2a\u6a21\u578b\u53ef\u80fd\u4f1a\u5f88\u6709\u8da3\u3002\u4f8b\u5982\uff0c\u7eb3\u5165\u5438\u5f15\u529b\u7684\u5e42\u5f8b\u5206\u5e03\uff0c\u5982Yakubo\u6240\u505a\u7684\u90a3\u6837\uff0c\u6216\u8005\u4f7f\u7528\u5728\u5f15\u529b\u6a21\u578b\u80cc\u666f\u4e0b\u8ba8\u8bba\u7684\u53c2\u6570\u03b3\u6240\u4f53\u73b0\u7684\u4e92\u52a8\u8303\u56f4\u3002<\/span><\/p>\n


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

     <\/span><\/section>\n

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

    <\/section>\n
    \n
    <\/svg><\/section>\n<\/section>\n<\/section>\n
    \n

    \u56db\u3001\u603b\u7ed3\u4e0e\u8ba8\u8bba<\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

    \u5927\u591a\u6570\u57ce\u5e02\u5185\u90e8\u6a21\u578b\u8ba4\u4e3a\u57ce\u5e02\u6807\u5ea6\u7684\u51fa\u73b0\u6765\u81ea\u4e8e\u4eba\u7c7b\u7684\u4e92\u52a8\uff0c\u5373\u57ce\u5e02\u4e2d\u6709\u610f\u6216\u65e0\u610f\u5730\u4e0e\u4eba\u76f8\u9047\u3002\u4f8b\u5982\uff0cBettencourt\u63d0\u51fa\u7684\u6a21\u578b\u91c7\u7528\u4e86\u7269\u7406\u5b66\u4e2d\u5df2\u77e5\u7684\u6a2a\u622a\u9762\u6982\u5ff5\u8fdb\u884c\u7c7b\u6bd4\u3002\u5728\u57ce\u5e02\u5185\u90e8\u91c7\u7528\u4eba\u7c7b\u4e92\u52a8\u7684\u6a21\u578b\u662f\u57fa\u4e8e\u4e00\u4e2a\u7279\u5b9a\u7684\u4e92\u52a8\u6982\u7387\u3002\u8fd9\u4fc3\u4f7f\u6211\u4eec\u5c06\u8fd9\u79cd\u6982\u5ff5\u4e0a\u7684\u91cd\u53e0\u7edf\u4e00\u5230\u4e00\u4e2a\u5c06\u8fd9\u79cd\u6982\u7387\u6b63\u89c4\u5316\u7684\u6846\u67b6\u4e2d\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u7ec4\u6a21\u578b\u53ea\u662f\u5728\u5982\u4f55\u4f30\u8ba1\u4e92\u52a8\u6982\u7387\u7684\u63a8\u7406\u4e0a\u6709\u533a\u522b\u3002\u5728\u56de\u987e\u5f15\u529b\u6a21\u578b\u65f6\uff0c\u6709\u4e09\u7ec4\u4f5c\u8005\u72ec\u7acb\u5730\u91c7\u7528\u4e86\u4e0d\u540c\u7684\u89c2\u70b9\uff0c\u5bfc\u81f4\u4e86\u76f8\u540c\u7684\u7ed3\u679c<\/span>\uff08\u5728\u7ed9\u5b9a\u7684\u53c2\u6570\u7ec4\u5408\u4e2d\uff09<\/span>\u3002\u7269\u7406\u5b66\u4e2d\u5bf9\u5f15\u529b\u7684\u7c7b\u6bd4\u6709\u5f88\u957f\u7684\u5386\u53f2\uff0c\u5e76\u5728\u66f4\u5e7f\u6cdb\u7684\u80cc\u666f\u4e0b\u8fdb\u884c\u4e86\u7814\u7a76\u3002\u76f8\u5e94\u5730\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u5c0f\u7684\u5c55\u671b\uff0c\u8fdb\u4e00\u6b65\u7edf\u4e00\u5f15\u529b\u7684\u5e94\u7528\u5c06\u662f\u6709\u8da3\u7684\u3002<\/span><\/p>\n


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

    \u672c\u6587\u8fd8\u56de\u987e\u4e86\u57ce\u5e02\u95f4\u7684\u6a21\u578b\uff0c\u5e76\u53d1\u73b0\u8fd9\u4e00\u9886\u57df\u5f88\u6709\u524d\u9014\uff0c\u4f46\u8fdb\u5c55\u8f83\u5c11\u3002\u9996\u5148\uff0c\u8fd9\u4e2a\u5206\u652f\u7684\u6a21\u578b\u8f83\u5c11\u3002\u5176\u6b21\uff0c\u8fd9\u7c7b\u6a21\u578b\u4e0d\u592a\u660e\u786e\uff0c\u57ce\u5e02\u6807\u5ea6\u7684\u51fa\u73b0\u51e0\u4e4e\u6ca1\u6709\u63a8\u5bfc\uff0c\u800c\u662f\u4e0e\u5176\u4ed6\u89c4\u6a21\u6cd5\u5219<\/span>\u6709\u5173\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u672c\u6587\u4ecd\u7136\u8ba4\u4e3a\u57ce\u5e02\u4e0d\u662f\u5b64\u7acb\u7684\u5bf9\u8c61\uff0c\u5b83\u4eec\u4e4b\u95f4\u5b58\u5728\u7740\u91cd\u8981\u7684\u4e92\u52a8\u3002\u540c\u65f6\uff0c\u57ce\u5e02\u5185\u90e8\u7684\u6a21\u578b\u4e5f\u662f\u57fa\u4e8e\u5408\u7406\u7684\u5047\u8bbe\uff0c\u5e76\u88ab\u8bc1\u660e\u5728\u63cf\u8ff0\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u65b9\u9762\u662f\u6210\u529f\u7684\u3002\u56e0\u6b64\u6709\u7406\u7531\u8ba4\u4e3a\uff0c\u57ce\u5e02\u5185\u90e8\u548c\u57ce\u5e02\u4e4b\u95f4\u7684\u6a21\u578b\u7684\u53d1\u5c55\u662f\u8fc8\u5411\u7edf\u4e00\u57ce\u5e02\u7406\u8bba<\/span>\uff08Uni\ufb01ed Urban Theory\uff09<\/span>\u7684\u91cd\u8981\u4e00\u6b65\u3002<\/span><\/p>\n


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

    \u6700\u540e\uff0c\u6709\u5fc5\u8981\u63d0\u53ca\u6700\u8fd1\u53d1\u8868\u7684\u5176\u4ed6\u6a21\u578b\u548c\u65b9\u6cd5\uff0c\u8fd9\u4e9b\u6a21\u578b\u548c\u65b9\u6cd5\u4e5f\u6709\u52a9\u4e8e\u7406\u89e3\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u7684\u7279\u6027\uff0c\u4f46\u4e0e\u672c\u6587\u4ecb\u7ecd\u7684\u6a21\u578b\u6709\u4e00\u5b9a\u7684\u533a\u522b\u3002\u4f8b\u5982\uff0c\u4e00\u4e9b\u6587\u7ae0\u5c06\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u4f5c\u4e3a\u5176\u4ed6\u5e42\u5f8b\u51fd\u6570\u6216\u5206\u5e03\u7684\u7ed3\u679c\u6765\u5206\u6790\uff0c\u5982Bettencourt\u7684\u80fd\u91cf\u8017\u6563\u6a21\u578b\u3002\u8fd9\u79cd\u65b9\u6cd5\u5bf9\u4e8e\u63cf\u8ff0\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219<\/span>\u5f88\u91cd\u8981\uff0c\u4f46\u5b83\u5e76\u6ca1\u6709\u4ece\u6839\u672c\u4e0a\u89e3\u91ca\u6216\u63a8\u5bfc\u51fa\u6807\u5ea6\u56e0\u5b50\u3002\u53e6\u4e00\u4e9b\u540c\u6837\u81f4\u529b\u4e8e\u89e3\u91ca\u6807\u5ea6\u56e0\u5b50\u7684\u7814\u7a76\u5219\u91c7\u7528\u4e86\u6570\u636e\u9a71\u52a8\u7684\u65b9\u6cd5\u3002<\/span><\/p>\n


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

    \u8fd8\u9700\u7279\u522b\u6307\u51fa\u7684\u662f\uff0c\u8fd9\u7bc7\u6587\u7ae0\u53ea\u8003\u8651\u4e86\u57ce\u5e02\u6807\u5ea6\u53d1\u5c55\u7684\u6a2a\u622a\u9762\u3002\u6a2a\u622a\u9762<\/span>\uff08\u6a2a\u5411\uff09<\/span>\u548c\u65f6\u95f4\u6807\u5ea6<\/span>\uff08\u7eb5\u5411\uff09<\/span>\u662f\u540c\u6837\u91cd\u8981\u7684\u3002\u4ece\u672c\u8d28\u4e0a\u8bb2\uff0c\u8003\u8651\u5230\u57ce\u5e02\u6709\u8db3\u591f\u5927\u7684\u589e\u957f\u7387\u4e14\u6ca1\u6709\u5916\u751f\u56e0\u7d20\u5e72\u6270\u7684\u60c5\u51b5\u4e0b\uff0c\u65f6\u95f4\u6807\u5ea6\u5f8b\u548c\u6a2a\u622a\u9762\u7684\u6807\u5ea6\u5f8b\u662f\u4e00\u6837\u7684\u3002\u6700\u8fd1\uff0c\u6709\u4e24\u4e2a\u7814\u7a76\u5c0f\u7ec4\u72ec\u7acb\u800c\u4e00\u81f4\u5730\u63d0\u4f9b\u4e86\u5173\u4e8e\u8fd9\u65b9\u9762\u7406\u8bba\u4e0a\u7684\u63cf\u8ff0\u3002<\/span> <\/span><\/p>\n


    <\/p>\n


    <\/p>\n

    \n
    \n
    \n

    \u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

    \n
    \n
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    \n

    1. Arbesman, S., Kleinberg, J. M., & Strogatz, S. H. (2009). Superlinear scaling for innovation in cities. Physical Review E<\/em>, 79<\/em>(1), 016115.<\/p>\n

    2. Batty, M. (2013). The new science of cities<\/em>. MIT press.<\/p>\n

    3. Bettencourt, L. M. (2013). The origins of scaling in cities. science<\/em>, 340<\/em>(6139), 1438-1441.<\/p>\n

    4. Molinero, C., & Thurner, S. (2019). How the geometry of cities explains urban scaling laws and determines their exponents. arXiv preprint arXiv:1908.07470<\/em>.<\/p>\n

    5. Ribeiro, F. L., Meirelles, J., Ferreira, F. F., & Neto, C. R. (2017). A model of urban scaling laws based on distance dependent interactions. Royal Society open science<\/em>, 4<\/em>(3), 160926.<\/p>\n

    6. Yang, V. C., Papachristos, A. V., & Abrams, D. M. (2019). Modeling the origin of urban-output scaling laws. Physical Review E<\/em>, 100<\/em>(3), 032306.<\/p>\n

    7. Yakubo, K., & Koro\u0161ak, D. (2011). Scale-free networks embedded in fractal space. Physical Review E<\/em>, 83<\/em>(6), 066111.<\/p>\n

    8. Yakubo, K., Saijo, Y., & Koro\u0161ak, D. (2014). Superlinear and sublinear urban scaling in geographical networks modeling cities. Physical Review E<\/em>, 90<\/em>(2), 022803.<\/p>\n

    9. G\u00f3mez-Li\u00e9vano, A., Vysotsky, V., & Lobo, J. (2021). Artificial increasing returns to scale and the problem of sampling from lognormals. Environment and Planning B: Urban Analytics and City Science<\/em>, 48<\/em>(6), 1574-1590.<\/p>\n

    10. Leitao, J. C., Miotto, J. M., Gerlach, M., & Altmann, E. G. (2016). Is this scaling nonlinear?. Royal Society open science<\/em>, 3<\/em>(7), 150649.<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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    \uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n


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    \u57ce\u5e02\u662f\u4e00\u573a\u6d41\u52a8\u7684\u76db\u5bb4\uff0c\u8fd9\u91cc\u805a\u96c6\u591a\u6837\u5316\u7684\u4eba\u7fa4\u3001\u5b55\u80b2\u79d1\u6280\u6587\u5316\u521b\u65b0\uff0c\u5374\u4e5f\u6ecb\u751f\u4ea4\u901a\u62e5\u5835\u3001\u73af\u5883\u6c61\u67d3\u7b49\u95ee\u9898\u3002\u6211\u4eec\u8feb\u5207\u9700\u8981\u5bf9\u57ce\u5e02\u7684\u57fa\u672c\u8fd0\u884c\u89c4\u5f8b\u6709\u79d1\u5b66\u7684\u8ba4\u77e5\u3002\u8fd1\u5341\u51e0\u5e74\u6765\uff0c\u667a\u80fd\u624b\u673a\u3001\u7269\u8054\u7f51\u3001\u536b\u661f\u9065\u611f\u53ef\u4ee5\u5e2e\u52a9\u83b7\u53d6\u9ad8\u7cbe\u5ea6\u7684\u57ce\u5e02\u6570\u636e\uff1b\u673a\u5668\u5b66\u4e60\u3001\u4eba\u5de5\u667a\u80fd\u7684\u53d1\u5c55\uff0c\u4e3a\u5904\u7406\u5927\u89c4\u6a21\u591a\u6e90\u5f02\u6784\u6570\u636e\u63d0\u4f9b\u4e86\u6280\u672f\u624b\u6bb5\u3002\u6b64\u5916\uff0c\u590d\u6742\u79d1\u5b66\u4ece\u6f14\u751f\u89c6\u89d2\uff0c\u5728\u4e0d\u540c\u65f6\u7a7a\u5c3a\u5ea6\u4e0a\u7814\u7a76\u57ce\u5e02\u73b0\u8c61\u7684\u57fa\u7840\u89c4\u5f8b\uff0c\u4e30\u5bcc\u4e86\u57ce\u5e02\u79d1\u5b66\u7684\u7406\u8bba\u6846\u67b6\uff1b\u57fa\u4e8e\u590d\u6742\u7cfb\u7edf\u7684\u6a21\u62df\u65b9\u6cd5\u4e5f\u5728\u5b9e\u8df5\u4e2d\u6709\u5e7f\u9614\u7684\u5e94\u7528\u524d\u666f\u3002<\/span><\/p>\n


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    \u5728\u8fd9\u4e2a\u5927\u80cc\u666f\u4e0b\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u201c\u57ce\u5e02\u79d1\u5b66\u201d\u8bfb\u4e66\u4f1a<\/a>\u7531\u5317\u4eac\u5927\u5b66\u52a9\u7406\u6559\u6388\u8463\u78ca\u8054\u5408\u660e\u5c3c\u82cf\u8fbe\u5927\u5b66\u52a9\u7406\u6559\u6388\u6731\u9012\u3001\u4e2d\u5357\u5927\u5b66\u5730\u7403\u79d1\u5b66\u4e0e\u4fe1\u606f\u7269\u7406\u5b66\u9662\u6559\u6388\u674e\u6d77\u5cf0\u3001\u5317\u4eac\u822a\u7a7a\u822a\u5929\u5927\u5b66\u8ba1\u7b97\u673a\u5b66\u9662\u535a\u58eb\u5bc4\u5bb6\u8c6a\u5171\u540c\u53d1\u8d77\uff0c\u5206\u4eab\u3001\u8ba8\u8bba\u548c\u68b3\u7406\u201c\u57ce\u5e02\u4f5c\u4e3a\u590d\u6742\u7cfb\u7edf\u201d\u7684\u7406\u8bba\u3001\u7814\u7a76\u65b9\u6cd5\u53ca\u5e94\u7528\uff0c\u5e0c\u671b\u4fc3\u8fdb\u76f8\u5173\u9886\u57df\u5b66\u8005\u7684\u4ea4\u6d41\uff0c\u63a8\u52a8\u4ea4\u53c9\u5b66\u79d1\u95f4\u7684\u5408\u4f5c\uff0c\u4fc3\u8fdb\u57ce\u5e02\u79d1\u5b66\u7684\u53d1\u5c55\u548c\u7814\u7a76\u3002\u8bfb\u4e66\u4f1a\u4ece2023\u5e747\u67081\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u516d\u665a 20:00-22:00\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba110\u5468\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/p>\n


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

    \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>\u57ce\u5e02\u79d1\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1aAI\u4e0e\u56e0\u679c\u4ea4\u7ec7\u7684\u57ce\u5e02\u590d\u6742\u7cfb\u7edf<\/a><\/span><\/strong><\/p>\n

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    <\/p>\n

    \n

    \u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n

    1. <\/strong>Luis Bettencourt\uff1a\u4e2d\u56fd\u57ce\u5e02\u53d1\u5c55\uff0c\u4ecd\u7136\u9075\u5faa\u666e\u904d\u7684\u89c4\u6a21\u6cd5\u5219<\/a>  <\/strong><\/span><\/section>\n
    2.<\/strong> Nat. Comput. Sci. \u6700\u65b0\uff1a\u4eba\u7c7b\u79fb\u52a8\u884c\u4e3a\u6d8c\u73b0\u57ce\u5e02\u53d1\u5c55\u89c4\u5f8b<\/a><\/strong><\/span><\/strong><\/section>\n
    3.<\/strong><\/strong> \u57ce\u5e02\u7b49\u7ea7\u5982\u4f55\u5f71\u54cd\u521b\u65b0\u7684\u7a7a\u95f4\u6269\u6563?\u2014\u2014\u5bf9300\u4e07\u4e2a\u4f20\u64ad\u4e8b\u4ef6\u7684\u7814\u7a76<\/a><\/strong><\/span><\/section>\n
    4. \u300a\u5f20\u6c5f\u00b7\u590d\u6742\u79d1\u5b66\u524d\u6cbf27\u8bb2\u300b\u5b8c\u6574\u4e0a\u7ebf\uff01<\/strong><\/a><\/strong><\/strong><\/strong><\/section>\n
    <\/strong><\/a><\/strong><\/strong><\/strong><\/section>\n
    5. \u6210\u4e3a\u96c6\u667aVIP\uff0c\u89e3\u9501\u5168\u7ad9\u8bfe\u7a0b\uff0f\u8bfb\u4e66\u4f1a<\/span><\/strong><\/a><\/strong><\/strong><\/strong><\/strong><\/section>\n
    6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/a><\/strong><\/strong><\/strong><\/span><\/section>\n


    <\/p>\n<\/section>\n


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

    \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a <\/span><\/strong><\/span><\/strong><\/span><\/strong>
    <\/p>\n<\/section>\n

    <\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    \u5bfc\u8bed \u4eba\u7c7b\u9762\u4e34\u7740\u57ce\u5e02\u5316\u548c\u57ce\u5e02\u4eba\u53e3\u5bc6\u5ea6\u4e0d\u65ad\u589e\u52a0\u7684\u6311\u6218\uff0c\u5bfb\u6c42\u4e00\u79cd\u80fd\u591f\u4e3a\u7ba1\u7406\u57ce\u5e02\u63d0\u4f9b\u91cf\u5316\u548c\u7cfb\u7edf\u5316\u65b9\u6cd5\u7684\u57ce\u5e02\u7406\u8bba\u662f\u5f53\u52a1\u4e4b\u6025\u3002\u5982\u679c\u8fd9\u6837\u7684\u7406\u8bba\u662f\u53ef\u884c\u7684\uff0c\u90a3\u4e48\u5b83\u5fc5\u987b\u4ee5\u6570\u5b66\u7684\u65b9\u5f0f\u6765\u8868\u8ff0\u3002\u6700\u8fd1\u53d1\u8868\u5728 Physics Reports \u7684\u4e00\u7bc7\u6587\u7ae0\u7efc\u8ff0\u4e86\u5173\u4e8e\u7cfb\u7edf\u7406\u89e3\u57ce\u5e02\u73b0\u8c61\u7684\u6570\u5b66\u601d\u60f3\u3002\u6587\u7ae0\u9996\u5148\u6eaf\u6e90\u4e86\u76f8\u5173\u6587\u732e\u4e2d\u57ce\u5e02\u89c4\u6a21\u6cd5\u5219\uff08…<\/p>\n","protected":false},"author":0,"featured_media":43159,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/43199"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=43199"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/43199\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/43159"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=43199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=43199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=43199"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=43199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}