{"id":103,"date":"2016-05-02T02:00:52","date_gmt":"2016-05-02T02:00:52","guid":{"rendered":"http:\/\/blogs.softwareclue.com\/?p=103"},"modified":"2016-05-02T02:23:56","modified_gmt":"2016-05-02T02:23:56","slug":"%e7%ba%af%e7%b2%b9%e6%95%b0%e5%ad%a6%e7%9a%84%e9%9b%aa%e5%b4%a9%e6%95%88%e5%ba%94%ef%bc%9a%e5%ba%9e%e5%8a%a0%e8%8e%b1%e7%8c%9c%e6%83%b3%e4%bd%95%e4%bb%a5%e9%80%a0%e7%a6%8f%e4%ba%86%e7%b2%be%e5%87%86","status":"publish","type":"post","link":"http:\/\/blog.softwareclues.com\/zh\/%e7%ba%af%e7%b2%b9%e6%95%b0%e5%ad%a6%e7%9a%84%e9%9b%aa%e5%b4%a9%e6%95%88%e5%ba%94%ef%bc%9a%e5%ba%9e%e5%8a%a0%e8%8e%b1%e7%8c%9c%e6%83%b3%e4%bd%95%e4%bb%a5%e9%80%a0%e7%a6%8f%e4%ba%86%e7%b2%be%e5%87%86","title":{"rendered":"\u7eaf\u7cb9\u6570\u5b66\u7684\u96ea\u5d29\u6548\u5e94\uff1a\u5e9e\u52a0\u83b1\u731c\u60f3\u4f55\u4ee5\u9020\u798f\u4e86\u7cbe\u51c6\u533b\u7597\uff1f"},"content":{"rendered":"

\u539f\u521b<\/span> 2016-04-12<\/em> \u987e\u9669\u5cf0<\/em> \u8d5b\u5148\u751f<\/span><\/p>\n

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\u56fe1 \u5e9e\u52a0\u83b1\u731c\u60f3\u7535\u8111\u4e09\u7ef4\u6a21\u578b<\/span><\/strong>
\n<\/span><\/p>\n

\u987e\u9669\u5cf0\u00a0(\u7ebd\u7ea6\u5dde\u7acb\u5927\u5b66\u77f3\u6eaa\u5206\u6821\u7ec8\u8eab\u6559\u6388\uff0c\u6e05\u534e\u5927\u5b66\u4e18\u6210\u6850\u6570\u5b66\u79d1\u5b66\u4e2d\u5fc3\u8bbf\u95ee\u6559\u6388\uff0c\u8ba1\u7b97\u5171\u5f62\u51e0\u4f55\u521b\u59cb\u4eba)<\/p><\/blockquote>\n

\u6700\u8fd1\u82f1\u56fd\u4e0a\u8bae\u9662\u8bae\u5458\u9a6c\u7279\u745e\u5fb7\u5229\uff08Matt Ridley\uff09\u5728\u300a\u534e\u5c14\u8857\u65e5\u62a5\u300b\u4e0a\u64b0\u6587\u300a\u57fa\u7840\u79d1\u5b66\u7684\u8ff7\u601d\u300b<\/a>\uff08The Myth of Basic Science\uff09\u3002\u4ed6\u8ba4\u4e3a\u201c\u79d1\u5b66\u9a71\u52a8\u521b\u65b0\uff0c\u521b\u65b0\u9a71\u52a8\u5546\u4e1a\u201d\u8fd9\u4e00\u8bf4\u6cd5\u57fa\u672c\u4e0a\u662f\u9519\u8bef\u7684\uff0c\u53cd\u800c\u662f\u5546\u4e1a\u9a71\u52a8\u4e86\u521b\u65b0\uff0c\u521b\u65b0\u9a71\u52a8\u4e86\u79d1\u5b66\uff0c\u6b63\u5982\u79d1\u5b66\u5bb6\u88ab\u5b9e\u9645\u9700\u6c42\u6240\u9a71\u52a8\uff0c\u800c\u4e0d\u662f\u79d1\u5b66\u5bb6\u9a71\u52a8\u5b9e\u9645\u9700\u6c42\u4e00\u6837\u3002\u603b\u4e4b\uff0c\u4ed6\u8ba4\u4e3a\u201c\u79d1\u5b66\u7a81\u7834\u662f\u6280\u672f\u8fdb\u6b65\u7684\u7ed3\u679c\uff0c\u800c\u4e0d\u662f\u539f\u56e0\u201d\u3002<\/p>\n

\u745e\u5fb7\u5229\u5148\u751f\u7684\u8a00\u8bba\u53cd\u6620\u4e86\u8bb8\u591a\u4eba\u5bf9\u57fa\u7840\u79d1\u5b66\u7684\u4e25\u91cd\u8bef\u89e3\uff0c\u4f1a\u7ed9\u5e74\u8f7b\u5b66\u5b50\u4eec\u5e26\u6765\u601d\u60f3\u6df7\u4e71\u548c\u4ef7\u503c\u89c2\u5ff5\u4e0a\u7684\u56f0\u6270\uff0c\u6709\u5fc5\u8981\u52a0\u4ee5\u6f84\u6e05\u3002\u8bda\u7136\uff0c\u5546\u4e1a\u9700\u6c42\u548c\u5de5\u7a0b\u5b9e\u8df5\u4f1a\u4e3a\u57fa\u7840\u79d1\u5b66\u63d0\u4f9b\u7814\u7a76\u7684\u7d20\u6750\uff0c\u6bd4\u5982\u5386\u53f2\u4e0a\u6700\u4f18\u4f20\u8f93\u7406\u8bba\uff08OptimalMass Transportation Theory\uff09\u548c\u8499\u65e5-\u5b89\u57f9\u65b9\u7a0b\uff08Monge-Ampere\uff09\u8d77\u6e90\u4e8e\u571f\u77f3\u65b9\u7684\u8fd0\u8f93\uff0c\u6700\u540e\u731c\u60f3\u88ab\u5eb7\u5854\u6d1b\u7ef4\u5947\u89e3\u51b3\uff0c\u5eb7\u5854\u6d1b\u7ef4\u5947\u4e3a\u6b64\u83b7\u5f97\u4e86\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5b66\u5956\u3002\u6570\u5e74\u524d\uff0c\u4e3a\u4e86\u89e3\u51b3\u533b\u5b66\u56fe\u50cf\u7684\u538b\u7f29\u95ee\u9898\uff0c\u9676\u54f2\u8f69\u63d0\u51fa\u4e86\u538b\u7f29\u611f\u77e5\uff08Compressive Sensing\uff09\u7406\u8bba\u3002\u4f46\u662f\uff0c\u4ece\u6839\u672c\u4e0a\u800c\u8a00\uff0c\u57fa\u7840\u79d1\u5b66\u7684\u6e90\u52a8\u529b\u6765\u81ea\u4e8e\u79d1\u5b66\u5bb6\u5bf9\u4e8e\u81ea\u7136\u771f\u7406\u7684\u597d\u5947\u548c\u5bf9\u7f8e\u5b66\u4ef7\u503c\u7684\u8ffd\u6c42\u3002\u57fa\u7840\u79d1\u5b66\u4e0a\u7684\u7a81\u7834\uff0c\u56e0\u4e3a\u63ed\u793a\u4e86\u81ea\u7136\u754c\u7684\u5ba2\u89c2\u771f\u7406\uff0c\u5f80\u5f80\u4f1a\u5f15\u53d1\u5e94\u7528\u79d1\u5b66\u7684\u9769\u547d\u3002\u7eaf\u7cb9\u6570\u5b66\u7684\u7814\u7a76\u56e0\u4e3a\u5176\u6666\u6da9\u62bd\u8c61\uff0c\u5b9e\u7528\u4ef7\u503c\u5e76\u4e0d\u660e\u663e\u76f4\u89c2\uff0c\u666e\u7f57\u5927\u4f17\u4e00\u76f4\u503e\u5411\u4e8e\u8ba4\u4e3a\u5176\u201c\u65e0\u7528\u201d\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u7eaf\u7cb9\u6570\u5b66\u5bf9\u5e94\u7528\u79d1\u5b66\u7684\u6307\u5bfc\u4f5c\u7528\u662f\u65e0\u53ef\u66ff\u4ee3\u7684\u3002<\/span><\/p>\n

\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u6280\u672f\u53d1\u5c55\u7684\u4e00\u4e2a\u4fa7\u9762\u5c31\u5728\u4e8e\u5c06\u4eba\u7c7b\u6570\u5343\u5e74\u79ef\u7d2f\u7684\u77e5\u8bc6\u8f6c\u6362\u6210\u7b97\u6cd5\uff0c\u4f7f\u5f97\u6ca1\u6709\u7ecf\u5386\u8fc7\u804c\u4e1a\u8bad\u7ec3\u7684\u4eba\u4e5f\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u6700\u4e3a\u8270\u6df1\u7684\u6570\u5b66\u7406\u8bba\u3002\u5728\u62d3\u6251\u548c\u51e0\u4f55\u9886\u57df\uff0c\u5f80\u5f80\u5f88\u591a\u5177\u6709\u6570\u767e\u5e74\u5386\u53f2\u7684\u5b9a\u7406\u4ec5\u4ec5\u5728\u6700\u8fd1\u624d\u88ab\u8f6c\u6362\u6210\u7b97\u6cd5\u3002\u4f46\u662f\uff0c\u4f9d\u968f\u8ba1\u7b97\u673a\u6280\u672f\u7684\u8fc5\u731b\u53d1\u5c55\uff0c\u4ece\u5b9a\u7406\u5230\u7b97\u6cd5\u7684\u8fc7\u7a0b\u65e5\u76ca\u52a0\u901f\u3002\u5f88\u591a\u65b0\u8fd1\u53d1\u5c55\u7684\u6570\u5b66\u7406\u8bba\u88ab\u8fc5\u901f\u8f6c\u6362\u6210\u5f3a\u6709\u529b\u7684\u7b97\u6cd5\uff0c\u5e76\u5728\u5de5\u7a0b\u548c\u533b\u7597\u9886\u57df\u88ab\u5e7f\u6cdb\u5e94\u7528\u3002<\/span><\/p>\n

\u5386\u53f2\u4e00\u518d\u8868\u660e\uff0c\u4ee5\u6ee1\u8db3\u4eba\u7c7b\u597d\u5947\u5fc3\u4e3a\u51fa\u53d1\u70b9\u7684\u57fa\u7840\u7406\u8bba\u7814\u7a76\uff0c\u5176\u672c\u8d28\u7a81\u7834\u5f80\u5f80\u4e0d\u80fd\u5f15\u8d77\u5f53\u65f6\u4eba\u7c7b\u793e\u4f1a\u7684\u91cd\u89c6\uff0c\u5b9b\u82e5\u51b0\u5ddd\u65f7\u8c37\u4e2d\u4e00\u58f0\u5fae\u5f31\u7684\u5450\u558a\uff0c\u8f6c\u77ac\u95f4\u968f\u98ce\u6d88\u901d\uff0c\u4f46\u662f\u8fd9\u4e00\u58f0\u5f80\u5f80\u4f1a\u5f15\u53d1\u4ee4\u5929\u7a7a\u53d8\u8272\uff0c\u5927\u5730\u98a4\u6296\u7684\u96ea\u5d29\u3002<\/span><\/strong>\u5e9e\u52a0\u83b1\u731c\u60f3\u7684\u8bc1\u660e\u5c31\u662f\u4e00\u4e2a\u9c9c\u660e\u7684\u5b9e\u4f8b\uff0c\u867d\u7136\u96ea\u5d29\u6548\u5e94\u8fd8\u6ca1\u6709\u88ab\u5927\u4f17\u6240\u5bdf\u89c9\uff0c\u4f46\u662f\u96ea\u5d29\u5df2\u7ecf\u4e0d\u53ef\u9006\u8f6c\u5730\u5f00\u59cb\u4e86\uff01<\/span><\/p>\n

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1\u00a0 \u5e9e\u52a0\u83b1\u731c\u60f3<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u6cd5\u56fd\u6570\u5b66\u5bb6\u5e9e\u52a0\u83b1\uff08Jules Henri Poincar\u00e9\uff09\u662f\u73b0\u4ee3\u62d3\u6251\u5b66\u7684\u5960\u57fa\u4eba\u3002\u62d3\u6251\u5b66\u7814\u7a76\u51e0\u4f55\u4f53\uff0c\u4f8b\u5982\u6d41\u5f62\uff0c\u5728\u8fde\u7eed\u5f62\u53d8\u4e0b\u7684\u4e0d\u53d8\u6027\u8d28\u3002\u6211\u4eec\u53ef\u4ee5\u60f3\u8c61\u66f2\u9762\u7531\u6a61\u76ae\u819c\u5236\u6210\uff0c\u6211\u4eec\u5bf9\u6a61\u76ae\u819c\u62c9\u4f38\u538b\u7f29\uff0c\u626d\u8f6c\u8737\u66f2\uff0c\u4f46\u662f\u4e0d\u4f1a\u6495\u7834\u6216\u7c98\u8054\uff0c\u90a3\u4e48\u8fd9\u4e9b\u5f62\u53d8\u90fd\u662f\u8fde\u7eed\u5f62\u53d8\uff0c\u6216\u88ab\u79f0\u4e4b\u4e3a\u62d3\u6251\u5f62\u53d8\uff0c\u5728\u8fd9\u4e9b\u5f62\u53d8\u4e0b\u4fdd\u6301\u4e0d\u53d8\u7684\u91cf\u5c31\u662f\u62d3\u6251\u4e0d\u53d8\u91cf\u3002\u5982\u679c\u4e00\u5f20\u6a61\u76ae\u819c\u66f2\u9762\u7ecf\u7531\u62d3\u6251\u5f62\u53d8\u5f97\u5230\u53e6\u5916\u4e00\u5f20\u6a61\u76ae\u819c\u66f2\u9762\uff0c\u5219\u8fd9\u4e24\u5f20\u66f2\u9762\u5177\u6709\u76f8\u540c\u7684\u62d3\u6251\u4e0d\u53d8\u91cf\uff0c\u5b83\u4eec\u5f7c\u6b64\u62d3\u6251\u7b49\u4ef7\u3002\u5982\u56fe2 \u6240\u793a\uff0c\u5047\u8bbe\u5154\u5b50\u66f2\u9762\u7531\u6a61\u76ae\u819c\u505a\u6210\uff0c\u6211\u4eec\u8c61\u5439\u6c14\u7403\u4e00\u6837\u5c06\u5176\u81a8\u80c0\u6210\u6807\u51c6\u5355\u4f4d\u7403\u9762\uff0c\u56e0\u6b64\u5154\u5b50\u66f2\u9762\u548c\u5355\u4f4d\u7403\u9762\u62d3\u6251\u7b49\u4ef7\u3002<\/span><\/p>\n

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\u56fe2. \u5154\u5b50\u66f2\u9762\u53ef\u4ee5\u8fde\u7eed\u5f62\u53d8\u6210\u5355\u4f4d\u7403\u9762\uff0c\u56e0\u6b64\u5154\u5b50\u66f2\u9762\u548c\u7403\u9762\u62d3\u6251\u7b49\u4ef7\u3002<\/strong><\/p>\n

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\n<\/span>\u56fe3. \u4e8f\u683c\u4e3a2\u7684\u5c01\u95ed\u66f2\u9762\u3002\u4e8f\u683c\u662f\u66f2\u9762\u6700\u91cd\u8981\u7684\u62d3\u6251\u4e0d\u53d8\u91cf\u3002<\/strong><\/p>\n

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\u4f46\u662f\u53e6\u4e00\u65b9\u9762\uff0c\u5047\u8bbe\u6709\u4e00\u53ea\u8682\u8681\u81ea\u5e7c\u751f\u6d3b\u5728\u4e00\u5f20\u66f2\u9762\u4e0a\uff0c\u4ece\u672a\u8df3\u79bb\u8fc7\u66f2\u9762\uff0c\u56e0\u6b64\u4ece\u672a\u770b\u5230\u8fc7\u66f2\u9762\u7684\u6574\u4f53\u60c5\u5f62\u3002\u8682\u8681\u53ea\u6709\u4e8c\u7ef4\u6982\u5ff5\uff0c\u6ca1\u6709\u4e09\u7ef4\u6982\u5ff5\u3002\u5047\u8bbe\u8fd9\u53ea\u8682\u8681\u5177\u6709\u9ad8\u5ea6\u53d1\u8fbe\u7684\u667a\u529b\uff0c\u90a3\u4e48\u8fd9\u53ea\u8682\u8681\u80fd\u5426\u5224\u65ad\u5b83\u6240\u751f\u6d3b\u7684\u66f2\u9762\u662f\u4e2a\u4e8f\u683c\u4e3a0\u7684\u62d3\u6251\u7403\u9762\uff0c\u8fd8\u662f\u9ad8\u4e8f\u683c\u66f2\u9762\uff1f<\/p>\n

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\u56fe5. \u4e8f\u683c\u4e3a1\u7684\u66f2\u9762\u4e0a\uff0c\u65e0\u6cd5\u7f29\u6210\u70b9\u7684\u95ed\u5708\u3002<\/strong><\/p>\n

\u5e9e\u52a0\u83b1\u6700\u7ec8\u609f\u5230\u4e00\u4e2a\u7b80\u5355\u800c\u53c8\u6df1\u523b\u7684\u65b9\u6cd5\u6765\u5224\u65ad\u66f2\u9762\u662f\u5426\u662f\u4e8f\u683c\u4e3a0\u7684\u62d3\u6251\u7403\u9762\uff1a\u5982\u679c\u66f2\u9762\u4e0a\u6240\u6709\u7684\u5c01\u95ed\u66f2\u7ebf\u90fd\u80fd\u5728\u66f2\u9762\u4e0a\u9010\u6e10\u7f29\u6210\u4e00\u4e2a\u70b9\uff0c\u90a3\u4e48\u66f2\u9762\u5fc5\u4e3a\u62d3\u6251\u7403\u9762\u3002<\/strong>\u6bd4\u5982\uff0c\u6211\u4eec\u8003\u8651\u56fe5\u4e2d\u5c0f\u732b\u7684\u66f2\u9762\uff0c\u56f4\u7ed5\u8116\u5b50\u7684\u4e00\u6761\u5c01\u95ed\u66f2\u7ebf\uff0c\u5728\u66f2\u9762\u4e0a\u65e0\u8bba\u600e\u6837\u53d8\u5f62\uff0c\u90fd\u65e0\u6cd5\u7f29\u6210\u4e00\u4e2a\u70b9\u3002\u6362\u8a00\u4e4b\uff0c\u53ea\u8981\u66f2\u9762\u4e8f\u683c\u975e\u96f6\uff0c\u5c31\u5b58\u5728\u4e0d\u53ef\u6536\u7f29\u6210\u70b9\u7684\u95ed\u5708\u3002\u5982\u679c\u6d41\u5f62\u5185\u6240\u6709\u7684\u5c01\u95ed\u5708\u90fd\u80fd\u7f29\u6210\u70b9\uff0c\u5219\u6d41\u5f62\u88ab\u79f0\u4e3a\u662f\u5355\u8fde\u901a\u7684\u3002\u5e9e\u52a0\u83b1\u5c06\u8fd9\u4e00\u7ed3\u679c\u5411\u9ad8\u7ef4\u63a8\u5e7f\uff0c\u63d0\u51fa\u4e86\u8457\u540d\u7684\u5e9e\u52a0\u83b1\u731c\u60f3\uff1a\u5047\u8bbeM\u662f\u4e00\u4e2a\u5c01\u95ed\u7684\u5355\u8fde\u901a\u4e09\u7ef4\u6d41\u5f62\uff0c\u5219M\u548c\u4e09\u7ef4\u7403\u9762\u62d3\u6251\u7b49\u4ef7\u3002<\/p>\n

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\u56fe6. \u5e26\u8fb9\u754c\u7684\u4e09\u6d41\u5f62\uff0c\u7528\u4e09\u89d2\u5256\u5206\u8868\u793a\u3002<\/strong><\/p>\n

\u5728\u73b0\u5b9e\u4e16\u754c\u4e2d\uff0c\u65e0\u6cd5\u770b\u5230\u5c01\u95ed\u7684\u4e09\u7ef4\u6d41\u5f62\uff1a\u6b63\u5982\u4e8c\u7ef4\u5c01\u95ed\u66f2\u9762\u65e0\u6cd5\u5728\u4e8c\u7ef4\u5e73\u9762\u4e0a\u5b9e\u73b0\uff0c\u4e09\u7ef4\u5c01\u95ed\u6d41\u5f62\u65e0\u6cd5\u5728\u4e09\u7ef4\u6b27\u5f0f\u7a7a\u95f4\u4e2d\u5b9e\u73b0\u3002\u56fe6\u663e\u793a\u4e86\u5e26\u6709\u8fb9\u754c\u7684\u4e09\u7ef4\u6d41\u5f62\uff0c\u4f8b\u5982\u5b9e\u5fc3\u7684\u5154\u5b50\u548c\u5b9e\u5fc3\u7684\u7403\u4f53\u62d3\u6251\u7b49\u4ef7\u3002\u8fd9\u4e9b\u4e09\u7ef4\u6d41\u5f62\u7528\u4e09\u89d2\u5256\u5206\u6765\u8868\u793a\uff0c\u5c31\u662f\u7528\u8bb8\u591a\u56db\u9762\u4f53\u7c98\u5408\u800c\u6210\u3002\u5982\u56fe\u6240\u793a\uff0c\u4f53\u7684\u4e09\u89d2\u5256\u5206\u8bf1\u5bfc\u4e86\u5176\u4e8c\u7ef4\u8fb9\u754c\u66f2\u9762\u7684\u4e09\u89d2\u5256\u5206\u3002\u5b9e\u5fc3\u7403\u5b9e\u9645\u4e0a\u662f\u4e09\u7ef4\u62d3\u6251\u5706\u76d8\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e24\u4e2a\u4e09\u7ef4\u62d3\u6251\u5706\u76d8\u6cbf\u7740\u8fb9\u754c\u7c98\u5408\uff0c\u5c31\u5f97\u5230\u4e09\u7ef4\u7403\u9762\uff0c\u6070\u5982\u6211\u4eec\u53ef\u4ee5\u5c06\u4e24\u4e2a\u4e8c\u7ef4\u62d3\u6251\u5706\u76d8\u6cbf\u7740\u8fb9\u754c\u7c98\u5408\u800c\u5f97\u5230\u4e8c\u7ef4\u7403\u9762\u4e00\u6837\u3002\u5f53\u7136\uff0c\u8fd9\u5df2\u7ecf\u8d85\u51fa\u4eba\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u7ecf\u9a8c\u3002<\/p>\n

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2\u00a0 \u66f2\u9762\u5355\u503c\u5316\u5b9a\u7406<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u8fd1\u767e\u5e74\u6765\uff0c\u5e9e\u52a0\u83b1\u731c\u60f3\u4e00\u76f4\u662f\u62d3\u6251\u5b66\u6700\u4e3a\u57fa\u672c\u7684\u95ee\u9898\uff0c\u65e0\u6570\u62d3\u6251\u5b66\u5bb6\u548c\u51e0\u4f55\u5b66\u5bb6\u4e3a\u8bc1\u660e\u5e9e\u52a0\u83b1\u731c\u60f3\u800c\u97a0\u8eac\u5c3d\u7601\u6b7b\u800c\u540e\u5df2\u3002\u76f8\u6bd4\u90a3\u4e9b\u6700\u540e\u6210\u529f\u7684\u5e78\u8fd0\u513f\uff0c\u4f17\u591a\u9ed8\u9ed8\u65e0\u95fb\uff0c\u6f66\u5012\u7ec8\u751f\u7684\u5931\u8d25\u8005\u66f4\u52a0\u4ee4\u4eba\u8083\u7136\u8d77\u656c\u3002\u8001\u987e\u66fe\u7ecf\u8bbf\u95ee\u8fc7\u5409\u6797\u5927\u5b66\u6570\u5b66\u5b66\u9662\uff0c\u542c\u95fb\u4e86\u6709\u5173\u4f55\u4f2f\u548c\u6559\u6388\u7684\u751f\u5e73\u4e8b\u8ff9\u3002\u4f55\u6559\u6388\u7ec8\u751f\u75f4\u8ff7\u4e8e\u5e9e\u52a0\u83b1\u731c\u60f3\u7684\u8bc1\u660e\uff0c\u82e6\u5fc3\u5b64\u8be3\uff0c\u5e9f\u5bdd\u5fd8\u98df\uff0c\u6108\u632b\u6108\u594b\uff0c\u4e5d\u6b7b\u4e0d\u6094\uff0c\u76f4\u81f3\u751f\u547d\u7ec8\u7ed3\uff0c\u5bf9\u4e8e\u5e9e\u52a0\u83b1\u731c\u60f3\u4f9d\u7136\u5ff5\u5ff5\u4e0d\u5fd8\u3002\u4f55\u6559\u6388\u7edd\u5bf9\u4e0d\u662f\u4e3a\u4e86\u4efb\u4f55\u5b9e\u7528\u4ef7\u503c\u6216\u8005\u5546\u4e1a\u5229\u76ca\u800c\u594b\u6597\u7ec8\u751f\u7684\uff0c\u800c\u662f\u4e3a\u4e86\u5bf9\u4e8e\u81ea\u7136\u754c\u5965\u79d8\u7684\u597d\u5947\uff0c\u5bf9\u4e8e\u7f8e\u5b66\u4ef7\u503c\u7684\u70ed\u5207\u8ffd\u6c42\uff0c\u8fd9\u79cd\u7eaf\u7cb9\u548c\u5d07\u9ad8\uff0c\u662f\u4eba\u7c7b\u8fdb\u6b65\u7684\u771f\u6b63\u52a8\u529b\uff01<\/p>\n


\n\u56fe7. \u4eba\u8138\u66f2\u9762\u4e0a\u8fde\u63a5\u4e24\u70b9\u7684\u6d4b\u5730\u7ebf\u3002<\/strong><\/p>\n

\u4f5c\u4e3a\u62d3\u6251\u5b66\u6700\u4e3a\u57fa\u672c\u7684\u95ee\u9898\uff0c\u5e9e\u52a0\u83b1\u731c\u60f3\u7684\u672c\u8d28\u7a81\u7834\u5374\u6765\u81ea\u4e8e\u51e0\u4f55\u3002\u7ed9\u5b9a\u4e00\u4e2a\u62d3\u6251\u6d41\u5f62\uff0c\u5982\u7ed9\u5b9a\u56fe6\u4e2d\u56db\u9762\u4f53\u7f51\u683c\u7684\u7ec4\u5408\u7ed3\u6784\uff0c\u6211\u4eec\u53ef\u4ee5\u4e3a\u6bcf\u6761\u8fb9\u6307\u5b9a\u4e00\u4e2a\u957f\u5ea6\uff0c\u4f7f\u5f97\u6bcf\u4e2a\u56db\u9762\u4f53\u90fd\u662f\u4e00\u4e2a\u6b27\u5f0f\u7684\u56db\u9762\u4f53\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u7ed9\u51fa\u4e86\u4e00\u4e2a\u9ece\u66fc\u5ea6\u91cf\u3002\u6240\u8c13\u9ece\u66fc\u5ea6\u91cf\uff0c\u5c31\u662f\u5b9a\u4e49\u5728\u6d41\u5f62\u4e0a\u7684\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u4efb\u610f\u4e24\u70b9\u95f4\u7684\u6700\u77ed\u6d4b\u5730\u7ebf\u3002\u56fe7\u663e\u793a\u4e86\u4eba\u8138\u66f2\u9762\u4e0a\u7684\u4e24\u6761\u6d4b\u5730\u7ebf\u3002\u9ece\u66fc\u5ea6\u91cf\u81ea\u7136\u8bf1\u5bfc\u4e86\u6d41\u5f62\u7684\u66f2\u7387\u3002\u66f2\u7387\u662f\u8868\u5f81\u7a7a\u95f4\u5f2f\u66f2\u7684\u4e00\u79cd\u7cbe\u786e\u63cf\u8ff0\u3002\u7ed9\u5b9a\u66f2\u9762\u4e0a\u4e09\u4e2a\u70b9\uff0c\u6211\u4eec\u7528\u6d4b\u5730\u7ebf\u8fde\u63a5\u5b83\u4eec\u6210\u4e00\u4e2a\u6d4b\u5730\u4e09\u89d2\u5f62\u3002\u5982\u679c\u66f2\u9762\u4e3a\u6b27\u51e0\u91cc\u5fb7\u5e73\u9762\uff0c\u90a3\u4e48\u6d4b\u5730\u4e09\u89d2\u5f62\u5185\u89d2\u548c\u4e3a180\u5ea6\u3002\u7403\u9762\u6d4b\u5730\u4e09\u89d2\u5f62\u7684\u5185\u89d2\u548c\u5927\u4e8e180\u5ea6\uff0c\u9a6c\u978d\u9762\u7684\u6d4b\u5730\u4e09\u89d2\u5f62\u7684\u5185\u89d2\u548c\u5c0f\u4e8e180\u5ea6\u3002\u6d4b\u5730\u4e09\u89d2\u5f62\u5185\u89d2\u548c\u4e0e180\u5ea6\u7684\u5dee\u522b\u5c31\u662f\u4e09\u89d2\u5f62\u7684\u603b\u66f2\u7387\u3002\u90a3\u4e48\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u62d3\u6251\u6d41\u5f62\uff0c\u6211\u4eec\u80fd\u5426\u9009\u62e9\u4e00\u4e2a\u6700\u4e3a\u7b80\u5355\u7684\u9ece\u66fc\u5ea6\u91cf\uff0c\u4f7f\u5f97\u66f2\u7387\u4e3a\u5e38\u6570\u5462\uff1f<\/strong>
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\n\u56fe8. \u66f2\u9762\u5355\u503c\u5316\u5b9a\u7406\uff0c\u6240\u6709\u5c01\u95ed\u66f2\u9762\u90fd\u53ef\u4ee5\u4fdd\u89d2\u5730\u5f62\u53d8\u6210\u5e38\u66f2\u7387\u66f2\u9762\u3002<\/strong><\/p>\n

\u8fd9\u4e00\u95ee\u9898\u7684\u7b54\u6848\u662f\u80af\u5b9a\u7684\uff0c\u8fd9\u5c31\u662f\u66f2\u9762\u5fae\u5206\u51e0\u4f55\u4e2d\u6700\u4e3a\u6839\u672c\u7684\u5355\u503c\u5316\u5b9a\u7406\u3002\u5355\u503c\u5316\u5b9a\u7406\u662f\u8bf4\u5927\u5343\u4e16\u754c\uff0c\u5404\u79cd\u51e0\u4f55\u5f62\u72b6\u5343\u53d8\u4e07\u5316\uff0c\u4f46\u662f\u65e0\u8bba\u5b83\u4eec\u5982\u4f55\u53d8\u5316\uff0c\u90fd\u662f\u4e07\u53d8\u4e0d\u79bb\u5176\u5b97\uff1a\u6240\u6709\u7684\u66f2\u9762\u90fd\u53ef\u4ee5\u5171\u5f62\u5730\u53d8\u6362\u6210\u4e09\u79cd\u6807\u51c6\u66f2\u9762\u4e2d\u7684\u4e00\u79cd\uff0c\u5355\u4f4d\u7403\u9762\uff0c\u6b27\u51e0\u91cc\u5fb7\u5e73\u9762\u548c\u53cc\u66f2\u5e73\u9762\u3002\u6807\u51c6\u7a7a\u95f4\u5bf9\u5e94\u7740\u5e38\u6570\u503c\u66f2\u7387\uff0c+1\uff0c0\u548c-1\uff0c\u5982\u56fe8\u6240\u793a\u3002\u6240\u8c13\u5171\u5f62\u53d8\u6362\uff0c\u5c31\u662f\u4fdd\u6301\u5c40\u90e8\u5f62\u72b6\u7684\u53d8\u6362\uff0c\u5c40\u90e8\u4e0a\u770b\u5c31\u662f\u76f8\u4f3c\u53d8\u6362\u3002\u76f8\u4f3c\u53d8\u6362\u4fdd\u6301\u89d2\u5ea6\u4e0d\u53d8\uff0c\u56e0\u6b64\u5171\u5f62\u53d8\u6362\u4e5f\u88ab\u79f0\u4e3a\u662f\u4fdd\u89d2\u53d8\u6362\u3002\u56fe9\u663e\u793a\u4e86\u4ece\u66f2\u9762\u5230\u5e73\u9762\u7684\u4e00\u4e2a\u5171\u5f62\u53d8\u6362\u3002\u5355\u503c\u5316\u5b9a\u7406\u65ad\u8a00\u4e86\u6240\u6709\u5c01\u95ed\u66f2\u9762\u53ef\u4ee5\u914d\u6709\u4e09\u79cd\u51e0\u4f55\u4e2d\u7684\u4e00\u79cd\uff1a\u7403\u9762\u51e0\u4f55\uff0c\u6b27\u6c0f\u51e0\u4f55\u548c\u53cc\u66f2\u51e0\u4f55<\/strong>\u3002\u66f2\u9762\u5fae\u5206\u51e0\u4f55\u4e2d\u51e0\u4e4e\u6240\u6709\u7684\u91cd\u8981\u5b9a\u7406\u90fd\u7ed5\u4e0d\u8fc7\u5355\u503c\u5316\u5b9a\u7406\u3002<\/p>\n


\n\u56fe9. \u5171\u5f62\u53d8\u6362\u4fdd\u6301\u5c40\u90e8\u5f62\u72b6\u3002<\/strong><\/p>\n

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3\u00a0 \u745f\u65af\u987f\u51e0\u4f55\u5316\u731c\u60f3<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u4e3a\u4e86\u8bc1\u660e\u5e9e\u52a0\u83b1\u731c\u60f3\uff0c\u83f2\u5c14\u5179\u5956\u5f97\u4e3b\u745f\u65af\u987f\u63a8\u5e7f\u4e86\u5355\u503c\u5316\u5b9a\u7406\u5230\u4e09\u7ef4\u6d41\u5f62\u60c5\u5f62\u3002\u4efb\u4f55\u4e09\u7ef4\u6d41\u5f62\uff0c\u90fd\u53ef\u4ee5\u7ecf\u5386\u4e00\u5957\u6807\u51c6\u624b\u7eed\u5206\u89e3\u6210\u4e00\u7cfb\u5217\u7684\u6700\u4e3a\u7b80\u5355\u7684\u4e09\u7ef4\u6d41\u5f62\uff0c\u5373\u6240\u8c13\u7684\u7d20\u6d41\u5f62\u3002\u7d20\u6d41\u5f62\u672c\u8eab\u65e0\u6cd5\u88ab\u8fdb\u4e00\u6b65\u5206\u89e3\uff0c\u540c\u65f6\u8fd9\u79cd\u5206\u89e3\u672c\u8d28\u4e0a\u662f\u552f\u4e00\u7684\u3002\u745f\u65af\u987f\u63d0\u51fa\u4e86\u77f3\u7834\u5929\u60ca\u7684\u51e0\u4f55\u5316\u731c\u60f3\uff1a\u6240\u6709\u7684\u7d20\u4e09\u7ef4\u6d41\u5f62\u53ef\u4ee5\u914d\u6709\u6807\u51c6\u9ece\u66fc\u5ea6\u91cf\uff0c\u4ece\u800c\u5177\u67098\u79cd\u51e0\u4f55\u4e2d\u7684\u4e00\u79cd\u3002\u7279\u522b\u5730\uff0c\u5355\u8fde\u901a\u7684\u4e09\u7ef4\u6d41\u5f62\u53ef\u88ab\u914d\u6709\u6b63\u7684\u5e38\u503c\u66f2\u7387\u5ea6\u91cf\uff0c\u914d\u6709\u6b63\u7684\u5e38\u503c\u66f2\u7387\u76843\u7ef4\u6d41\u5f62\u5fc5\u4e3a3\u7ef4\u7403\u9762\u3002\u56e0\u6b64\u5e9e\u52a0\u83b1\u731c\u60f3\u662f\u745f\u65af\u987f\u51e0\u4f55\u5316\u731c\u60f3\u7684\u4e00\u4e2a\u7279\u4f8b\u3002<\/p>\n

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\u56fe10. \u745f\u65af\u987f\u7684\u82f9\u679c\uff0c\u51e0\u4f55\u5316\u731c\u60f3\u3002<\/strong><\/p>\n

\u56fe10\u663e\u793a\u4e86\u745f\u65af\u987f\u51e0\u4f55\u5316\u7684\u4e00\u4e2a\u5b9e\u4f8b\u3002\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u82f9\u679c\uff0c\u4e09\u53ea\u86c0\u866b\u86c0\u8680\u4e86\u4e09\u6761\u7ba1\u9053\uff0c\u5982\u5de6\u5e27\u6240\u793a\uff0c\u8fd9\u6837\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u5e26\u8fb9\u754c\u7684\u4e09\u7ef4\u6d41\u5f62\u3002\u6839\u636e\u51e0\u4f55\u5316\u7eb2\u9886\uff0c\u8fd9\u4e2a\u88ab\u86c0\u8680\u7684\u82f9\u679c\u5185\u90e8\u5bb9\u8bb8\u4e00\u4e2a\u53cc\u66f2\u9ece\u66fc\u5ea6\u91cf\uff0c\u4f7f\u5f97\u5176\u8fb9\u754c\u66f2\u9762\u7684\u66f2\u7387\u5904\u5904\u4e3a-1\u3002\u6211\u4eec\u5c06\u914d\u6709\u53cc\u66f2\u5ea6\u91cf\u7684\u82f9\u679c\u5468\u671f\u6027\u5730\u5d4c\u5728\u4e09\u7ef4\u53cc\u66f2\u7a7a\u95f4\u4e4b\u4e2d\uff0c\u5f97\u5230\u53f3\u5e27\u6240\u793a\u56fe\u5f62\u3002<\/p>\n

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4\u00a0 \u54c8\u5bc6\u5c14\u987f\u7684\u91cc\u5947\u66f2\u7387<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u56fe11. \u66f2\u7387\u6d41\u4f7f\u5f97\u66f2\u7387\u8d8a\u6765\u8d8a\u5747\u5300\uff0c\u76f4\u81f3\u53d8\u6210\u5e38\u6570\uff0c\u66f2\u9762\u53d8\u6210\u7403\u9762\u3002<\/strong><\/p>\n

\u5728\u4e8c\u7ef4\u66f2\u9762\u60c5\u5f62\uff0c\u54c8\u5bc6\u5c14\u987f\u548cBen Chow\u8bc1\u660e\u4e86\u66f2\u7387\u6d41\u7684\u786e\u5c06\u4efb\u4f55\u4e00\u4e2a\u9ece\u66fc\u5ea6\u91cf\u5f62\u53d8\u6210\u5e38\u503c\u66f2\u7387\u5ea6\u91cf\uff0c\u4ece\u800c\u7ed9\u51fa\u4e86\u66f2\u9762\u5355\u503c\u5316\u5b9a\u7406\u7684\u4e00\u4e2a\u6784\u9020\u6027\u8bc1\u660e\u3002\u4f46\u662f\u5728\u4e09\u7ef4\u6d41\u5f62\u60c5\u5f62\uff0c\u91cc\u5947\u66f2\u7387\u6d41\u9047\u5230\u4e86\u5de8\u5927\u7684\u6311\u6218\u3002\u5728\u4e8c\u7ef4\u66f2\u9762\u60c5\u5f62\uff0c\u5728\u66f2\u7387\u6d41\u8fc7\u7a0b\u4e2d\uff0c\u5728\u4efb\u610f\u65f6\u523b\uff0c\u66f2\u9762\u4e0a\u4efb\u610f\u4e00\u70b9\u7684\u66f2\u7387\u90fd\u662f\u6709\u9650\u7684\uff1b\u5728\u4e09\u7ef4\u6d41\u5f62\u60c5\u5f62\uff0c\u5728\u6709\u9650\u65f6\u95f4\u5185\uff0c\u6d41\u5f62\u7684\u67d0\u4e00\u70b9\u5904\uff0c\u66f2\u7387\u6709\u53ef\u80fd\u8d8b\u5411\u4e8e\u65e0\u7a77\uff0c\u8fd9\u79cd\u60c5\u51b5\u88ab\u79f0\u4e3a\u662f\u66f2\u7387\u7206\u7834\uff08blowup\uff09\uff0c\u7206\u7834\u70b9\u88ab\u79f0\u4e3a\u662f\u5947\u5f02\u70b9\uff08singularity\uff09\u3002<\/p>\n

\u5982\u679c\u53d1\u751f\u66f2\u7387\u7206\u7834\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6d41\u5f62\u6cbf\u7740\u7206\u7834\u70b9\u4e00\u5207\u4e24\u534a\uff0c\u7136\u540e\u5c06\u6bcf\u4e00\u534a\u63a5\u7740\u5b9e\u65bd\u66f2\u7387\u6d41\u3002\u5982\u679c\u6211\u4eec\u80fd\u591f\u8bc1\u660e\u5728\u66f2\u7387\u6d41\u7684\u8fc7\u7a0b\u4e2d\uff0c\u66f2\u7387\u7206\u7834\u53d1\u751f\u7684\u6b21\u6570\u6709\u9650\uff0c\u90a3\u4e48\u6d41\u5f62\u88ab\u5206\u5272\u6210\u6709\u9650\u4e2a\u5b50\u6d41\u5f62\uff0c\u6bcf\u4e2a\u5b50\u6d41\u5f62\u6700\u7ec8\u53d8\u6210\u4e86\u4e09\u7ef4\u7403\u9762\u3002\u5982\u679c\u8fd9\u6837\uff0c\u539f\u6765\u6d41\u5f62\u7531\u6709\u9650\u4e2a\u7403\u7c98\u5408\u800c\u6210\uff0c\u56e0\u800c\u662f\u4e09\u7ef4\u7403\u9762\uff0c\u8fd9\u6837\u5c31\u8bc1\u660e\u4e86\u5e9e\u52a0\u83b1\u731c\u60f3\u3002\u7531\u6b64\u53ef\u89c1\uff0c\u5bf9\u4e8e\u5947\u5f02\u70b9\u7684\u7cbe\u7ec6\u5206\u6790\u6210\u4e3a\u95ee\u9898\u7684\u5173\u952e\u3002\u54c8\u5bc6\u5c14\u987f\u5398\u6e05\u4e86\u5927\u591a\u6570\u79cd\u7c7b\u5947\u5f02\u70b9\u7684\u60c5\u51b5\uff0c\u4f69\u96f7\u5c14\u66fc\u89e3\u51b3\u4e86\u5269\u4f59\u7684\u5947\u5f02\u70b9\u79cd\u7c7b\u3002\u540c\u65f6\uff0c\u4f69\u96f7\u5c14\u66fc\u654f\u9510\u5730\u6d1e\u5bdf\u5230\u54c8\u5bc6\u5c14\u987f\u7684\u91cc\u5947\u6d41\u662f\u6240\u8c13\u71b5\u80fd\u91cf\u7684\u68af\u5ea6\u6d41\uff0c\u4ece\u800c\u5c06\u91cc\u5947\u6d41\u7eb3\u5165\u4e86\u53d8\u5206\u7684\u6846\u67b6\u3002\u4f69\u96f7\u5c14\u66fc\u7ed9\u51fa\u4e86\u8bc1\u660e\u7684\u5173\u952e\u601d\u60f3\u548c\u4e3b\u8981\u6897\u6982\uff0c\u8bc1\u660e\u7684\u7ec6\u8282\u88ab\u4f17\u591a\u6570\u5b66\u5bb6\u8fdb\u4e00\u6b65\u8865\u5145\u5b8c\u6210\u3002\u81f3\u6b64\uff0c\u745f\u65af\u987f\u51e0\u4f55\u5316\u731c\u60f3\u88ab\u5b8c\u5168\u8bc1\u660e\uff0c\u5e9e\u52a0\u83b1\u731c\u60f3\u5386\u7ecf\u767e\u5e74\u63a2\u7d22\uff0c\u7ec8\u4e8e\u88ab\u5f7b\u5e95\u89e3\u51b3\u3002<\/p>\n

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5 \u5e9e\u52a0\u83b1\u731c\u60f3\u5e26\u6765\u7684\u8ba1\u7b97\u6280\u672f<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u5e9e\u52a0\u83b1\u731c\u60f3\u672c\u8eab\u5f02\u5e38\u62bd\u8c61\u800c\u67af\u71e5\uff1a\u5355\u8fde\u901a\u7684\u95ed3-\u6d41\u5f62\u662f\u4e09\u7ef4\u7403\u9762\uff0c\u4f3c\u4e4e\u6ca1\u6709\u4efb\u4f55\u5b9e\u7528\u4ef7\u503c\u3002\u4f46\u662f\u4e3a\u4e86\u8bc1\u660e\u5e9e\u52a0\u83b1\u731c\u60f3\uff0c\u4eba\u7c7b\u53d1\u5c55\u4e86\u745f\u65af\u987f\u51e0\u4f55\u5316\u7eb2\u9886\uff0c\u53d1\u660e\u4e86\u54c8\u5bc6\u5c14\u987f\u7684\u91cc\u5947\u66f2\u7387\u6d41\uff0c\u6df1\u523b\u5730\u7406\u89e3\u4e86\u4e09\u7ef4\u6d41\u5f62\u7684\u62d3\u6251\u548c\u51e0\u4f55\uff0c\u5c06\u5947\u5f02\u70b9\u7684\u5f62\u6210\u8fc7\u7a0b\u7eb3\u5165\u4e86\u6570\u5b66\u7684\u89c6\u91ce\u3002\u8fd9\u4e9b\u57fa\u7840\u6570\u5b66\u4e0a\u7684\u8fdb\u5c55\uff0c\u5fc5\u5c06\u5f15\u8d77\u5de5\u7a0b\u79d1\u5b66\u548c\u5b9e\u7528\u6280\u672f\u9886\u57df\u7684\u201c\u96ea\u5d29\u201d\u3002\u6bd4\u5982\uff0c\u91cc\u5947\u66f2\u7387\u6d41\u6280\u672f\u5b9e\u9645\u4e0a\u7ed9\u51fa\u4e86\u4e00\u79cd\u5f3a\u6709\u529b\u7684\u65b9\u6cd5\uff0c\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u7528\u66f2\u7387\u6765\u6784\u9020\u9ece\u66fc\u5ea6\u91cf<\/strong>\u3002<\/span><\/p>\n

\u91cc\u5947\u66f2\u7387\u6d41\u5c5e\u4e8e\u975e\u7ebf\u6027\u51e0\u4f55\u504f\u5fae\u5206\u65b9\u7a0b\uff0c\u91cc\u5947\u6d41\u7684\u65b9\u6cd5\u5b9e\u9645\u4e0a\u662f\u5178\u578b\u7684\u51e0\u4f55\u5206\u6790\u65b9\u6cd5\uff0c\u5373\u7528\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u6280\u672f\u6765\u8bc1\u660e\u51e0\u4f55\u95ee\u9898\u3002\u51e0\u4f55\u5206\u6790\u7531\u4e18\u6210\u6850\u5148\u751f\u521b\u7acb<\/span>\uff0c\u5e9e\u52a0\u83b1\u731c\u60f3\u7684\u8bc1\u660e\u662f\u51e0\u4f55\u5206\u6790\u7684\u53c8\u4e00\u5de8\u5927\u80dc\u5229\u3002\u5f53\u5e74\u745f\u65af\u987f\u63d0\u5021\u7528\u76f8\u5bf9\u4f20\u7edf\u7684\u62d3\u6251\u548c\u51e0\u4f55\u65b9\u6cd5\uff0c\u4f8b\u5982\u6cf0\u897f\u7c73\u52d2\u7406\u8bba\u548c\u53cc\u66f2\u51e0\u4f55\u7406\u8bba\u6765\u8bc1\u660e\uff0c\u4e5f\u6709\u6570\u5b66\u5bb6\u4e3b\u5f20\u7528\u76f8\u5bf9\u7ec4\u5408\u7684\u65b9\u6cd5\u6765\u8bc1\u660e\uff0c\u6700\u7ec8\u8fd8\u662f\u51e0\u4f55\u5206\u6790\u7684\u65b9\u6cd5\u62d4\u5f97\u5934\u7b79\u3002<\/span><\/p>\n

\u54c8\u5bc6\u5c14\u987f\u7684\u91cc\u5947\u6d41\u662f\u5b9a\u4e49\u5728\u5149\u6ed1\u6d41\u5f62\u4e0a\u7684\uff0c\u5728\u8ba1\u7b97\u673a\u7684\u8868\u793a\u4e2d\uff0c\u6240\u6709\u7684\u6d41\u5f62\u90fd\u88ab\u79bb\u6563\u5316\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5efa\u7acb\u4e00\u5957\u79bb\u6563\u91cc\u5947\u6d41\u7406\u8bba\u6765\u53d1\u5c55\u76f8\u5e94\u7684\u8ba1\u7b97\u65b9\u6cd5\u3002\u5386\u7ecf\u591a\u5e74\u7684\u52aa\u529b\uff0c\u7b14\u8005\u548c\u5408\u4f5c\u8005\u4eec\u5efa\u7acb\u4e86\u79bb\u6563\u66f2\u9762\u7684\u91cc\u5947\u66f2\u7387\u6d41\u7406\u8bba\uff0c\u8bc1\u660e\u4e86\u79bb\u6563\u89e3\u7684\u5b58\u5728\u6027\u548c\u552f\u4e00\u6027\u3002\u56e0\u4e3a\u51e0\u4e4e\u6240\u6709\u66f2\u9762\u5fae\u5206\u51e0\u4f55\u7684\u91cd\u8981\u95ee\u9898\uff0c\u90fd\u65e0\u6cd5\u7ed5\u8fc7\u5355\u503c\u5316\u5b9a\u7406\u3002\u6211\u4eec\u76f8\u4fe1\u79bb\u6563\u66f2\u7387\u6d41\u7684\u8ba1\u7b97\u65b9\u6cd5\u5fc5\u5c06\u5728\u5de5\u7a0b\u5b9e\u8df5\u4e2d\u53d1\u6325\u8d8a\u6765\u8d8a\u91cd\u8981\u7684\u4f5c\u7528 [1]<\/sup><\/strong>\u3002<\/span><\/p>\n


\n<\/span>\u56fe12. \u79bb\u6563\u91cc\u5947\u6d41\u8ba1\u7b97\u7684\u5e26\u8fb9\u66f2\u9762\u5355\u503c\u5316\u3002<\/strong><\/p>\n

\u56fe8\u548c\u56fe12\u663e\u793a\u4e86\u79bb\u6563\u91cc\u5947\u6d41\u7b97\u51fa\u7684\u5c01\u95ed\u66f2\u9762\u548c\u5e26\u8fb9\u754c\u66f2\u9762\u7684\u5355\u503c\u5316\u3002\u672c\u8d28\u4e0a\uff0c\u8fd9\u4e24\u5e45\u56fe\u7edf\u6444\u4e86\u73b0\u5b9e\u751f\u6d3b\u4e2d\u6240\u6709\u53ef\u80fd\u7684\u66f2\u9762\uff0c\u5b83\u4eec\u90fd\u88ab\u5171\u5f62\u5730\u6620\u5230\u4e86\u4e09\u79cd\u6807\u51c6\u66f2\u9762\u4e0a\uff0c\u7403\u9762\u3001\u6b27\u6c0f\u5e73\u9762\u548c\u53cc\u66f2\u5e73\u9762\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5982\u679c\u6211\u4eec\u53d1\u660e\u4e86\u4e00\u79cd\u65b0\u7684\u51e0\u4f55\u7b97\u6cd5\uff0c\u9002\u7528\u4e8e\u8fd9\u4e09\u79cd\u6807\u51c6\u66f2\u9762\uff0c\u90a3\u4e48\u8fd9\u4e00\u7b97\u6cd5\u4e5f\u9002\u7528\u4e8e\u6240\u6709\u66f2\u9762\u3002\u56e0\u6b64\uff0c\u79bb\u6563\u66f2\u7387\u6d41\u7684\u6280\u672f\u6781\u5927\u5730\u7b80\u5316\u4e86\u51e0\u4f55\u7b97\u6cd5\u8bbe\u8ba1\u3002<\/p>\n

\n
\n
\n
\n
\n
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\n
\n
6 \u7cbe\u51c6\u533b\u7597<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u5e9e\u52a0\u83b1\u731c\u60f3\u6240\u8bf1\u53d1\u7684\u79bb\u6563\u66f2\u7387\u6d41\u65b9\u6cd5\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u7cbe\u51c6\u533b\u7597\u9886\u57df\u3002\u4eba\u4f53\u7684\u5404\u79cd\u5668\u5b98\u672c\u8d28\u4e0a\u90fd\u662f\u4e8c\u7ef4\u66f2\u9762\u6216\u4e09\u7ef4\u6d41\u5f62\uff0c\u66f2\u7387\u6d41\u65b9\u6cd5\u5bf9\u4e8e\u8fd9\u4e9b\u5668\u5b98\u51e0\u4f55\u7279\u5f81\u7684\u5206\u6790\u548c\u6bd4\u8f83\u8d77\u5230\u4e86\u4e0d\u53ef\u66ff\u4ee3\u7684\u4f5c\u7528\u3002<\/p>\n


\n\u56fe13. \u865a\u62df\u80a0\u955c\u6280\u672f\u3002<\/strong><\/p>\n

\u865a\u62df\u80a0\u955c\u00a0<\/strong><\/p>\n

\u76f4\u80a0\u764c\u662f\u7537\u5b50\u7684\u7b2c\u56db\u53f7\u6740\u624b\uff0c\u4ec5\u5728\u5fc3\u8111\u8840\u7ba1\u75be\u75c5\u4e4b\u540e\u3002\u4e2d\u5e74\u4e4b\u540e\uff0c\u6bcf\u4e2a\u4eba\u90fd\u4f1a\u81ea\u7136\u957f\u51fa\u76f4\u80a0\u606f\u8089\uff0c\u606f\u8089\u4f1a\u9010\u5e74\u589e\u957f\uff0c\u5982\u679c\u606f\u8089\u76f4\u5f84\u8fbe\u5230\u4e00\u5b9a\u5c3a\u5bf8\uff0c\u7531\u4e8e\u6469\u64e6\u606f\u8089\u4f1a\u53d1\u751f\u6e83\u75a1\uff0c\u957f\u671f\u6e83\u75a1\u4f1a\u5bfc\u81f4\u764c\u53d8\u3002\u4f46\u662f\u76f4\u80a0\u606f\u8089\u7684\u751f\u957f\u975e\u5e38\u7f13\u6162\uff0c \u4e00\u822c\u4ece\u606f\u8089\u51fa\u73b0\u76f4\u5230\u4e34\u754c\u5c3a\u5bf8\u9700\u8981\u4e03\u516b\u5e74\uff0c\u56e0\u6b64\u5bf9\u606f\u8089\u7684\u76d1\u63a7\u5bf9\u4e8e\u9884\u9632\u76f4\u80a0\u764c\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002\u4e2d\u5e74\u4eba\u5e94\u8be5\u6bcf\u4e24\u5e74\u505a\u4e00\u6b21\u80a0\u955c\u68c0\u67e5\u3002\u4f20\u7edf\u7684\u80a0\u955c\u68c0\u67e5\u65b9\u6cd5\u9700\u8981\u5bf9\u53d7\u68c0\u8005\u5168\u8eab\u9ebb\u9189\uff0c\u5c06\u5149\u5b66\u5185\u7aa5\u955c\u63a2\u5165\u76f4\u80a0\u3002\u8001\u5e74\u4eba\u80a0\u58c1\u6bd4\u8f83\u8584\u5f31\uff0c\u5bb9\u6613\u4ea7\u751f\u5e76\u53d1\u75c7\u3002\u540c\u65f6\uff0c\u80a0\u58c1\u4e0a\u6709\u5f88\u591a\u76b1\u8936\uff0c\u5982\u679c\u606f\u8089\u9690\u85cf\u5728\u76b1\u8936\u4e2d\uff0c\u533b\u751f\u4f1a\u65e0\u6cd5\u770b\u5230\u800c\u4ea7\u751f\u6f0f\u68c0\u3002<\/p>\n

\u8fd1\u4e9b\u5e74\u6765\uff0c\u5317\u7f8e\u548c\u65e5\u672c\u91c7\u7528\u4e86\u865a\u62df\u80a0\u955c\u6280\u672f\u3002\u53d7\u68c0\u8005\u7684\u76f4\u80a0\u56fe\u50cf\u7531\u65ad\u5c42\u626b\u63cf\u6280\u672f\u6765\u83b7\u53d6\uff0c\u76f4\u80a0\u66f2\u9762\u53ef\u4ee5\u4ece\u56fe\u50cf\u91cd\u5efa\u51fa\u6765\uff0c\u5982\u56fe14\u6240\u793a\u3002\u6211\u4eec\u9700\u8981\u5c06\u76f4\u80a0\u5c55\u5f00\u644a\u5e73\uff0c\u4ece\u800c\u4f7f\u6240\u6709\u76b1\u8936\u66b4\u9732\u51fa\u6765\uff0c\u4ee5\u4fbf\u4e8e\u5bfb\u627e\u606f\u8089\u548c\u6d4b\u91cf\u5b83\u4eec\u7684\u5c3a\u5bf8\u3002\u540c\u65f6\uff0c\u5982\u56fe13\u6240\u793a\uff0c\u5728\u68c0\u67e5\u4e2d\u540c\u4e00\u53d7\u68c0\u8005\u7684\u76f4\u80a0\u88ab\u626b\u63cf\u4e24\u6b21\uff0c\u6bcf\u6b21\u626b\u63cf\u90fd\u662f\u91c7\u7528\u4e0d\u540c\u7684\u59ff\u6001\u3002\u76f4\u80a0\u66f2\u9762\u67d4\u8f6f\u800c\u5bcc\u6709\u5f39\u6027\uff0c\u4e0d\u540c\u7684\u626b\u63cf\u5f97\u5230\u7684\u66f2\u9762\u4e4b\u95f4\u76f8\u5dee\u5f88\u5927\u7684\u5f39\u6027\u5f62\u53d8\u3002\u6211\u4eec\u9700\u8981\u5728\u4e24\u5f20\u66f2\u9762\u95f4\u5efa\u7acb\u5149\u6ed1\u53cc\u5c04\u3002\u5728\u4e24\u5f20\u4e09\u7ef4\u66f2\u9762\u95f4\u5efa\u7acb\u6620\u5c04\u76f8\u5bf9\u56f0\u96be\uff0c\u5f53\u6211\u4eec\u5c06\u66f2\u9762\u644a\u5f00\u5c55\u5e73\u6210\u5e73\u9762\u957f\u65b9\u5f62\u540e\uff0c\u5728\u5e73\u9762\u533a\u57df\u95f4\u8ba1\u7b97\u6620\u5c04\u4f1a\u7b80\u5355\u5f88\u591a\u3002\u5c06\u76f4\u80a0\u66f2\u9762\u644a\u5f00\u5c55\u5e73\u7b49\u4ef7\u4e8e\u4e3a\u66f2\u9762\u8d4b\u4e0a\u4e00\u4e2a\u66f2\u7387\u5904\u5904\u4e3a0\u7684\u9ece\u66fc\u5ea6\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5e94\u7528\u91cc\u5947\u66f2\u7387\u6d41\u7684\u7b97\u6cd5\u52a0\u4ee5\u5b9e\u73b0\uff0c\u5982\u56fe14\u6240\u793a\u3002<\/p>\n

\u56fe14. \u7528\u91cc\u5947\u66f2\u7387\u6d41\u5c06\u76f4\u80a0\u66f2\u9762\u644a\u5f00\u5c55\u5e73\u3002<\/strong><\/p>\n

\u76ee\u524d\uff0c\u865a\u62df\u80a0\u955c\u6280\u672f\u5728\u5317\u7f8e\u548c\u65e5\u672c\u88ab\u5e7f\u6cdb\u91c7\u7528\uff0c\uff08\u4f46\u5728\u4e2d\u56fd\u8fd8\u6ca1\u6709\u666e\u53ca\uff09\uff0c\u4e3b\u8981\u662f\u56e0\u4e3a\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u63d0\u9ad8\u5b89\u5168\u6027\uff0c\u964d\u4f4e\u6f0f\u68c0\u7387\uff0c\u964d\u4f4e\u4eba\u529b\u6210\u672c\u3002\u865a\u62df\u80a0\u955c\u6280\u672f\u7684\u666e\u53ca\u6781\u5927\u5730\u63d0\u9ad8\u4e86\u65e9\u671f\u76f4\u80a0\u764c\u7684\u53d1\u73b0\u51e0\u7387\uff0c\u964d\u4f4e\u4e86\u76f4\u80a0\u764c\u7684\u6b7b\u4ea1\u7387\uff0c\u4e3a\u4eba\u7c7b\u7684\u5065\u5eb7\u4e8b\u4e1a\u505a\u51fa\u4e86\u5de8\u5927\u8d21\u732e\u3002<\/p>\n


\n\u56fe15. \u865a\u62df\u8180\u80f1\u955c\u3002<\/strong><\/p>\n

\u540c\u6837\u7684\u65b9\u6cd5\u53ef\u4ee5\u7528\u4e8e\u8180\u80f1\u7b49\u5176\u4ed6\u5668\u5b98\uff0c\u5982\u56fe15\u6240\u793a\u3002\u8180\u80f1\u764c\u7684\u6700\u4e3b\u8981\u7279\u5f81\u662f\u8180\u80f1\u58c1\u53d8\u539a\uff0c\u540c\u65f6\u5185\u58c1\u4e0d\u518d\u5149\u6ed1\uff0c\u51fa\u73b0\u83dc\u82b1\u72b6\u7684\u51e0\u4f55\u7eb9\u7406\u3002\u8fd9\u4e9b\u75c7\u72b6\u53ef\u4ee5\u7528\u865a\u62df\u8180\u80f1\u955c\u7684\u65b9\u6cd5\u5b9a\u91cf\u5f97\u5230\u3002\u4f20\u7edf\u8180\u80f1\u955c\u7684\u65b9\u6cd5\u75c5\u4eba\u9700\u8981\u5fcd\u53d7\u5f88\u5927\u7684\u75db\u82e6\uff0c\u865a\u62df\u8180\u80f1\u955c\u7684\u65b9\u6cd5\u6781\u5927\u5730\u51cf\u8f7b\u4e86\u75c5\u60a3\u7684\u75bc\u75db\uff0c\u56e0\u800c\u5177\u6709\u5f88\u5927\u7684\u4f18\u52bf\u3002<\/p>\n


\n\u56fe16. \u7528\u91cc\u5947\u66f2\u7387\u6d41\u5c06\u5927\u8111\u76ae\u5c42\u66f2\u9762\u5171\u5f62\u6620\u5230\u5355\u4f4d\u7403\u9762\uff0c\u4ee5\u4fbf\u4e8e\u5bf9\u7167\u6bd4\u8f83\u3002<\/strong><\/p>\n

\u8111\u795e\u7ecf\u75be\u75c5\u7684\u9884\u9632\u8bca\u65ad<\/strong><\/p>\n

\u8111\u9000\u5316\u75c7\uff08Alzheimer\u2019s disease\uff0c\u4fd7\u79f0\u8001\u5e74\u75f4\u5446\u75c7\uff09\uff0c\u766b\u75eb\uff0c\u513f\u7ae5\u81ea\u95ed\u75c7\u7b49\u8111\u795e\u7ecf\u75be\u75c5\u4e25\u91cd\u5730\u5a01\u80c1\u7740\u4eba\u7c7b\u7684\u5065\u5eb7\u5b89\u5168\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u75be\u75c5\u7684\u9884\u9632\u548c\u8bca\u65ad\u5177\u6709\u91cd\u8981\u7684\u73b0\u5b9e\u610f\u4e49\u3002\u901a\u8fc7\u6838\u78c1\u5171\u632f\u6210\u50cf\u6280\u672f\uff0c\u6211\u4eec\u80fd\u591f\u83b7\u53d6\u4eba\u7c7b\u7684\u5927\u8111\u76ae\u5c42\u66f2\u9762\uff0c\u5982\u56fe16\u6240\u793a\u3002\u5927\u8111\u76ae\u5c42\u66f2\u9762\u7684\u51e0\u4f55\u975e\u5e38\u590d\u6742\uff0c\u6709\u5927\u91cf\u7684\u76b1\u8936\u6c9f\u56de\u7ed3\u6784\uff0c\u5e76\u4e14\u8fd9\u4e9b\u51e0\u4f55\u7ed3\u6784\u56e0\u4eba\u800c\u5f02\uff0c\u4f9d\u968f\u5e74\u9f84\u53d8\u5316\u800c\u53d8\u5316\u3002\u4f8b\u5982\u8001\u5e74\u75f4\u5446\u75c7\u5f80\u5f80\u4f34\u968f\u5927\u8111\u76ae\u5c42\u4e00\u90e8\u5206\u533a\u57df\u7684\u840e\u7f29\u3002\u4e3a\u4e86\u76d1\u63a7\u75c5\u60c5\u7684\u53d1\u5c55\uff0c\u6211\u4eec\u9700\u8981\u6bcf\u9694\u51e0\u4e2a\u6708\u5c31\u626b\u63cf\u4e00\u4e0b\u75c5\u4eba\u7684\u5927\u8111\uff0c\u7136\u540e\u5c06\u4e0d\u540c\u65f6\u671f\u5f97\u5230\u7684\u5927\u8111\u76ae\u5c42\u66f2\u9762\u8fdb\u884c\u7cbe\u786e\u5730\u5bf9\u6bd4\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u76f4\u63a5\u5bf9\u6bd4\u96be\u5ea6\u5f88\u9ad8\uff0c\u6211\u4eec\u975e\u5e38\u5bb9\u6613\u5c06\u4e0d\u540c\u7684\u6c9f\u56de\u9519\u8bef\u5730\u5bf9\u9f50\uff0c\u7b97\u6cd5\u843d\u5165\u5728\u5c40\u90e8\u6700\u4f18\u9677\u9631\u4e2d\u3002\u5982\u56fe16\u6240\u793a\uff0c\u6211\u4eec\u5c06\u5927\u8111\u76ae\u5c42\u66f2\u9762\u5171\u5f62\u5730\u6620\u5230\u7403\u9762\u4e0a\uff0c\u7136\u540e\u5728\u7403\u9762\u4e4b\u95f4\u5efa\u7acb\u5149\u6ed1\u6620\u5c04\uff0c\u8fd9\u79cd\u65b9\u6cd5\u66f4\u52a0\u7b80\u5355\u800c\u7cbe\u786e\u3002\u5c06\u5927\u8111\u76ae\u5c42\u6620\u5230\u7403\u9762\u7b49\u4ef7\u4e8e\u4e3a\u5927\u8111\u76ae\u5c42\u66f2\u9762\u8d4b\u4ee5\u66f2\u7387\u4e3a+1\u7684\u9ece\u66fc\u5ea6\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u91cc\u5947\u66f2\u7387\u6d41\u7684\u65b9\u6cd5\u5f97\u5230\u3002<\/p>\n


\n\u56fe17. \u5927\u8111\u6d77\u9a6c\u4f53\u7684\u51e0\u4f55\u5206\u6790\u3002<\/strong><\/p>\n

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<\/p>\n

\u56fe18. \u4eba\u8138\u66f2\u9762\u7684\u7cbe\u786e\u5339\u914d\u3002<\/strong><\/p>\n

\u7f8e\u5bb9\u6280\u672f<\/strong><\/p>\n

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\n\u56fe19. \u4e09\u7ef4\u4eba\u8138\u66f2\u9762\u88ab\u5171\u5f62\u5730\u6620\u5230\u4e8c\u7ef4\u5e73\u9762\u4e0a\uff0c\u6240\u7528\u65b9\u6cd5\u5c31\u662f\u91cc\u5947\u66f2\u7387\u6d41\u3002<\/strong><\/p>\n

\u5982\u56fe19\u6240\u793a\uff0c\u6211\u4eec\u7528\u91cc\u5947\u66f2\u7387\u6d41\u65b9\u6cd5\uff0c\u5c06\u4eba\u8138\u66f2\u9762\u7684\u9ece\u66fc\u5ea6\u91cf\u53d8\u6210\u66f2\u7387\u4e3a0\u7684\u5e73\u76f4\u5ea6\u91cf\uff0c\u5c06\u4e09\u7ef4\u4eba\u8138\u66f2\u9762\u5e73\u94fa\u5230\u4e8c\u7ef4\u5e73\u9762\u4e0a\u9762\uff0c\u7136\u540e\u5728\u4e8c\u7ef4\u5e73\u9762\u533a\u57df\u4e4b\u95f4\u5efa\u7acb\u5149\u6ed1\u53cc\u5c04\uff0c\u4ece\u800c\u8bf1\u5bfc\u4e09\u7ef4\u4eba\u8138\u66f2\u9762\u95f4\u7684\u53cc\u5c04\u3002\u5f53\u7136\uff0c\u8fd9\u79cd\u65b9\u6cd5\u4e5f\u53ef\u4ee5\u7528\u4e8e\u4e09\u7ef4\u4eba\u8138\u8bc6\u522b\uff0c\u4f46\u662f\u4eba\u8138\u8bc6\u522b\u5bf9\u4e8e\u6620\u5c04\u7684\u7cbe\u786e\u5ea6\u8981\u6c42\u6ca1\u6709\u5982\u6b64\u4e4b\u9ad8\u3002<\/p>\n

\u5728\u7cbe\u51c6\u533b\u7597\u7684\u5176\u4ed6\u9886\u57df\uff0c\u4f8b\u5982\u7259\u9f7f\u6574\u5f62\u3001\u4eba\u9020\u5fc3\u810f\u74e3\u819c\u3001\u4eba\u9020\u9aa8\u9abc\u3001\u653e\u5c04\u6cbb\u7597\u5b9e\u65f6\u76d1\u63a7\u3001\u809d\u810f\u624b\u672f\u8ba1\u5212\u7b49\u7b49\uff0c\u90fd\u9700\u8981\u5bf9\u5404\u79cd\u4eba\u4f53\u5668\u5b98\u8fdb\u884c\u5f71\u50cf\u83b7\u53d6\u3001\u51e0\u4f55\u91cd\u5efa\u3001\u7279\u5f81\u5206\u6790\u7b49\uff0c\u91cc\u5947\u6d41\u65b9\u6cd5\u90fd\u4f1a\u8d77\u5230\u91cd\u8981\u7684\u4f5c\u7528\u3002<\/p>\n

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7 \u603b\u7ed3\u548c\u5c55\u671b<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\n

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

[1] W. Zeng and X. Gu, Ricci Flow for Shape Analysis and Surface Registration Theories, Algorithms and Applications, Springer 2013<\/p><\/blockquote>\n<\/section>\n

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