{"id":22736,"date":"2020-12-17T17:30:16","date_gmt":"2020-12-17T09:30:16","guid":{"rendered":"https:\/\/swarma.org\/?p=22736"},"modified":"2020-12-17T17:30:16","modified_gmt":"2020-12-17T09:30:16","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e8%9d%b4%e8%9d%b6%e6%95%88%e5%ba%94-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=22736","title":{"rendered":"\u4ec0\u4e48\u662f\u8774\u8776\u6548\u5e94 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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1963\u5e74\uff0c\u7231\u5fb7\u534e\u00b7\u6d1b\u4f26\u8328 Edward N. Lorenz \u5728\u4e00\u7bc7\u53d1\u8868\u4e8e\u300a\u5927\u6c14\u79d1\u5b66\u6742\u5fd7\u300bJournal of Atmospheric Sciences <\/em>\u7684\u8bba\u6587\u300a\u786e\u5b9a\u6027\u975e\u5468\u671f\u6d41\u300b<\/span>Deterministic Nonperiodic Flow<\/span><\/em> \u4e2d\u9996\u6b21\u89c2\u5bdf\u5e76\u5206\u6790\u4e86\u8fd9\u4e2a\u6548\u5e94\u3002\u4ed6\u5728\u540c\u5e74\u53d1\u8868\u4e8e\u300a\u7ebd\u7ea6\u79d1\u5b66\u9662\u5b66\u62a5\u300b<\/span>Transactions of the New York Academy of Sciences<\/span><\/em> \u7684\u8bba\u6587\u300a\u6d41\u4f53\u52a8\u529b\u6d41\u7684\u53ef\u9884\u6d4b\u6027\u300b<\/span>The Predictability of Hydrodynamic Flow<\/span><\/em> \u4e2d\u8bc4\u8bba\u8bf4\uff1a<\/span><\/p>\n


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\u201c\u4e00\u4e2a\u6c14\u8c61\u5b66\u5bb6\u66fe\u8bc4\u8bba\u8bf4\uff1a\u2018\u5982\u679c\u8fd9\u4e2a\u7406\u8bba\u662f\u6b63\u786e\u7684\uff0c\u90a3\u4e48\u6d77\u9e25\u6247\u52a8\u4e00\u6b21\u7fc5\u8180\u5c31\u8db3\u4ee5\u6c38\u8fdc\u6539\u53d8\u5929\u6c14\u7684\u53d8\u5316\u8fdb\u7a0b\u3002\u2019 \u201d<\/section>\n<\/section>\n<\/blockquote>\n

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\u5728\u540e\u6765\u7684\u6f14\u8bb2\u548c\u8bba\u6587\u4e2d\u4ed6\u7528\u4e86\u66f4\u52a0\u6709\u8bd7<\/span>\u610f\u7684\u8868\u8fbe\u2014\u2014”\u8774\u8776\u6548\u5e94”\u3002<\/span><\/p>\n


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\u5bf9\u4e8e\u8fd9\u4e2a\u6548\u5e94\u6700\u5e38\u89c1\u7684\u9610\u8ff0\u662f\uff1a\u201c\u4e00\u53ea\u5357\u7f8e\u6d32\u4e9a\u9a6c\u900a\u6cb3\u6d41\u57df\u70ed\u5e26\u96e8\u6797\u4e2d\u7684\u8774\u8776\uff0c\u5076\u5c14\u6247\u52a8\u51e0\u4e0b\u7fc5\u8180\uff0c\u53ef\u4ee5\u5728\u4e24\u5468\u4ee5\u540e\u5f15\u8d77\u7f8e\u56fd\u5f97\u514b\u8428\u65af\u5dde\u7684\u4e00\u573a\u9f99\u5377\u98ce\u3002\u201d<\/span><\/p>\n


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\u4e00\u822c\u6765\u8bf4\uff0c\u5fae\u89c2\u5c3a\u5ea6\u4e0a\u8774\u8776\u5fae\u5f31\u7684\u5e72\u6270\uff0c\u4e0d\u4f1a\u5f71\u54cd\u5b8f\u89c2\u5c3a\u5ea6\u4e0a\u6574\u4e2a\u5929\u6c14\u53d8\u5316\u3002\u7136\u800c\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u6b63\u597d\u662f\u8774\u8776\u591a\u6247\u52a8\u4e86\u4e00\u6b21\u7fc5\u8180\u6240\u9020\u6210\u7684\u5fae\u89c2\u6548\u679c\uff0c\u7531\u6b64\u5f15\u8d77\u4e86\u8fde\u9501\u53cd\u5e94\uff0c\u968f\u540e\u5728\u5929\u6c14\u7684\u53d8\u5316\u4e2d\u4e0d\u65ad\u6269\u5927\u81ea\u8eab\uff0c\u4e43\u81f3\u4e8e\u540e\u6765\u6210\u4e3a\u9f99\u5377\u98ce\u8fd9\u6837\u5b8f\u89c2\u5c3a\u5ea6\u7684\u5929\u6c14\u73b0\u8c61\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u5728\u5229\u7528\u6570\u503c\u5de5\u5177\u9884\u6d4b\u5929\u6c14\u53d8\u5316\u65f6\uff0c\u89c2\u5bdf\u5230\u4e86\u8fd9\u6837\u7684\u6548\u5e94\u3002\u4ed6\u53d1\u73b0\uff0c\u5c06\u5929\u6c14\u6a21\u578b\u7684\u521d\u59cb\u6761\u4ef6\u8fdb\u884c\u770b\u4f3c\u65e0\u5173\u7d27\u8981\u7684\u56db\u820d\u4e94\u5165\u4e4b\u540e\uff0c\u6a21\u578b\u6240\u9884\u6d4b\u7684\u5929\u6c14\u53d8\u5316\u5b8c\u5168\u4e0d\u540c\u4e8e\u56db\u820d\u4e94\u5165\u4e4b\u524d\u6240\u9884\u6d4b\u7684\u90a3\u6837\u3002\u5b9e\u9645\u4e0a\uff0c\u8fd9\u79cd\u73b0\u8c61\u66fe\u5728\u6570\u5b66\u548c\u79d1\u5b66\u5386\u53f2\u4e0a\u88ab\u53cd\u590d\u53d1\u73b0\u8fc7\uff0c\u81f3\u5c11\u8ffd\u6eaf\u5230\u9ea6\u514b\u65af\u97e6 James Clerk Maxwell \u548c\u5e9e\u52a0\u83b1  Henri Poincar\u00e9 \uff0c\u4f46\u662f\u4e00\u76f4\u6ca1\u6709\u5f15\u8d77\u5b66\u672f\u754c\u8db3\u591f\u7684\u91cd\u89c6\uff0c\u76f4\u52301972\u5e74\uff0c\u6d1b\u4f26\u5179\u5728\u4e00\u573a\u4e8e\u534e\u76db\u987f\u53ec\u5f00\u7684\u5b66\u672f\u4f1a\u8bae\u4e0a\uff0c\u505a\u4e86\u90a3\u573a\u8457\u540d\u7684\u6f14\u8bb2\uff0c\u9898\u4e3a\u300a\u53ef\u9884\u6d4b\u6027\uff1a\u5728\u5df4\u897f\u7684\u4e00\u53ea\u8774\u8776\u6247\u6247\u7fc5\u8180\u4f1a\u5f15\u8d77\u5728\u7279\u514b\u8428\u65af\u5dde\u7684\u9f99\u5377\u98ce\u5417\u300bPredictability: Does the flap of a butterfly\u2019s wings in Brazil set off a tornado in Texas? <\/em>\u3002<\/span><\/p>\n


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\u5728\u6b64\u4e4b\u540e\uff0c\u8774\u8776\u6548\u5e94\u4ee5\u53ca\u8fd9\u4e2a\u73b0\u8c61\u80cc\u540e\u7684\u539f\u7406\u5f00\u59cb\u5f15\u8d77\u5b66\u672f\u754c\u7684\u5e7f\u6cdb\u5173\u6ce8\u30021975\u5e74\uff0c\u674e\u5929\u5ca9Tien-Yien Li \u548c\u8a79\u59c6\u65af\u00b7\u7ea6\u514b James Yorke\u53d1\u8868\u4e86\u9898\u4e3a\u300a\u5468\u671f\u4e09\u610f\u5473\u7740\u6df7\u6c8c\u300bPeriod three implies chaos<\/em>\uff0c\u6b63\u5f0f\u4f7f\u7528\u4e86\u6df7\u6c8c\u4e00\u8bcd\u6765\u547d\u540d\u8fd9\u4e2a\u9886\u57df\u7684\u7814\u7a76\u3002\u968f\u7740\u4e4b\u540e\u6df7\u6c8c\u7406\u8bba\u7684\u53d1\u5c55\uff0c\u201c\u8774\u8776\u6548\u5e94\u201d\u8fd9\u4e2a\u5f62\u8c61\u53c8\u751f\u52a8\u7684\u6bd4\u55bb\u9010\u6e10\u5e7f\u4e3a\u4eba\u77e5 \u2014\u2014 \u4e00\u4e2a\u4e0d\u8d77\u773c\u7684\u5c0f\u52a8\u4f5c\u5374\u6709\u53ef\u80fd\u4f1a\u5f15\u8d77\u4e00\u8fde\u4e32\u7684\u5de8\u5927\u53cd\u5e94\u3002<\/span><\/p>\n


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\u7406\u8bba\u5b9a\u4e49<\/span><\/strong><\/p>\n

\u5728\u6df7\u6c8c\u7406\u8bba chaos theory \u4e2d\uff0c\u8774\u8776\u6548\u5e94\u6307\u7684\u662f\u52a8\u529b\u7cfb\u7edf dynamical system \u7684\u4e00\u79cd\u5c5e\u6027\uff0c\u5373\u5176\u5173\u4e8e\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u4f9d\u8d56\u6027 the sensitive dependence on initial conditions \u3002\u5bf9\u4e8e\u5177\u5907\u8fd9\u79cd\u5c5e\u6027\u7684\u786e\u5b9a\u6027\u52a8\u529b\u7cfb\u7edf deterministic system\uff0c \u67d0\u4e2a\u72b6\u6001\u91cf\u7684\u5fae\u5c0f\u6539\u53d8\u90fd\u6709\u53ef\u80fd\u5bfc\u81f4\u8fd9\u4e2a\u7cfb\u7edf\u4e4b\u540e\u6f14\u5316\u8fc7\u7a0b\u7684\u5de8\u5927\u5dee\u5f02\u3002<\/span><\/p>\n


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\u6839\u636e\u8a79\u59c6\u65af\u00b7\u683c\u96f7\u514b James Gleick\u7684\u8003\u8bc1[1]\uff0c\u201c\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u4f9d\u8d56\u6027\u201c\u5e76\u4e0d\u662f\u4e2a\u5168\u65b0\u7684\u6982\u5ff5\uff0c\u4e4b\u524d\u4eba\u4eec\u6240\u4f20\u9882\u7684\u8c1a\u8bed\u4e2d\u5c31\u6709\u63d0\u5230\uff1a<\/span><\/p>\n


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\u201c\u4e22\u4e86\u4e00\u53ea\u9a6c\u8e44\u94c1\uff0c\u6298\u4e86\u4e00\u5339\u6218\u9a6c\uff1b<\/span><\/p>\n

\u6298\u4e86\u4e00\u5339\u6218\u9a6c\uff0c\u635f\u4e86\u4e00\u4f4d\u56fd\u738b\uff1b<\/span><\/p>\n

\u635f\u4e86\u4e00\u4f4d\u56fd\u738b\uff0c\u8f93\u4e86\u4e00\u573a\u6218\u4e89\uff1b<\/span><\/p>\n

\u8f93\u4e86\u4e00\u573a\u6218\u4e89\uff0c\u4ea1\u4e86\u4e00\u4e2a\u5e1d\u56fd\u3002\u201d<\/span><\/p>\n


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\u201cFor want of a nail, the shoe was lost;<\/span><\/p>\n

For want of a shoe, the horse was lost;<\/span><\/p>\n

For want of a horse, the rider was lost;<\/span><\/p>\n

For want of a rider, the battle was lost;<\/span><\/p>\n

For want of a battle, the kingdom was lost!\u201d<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u770b\u8d77\u6765\u4e22\u4e86\u4e00\u53ea\u9a6c\u8e44\u8dcc\u53ea\u662f\u4e00\u4ef6\u65e0\u5173\u75db\u75d2\u7684\u5c0f\u4e8b\uff0c\u4f46\u662f\u968f\u7740\u4e8b\u7269\u4e4b\u540e\u7684\u53d1\u5c55\uff0c\u8fd9\u5374\u6709\u53ef\u80fd\u5f15\u8d77\u5b8c\u5168\u65e0\u6cd5\u9884\u77e5\u7684\u5927\u540e\u679c\u3002<\/span><\/p>\n


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<\/p>\n

\u8774\u8776\u6548\u5e94\u7684\u6210\u56e0\u5206\u6790<\/span><\/strong><\/p>\n

\u5982\u524d\u6587\u6240\u8bf4\uff0c\u8774\u8776\u6548\u5e94\u6307\u7684\u662f\u52a8\u529b\u7cfb\u7edf\u7684\u521d\u59cb\u6761\u4ef6\u654f\u611f\u4f9d\u8d56\u6027\uff0c\u90a3\u4e48\u4ec0\u4e48\u6837\u7684\u52a8\u529b\u7cfb\u7edf\u4f1a\u6709\u8fd9\u6837\u7684\u6027\u8d28\uff1f<\/span><\/p>\n


<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

\u6570\u5b66\u5b9a\u4e49<\/span><\/strong><\/p>\n

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<\/p>\n

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    \n
  1. \n
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  2. \n
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  3. \n
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    <\/p>\n
    <\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/section>\n

    <\/span><\/section>\n

    \u8fd9\u91cc\u7684\u4e2d\u5fc3\u601d\u60f3\u662f\uff0c\u53ea\u8981\u52a8\u529b\u7cfb\u7edf\u5bf9\u4e8e\u4efb\u610f\u521d\u59cb\u72b6\u6001<\/path><\/g><\/g><\/g><\/svg><\/span>\uff0c\u5b58\u5728\u4e00\u4e2a\u4efb\u610f\u63a5\u8fd1<\/path><\/g><\/g><\/g><\/svg><\/span>\u7684\u7cfb\u7edf\u72b6\u6001\u91cf<\/path><\/g><\/g><\/g><\/svg><\/span>\uff0c\u5b83\u80fd\u9010\u6e10\u6f14\u5316\u8fdc\u79bb<\/path><\/g><\/g><\/g><\/svg><\/span>\uff0c\u90a3\u4e48\u8fd9\u4e2a\u52a8\u529b\u7cfb\u7edf\u5c31\u5177\u5907\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u4f9d\u8d56\u6027\u3002\u8fd9\u91cc\u8981\u5f3a\u8c03\uff0c\u6ca1\u6709\u5fc5\u8981\u8981\u6c42<\/path><\/g><\/g><\/g><\/svg><\/span>\u9644\u8fd1\u7684\u6240\u6709<\/path><\/g><\/g><\/g><\/svg><\/span>\u90fd\u6ee1\u8db3\uff1a\u6700\u7ec8<\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u4e0d\u8d8b\u8fd1<\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\uff1b\u53ea\u8981\u81f3\u5c11\u6709\u4e00\u4e2a\u8fd9\u6837\u7684<\/path><\/g><\/g><\/g><\/svg><\/span>\u5c31\u53ef\u4ee5\u4e86\u3002<\/span><\/section>\n
    \u5982\u679c\u5bf9\u4e8e\u9644\u8fd1\u7684\u6240\u6709<\/path><\/g><\/g><\/g><\/svg><\/span>\u90fd\u6ee1\u8db3\uff0c\u6700\u7ec8<\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u4e0d\u8d8b\u8fd1<\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u8fd9\u4e2a\u7cfb\u7edf\u5177\u6709\u6269\u5f20\u6027(expansiveness)<\/span><\/section>\n
    \u6211\u4eec\u4e5f\u7528\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570 Lyapunov exponent \u6765\u5b9a\u4e49\u521d\u59cb\u6761\u4ef6\u654f\u611f\u4f9d\u8d56\u6027\u3002<\/span><\/section>\n
    \u8003\u8651\u5ea6\u91cf\u7a7a\u95f4<\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u4e2d\u52a8\u529b\u7cfb\u7edf<\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\uff0c\u5176\u628a\u521d\u59cb\u72b6\u6001<\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u6620\u5c04\u4e3a<\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u65f6\u523b\u7684\u7cfb\u7edf\u72b6\u6001<\/path><\/g><\/path><\/g><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u3002\u52a8\u529b\u7cfb\u7edf\u7684\u521d\u59cb\u6761\u4ef6\u654f\u611f\u4f9d\u8d56\u6027\u88ab\u5b9a\u4e49\u4e3a[4]\uff0c\u5b58\u5728\u6b63\u6570<\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>  \u6ee1\u8db3\uff1a\u5bf9\u4e8e\u4efb\u610f <\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u4ee5\u53ca<\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u90fd\u5b58\u5728\u6ee1\u8db3<\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u7684<\/path><\/g><\/g><\/g><\/svg><\/span>\u4ee5\u53ca\u65f6\u523b<\/path><\/g><\/path><\/g><\/path><\/g><\/g><\/g><\/svg><\/span>\u6ee1\u8db3<\/span><\/section>\n
    <\/p>\n
    <\/embed><\/section>\n

    <\/span><\/section>\n

    \u8fd9\u91cc\u7684<\/path><\/g><\/g><\/g><\/svg><\/span>\u5c31\u88ab\u79f0\u4e3a\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u3002\u6211\u4eec\u4e5f\u79f0\u5177\u6709\u6b63\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u7684\u52a8\u529b\u7cfb\u7edf\uff0c\u5177\u6709\u521d\u59cb\u6761\u4ef6\u654f\u611f\u4f9d\u8d56\u6027\u3002<\/span><\/section>\n
    \u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u5f97\u77e5\uff0c\u521d\u59cb\u6761\u4ef6\u654f\u611f\u4f9d\u8d56\u6027\uff0c\u5e76\u6ca1\u6709\u7ea6\u675f\u7cfb\u7edf\u7684\u957f\u671f\u884c\u4e3a\u662f\u4e0d\u662f\u8d8b\u8fd1\u4e8e\u67d0\u4e00\u5e73\u8861\u6001\u6216\u8005\u5468\u671f\u8f68\u9053\uff1b\u800c\u4ec5\u4ec5\u8981\u6c42\u4e86\uff0c\u4efb\u610f\u4ece\u4efb\u610f\u4e24\u4e2a\u4efb\u610f\u63a5\u8fd1\u7684\u521d\u59cb\u72b6\u6001\u51fa\u53d1\uff0c\u7cfb\u7edf\u7684\u4e24\u6761\u6f14\u5316\u8f68\u8ff9\u5728\u4e00\u5b9a\u65f6\u95f4\u5185\u5feb\u901f\u5206\u5f00\u3002<\/span><\/section>\n
    \u4e8e\u662f\uff0c\u5bf9\u4e8e\u5177\u6709\u521d\u59cb\u6761\u4ef6\u654f\u611f\u4f9d\u8d56\u6027\u7684\u7cfb\u7edf\uff08\u5982\u5929\u6c14\u7cfb\u7edf\uff09\uff0c\u7531\u4e8e\u65e0\u6cd5\u5b8c\u5168\u51c6\u786e\u5730\u6d4b\u91cf\u548c\u521d\u59cb\u6761\u4ef6\uff0c\u4ee5\u53ca\u4eff\u771f\u8ba1\u7b97\u7cfb\u7edf\u7684\u6f14\u5316\uff0c\u56e0\u6b64\u6211\u4eec\u96be\u4ee5\u8fdb\u884c\u8d85\u8fc7\u7279\u5b9a\u65f6\u95f4\u8303\u56f4\u7684\u9884\u6d4b\uff0c\u4f8b\u5982\u5bf9\u4e8e\u5929\u6c14\u9884\u6d4b\u6682\u65f6\u65e0\u6cd5\u8d85\u8fc7\u4e00\u4e2a\u6708\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u8fd8\u53cd\u6620\u51fa\uff0c\u8bef\u5dee\u5728\u4e00\u5b9a\u8303\u56f4\u5185\u662f\u6307\u6570\u589e\u52a0\u7684\u3002\u8fd9\u4e5f\u610f\u5473\u7740\uff0c\u53ea\u6709\u6211\u4eec\u7684\u6d4b\u91cf\u7cbe\u5ea6\u548c\u8ba1\u7b97\u7cbe\u5ea6\u6307\u6570\u589e\u957f\uff0c\u6211\u4eec\u80fd\u9884\u6d4b\u7684\u65f6\u957f\u624d\u53ea\u80fd\u7ebf\u6027\u589e\u957f\u3002\u53c2\u9605\u6587\u732e[4]\u7b2c329-330\u9875\u7684\u4f8b\u5b50\uff0c\u4ee5\u53ca\u6587\u732e[5]\u4e2d\u7684\u7cbe\u5f69\u8ba8\u8bba\u3002<\/span><\/section>\n
    \u5f53\u7136\uff0c\u5bf9\u4e8e\u65e2\u4e0d\u53d1\u6563\u4e5f\u4e0d\u6536\u655b\u3001\u521d\u59cb\u6761\u4ef6\u654f\u611f\u3001\u975e\u5468\u671f\u53d8\u5316\u3001\u786e\u5b9a\u6027\u6df7\u6c8c\u7cfb\u7edf\u800c\u8a00\uff0c\u8fd9\u6837\u7684\u8bef\u5dee\u4e00\u822c\u4e0d\u662f\u65e0\u9650\u6307\u6570\u589e\u52a0\u7684\uff0c\u800c\u662f\u4f1a\u6709\u4e2a\u9650\u5ea6\u3002\u5bf9\u4e8e\u5b58\u5728\u5947\u602a\u5438\u5f15\u5b50 strange attractor\u7684\u6df7\u6c8c\u7cfb\u7edf\uff0c\u4f8b\u5982\u6d1b\u4f26\u8328\u53d1\u73b0\u7684\u7cfb\u7edf[6]\uff0c\u5176\u6700\u5927\u8bef\u5dee\u4e0d\u4f1a\u5927\u4e8e\u5947\u602a\u5438\u5f15\u5b50\u7684\u76f4\u5f84\u3002<\/span><\/section>\n
    \u5bf9\u4e8e\u7ed9\u5b9a\u52a8\u529b\u7cfb\u7edf\u7684\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u8ba1\u7b97\uff0c\u53c2\u9605\u6587\u732e[4]\u7b2c373-376\u9875\u3002  <\/span><\/section>\n


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    3.\u6d1b\u4f26\u8328\u7cfb\u7edf\u6f14\u5316\u7684\u4eff\u771f\u56fe\u793a<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

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


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    \u65f6\u95f4 0 \u2264 t \u2264 30<\/span><\/p>\n

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    z \u5750\u6807<\/span><\/section>\n

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

    \u8fd9\u4e24\u5e45\u56fe\u8868\u793a\u4e86\u6d1b\u4f26\u8328\u7cfb\u7edf\u4ece\u4e24\u4e2a\u76f8\u5dee\u65e0\u51e0\u7684\u521d\u59cb\u72b6\u6001\uff08\u4ec5\u5728\u67d0\u4e00\u65b9\u5411\u4e0a\u5dee<\/span>10<\/span>-5<\/span><\/sup>\uff09\u800c\u6f14\u5316\u7684\u8fc7\u7a0b\u3002<\/span><\/span><\/p>\n


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

    \u4e0a\u56fe\u4e2d\uff0c\u84dd\u8272\u66f2\u7ebf\u7531\u5916\u4fa7\u7684\u84dd\u8272\u690e\u4f53\u5f00\u59cb\uff0c\u6f14\u531630\u500d\u5355\u4f4d\u65f6\u95f4\u4e4b\u540e\uff0c\u5230\u8fbe\u5185\u4fa7\u7684\u84dd\u8272\u690e\u4f53\uff1b\u9ec4\u8272\u66f2\u7ebf\u7531\u5916\u4fa7\u7684\u9ec4\u8272\u690e\u4f53\u5f00\u59cb\uff0c\u6f14\u531630\u500d\u5355\u4f4d\u65f6\u95f4\u4e4b\u540e\uff0c\u5230\u8fbe\u5185\u4fa7\u7684\u9ec4\u8272\u690e\u4f53\u3002<\/span>
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    \u8fd9\u91cc\u628a\u8fd9\u4e24\u6761\u66f2\u7ebf\u5206\u5f00\u7ed8\u5236\u7684\u539f\u56e0\u662f\uff0c\u4e24\u6761\u66f2\u7ebf\u7684\u5927\u90e8\u5206\u9ad8\u5ea6\u76f8\u8fd1\uff0c\u82e5\u7ed8\u5236\u5728\u4e00\u8d77\uff0c\u5219\u4f1a\u770b\u8d77\u6765\u91cd\u5408\u5728\u4e00\u8d77\uff0c\u800c\u4e0d\u65b9\u4fbf\u6211\u4eec\u5bf9\u6bd4\u8fd9\u4e24\u6761\u66f2\u7ebf\u7684\u4e0d\u540c\u3002\u901a\u8fc7\u5bf9\u6bd4\u8fd9\u4e24\u6761\u66f2\u7ebf\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e24\u6761\u6f14\u5316\u8f68\u8ff9\u5728\u6700\u540e\u4e00\u6bb5\u65f6\u95f4\u5b8c\u5168\u4e0d\u540c\uff0c\u7279\u522b\u662f\u6700\u7ec8\u4f4d\u7f6e\u660e\u663e\u5dee\u4e86\u4e00\u622a\u3002\u4e0b\u56fe\u5bf9\u6bd4\u4e86\u4e24\u6761\u66f2\u7ebf\u7684\u6cbf\u67d0\u4e00\u56fa\u5b9a\u65b9\u5411\u7684\u5750\u6807\u53d8\u5316\u3002\u5176\u4e2d\u4e0a\u534a\u5b50\u56fe\u662f\u4e24\u6761\u66f2\u7ebf\u7684\u5e73\u5747\u5750\u6807\u53d8\u5316\uff0c\u4e0b\u534a\u5b50\u56fe\u662f\u4e24\u6761\u66f2\u7ebf\u5750\u6807\u5dee\u5f02\u7684\u53d8\u5316\u3002<\/span><\/p>\n


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

    \u53ef\u4ee5\u770b\u51fa\uff0c\u6700\u521d\uff0c\u4e24\u6761\u8f68\u8ff9\u51e0\u4e4e\u662f\u91cd\u5408\u7684\uff0c\u800c\u5f53\u6f14\u5316\u65f6\u95f4\u8d85\u8fc723\u500d\u5355\u4f4d\u65f6\u95f4\u7684\u65f6\u5019\uff0c\u4e24\u6761\u6f14\u5316\u66f2\u7ebf\u5f00\u59cb\u4e0d\u518d\u4e00\u81f4\uff0c\u5e76\u4e14\u4ed6\u4eec\u7684\u5dee\u5f02\u5f00\u59cb\u65e0\u89c4\u5f8b\u9707\u8361\uff0c\u5230\u6700\u7ec830\u500d\u5355\u4f4d\u65f6\u95f4\u65f6\uff0c\u4e24\u6761\u66f2\u7ebf\u5927\u6982\u76f8\u5dee15\u500d\u5355\u4f4d\u5750\u6807\u3002\u7531\u6b64\u53ef\u89c1\uff0c\u521d\u59cb\u6761\u4ef6\u7684\u5fae\u5c0f\u4e0d\u540c\uff08\u4ec5\u5728\u67d0\u4e00\u65b9\u5411\u4e0a\u5dee10<\/span>-5<\/span><\/sup>\u500d\u5355\u4f4d\u5750\u6807\uff09\uff0c\u5728\u7ecf\u8fc730\u500d\u5355\u4f4d\u65f6\u95f4\u7684\u6f14\u5316\u540e\uff0c\u653e\u5927\u4e8610\u4e07\u500d\uff0c\u6210\u4e86\u5de8\u5927\u7684\u5dee\u5f02\uff0815\u500d\u5355\u4f4d\u5750\u6807\uff09\u3002<\/span><\/section>\n


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    4. \u5404\u9886\u57df\u4e2d\u7684\u8774\u8776\u6548\u5e94<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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

    \u5173\u4e8e\u79d1\u5b66<\/span><\/strong><\/p>\n

    \u5929\u6c14\u7cfb\u7edf\u65b9\u9762<\/span><\/p>\n

    \u8774\u8776\u6548\u5e94\u5728\u6c14\u8c61\u9886\u57df\u662f\u6700\u4e3a\u4eba\u6240\u719f\u77e5\u7684\uff0c\u4f8b\u5982\u6807\u51c6\u5929\u6c14\u9884\u62a5\u6a21\u578b\u5c31\u53ef\u4ee5\u8f7b\u800c\u6613\u4e3e\u5730\u7684\u6f14\u793a\u8fd9\u4e00\u6548\u5e94\u3002\u6c14\u5019\u79d1\u5b66\u5bb6\u8a79\u59c6\u65af\u00b7\u5b89\u5357 James Annan \u548c\u5a01\u5ec9\u00b7\u5eb7\u8bfa\u5229 William Connolley \u89e3\u91ca\u8bf4\uff0c\u6df7\u6c8c\u5bf9\u5929\u6c14\u9884\u62a5\u65b9\u6cd5\u7684\u53d1\u5c55\u5f88\u91cd\u8981; \u5929\u6c14\u6a21\u578b\u5bf9\u521d\u59cb\u6761\u4ef6\u5f88\u654f\u611f\u3002<\/span><\/p>\n


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

    \u4ed6\u4eec\u4e5f\u8865\u5145\u544a\u8beb\u8bf4: \u201c\u5f53\u7136\uff0c\u662f\u5426\u6709\u4e00\u53ea\u672a\u77e5\u8774\u8776\u6247\u52a8\u4e86\u7fc5\u8180\u4e0d\u4f1a\u76f4\u63a5\u663e\u793a\u5728\u5929\u6c14\u9884\u62a5\u4e0a\uff0c\u56e0\u4e3a\u8fd9\u6837\u4e00\u4e2a\u5fae\u5c0f\u7684\u6270\u52a8\u9700\u8981\u5f88\u957f\u65f6\u95f4\u624d\u4f1a\u53d1\u5c55\u5230\u4e00\u4e2a\u663e\u8457\u7684\u89c4\u6a21\uff0c\u800c\u4e14\u8fd8\u6709\u8bb8\u591a\u66f4\u76f4\u63a5\u7684\u4e0d\u786e\u5b9a\u56e0\u7d20\u9700\u8981\u6211\u4eec\u62c5\u5fc3\u3002\u56e0\u6b64\uff0c\u5982\u679c\u8bf4\u8774\u8776\u6548\u5e94\u8fd9\u4e00\u73b0\u8c61\u76f4\u63a5\u5bf9\u5929\u6c14\u9884\u62a5\u9020\u6210\u4e86\u4ec0\u4e48\u5f71\u54cd\uff0c\u8fd9\u4e00\u8bf4\u6cd5\u5f80\u5f80\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u662f\u9519\u8bef\u7684\u3002<\/span><\/p>\n


    <\/p>\n

    \u91cf\u5b50\u529b\u5b66\u65b9\u9762<\/span><\/strong><\/span><\/p>\n

    \u4e00\u4e9b\u5b66\u8005\u5df2\u7ecf\u5728\u4e00\u4e9b\u534a\u7ecf\u5178\u7269\u7406\u5b66\u548c\u91cf\u5b50\u7269\u7406\u5b66\u6848\u4f8b\u4e2d\uff0c\u5305\u62ec\u5f3a\u573a\u4e2d\u7684\u6c22\u539f\u5b50\u8c31\u548c\u9006\u78c1\u5f00\u666e\u52d2\u95ee\u9898diamagnetic Kepler problem\uff0c\u7814\u7a76\u4e86\u5b58\u5728\u521d\u59cb\u6761\u4ef6\u654f\u611f\u4f9d\u8d56\uff08\u8774\u8776\u6548\u5e94\uff09\u7684\u53ef\u80fd\u6027[7]\u3002  \u4e00\u4e9b\u5b66\u8005\u5df2\u7ecf\u8bba\u8bc1\u4e86\uff0c\u91cf\u5b50\u529b\u5b66\u7cfb\u7edf\u4e2d\u4e0d\u5b58\u5728”\u521d\u59cb\u6761\u4ef6\u7684\u6781\u7aef\uff08\u6307\u6570\uff09\u654f\u611f\u4f9d\u8d56\u6027”\uff0c\u4f46\u662f\u91cf\u5b50\u7cfb\u7edf\u80fd\u4ee5\u4e00\u4e9b\u91cf\u5b50\u73b0\u8c61\u53cd\u6620\u7ecf\u5178\u529b\u5b66\u4e2d\u7684\u6df7\u6c8c\u73b0\u8c61\uff08\u901a\u8fc7\u8003\u8651\u968f\u673a\u77e9\u9635\u7684\u7279\u5f81\u503c\uff09[8,9]\u3002\u968f\u673a\u77e9\u9635\u7406\u8bba\u548c\u57fa\u4e8e\u91cf\u5b50\u8ba1\u7b97\u673a\u7684\u4eff\u771f\u4e5f\u9a8c\u8bc1\u4e86\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\u4e0d\u5b58\u5728\u8774\u8776\u6548\u5e94[10]\u3002<\/span><\/p>\n


    <\/p>\n

    \u4e5f\u6709\u5176\u4ed6\u5b66\u8005\u8ba4\u4e3a\uff0c\u5982\u679c\u6211\u4eec\u6362\u4e2a\u89d2\u5ea6\uff0c\u4e5f\u53ef\u4ee5\u5728\u91cf\u5b50\u7cfb\u7edf\u4e2d\u53ef\u4ee5\u89c2\u6d4b\u5230\u67d0\u79cd\u6f14\u5316\u8fc7\u7a0b\u7684\u654f\u611f\u6027\uff0c\u7c7b\u4f3c\u7ecf\u5178\u529b\u5b66\u4e2d\u7684\u8774\u8776\u6548\u5e94\u3002\u5728\u7ecf\u5178\u529b\u5b66\u4e2d\uff0c\u6211\u4eec\u6240\u8ba8\u8bba\u7684\u8774\u8776\u6548\u5e94\uff0c\u662f\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u54c8\u5bc6\u987f\u4e3b\u51fd\u6570\uff08\u7cfb\u7edf\u52a8\u529b\u5b66\u65b9\u7a0b\uff09\uff0c\u8003\u8651\u53d7\u5fae\u6270\u7684\u7cfb\u7edf\u72b6\u6001\u91cf\uff0c\u4ece\u800c\u89c2\u5bdf\u5230\u4e86\u7cfb\u7edf\u72b6\u6001\u91cf\u5728\u5fae\u6270\u4f5c\u7528\u540e\u7684\u6f14\u5316\u5dee\u5f02\u3002<\/span><\/p>\n


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

    \u800c\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\uff0c\u7cfb\u7edf\u72b6\u6001\u91cf\u662f\u6ce2\u51fd\u6570\uff0c\u5e76\u4e0d\u5b58\u5728\u76f8\u5bf9\u4e8e\u65f6\u95f4\u7684\u72b6\u6001\u53d1\u6563\u3002\u4e8e\u662f\u8fd9\u4e9b\u5b66\u8005\u8003\u8651\uff0c\u6211\u4eec\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\uff0c\u6211\u4eec\u56fa\u5b9a\u7cfb\u7edf\u521d\u59cb\u72b6\u6001\u91cf\uff0c\u800c\u8003\u8651\u53d7\u5fae\u6270\u7684\u54c8\u5bc6\u987f\u4e3b\u51fd\u6570\uff0c\u518d\u89c2\u5bdf\u7cfb\u7edf\u72b6\u6001\u91cf\u7684\u6f14\u5316\u5dee\u5f02[11]\u3002<\/span><\/p>\n


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

    \u4ece\u8fd9\u4e2a\u65b9\u9762\u8003\u8651\uff0c\u5361\u5e93\u8c22\u592b\u65af\u57fa Karkuszewski \u7b49\u5b66\u8005\uff0c\u4ee5\u7cfb\u7edf\u72b6\u6001\u91cf\u7684\u91cd\u53e0\u7a0b\u5ea6\u4f5c\u4e3a\u201c\u6807\u5ea6\u201dmeasure\uff0c\u7814\u7a76\u4e86\u5bf9\u4e8e\u540c\u4e00\u521d\u59cb\u72b6\u6001\uff0c\u4e0d\u540c\u54c8\u5bc6\u987f\u91cf\u7684\u654f\u611f\u6027\u6c34\u5e73[12] \u3002\u8fd9\u4e00\u89c6\u89d2\u662f\u601d\u8003\u91cf\u5b50\u6df7\u6c8c\u7684\u4e00\u6761\u8def\u5f84\uff0c\u4e0d\u8fc7\u57fa\u672c\u4e0a\u4e0d\u88ab\u7b97\u4f5c\u91cf\u5b50\u529b\u5b66\u7248\u672c\u7684\u8774\u8776\u6548\u5e94\u3002<\/span><\/p>\n


    <\/p>\n

    \u5173\u4e8e\u6587\u5316<\/span><\/strong><\/p>\n

    \u4e2d\u56fd\u53e4\u7c4d\u4e2d\u7684\u8774\u8776\u6548\u5e94<\/span><\/p>\n

    \u539f\u6587\uff08\u300a\u5415\u6c0f\u6625\u79cb\u00b7\u5bdf\u5fae\u300b\uff09\uff1a\u695a\u4e4b\u8fb9\u9091\u66f0\u5351\u6881\uff0c\u5176\u5904\u5973\u4e0e\u5434\u4e4b\u8fb9\u9091\u5904\u5973\u6851\u4e8e\u5883\u4e0a\uff0c\u620f\u800c\u4f24\u5351\u6881\u4e4b\u5904\u5973\u3002\u5351\u6881\u4eba\u64cd\u5176\u4f24\u5b50\u4ee5\u8ba9\u5434\u4eba\uff0c\u5434\u4eba\u5e94\u4e4b\u4e0d\u606d\uff0c\u6012\uff0c\u6740\u800c\u53bb\u4e4b\u3002\u5434\u4eba\u5f80\u62a5\u4e4b\uff0c\u5c3d\u5c60\u5176\u5bb6\u3002\u5351\u6881\u516c\u6012\uff0c\u66f0\uff1a\u201c\u5434\u4eba\u7109\u6562\u653b\u543e\u9091\uff1f\u201d\u4e3e\u5175\u53cd\u653b\u4e4b\uff0c\u8001\u5f31\u5c3d\u6740\u4e4b\u77e3\u3002\u5434\u738b\u5937\u6627\u95fb\u4e4b\uff0c\u6012\uff0c\u4f7f\u4eba\u4e3e\u5175\u4fb5\u695a\u4e4b\u8fb9\u9091\uff0c\u514b\u5937\u800c\u540e\u53bb\u4e4b\u3002<\/span><\/p>\n


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

    \u5434\u3001\u695a\u4ee5\u6b64\u5927\u9686\u3002\u5434\u516c\u5b50\u5149\u53c8\u7387\u5e08\u4e0e\u695a\u4eba\u6218\u4e8e\u9e21\u7236\uff0c\u5927\u8d25\u695a\u4eba\uff0c\u83b7\u5176\u5e05\u6f58\u5b50\u81e3\u3001\u5c0f\u5e37\u5b50\u3001\u9648\u590f\u556e\u3002\u53c8\u53cd\u4f10\u90e2\uff0c\u5f97\u8346\u5e73\u738b\u4e4b\u592b\u4eba\u4ee5\u5f52\uff0c\u5b9e\u4e3a\u9e21\u7236\u4e4b\u6218\u3002\u51e1\u6301\u56fd\uff0c\u592a\u4e0a\u77e5\u59cb\uff0c\u5176\u6b21\u77e5\u7ec8\uff0c\u5176\u6b21\u77e5\u4e2d\u3002\u4e09\u8005\u4e0d\u80fd\uff0c\u56fd\u5fc5\u5371\uff0c\u8eab\u5fc5\u7a77\u3002<\/span><\/p>\n


    <\/p>\n

    \u300a\u5b5d\u7ecf\u300b\u66f0\uff1a\u201c\u9ad8\u800c\u4e0d\u5371\uff0c\u6240\u4ee5\u957f\u5b88\u8d35\u4e5f\uff1b\u6ee1\u800c\u4e0d\u6ea2\uff0c\u6240\u4ee5\u957f\u5b88\u5bcc\u4e5f\u3002\u5bcc\u8d35\u4e0d\u79bb\u5176\u8eab\uff0c\u7136\u540e\u80fd\u4fdd\u5176\u793e\u7a37\uff0c\u800c\u548c\u5176\u6c11\u4eba\u3002\u201d\u695a\u4e0d\u80fd\u4e4b\u4e5f\u3002<\/span><\/p>\n


    <\/p>\n

    \u8bd1\u6587\uff1a\u695a\u56fd\u6709\u4e2a\u8fb9\u5883\u57ce\u9091\u53eb\u5351\u6881\uff0c\u90a3\u91cc\u7684\u59d1\u5a18\u548c\u5434\u56fd\u8fb9\u5883\u57ce\u9091\u7684\u59d1\u5a18\u540c\u5728\u8fb9\u5883\u4e0a\u91c7\u6851\u53f6\uff0c\u6e38\u620f\u65f6\uff0c\u5434\u56fd\u7684\u59d1\u5a18\u5f04\u4f24\u4e86\u5351\u6881\u7684\u59d1\u5a18\u3002\u5351\u6881\u7684\u4eba\u5e26\u7740\u53d7\u4f24\u7684\u59d1\u5a18\u53bb\u8d23\u5907\u5434\u56fd\u4eba\u3002\u5434\u56fd\u4eba\u51fa\u8a00\u4e0d\u606d\uff0c\u5351\u6881\u4eba\u5341\u5206\u607c\u706b\uff0c\u6740\u6b7b\u5434\u4eba\u8d70\u4e86\u3002\u5434\u56fd\u4eba\u53bb\u5351\u6881\u62a5\u590d\uff0c\u628a\u90a3\u4e2a\u5351\u6881\u4eba\u5168\u5bb6\u90fd\u6740\u4e86\u3002<\/span><\/p>\n


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

    \u5351\u6881\u7684\u5b88\u9091\u5927\u592b\u5927\u6012\uff0c\u8bf4\uff1a\u201c\u5434\u56fd\u4eba\u600e\u4e48\u6562\u653b\u6253\u6211\u7684\u57ce\u9091\uff1f\u201d\u4e8e\u662f\u53d1\u5175\u53cd\u51fb\u5434\u4eba\uff0c\u628a\u5434\u4eba\u8001\u5e7c\u5168\u90fd\u6740\u6b7b\u4e86\u3002\u5434\u738b\u5937\u6627\u542c\u5230\u8fd9\u4ef6\u4e8b\u540e\u5f88\u751f\u6c14\uff0c\u6d3e\u4eba\u9886\u5175\u5165\u4fb5\u695a\u56fd\u7684\u8fb9\u5883\u57ce\u9091\uff0c\u653b\u5360\u5937\u4ee5\u540e\u624d\u79bb\u53bb\u3002<\/span><\/p>\n


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

    \u5434\u56fd\u548c\u695a\u56fd\u56e0\u6b64\u53d1\u751f\u4e86\u5927\u89c4\u6a21\u7684\u51b2\u7a81\u3002\u5434\u56fd\u516c\u5b50\u5149\u53c8\u7387\u9886\u519b\u961f\u5728\u9e21\u7236\u548c\u695a\u56fd\u4eba\u4ea4\u6218\uff0c\u5927\u8d25\u695a\u519b\uff0c\u4fd8\u83b7\u4e86\u695a\u519b\u7684\u4e3b\u5e05\u6f58\u5b50\u81e3\u3001\u5c0f\u5e37\u5b50\u4ee5\u53ca\u9648\u56fd\u7684\u5927\u592b\u590f\u556e\u3002\u53c8\u63a5\u7740\u653b\u6253\u90e2\u90fd\uff0c\u83b7\u5f97\u695a\u5e73\u738b\u7684\u592b\u4eba\u800c\u56de\u3002\u8fd9\u5c31\u662f\u9e21\u7236\u4e4b\u6218\u3002<\/span><\/p>\n


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

    \u51e1\u662f\u4e3b\u6301\u56fd\u4e8b\uff0c\u6700\u4e0a\u7b49\u7684\u662f\u8981\u4e86\u89e3\u4e8b\u60c5\u5f00\u59cb\u65f6\u7684\u60c5\u52bf\uff0c\u5176\u6b21\u662f\u8981\u9884\u89c1\u5230\u4e8b\u60c5\u7684\u7ed3\u5c40\uff0c\u518d\u6b21\u662f\u8981\u77e5\u9053\u4e8b\u60c5\u53d1\u5c55\u7684\u7ecf\u8fc7\u3002\u8fd9\u4e09\u70b9\u90fd\u505a\u4e0d\u5230\uff0c\u56fd\u5bb6\u4e00\u5b9a\u5371\u9669\uff0c\u81ea\u8eab\u4e00\u5b9a\u56f0\u7a98\u3002<\/span><\/p>\n


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

    \u300a\u5b5d\u7ecf\u300b\u4e0a\u8bf4\uff1a\u201c\u9ad8\u5374\u4e0d\u503e\u5371\uff0c\u5c31\u80fd\u957f\u671f\u4fdd\u6301\u5c0a\u8d35\uff1b\u6ee1\u5374\u4e0d\u5916\u6ea2\uff0c\u5c31\u80fd\u957f\u671f\u4fdd\u6301\u5bcc\u8db3\u3002\u5bcc\u8d35\u4e0d\u79bb\u5176\u8eab\uff0c\u7136\u540e\u624d\u80fd\u4fdd\u4f4f\u4ed6\u7684\u56fd\u5bb6\uff0c\u800c\u4e14\u5b89\u5b9a\u4ed6\u7684\u4eba\u6c11\u3002\u201d\u53ef\u662f\u695a\u56fd\u505a\u4e0d\u5230\u8fd9\u4e00\u70b9\u3002<\/span><\/p>\n


    <\/p>\n

    \u6d41\u884c\u6587\u5316\u4e2d\u7684\u8774\u8776\u6548\u5e94<\/span><\/strong><\/span><\/p>\n

    2008\u5e74\uff0c\u8bb0\u8005\u5f7c\u5f97\u00b7\u8fea\u9f50\u514b\u65af Peter Dizikes \u5728\u300a\u6ce2\u58eb\u987f\u73af\u7403\u62a5 \u300bThe Boston Globe<\/em>\u4e0a\u64b0\u6587\u6307\u51fa\uff0c\u6d41\u884c\u6587\u5316\u559c\u6b22\u8774\u8776\u6548\u5e94\u8fd9\u4e2a\u6982\u5ff5\uff0c\u4f46\u5374\u628a\u5b83\u641e\u9519\u4e86\u3002\u76f8\u6bd4\u4e8e\u6d1b\u4f26\u8328\u7528\u8774\u8776\u7684\u9690\u55bb\u6b63\u786e\u5730\u6307\u51fa\u4e86\u53ef\u9884\u6d4b\u6027\u201c\u672c\u8d28\u4e0a\u662f\u6709\u9650\u7684\u201d \uff0c\u6d41\u884c\u6587\u5316\u5374\u5047\u5b9a\uff0c\u6bcf\u4e00\u4e2a\u53d1\u751f\u7684\u4e8b\u4ef6\u90fd\u53ef\u4ee5\u7531\u5bfb\u627e\u5f15\u8d77\u5b83\u7684\u57fa\u672c\u6761\u4ef6\u6765\u8fdb\u884c\u89e3\u91ca\u3002<\/span><\/p>\n


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

    \u201c\u8fd9\u8bf4\u660e\u4e86\u6211\u4eec\u66f4\u5927\u7684\u671f\u671b\uff0c\u90a3\u5c31\u662f\u8fd9\u4e2a\u4e16\u754c\u5e94\u8be5\u662f\u53ef\u4ee5\u7406\u89e3\u7684 \u2014\u2014 \u4e5f\u5c31\u662f\u6bcf\u4ef6\u4e8b\u7684\u53d1\u751f\u90fd\u662f\u5408\u7406\u7684\uff08\u53ef\u4ee5\u7528\u7406\u6027\u53bb\u63a2\u7a76\u63a8\u7406\u7684\uff09\uff0c\u5e76\u4e14\u6211\u4eec\u53ef\u4ee5\u660e\u786e\u4e14\u51c6\u786e\u7684\u8fdb\u884c\u89e3\u91ca\uff0c\u65e0\u8bba\u8fd9\u4e9b\u89e3\u91ca\u6240\u7528\u7684\u57fa\u672c\u6761\u4ef6\u6709\u591a\u4e48\u7ec6\u5fae\u3002\u7136\u800c\uff0c\u5927\u81ea\u7136\u672c\u8eab\u5c31\u6f20\u89c6\u4e86\u8fd9\u79cd\u671f\u671b\u201d \u3002<\/span><\/p>\n


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    5. \u76f8\u5173\u8d44\u6e90\u63a8\u8350<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

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


    <\/p>\n

    \u4e66\u7c4d\u63a8\u8350<\/span><\/strong><\/p>\n

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    \u300a\u8774\u8776\u6548\u5e94\u4e4b\u8c1c\uff1a\u8d70\u8fd1\u5206\u5f62\u4e0e\u6df7\u6c8c\u300b\u5c01\u9762<\/span><\/section>\n

    \u5185\u5bb9\u7b80\u4ecb:\u6709\u4eba\u5c06\u5206\u5f62\u548c\u6df7\u6c8c\u7406\u8bba\u8a89\u4e3a\u7ee7\u76f8\u5bf9\u8bba\u548c\u91cf\u5b50\u529b\u5b66\u4e4b\u540e\u768420\u4e16\u7eaa\u7269\u7406\u5b66\u7684\u7b2c\u4e09\u6b21\u9769\u547d\u3002\u672c\u4e66\u9996\u5148\u63cf\u8ff0\u4e86\u5404\u79cd\u5206\u5f62\u7684\u57fa\u7840\u77e5\u8bc6\u548c\u7279\u6027\uff0c\u5305\u62ec\u7ebf\u6027\u8fed\u4ee3\u4ea7\u751f\u7684\u5206\u5f62\u5982\u5206\u5f62\u9f99\u3001\u79d1\u548c\u66f2\u7ebf\u7b49\uff0c\u4ee5\u53ca\u975e\u7ebf\u6027\u8fed\u4ee3\u4ea7\u751f\u7684\u66fc\u5fb7\u52c3\u7f57\u96c6\u3001\u6731\u5229\u4e9a\u96c6\u7b49\u3002<\/span><\/p>\n


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    \u901a\u8fc7\u8fd9\u4e9b\u4f8b\u5b50\uff0c\u4ecb\u7ecd\u4e86\u81ea\u76f8\u4f3c\u6027\u53ca\u5206\u6570\u7ef4\u7684\u6982\u5ff5\u3002\u7136\u540e\uff0c\u9075\u5faa\u6df7\u6c8c\u73b0\u8c61\u53d1\u5c55\u7684\u5386\u53f2\uff0c\u901a\u8fc7\u8bb2\u8ff0\u5e9e\u52a0\u83b1\u7684\u4e09\u4f53\u95ee\u9898\u3001\u6d1b\u4f26\u8328\u7684\u8774\u8776\u6548\u5e94\u7b49\u7b49\u6545\u4e8b\u548c\u8da3\u95fb\uff0c\u5c06\u8bfb\u8005\u5e26\u8fdb\u795e\u5947\u6df7\u6c8c\u7406\u8bba\u7684\u5929\u5730\u4e2d\u3002\u518d\u8fdb\u4e00\u6b65\u901a\u8fc7\u5bf9\u4e00\u4e2a\u7b80\u5355\u6df7\u6c8c\u7cfb\u7edf–\u903b\u8f91\u65af\u8482\u6620\u5c04\u7684\u63a2\u8ba8\uff0c\u8be6\u7ec6\u4ecb\u7ecd\u5206\u5c94\u7406\u8bba\u3001\u7a33\u5b9a\u6027\u3001\u53ca\u8d39\u6839\u9c8d\u59c6\u666e\u9002\u5e38\u6570\u7b49\u6982\u5ff5\u3002<\/span><\/p>\n


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    \u300a\u8774\u8776\u6548\u5e94\uff08\u77e5\u5fae\u89c1\u8457\uff0c\u5f71\u54cd\u6211\u4eec\u751f\u6d3b\u7684\uff0c\u5f80\u5f80\u662f\u4ece\u5c0f\u4e8b\u5f00\u59cb\u3002\uff09\u300b<\/span><\/p>\n

    \u5185\u5bb9\u7b80\u4ecb:\u672c\u4e66\u5256\u6790\u4e86\u4ee5\u201c\u8774\u8776\u6548\u5e94\u201d\u4e3a\u4ee3\u8868\u7684\u8bf8\u591a\u5fc3\u7406\u5b66\u89c4\u5f8b\u3001\u6cd5\u5219\u5728\u4eba\u4eec\u751f\u6d3b\u3001\u5de5\u4f5c\u7b49\u65b9\u9762\u8fd0\u884c\u7684\u5fc3\u7406\u673a\u5236\uff1a\u521d\u59cb\u6761\u4ef6\u5341\u5206\u5fae\u5c0f\u7684\u53d8\u5316\u7ecf\u8fc7\u4e0d\u65ad\u653e\u5927\uff0c\u5bf9\u5176\u672a\u6765\u72b6\u6001\u4f1a\u9020\u6210\u6781\u5176\u5de8\u5927\u7684\u5dee\u522b\u3002\u672c\u4e66\u8bed\u8a00\u751f\u52a8\u6d41\u7545\uff0c\u6848\u4f8b\u4e0e\u7406\u8bba\u9c9c\u660e\u800c\u4e0d\u67af\u71e5\uff0c\u80fd\u5e2e\u52a9\u8bfb\u8005\u4ece\u5bb9\u5e94\u5bf9\u79cd\u79cd\u4e0d\u53ef\u63a7\u5374\u5bf9\u751f\u6d3b\u5f71\u54cd\u81f3\u6df1\u7684\u4e8b\u4ef6\u2026\u2026<\/span><\/p>\n


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    \u300a\u8774\u8776\u6548\u5e94 \u7ecf\u6d4e\u548c\u793e\u4f1a\u4e2d\u90a3\u4e9b\u4e0d\u53ef\u5ffd\u7565\u7684\u5c0f\u4e8b\u4ef6\u300b<\/span><\/p>\n

    \u5185\u5bb9\u7b80\u4ecb:\u793e\u4f1a\u79d1\u5b66\u7279\u522b\u662f\u7ecf\u6d4e\u5b66\u4f20\u7edf\u7684\u601d\u7ef4\u65b9\u5f0f\u5c06\u4e16\u754c\u770b\u4f5c\u4e00\u90e8\u673a\u5668\uff0c\u867d\u7136\u590d\u6742\u4f46\u5374\u53ef\u4ee5\u88ab\u7406\u89e3\u4f20\u7edf\u7684\u7ecf\u6d4e\u5b66\u601d\u7ef4\u65b9\u5f0f\u5f80\u5f80\u5c06\u4e16\u754c\u770b\u4f5c\u4e00\u90e8\u673a\u5668\uff0c\u867d\u7136\u590d\u6742\u4f46\u5374\u53ef\u4ee5\u88ab\u7406\u89e3\u751a\u81f3\u63a7\u5236\u3002\u8fd9\u79cd\u601d\u7ef4\u81f3\u591a\u53ea\u80fd\u7247\u9762\u5730\u8bf4\u660e\u4e16\u754c\u662f\u5982\u4f55\u8fd0\u8f6c\u7684\uff0c\u800c\u65e0\u6cd5\u770b\u5230\u4e16\u754c\u7684\u672c\u8d28\u3002<\/span><\/p>\n


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

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

    \u8fd9\u4e9b\u90fd\u662f\u4e3b\u6d41\u7ecf\u6d4e\u5b66\u6ca1\u80fd\u5b8c\u7f8e\u5730\u89e3\u91ca\u7684\u95ee\u9898\u3002\u5728\u672c\u4e66\u4e2d\uff0c\u4f5c\u8005\u4ece\u8682\u8681\u6a21\u578b\u51fa\u53d1\uff0c\u901a\u8fc7\u5927\u91cf\u7684\u4e8b\u4f8b\uff0c\u8be6\u7ec6\u5730\u89e3\u91ca\u4e86\u8774\u8776\u6548\u5e94\u5728\u793e\u4f1a\u4e0e\u7ecf\u6d4e\u8fd0\u884c\u4e2d\u7684\u4f5c\u7528\u3002\u4e2a\u4f53\u7684\u54c1\u4f4d\u548c\u504f\u597d\u4f1a\u53d7\u5230\u793e\u4f1a\u4e2d\u5176\u4ed6\u4eba\u7684\u5f71\u54cd\uff0c\u5c06\u8fd9\u4e00\u7406\u5ff5\u52a0\u5165\u5230\u7ecf\u6d4e\u5b66\u5206\u6790\u4e2d\u53ef\u4ee5\u89e3\u91ca\u5f88\u591a\u793e\u4f1a\u73b0\u8c61\u3002\u672c\u4e66\u4e3a\u653f\u5e9c\u51b3\u7b56\u4eba\u3001\u7ecf\u6d4e\u5b66\u5b66\u8005\u3001\u7ecf\u6d4e\u5b66\u4e13\u4e1a\u5b66\u751f\u4ee5\u53ca\u5bf9\u7ecf\u6d4e\u5b66\u611f\u5174\u8da3\u7684\u8bfb\u8005\u63d0\u4f9b\u4e86\u591a\u5143\u7684\u89c6\u89d2\u3001\u751f\u52a8\u7684\u6848\u4f8b\u548c\u53d8\u9769\u6027\u7684\u65b9\u6cd5\u3002<\/span><\/p>\n


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    \u89c6\u9891\u63a8\u8350<\/span><\/strong><\/p>\n

    \u7535\u5f71\u300a\u8774\u8776\u6548\u5e94\u300b<\/span><\/p>\n

    \u5267\u60c5\u7b80\u4ecb: \u4f0a\u4e07\uff08\u827e\u4ec0\u987f\u00b7\u5e93\u5947 Ashton Kutcher \u9970\uff09\u66fe\u7ecf\u6709\u4e00\u4e2a\u7cdf\u7cd5\u7684\u7ae5\u5e74\uff0c\u56e0\u4e3a\u4ed6\u884c\u4e3a\u95ef\u4e0b\u4e86\u5927\u7978\uff0c\u4ee4\u4ed6\u7ae5\u5e74\u5145\u6ee1\u4e0d\u582a\u56de\u5fc6\u7684\u5f80\u4e8b\u3002\u800c\u4e8b\u5b9e\u4e0a\uff0c\u4ed6\u786e\u5b9e\u53ea\u662f\u4f9d\u7a00\u8bb0\u5f97\u4e00\u70b9\u53ef\u6015\u7684\u60c5\u666f\uff0c\u8fd9\u4e9b\u60c5\u666f\u4e00\u76f4\u7ea0\u7f20\u7740\u4ed6\u7684\u6b63\u5e38\u751f\u6d3b\u3002\u4f0a\u4e07\u63a5\u53d7\u5fc3\u7406\u5b66\u5bb6\u5efa\u8bae\uff0c\u628a\u7410\u788e\u751f\u6d3b\u8bb0\u5728\u8bb0\u4e8b\u672c\u91cc\uff0c\u5374\u5076\u7136\u53d1\u73b0\u901a\u8fc7\u8bb0\u4e8b\u672c\u56de\u5230\u8fc7\u53bb\u3002\u8fd9\u65f6\u4ed6\u624d\u6e05\u695a\u8bb0\u8d77\uff0c\u7ae5\u5e74\u65f6\u5019\u7684\u81ea\u5df1\u505a\u4e86\u90a3\u4e48\u591a\u7684\u9519\u4e8b\u3002\u4ed6\u5e7b\u60f3\u7740\u7528\u73b0\u5728\u7684\u610f\u8bc6\uff0c\u6f5c\u5165\u7ae5\u5e74\u7684\u8eab\u4f53\uff0c\u53bb\u5f25\u8865\u79cd\u79cd\u8fc7\u5931\u7ed9\u4eba\u4eec\u5e26\u6765\u7684\u4f24\u5bb3\uff0c\u5c24\u5176\u662f\u5e0c\u671b\u4e0e\u5f53\u5e74\u6697\u604b\u7684\u51ef\u897f\u6700\u7ec8\u8d70\u56de\u4e00\u8d77\u3002\u7136\u800c\u4ed6\u4e00\u6b21\u6b21\u7684\u8de8\u8d8a\u65f6\u7a7a\u7684\u66f4\u6539\uff0c\u53ea\u80fd\u8d8a\u6765\u8d8a\u62db\u81f4\u73b0\u5b9e\u4e16\u754c\u7684\u4e0d\u53ef\u6551\u836f\u3002\u4e00\u5207\u5c31\u50cf\u8774\u8776\u6548\u5e94\u822c\uff0c\u7275\u4e00\u53d1\u800c\u52a8\u5168\u8eab\u3002<\/span><\/p>\n


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    6. \u767e\u79d1\u9879\u76ee\u5fd7\u613f\u8005\u62db\u52df<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


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    \u4ee5\u4e0a\u5185\u5bb9\u90fd\u662f\u6211\u4eec\u505a\u8fd9\u9879\u76ee\u7684\u8d77\u70b9\uff0c\u4f5c\u4e3a\u6765\u81ea\u4e0d\u540c\u5b66\u79d1\u548c\u9886\u57df\u7684\u5fd7\u613f\u8005\uff0c\u6211\u4eec\u5efa\u7acb\u8d77\u4e00\u4e2a\u6709\u6548\u7684\u767e\u79d1\u56e2\u961f\uff0c\u5206\u914d\u6709\u5ba1\u6821\u3001\u7ffb\u8bd1\u3001\u7f16\u8f91\u3001\u5ba3\u4f20\u7b49\u5de5\u4f5c\u3002\u6211\u4eec\u79c9\u6301\uff1a\u77e5\u8bc6\u4ece\u6211\u800c\u6765\uff0c\u95ee\u9898\u5230\u6211\u4e3a\u6b62\u7684\u4fe1\u5ff5\uff0c\u8ba4\u771f\u8d1f\u8d23\u7f16\u64b0\u6bcf\u4e00\u4e2a\u8bcd\u6761\u3002<\/span><\/section>\n


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    <\/p>\n


    <\/p>\n

    \u5728\u8fd9\u91cc\u4ece\u590d\u6742\u6027\u77e5\u8bc6\u51fa\u53d1\u4e0e\u4f19\u4f34\u540c\u884c\uff0c\u540c\u65f6\u6211\u4eec\u5e0c\u671b\u6709\u66f4\u591a\u5fd7\u613f\u8005\u52a0\u5165\u8fd9\u4e2a\u56e2\u961f\uff0c\u4f7f\u767e\u79d1\u8bcd\u6761\u5185\u5bb9\u5f97\u5230\u6269\u5145\uff0c\u5e76\u4e3a\u6bcf\u4f4d\u5fd7\u613f\u8005\u63d0\u4f9b\u76f8\u5e94\u5956\u52b1\u4e0e\u8d44\u6e90\uff0c\u5efa\u7acb\u4e2a\u4eba\u4e3b\u9875\u4e0e\u8d21\u732e\u8bb0\u5f55\uff0c\u4f7f\u5176\u80fd\u591f\u7ee7\u7eed\u63a2\u7d22\u590d\u6742\u4e16\u754c\u3002<\/span><\/p>\n


    <\/p>\n

    \u5982\u679c\u4f60\u6709\u610f\u53c2\u4e0e\u66f4\u52a0\u7cfb\u7edf\u7cbe\u7ec6\u7684\u5206\u5de5\uff0c\u626b\u63cf\u4e8c\u7ef4\u7801\u586b\u5199\u62a5\u540d\u8868\uff0c\u6211\u4eec\u671f\u5f85\u4f60\u7684\u52a0\u5165\uff01<\/span><\/p>\n


    <\/p>\n

    <\/section>\n
    \u96c6\u667a\u767e\u79d1\u62a5\u540d\u8868<\/span><\/section>\n

    <\/section>\n
    \n
    \n

    \u53c2\u8003\u6587\u732e\uff1a<\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n

    \n