{"id":54727,"date":"2024-12-27T18:41:17","date_gmt":"2024-12-27T10:41:17","guid":{"rendered":"https:\/\/swarma.org\/?p=54727"},"modified":"2024-12-27T18:41:17","modified_gmt":"2024-12-27T10:41:17","slug":"%e9%9d%9e%e7%ba%bf%e6%80%a7%e7%b3%bb%e7%bb%9f%e7%9a%84%e7%ba%bf%e6%80%a7%e5%8c%96%ef%bc%8c%e9%9b%b7%e6%b1%a0%e7%9a%84%e8%b7%a8%e8%b6%8a%ef%bc%81%e4%b8%a8koopman%e5%88%86%e6%9e%90%e7%b3%bb%e5%88%97","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=54727","title":{"rendered":"\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u7ebf\u6027\u5316\uff0c\u96f7\u6c60\u7684\u8de8\u8d8a\uff01\u4e28Koopman\u5206\u6790\u7cfb\u5217\u8bfe\u7a0b"},"content":{"rendered":"
\n
\n
\n
\n

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

\n
\n
\n
\n
\n
\n

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

\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u7814\u7a76\u662f\u7406\u89e3\u81ea\u7136\u754c\u4e0e\u5de5\u7a0b\u9886\u57df\u590d\u6742\u73b0\u8c61\u7684\u91cd\u8981\u5de5\u5177\u3002\u65e0\u8bba\u662f\u6d41\u4f53\u6e4d\u6d41\u4e2d\u7684\u6da1\u65cb\u8fd0\u52a8\u3001\u4eba\u5de5\u6216\u751f\u7269\u795e\u7ecf\u7f51\u7edc\u7684\u529f\u80fd\u5b9e\u73b0\u3001\u751f\u6001\u7cfb\u7edf\u4e2d\u7684\u79cd\u7fa4\u53d8\u5316\uff0c\u8fd8\u662f\u5929\u6c14\u6216\u6c14\u5019\u7cfb\u7edf\u7684\u72b6\u6001\u8f6c\u53d8\u3001\u65b0\u578b\u667a\u80fd\u7535\u529b\u7f51\u7edc\u7684\u8c03\u63a7\u3001\u793e\u4ea4\u7f51\u7edc\u4e2d\u610f\u89c1\u4f20\u64ad\u7684\u52a8\u6001\uff0c\u975e\u7ebf\u6027\u7cfb\u7edf\u90fd\u5c55\u73b0\u4e86\u5468\u671f\u6027\u3001\u5206\u5c94\u4e0e\u6df7\u6c8c\u7b49\u590d\u6742\u884c\u4e3a\u3002\u800c\u627e\u5230\u8fd9\u4e9b\u590d\u6742\u975e\u7ebf\u6027\u73b0\u8c61\u80cc\u540e\u53ef\u89e3\u6790\u7684\u7ebf\u6027\u7ed3\u6784\uff0c\u662f\u79d1\u5b66\u7814\u7a76\u548c\u5de5\u7a0b\u5e94\u7528\u4e2d\u7684\u5173\u952e\u6311\u6218\u3002<\/span><\/strong><\/section>\n

<\/section>\n<\/section>\n
\n
\u5728\u300aKoopman\u5206\u6790\u5728\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2d\u7684\u5e94\u7528<\/a>\u300b\u7cfb\u5217<\/span><\/strong>\u8bfe\u7a0b\u7b2c\u4e8c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4e8e 12\u670828\u65e5\uff08\u5468\u516d\uff0914:00-16:00 \u7531\u5170\u5cb3\u6052\u6559\u6388\u7ee7\u7eed\u5e26\u9886\u5927\u5bb6\uff0c\u63a2\u7d22\u975e\u7ebf\u6027\u7cfb\u7edf\u5982\u4f55\u901a\u8fc7\u5c40\u90e8\u548c\u5168\u5c40\u7ebf\u6027\u5316\u8fdb\u884c\u5206\u6790\u3002\u8bfe\u7a0b\u4e2d\u4f1a\u5f15\u5165\u7ecf\u5178\u7684 Hartman-Grobman \u5b9a\u7406\u548c Kalman \u7ebf\u6027\u5316\u65b9\u6cd5\uff0c\u5e76\u7ed3\u5408 Koopman \u7b97\u7b26\u548c\u52a8\u529b\u5b66\u7684\u51e0\u4f55\u601d\u8003\u6846\u67b6\uff0c\u63ed\u793a\u8fd9\u4e9b\u5de5\u5177<\/span><\/strong>\u5728\u89e3\u6790\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u6f5c\u529b\u4e0e\u5c40\u9650\u6027\u3002<\/span><\/strong><\/span><\/strong><\/span><\/section>\n<\/section>\n
\n
<\/strong><\/section>\n
<\/strong><\/section>\n
<\/strong><\/section>\n
<\/strong><\/section>\n
<\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/section>\n
<\/strong><\/section>\n
<\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/section>\n
<\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n

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


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

\u4e3b\u9898\uff1a\u5c40\u90e8\u548c\u5168\u5c40\u7ebf\u6027\u5316<\/strong><\/span><\/h2>\n


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

\n
\n
\n
\n
\n

<\/section>\n

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

\u8bfe\u7a0b\u7b80\u4ecb<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

<\/h2>\n
\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u7684\u95ee\u9898\u5728\u4e8e\u5176\u590d\u6742\u6027\uff0c\u800c\u7ebf\u6027\u65b9\u7a0b\u7684\u4f18\u52bf\u5728\u4e8e\u53ef\u4ee5\u901a\u8fc7\u89e3\u7684\u53e0\u52a0\u6027\u548c\u672c\u5f81\u95ee\u9898\u7684\u6c42\u89e3\u5b9e\u73b0\u7cbe\u786e\u5206\u6790\u3002\u56e0\u6b64\uff0c\u5982\u679c\u80fd\u591f\u5c06\u975e\u7ebf\u6027\u95ee\u9898\u8f6c\u5316\u4e3a\u7ebf\u6027\u95ee\u9898\uff0c\u7814\u7a76\u548c\u5206\u6790\u5c31\u4f1a\u53d8\u5f97\u7b80\u5355\u5f97\u591a\u3002\u7136\u800c\uff0c\u5927\u591a\u6570\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u95ee\u9898\u4ec5\u80fd\u5728\u5c40\u90e8\u8303\u56f4\u5185\u5b9e\u73b0\u7ebf\u6027\u5316\uff0c\u5168\u5c40\u7ebf\u6027\u5316\u5f80\u5f80\u975e\u5e38\u56f0\u96be\uff0c\u751a\u81f3\u4e0d\u53ef\u80fd\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u672c\u8282\u8bfe\u7a0b\u5c06\u4ece\u8fd9\u4e00\u80cc\u666f\u51fa\u53d1\uff0c\u6df1\u5165\u63a2\u8ba8\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u7684\u7ebf\u6027\u5316\u65b9\u6cd5\u53ca\u5176\u5c40\u9650\u6027\u3002\u6211\u4eec\u5c06\u4ecb\u7ecd Hartman-Grobman \u5b9a\u7406\uff0c\u63ed\u793a\u975e\u7ebf\u6027\u7cfb\u7edf\u5728\u5e73\u8861\u70b9\u9644\u8fd1\u5982\u4f55\u901a\u8fc7\u5c40\u90e8\u7ebf\u6027\u5316\u5f97\u5230\u62d3\u6251\u7b49\u4ef7\u7684\u7ebf\u6027\u6a21\u578b\u3002\u6b64\u5916\uff0c\u8fd8\u4f1a\u8ba8\u8bba Kalman \u7ebf\u6027\u5316\u65b9\u6cd5\uff0c\u5229\u7528\u5f15\u5165\u65b0\u53d8\u91cf\u5c06\u590d\u6742\u7684\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u8f6c\u5316\u4e3a\u5f62\u5f0f\u4e0a\u7684\u7ebf\u6027\u7cfb\u7edf\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u5982\u4f55\u901a\u8fc7 Koopman \u5206\u6790\uff0c\u5728\u66f4\u5927\u8303\u56f4\u5185\u6216\u7279\u5b9a\u610f\u4e49\u4e0b\u5b9e\u73b0\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u7684\u5168\u5c40\u7ebf\u6027\u5316\uff0c\u4ece\u800c\u7aa5\u89c1\u89e3\u7a7a\u95f4\u7684\u6df1\u5c42\u7ed3\u6784\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u8981\u5e94\u5bf9\u8bf8\u591a\u6311\u6218\uff0c\u4f8b\u5982\u5bfb\u627e\u53ef\u9760\u7684\u8c31\u6027\u8d28\u8ba1\u7b97\u65b9\u6cd5\uff1b\u4ece\u5927\u91cf\u6a21\u5f0f\u4e2d\u9009\u62e9\u51fa\u76f8\u5173\u7684\u6a21\u5f0f\uff1b\u7406\u89e3\u91cd\u8981\u6a21\u5f0f\u7684\u7269\u7406\u610f\u4e49\uff1b\u6839\u636e\u91cd\u8981\u6a21\u5f0f\u6784\u5efa\u51fa\u6700\u5927\u7ebf\u6027\u5316\u533a\u57df\u7b49\u3002<\/span><\/section>\n

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

\u63a2\u7d22\u5982\u4e0b\u95ee\u9898\uff1a<\/span><\/p>\n

    \n
  1. \n

    \u5b9e\u73b0\u975e\u7ebf\u6027\u95ee\u9898\u7684\u5168\u5c40\u6216\u5c40\u90e8\u7ebf\u6027\u5316\u7684\u610f\u4e49\u548c\u6761\u4ef6\u662f\u4ec0\u4e48\uff1f<\/span><\/p>\n<\/li>\n

  2. \n

    \u5982\u4f55\u6700\u5927\u5316\u7ebf\u6027\u5316\u533a\u57df\uff0c\u975e\u7ebf\u6027\u7684\u672c\u8d28\u4f53\u73b0\u5728\u54ea\u91cc\uff1f<\/span><\/p>\n<\/li>\n

  3. \n
    \u5982\u4f55\u8054\u7cfb\u72b6\u6001\u7a7a\u95f4\u548c\u51fd\u6570\u7a7a\u95f4\u4e2d\u7684\u7ebf\u6027\u5316\uff1f<\/span><\/section>\n<\/li>\n<\/ol>\n


    <\/strong><\/span><\/h2>\n

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

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

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

    \u8bfe\u7a0b\u76ee\u6807<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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


    <\/p>\n

    \u5e2e\u52a9\u5b66\u751f\u638c\u63e1\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u7684\u6838\u5fc3\u5206\u6790\u5de5\u5177\uff0c\u5305\u62ec\u5982\u4f55\u5229\u7528 Hartman-Grobman \u5b9a\u7406\u8fdb\u884c\u5c40\u90e8\u7ebf\u6027\u5316\u4ee5\u63ed\u793a\u5e73\u8861\u70b9\u9644\u8fd1\u7684\u62d3\u6251\u7279\u6027\uff0c\u4f7f\u7528 Kalman \u7ebf\u6027\u5316\u65b9\u6cd5\u5c06\u975e\u7ebf\u6027\u7cfb\u7edf\u8f6c\u5316\u4e3a\u5f62\u5f0f\u4e0a\u7684\u7ebf\u6027\u7cfb\u7edf\uff0c\u4ee5\u53ca\u901a\u8fc7 Koopman \u5206\u6790\u5728\u66f4\u5927\u8303\u56f4\u6216\u7279\u5b9a\u610f\u4e49\u4e0b\u5b9e\u73b0\u5168\u5c40\u7ebf\u6027\u5316\uff0c\u4ece\u800c\u6df1\u5165\u7406\u89e3\u590d\u6742\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u884c\u4e3a\u548c\u89e3\u7a7a\u95f4\u7ed3\u6784\uff0c\u4e3a\u591a\u5b66\u79d1\u590d\u6742\u7cfb\u7edf\u5efa\u6a21\u63d0\u4f9b\u5f3a\u6709\u529b\u7684\u7406\u8bba\u652f\u6301\u4e0e\u5b9e\u8df5\u65b9\u6cd5\u3002<\/span><\/section>\n


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


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

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

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

    \u8bfe\u7a0b\u5927\u7eb2<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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

      <\/p>\n

    1.<\/span><\/strong> \u5c40\u90e8\u548c\u5168\u5c40\u7ebf\u6027\u5316<\/span><\/strong><\/span><\/section>\n
      \n
    1. \n

      \u63a2\u8ba8\u5c40\u90e8\u7ebf\u6027\u5316\u5728\u5e73\u8861\u70b9\u9644\u8fd1\u7684\u9002\u7528\u6027\uff0c\u5206\u6790\u5168\u5c40\u7ebf\u6027\u5316\u7684\u5b9e\u73b0\u96be\u70b9\u53ca\u5176\u5728\u7279\u5b9a\u6761\u4ef6\u4e0b\u7684\u53ef\u80fd\u6027\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n


      <\/p>\n

      2. \u5927\u8303\u56f4\u7ebf\u6027\u5316<\/span><\/strong><\/span><\/section>\n
        \n
      1. \n

        \u4ecb\u7ecd\u5982\u4f55\u901a\u8fc7\u5927\u8303\u56f4\u7ebf\u6027\u5316\u65b9\u6cd5\uff08\u5982 Koopman \u5206\u6790\uff09\u523b\u753b\u590d\u6742\u7cfb\u7edf\u7684\u5168\u5c40\u52a8\u529b\u5b66\u7279\u6027\uff0c\u89e3\u6790\u5438\u5f15\u57df\u548c\u5206\u5c94\u884c\u4e3a\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n


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

        3. Koopman \u7b97\u7b26\u4e0e\u7ebf\u6027\u5316<\/span><\/strong><\/span><\/section>\n
          \n
        1. \n

          \u4ecb\u7ecdKoopman\u7b97\u5b50\u7684\u5206\u6790\u601d\u8def\uff0c\u5e76\u6bd4\u8f83 Kalman \u7ebf\u6027\u5316\u4e0e Koopman \u5206\u6790\u7684\u5f02\u540c\uff0c\u63a2\u8ba8\u5176\u5728\u590d\u6742\u7cfb\u7edf\u5efa\u6a21\u4e2d\u7684\u7ed3\u5408\u5e94\u7528\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n


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

          4. \u8bfe\u7a0b\u603b\u7ed3<\/span><\/strong><\/section>\n
            \n
          1. \n
            \u5e93\u666e\u66fc\u7b97\u5b50\u63d0\u4f9b\u4e86\u4e00\u79cd\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u5c06\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7ebf\u6027\u5316\u7684\u65b9\u6cd5\uff1b<\/span><\/section>\n<\/li>\n
          2. \n
            \u53ef\u4ee5\u901a\u8fc7\u6570\u503c\u8ba1\u7b97\u6784\u5efa\u7279\u5f81\u6a21\u6001\uff0c\u63ed\u793a\u6700\u91cd\u8981\u7684\u52a8\u529b\u5b66\uff1b<\/span><\/section>\n<\/li>\n
          3. \n
            \u7279\u5f81\u51fd\u6570\u53ef\u7528\u4e8e\u6784\u5efa\u7b26\u53f7\u5206\u533a\u3001\u63ed\u793a\u5206\u5c94\u548c\u8bc6\u522b\u5728\u9ad8\u7ef4\u975e\u7ebf\u6027\u7cfb\u7edf\u4e2d\u5b58\u5728\u7684\u4e0d\u540c\u4e0d\u53d8\u7ed3\u6784\uff1b<\/span><\/section>\n<\/li>\n
          4. \n

            \u4e00\u822c\u5316\u548c\u6311\u6218<\/span><\/p>\n<\/li>\n<\/ol>\n

              \n

              <\/section>\n<\/ol>\n
              \u6d89\u53ca\u4e13\u4e1a\u672f\u8bed<\/strong><\/span><\/section>\n
              \u975e\u7ebf\u6027\u52a8\u529b\u5b66\uff08Nonlinear Dynamics\uff09\uff1b\u590d\u6742\u7cfb\u7edf\uff08Complex Systems\uff09\uff1b\u5c40\u90e8\u7ebf\u6027\u5316\uff08Local Linearization\uff09\uff1b\u5168\u5c40\u7ebf\u6027\u5316\uff08Global Linearization\uff09\uff1bHartman-Grobman \u5b9a\u7406\uff08Hartman-Grobman Theorem\uff09\uff1bKalman \u7ebf\u6027\u5316\uff08Kalman Linearization\uff09\uff1b\u83ab\u5c14\u65af\u5b9a\u7406\uff08Morse Theorem\uff09\uff1bKoopman \u5206\u6790\uff08Koopman Analysis\uff09\uff1b\u7279\u5f81\u51fd\u6570\uff08Eigenfunction\uff09\uff1b\u7279\u5f81\u6a21\u6001\uff08Eigenmode\uff09\uff1b\u8c31\u6027\u8d28\uff08Spectral Properties\uff09\uff1b\u5206\u5c94\uff08Bifurcation\uff09\uff1b\u6781\u9650\u73af\uff08Limit Cycle\uff09\uff1b\u7b26\u53f7\u5206\u5272\uff08Symbolic Partition\uff09\uff1b\u52a8\u6001\u6a21\u6001\u5206\u89e3\uff08Dynamic Mode Decomposition, DMD\uff09\u3002<\/span><\/section>\n

              <\/span><\/section>\n
              \u53c2\u8003\u6587\u732e\uff1a<\/span><\/strong><\/span><\/section>\n
              1. Lan, Yueheng, and Igor Mezi\u0107. “Linearization in the large of nonlinear systems and Koopman operator spectrum.” <\/span>Physica D: Nonlinear Phenomena<\/span><\/em> 242.1 (2013): 42-53.<\/span><\/section>\n


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


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

              \n
              \n
              \n
              \n
              \n

              <\/section>\n

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

              \u8bfe\u7a0b\u4fe1\u606f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

              \n

              <\/section>\n

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


              <\/p>\n

              \u8bfe\u7a0b\u4e3b\u9898\uff1a\u5c40\u90e8\u548c\u5168\u5c40\u7ebf\u6027\u5316<\/span><\/p>\n

              \u8bfe\u7a0b\u65f6\u95f4\uff1a2024\u5e7412\u670828\u65e5\uff08\u5468\u516d\uff09 14:00-16:00<\/strong><\/span><\/p>\n

              \u8bfe\u7a0b\u5f62\u5f0f\uff1a\u817e\u8baf\u4f1a\u8bae\uff08\u4f1a\u8bae\u4fe1\u606f\u89c1\u7fa4\u5185\u901a\u77e5\uff09\uff1b\u96c6\u667a\u5b66\u56ed\u7f51\u7ad9\u5f55\u64ad\uff083\u4e2a\u5de5\u4f5c\u65e5\u5185\u4e0a\u7ebf\uff09<\/span><\/section>\n


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


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

              \n
              \n
              \n
              \n
              \n

              <\/section>\n

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

              \u8bfe\u7a0b\u4e3b\u8bb2\u4eba<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

              \n

              <\/section>\n

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


              <\/p>\n

              <\/section>\n
              \u5170\u5cb3\u6052<\/strong>\uff0c\u5317\u4eac\u90ae\u7535\u5927\u5b66\u7406\u5b66\u9662\u6559\u6388\uff0c\u535a\u58eb\u5b66\u4f4d\u5728\u4f50\u6cbb\u4e9a\u7406\u5de5\u5b66\u9662\uff08Georgia Institute of Technology\uff09\u83b7\u5f97\u3002\u5148\u540e\u5728\u56fd\u5185\u5916\u591a\u4e2a\u8457\u540d\u5927\u5b66\u5b66\u4e60\u548c\u5de5\u4f5c\u8fc7\uff0c\u6709\u4e30\u5bcc\u7684\u5b66\u79d1\u4ea4\u53c9\u7814\u7a76\u7ecf\u5386\u3002\u4e3b\u8981\u4ece\u4e8b\u975e\u7ebf\u6027\u79d1\u5b66\u3001\u7edf\u8ba1\u7269\u7406\u3001\u751f\u7269\u7269\u7406\u3001\u590d\u6742\u4fe1\u606f\u548c\u667a\u80fd\u7cfb\u7edf\u7b49\u65b9\u9762\u7684\u7814\u7a76\u5de5\u4f5c\uff0c\u6ce8\u91cd\u57fa\u672c\u7406\u8bba\u65b9\u6cd5\u7684\u53d1\u5c55\u548c\u4e0e\u5b9e\u9a8c\u7d27\u5bc6\u7ed3\u5408\u7684\u5e94\u7528\u3002\u73b0\u4e3a\u5317\u4eac\u90ae\u7535\u5927\u5b66\u201c\u6570\u5b66\u4e0e\u4fe1\u606f\u7f51\u7edc\u201d\u6559\u80b2\u90e8\u91cd\u70b9\u5b9e\u9a8c\u5ba4\u526f\u4e3b\u4efb\uff0c\u591a\u6b21\u88ab\u9080\u8bf7\u5728\u56fd\u5185\u5916\u5b66\u672f\u4f1a\u8bae\u4e0a\u62a5\u544a\u81ea\u5df1\u7684\u5de5\u4f5c\uff0c\u540c\u65f6\u62c5\u4efb\u671f\u520a\u201c\u7406\u8bba\u7269\u7406\u901a\u4fe1\u201d\uff08Communications in Theoretical Physics\uff09\u548c\u201c\u73b0\u4ee3\u6570\u5b66\u7269\u7406\u201d\uff08Modern Mathematical Physics\uff09\u7684\u7f16\u59d4\uff0c\u4e5f\u662f\u591a\u4e2a\u56fd\u9645\u8457\u540d\u6742\u5fd7\u7684\u5ba1\u7a3f\u4eba\u3002\u53d1\u8868\u5b66\u672f\u8bba\u6587100\u4f59\u7bc7\uff0c\u5305\u62ec\u56fd\u9645\u9876\u7ea7\u6742\u5fd7PRL\uff0c PNAS\uff0c Nature\u5b50\u520a\u8bba\u6587\u591a\u7bc7<\/span><\/section>\n

              <\/section>\n


              <\/p>\n

              \n
              \n
              \n
              \n
              \n

              <\/section>\n

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

              \u7cfb\u5217\u8bfe\u7a0b\u4fe1\u606f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

              \n

              <\/section>\n

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


              <\/p>\n

              \u8bfe\u7a0b\u9002\u7528\u5bf9\u8c61<\/span><\/strong><\/span><\/h3>\n
                \n
              1. \n

                \u7406\u5de5\u79d1\u7814\u7a76\u751f\u6216\u9ad8\u5e74\u7ea7\u672c\u79d1\u751f<\/strong>\uff1a<\/span><\/p>\n<\/li>\n