{"id":32539,"date":"2022-02-19T21:09:24","date_gmt":"2022-02-19T13:09:24","guid":{"rendered":"https:\/\/swarma.org\/?p=32539"},"modified":"2022-02-19T21:09:24","modified_gmt":"2022-02-19T13:09:24","slug":"%e6%bc%ab%e8%b0%88%e7%a7%91%e6%8a%80%e8%ae%ba%e6%96%87%e5%86%99%e4%bd%9c%e4%b8%a8%e9%99%88%e5%85%b3%e8%8d%a3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=32539","title":{"rendered":"\u6f2b\u8c08\u79d1\u6280\u8bba\u6587\u5199\u4f5c\u4e28\u9648\u5173\u8363"},"content":{"rendered":"
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1\uff09\u9898\u76ee<\/span><\/strong><\/span><\/span><\/p>\n


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\u4e00\u822c\u6765\u8bf4\uff0c\u6587\u7ae0\u7684\u9898\u76ee\u5e94\u8be5\u7b80\u5355\u3001\u6e05\u6670\u3001\u51c6\u786e\u3001\u96c5\u81f4\u3002<\/span><\/p>\n


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\u9898\u76ee\u8981\u201c\u7b80\u5355\u201d\uff0c\u5c31\u662f\u5c3d\u53ef\u80fd\u6ca1\u6709\u591a\u4f59\u7684\u5b57\u548c\u8bcd\u3002\u90a3\u4e9b\u5220\u53bb\u4e86\u4e5f\u65e0\u59a8\u7684\u5b57\u8bcd\u5c31\u5220\u6389\u597d\u4e86\u3002\u4f8b\u5982\uff0c\u201cOn the study of …\u201d\u4e2d\u7684\u201cOn\u201d\u662f\u591a\u4f59\u7684\uff0c\u53ef\u4ee5\u53bb\u6389\u3002\u6b64\u5916\uff0c\u201cThe study of …\u201d\u548c\u201cTo study …\u201d\u90fd\u4e0d\u662f\u597d\u7684\u82f1\u6587\u9898\u76ee\uff0c\u800c\u7528\u52a8\u540d\u8bcd\u201cStudying …\u201d\u9886\u8d77\u6587\u7ae0\u9898\u76ee\u5728\u7ecf\u5178\u82f1\u6587\u6587\u732e\u4e2d\u5219\u6bd4\u8f83\u5e38\u89c1\u3002\u8fd8\u6709\uff0c\u7b80\u5355\u7684\u9898\u76ee\u6bd4\u8f83\u77ed\u5c0f\uff0c\u800c\u8fd9\u6837\u7684\u6587\u7ae0\u5f15\u7528\u7387\u5374\u8f83\u9ad8[2,3]\u3002\u8fd9\u662f\u56e0\u4e3a\u77ed\u5c0f\u9898\u76ee\u5bb9\u6613\u8bb0\u4f4f\uff0c\u4e5f\u65b9\u4fbf\u5f15\u7528\u548c\u63a8\u8350\u3002\u4e0d\u8981\u52a8\u4e0d\u52a8\u5c31\u5199\u4e2a\u4e09\u3001\u56db\u884c\u5b57\u7684\u957f\u6807\u9898\uff0c\u751f\u6015\u8bf4\u4e0d\u6e05\u695a\u3002\u8fd9\u6837\u7684\u6807\u9898\u8bfb\u8005\u770b\u5b8c\u4e86\u4e5f\u8bb0\u4e0d\u4f4f\uff0c\u6253\u7b97\u5f15\u7528\u65f6\u4e5f\u60f3\u4e0d\u8d77\u6765\uff0c\u4fbf\u4f1a\u56e0\u4e3a\u4e0d\u80fd\u987a\u624b\u67e5\u5230\u800c\u653e\u5f03\u5f15\u7528\u3002<\/span><\/p>\n


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\u9898\u76ee\u8981\u201c\u6e05\u6670\u201d\uff0c\u5c31\u662f\u544a\u8bc9\u8bfb\u8005\u8fd9\u7bc7\u6587\u7ae0\u662f\u5173\u4e8e\u4ec0\u4e48\u4e3b\u9898\u7684\u3002\u4e00\u822c\u4e0d\u5fc5\u628a\u80cc\u666f\u3001\u5185\u5bb9\u548c\u65b9\u6cd5\u5199\u8fdb\u53bb\u3002\u4f8b\u5982\uff0c\u201cStudying the stability of a nonlinear system by Lyapunov methods\u201d\u4e2d\u7684\u201cby Lyapunov methods\u201d\u53ef\u4ee5\u4e5f\u5e94\u8be5\u5220\u6389\u3002\u6240\u7528\u65b9\u6cd5\u5728\u6587\u7ae0\u91cc\u4ecb\u7ecd\u3002\u7279\u522b\u5730\uff0c\u8fd9\u662f\u4e00\u79cd\u4f20\u7edf\u65b9\u6cd5\uff0c\u65e0\u9700\u5728\u6807\u9898\u5f3a\u8c03\u3002\u53e6\u5916\uff0c\u201ca nonlinear system\u201d\u867d\u7136\u7b80\u5355\u4f46\u5e76\u4e0d\u6e05\u6670\uff1a\u4ec0\u4e48\u7c7b\u578b\u7684\u201cnonlinear system\u201d\u5462\uff1f\u5982\u679c\u6539\u6210\u201ca three-link robot-arm system\u201d\u3001\u201ca memristive system\u201d\u4e4b\u7c7b\u5c31\u6e05\u695a\u591a\u4e86\u3002\u5f53\u7136\uff0c\u6587\u7ae0\u7684\u9898\u76ee\u4e0d\u9700\u8981\u4e5f\u4e0d\u53ef\u80fd\u628a\u5185\u5bb9\u8868\u8fbe\u5f97\u975e\u5e38\u5177\u4f53\uff0c\u4f46\u662f\u9002\u5f53\u7684\u5185\u6db5\u4ecd\u662f\u5fc5\u8981\u7684\u3002\u4e0d\u7136\uff0c\u6ca1\u6709\u5185\u6db5\u7684\u5b57\u8bcd\u5199\u51fa\u6765\u548c\u4e0d\u5199\u4e5f\u5dee\u4e0d\u591a\u3002<\/span><\/p>\n


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\u9898\u76ee\u8981\u201c\u51c6\u786e\u201d\u3002\u8fd9\u5176\u5b9e\u662f\u62df\u9898\u7684\u4e00\u4e2a\u57fa\u672c\u51c6\u5219\uff0c\u65e0\u987b\u591a\u8bf4\u3002\u4f46\u662f\uff0c\u8fd9\u8981\u6c42\u6709\u65f6\u5019\u4f1a\u548c\u201c\u7b80\u5355\u201d\u76f8\u51b2\u7a81\u3002\u4f8b\u5982\uff0c\u201cDesigning a new algorithm that combines a fastest algorithm and an optimal algorithm\u201d\u662f\u4e00\u4e2a\u5341\u5206\u7cbe\u51c6\u7684\u9898\u76ee\u3002\u53ef\u662f\uff0c\u5b83\u5305\u542b\u4e86\u4e09\u4e2a\u201calgorithm\u201d\uff0c\u771f\u6709\u5fc5\u8981\u5417\uff1f\u6539\u4e3a\u201cDesigning a fast optimal algorithm\u201d\u5c31\u597d\u591a\u4e86\uff0c\u5c3d\u7ba1\u5b83\u4e0d\u50cf\u539f\u6765\u90a3\u6837\u53ef\u4ee5\u53cd\u6620\u51fa\u65b0\u7a0b\u5e8f\u7684\u5177\u4f53\u6765\u5386\uff0c\u4f46\u5b83\u786e\u5b9e\u8bf4\u51fa\u4e86\u8bba\u6587\u7684\u4e3b\u8981\u7ed3\u679c\uff0c\u662f\u51c6\u786e\u7684\u3002<\/span><\/p>\n


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\u9898\u76ee\u8981\u5199\u5f97\u201c\u96c5\u81f4\u201d\u4e0d\u5bb9\u6613\u3002\u4f46\u9898\u76ee\u751f\u52a8\u96c5\u81f4\uff0c\u5219\u8f83\u5bb9\u6613\u5f15\u8d77\u6ce8\u610f\u3002\u4f8b\u5982\uff0c\u201cReporting a new chaotic system\u201d\u6539\u6210\u201cA new chaotic system coined\u201d\uff0c\u867d\u7136\u610f\u601d\u6ca1\u53d8\uff0c\u4f46\u662f\u7b14\u8c03\u9ad8\u96c5\u591a\u4e86\u3002\u201cYet, another chaotic system\u201d\u4e5f\u53ef\u8868\u8fbe\u540c\u6837\u7684\u610f\u601d\uff0c\u4e14\u6709\u65b0\u5947\u611f\u3002\u8bfb\u8005\u770b\u5230\u6709\u8da3\u7684\u6807\u9898\uff0c\u54ea\u6015\u662f\u51fa\u4e8e\u597d\u5947\u5fc3\u4e5f\u4f1a\u6253\u5f00\u4f60\u7684\u6587\u7ae0\u770b\u770b\u3002\u4ed6\u4e0d\u770b\u7684\u8bdd\u5f53\u7136\u5c31\u4e0d\u4f1a\u5f15\u7528\u548c\u63a8\u8350\u4f60\u7684\u6587\u7ae0\uff0c\u66f4\u8c08\u4e0d\u4e0a\u53bb\u5b66\u4e60\u4f60\u6587\u7ae0\u62a5\u544a\u7684\u65b0\u6210\u679c\u3002\u5f53\u7136\uff0c\u62df\u9898\u65f6\u4e0d\u8981\u4e1c\u65bd\u6548\u98a6\uff0c\u66f4\u4e0d\u8981\u5f53\u201c\u6807\u9898\u515a\u201d\uff01\u300aNature\u300b\u65b0\u95fb\u57282015\u5e7412\u670814\u65e5\u62a5\u9053\u8bf4[4]\uff0c\u6709\u5b66\u8005\u5bf9PubMed\u533b\u5b66\u6587\u732e\u6570\u636e\u5e93\u4ece1974\u5e74\u52302014\u5e7440\u5e74\u95f4\u7684\u79d1\u7814\u8bba\u6587\u8fdb\u884c\u5206\u6790\u540e\uff0c\u53d1\u73b0\u8bf8\u5982\u201c\u65b0\u9896\u201d<\/span>\uff08novel\uff09<\/span>\u3001\u201c\u8ff7\u4eba\u201d<\/span>\uff08amazing\uff09<\/span>\u3001\u201c\u521b\u65b0\u201d<\/span>\uff08innovative\uff09<\/span>\u548c\u201c\u524d\u6240\u672a\u6709\u201d<\/span>\uff08unprecedented\uff09<\/span>\u7b49\u8bcd\u6c47\u5728\u8bba\u6587\u6807\u9898\u548c\u6458\u8981\u4e2d\u51fa\u73b0\u7684\u9891\u7387\u4e0a\u5347\u4e86\u5c06\u8fd19\u500d\u3002\u8fd9\u4e9b\u7528\u5b57\u6709\u81ea\u5356\u81ea\u5938\u4e4b\u5acc\uff0c\u4e00\u822c\u4e0d\u83b7\u597d\u8bc4\u3002<\/span><\/p>\n


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2\uff09\u4f5c\u8005<\/span><\/strong><\/span><\/span><\/p>\n


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\u5343\u4e07\u4e0d\u80fd\u672a\u7ecf\u540c\u610f\u5c31\u968f\u4fbf\u5730\u628a\u522b\u4eba<\/span>\uff08\u4f8b\u5982\u4f60\u7684\u5bfc\u5e08\uff09<\/span>\u7684\u540d\u5b57\u52a0\u5230\u4f60\u7684\u6587\u7ae0\u4e0a\u3001\u5355\u65b9\u9762\u53bb\u6295\u7a3f\u3002\u4f60\u6216\u8005\u4ee5\u4e3a\u65e5\u540e\u53ef\u4ee5\u7ed9\u670b\u53cb<\/span>\uff08\u5bfc\u5e08\uff09<\/span>\u4e00\u4e2a\u201c\u60ca\u559c\u201d\uff0c\u5176\u5b9e\u4f60\u53ef\u80fd\u4f1a\u88ab\u8ba4\u4e3a\u662f\u5728\u5229\u7528\u522b\u4eba<\/span>\uff08\u5bfc\u5e08\uff09<\/span>\u7684\u540d\u58f0\u53bb\u8c0b\u53d6\u79c1\u5229\u3002\u6240\u6709\u4f5c\u8005\u5bf9\u6587\u7ae0\u90fd\u8d1f\u6709\u51e0\u4e4e\u540c\u7b49\u7684\u8d23\u4efb\uff0c\u6bd4\u5982\u6587\u7ae0\u5f97\u5956\u65f6\u5927\u5bb6\u4f1a\u4e00\u8d77\u53bb\u9886\u5956\uff0c\u4f46\u6587\u7ae0\u53d7\u5230\u6279\u8bc4\u65f6\u5c31\u4e0d\u80fd\u4e92\u63a8\u8d23\u4efb\u3002\u67d0\u4e00\u7bc7\u6587\u7ae0\u5bf9\u4e8e\u4f60\u6765\u8bf4\u53ef\u80fd\u662f\u5f88\u9002\u5408\u6295\u7a3f\u548c\u53d1\u8868\u7684\uff0c\u4f46\u5bf9\u4e8e\u53e6\u5916\u4e00\u4e2a\u4eba\u6765\u8bf4\u5c31\u4e0d\u89c1\u5f97\u662f\u90a3\u4e48\u4e00\u56de\u4e8b\u3002\u6bd4\u5982\u540c\u4e00\u7bc7\u6587\u7ae0\uff0c\u4f60\u53d1\u8868\u7684\u8bdd\u4eba\u5bb6\u53ef\u80fd\u4f1a\u8bf4\u201c\u4e00\u4e2a\u7814\u7a76\u751f\u505a\u51fa\u8fd9\u6837\u7684\u6587\u7ae0\u771f\u4e0d\u9519\u201d\uff0c\u4f46\u4f60\u7684\u5bfc\u5e08\u62ff\u53bb\u53d1\u8868\u7684\u8bdd\u4eba\u5bb6\u4e5f\u8bb8\u4f1a\u8bf4\u201c\u4e00\u4e2a\u8001\u6559\u6388\u4e86\u8fd8\u53d1\u8fd9\u79cd\u6c34\u5e73\u7684\u6587\u7ae0\u201d\u3002\u4e0d\u540c\u4eba\u8bc4\u4ef7\u6807\u51c6\u662f\u4e0d\u4e00\u6837\u7684\u3002\u53e6\u5916\uff0c\u4e00\u7bc7\u6587\u7ae0\u5728\u5ba1\u7a3f\u540e\uff0c\u4e0d\u8981\u968f\u610f\u589e\u52a0\u6216\u8005\u51cf\u5c11\u4f5c\u8005\u7684\u540d\u5b57\u3002\u5982\u679c\u786e\u6709\u9700\u8981\uff0c\u5fc5\u987b\u5411\u7f16\u8f91\u90e8\u89e3\u91ca\u6e05\u695a\u3002\u4f5c\u8005\u7684\u6392\u540d\u4e00\u822c\u6309\u8d21\u732e\uff0c\u4f46\u6709\u65f6\u4e5f\u6309\u4e60\u60ef\uff0c\u8fd9\u548c\u56fd\u5916\u670b\u53cb\u5408\u4f5c\u65f6\u987b\u7279\u522b\u6ce8\u610f\u3002<\/span><\/p>\n


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

3\uff09\u6458\u8981<\/span><\/strong><\/span><\/span><\/p>\n


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

\u6458\u8981\u662f\u7b80\u8981\u5730\u5f52\u7eb3\u6587\u7ae0\u7684\u4e3b\u8981\u5185\u5bb9\uff0c\u4e0d\u5938\u5f20\u4e5f\u4e0d\u9057\u6f0f\u3002\u6458\u8981\u4e00\u822c\u4e0d\u52a0\u8bc4\u8bba\uff0c\u4e5f\u4e0d\u63cf\u8ff0\u5386\u53f2\u80cc\u666f\u3001\u5199\u4f5c\u52a8\u673a\u3001\u6587\u7ae0\u91cd\u8981\u6027\u7b49\u3002\u4f8b\u5982\uff0c\u4e0b\u9762\u8fd9\u53e5\u8bdd\u5c31\u662f\u6458\u8981\uff1a<\/span><\/p>\n


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

\u672c\u6587\u8bc1\u660e\u4e86\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u3002<\/span><\/p>\n


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

\u4f46\u4e0b\u9762\u8fd9\u6bb5\u8bdd\u5c31\u4e0d\u662f\u6458\u8981\uff0c\u800c\u662f\u4e00\u4e2a\u201c\u6269\u5c55\u6458\u8981\u201d<\/span>\uff08Extended Abstract\uff09<\/span>\uff1a<\/span><\/p>\n


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

\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u662f\u6307\u4efb\u4f55\u4e00\u4e2a\u5927\u4e8e2\u7684\u5076\u6570\u90fd\u53ef\u5199\u6210\u4e24\u4e2a\u8d28\u6570\u4e4b\u548c\uff0c\u4fd7\u79f0\u201c1+1\u201d\u95ee\u9898\u3002\u8be5\u731c\u60f3\u57281742\u5e74\u54e5\u5fb7\u5df4\u8d6b\u7ed9\u6b27\u62c9\u7684\u4fe1\u4e2d\u63d0\u51fa\uff0c\u662f\u6570\u8bba\u4e2d\u60ac\u800c\u672a\u51b3\u7684\u91cd\u5927\u95ee\u9898\u4e4b\u4e00\u3002\u8fc7\u53bb\u6700\u597d\u7684\u7ed3\u679c\u662f\u9648\u666f\u6da61966\u5e74\u8bc1\u660e\u7684\u201c1+2\u201d\uff0c\u4f46\u5c1a\u4e0d\u662f\u95ee\u9898\u7684\u7ec8\u7ed3\u3002\u672c\u6587\u5219\u5b8c\u5168\u8bc1\u660e\u4e86\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u3002<\/span><\/section>\n


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

\u5176\u4e2d\u5f88\u591a\u4fe1\u606f\u5e94\u8be5\u662f\u6b63\u6587\u7684\u5185\u5bb9\uff0c\u4e0d\u5fc5\u4e5f\u4e0d\u5e94\u5728\u6458\u8981\u91cc\u53d9\u8ff0\u548c\u63cf\u5199\u3002\u5f88\u591a\u4f5c\u8005\u751f\u6015\u8bfb\u8005\u4e0d\u7406\u89e3\u8be5\u6587\u7684\u610f\u4e49\uff0c\u5728\u6458\u8981\u91cc\u7279\u522b\u5f3a\u8c03\u6240\u7814\u7a76\u7684\u95ee\u9898\u5982\u4f55\u91cd\u8981\u548c\u5982\u4f55\u5bcc\u6709\u6311\u6218\u6027\uff0c\u5e0c\u671b\u8bfb\u8005\u7279\u522b\u662f\u7f16\u8f91\u548c\u5ba1\u7a3f\u4eba\u8ba4\u53ef\u3002\u4f46\u8fd9\u5176\u5b9e\u4e0d\u662f\u4e00\u7bc7\u6587\u7ae0\u5f00\u5934\u5199\u4e2a\u6458\u8981\u7684\u76ee\u7684\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u6458\u8981\u5e94\u8be5\u5e76\u4e14\u53ea\u9700\u628a\u6587\u7ae0\u8981\u70b9\u6458\u5f55\u51fa\u6765\uff0c\u8ba9\u8bfb\u8005\u7acb\u9a6c\u77e5\u9053\u8fd9\u662f\u4e0d\u662f\u4ed6\u60f3\u8981\u9605\u8bfb\u7684\u6587\u7ae0\uff0c\u662f\u7684\u8bdd\u5c31\u5f80\u4e0b\u770b\u5176\u5185\u5bb9\uff0c\u4e0d\u662f\u7684\u8bdd\u5c31\u6253\u4f4f\u4e0d\u8981\u6d6a\u8d39\u65f6\u95f4\u4e86\u3002<\/span><\/p>\n


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

\u6458\u8981\u5e94\u8be5\u662f\u81ea\u6211\u5b8c\u5907\u7684\uff0c\u8ba9\u8bfb\u8005\u9605\u8bfb\u65f6\u4e0d\u9700\u53bb\u67e5\u5bf9\u8d44\u6599\u5c31\u80fd\u7406\u89e3\u3002\u6458\u8981\u51fa\u73b0\u5728\u6587\u7ae0\u7684\u5f00\u5934\uff0c\u5199\u6458\u8981\u7684\u65f6\u5019\u4e0d\u80fd\u5047\u5b9a\u8bfb\u8005\u5df2\u7ecf\u770b\u8fc7\u4e86\u6587\u7ae0\uff0c\u56e0\u6b64\u8981\u907f\u514d\u4f7f\u7528\u5c1a\u672a\u5b9a\u4e49\u7684\u6982\u5ff5\u548c\u7b26\u53f7\u3002\u6240\u6709\u5185\u5bb9\u90fd\u987b\u7ed9\u51fa\u8bf4\u660e\u548c\u63cf\u8ff0\u3002\u6458\u8981\u4e2d\u5c3d\u53ef\u80fd\u4e0d\u8981\u51fa\u73b0\u6570\u5b66\u65b9\u7a0b\u3001\u516c\u5f0f\u3001\u56fe\u8868\u548c\u6570\u636e\u3002<\/span><\/p>\n


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

\u6587\u7ae0\u7684\u6458\u8981\u975e\u5e38\u91cd\u8981\uff0c\u5b83\u5411\u8bfb\u8005\u5c55\u793a\u4e86\u6587\u7ae0\u7684\u5168\u666f\u548c\u4e3b\u8981\u7ed3\u679c\uff0c\u53cd\u6620\u51fa\u6587\u7ae0\u7684\u6c34\u5e73\u548c\u8d21\u732e\u3002\u5efa\u8bae\u4f5c\u8005\u591a\u82b1\u70b9\u65f6\u95f4\u62df\u5199\u4e00\u4e2a\u7b80\u6d01\u51c6\u786e\u7684\u6458\u8981\u3002<\/span><\/p>\n


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

4\uff09\u5173\u952e\u8bcd<\/span><\/strong><\/span><\/span><\/p>\n


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

\u5f88\u591a\u4eba\u5728\u5217\u51fa\u5173\u952e\u8bcd\u65f6\u4e0d\u52a0\u601d\u8003\uff0c\u51ed\u611f\u89c9\u968f\u4fbf\u5199\u51e0\u4e2a\u4e86\u4e8b\uff0c\u4ee5\u4e3a\u53ea\u662f\u5e94\u4ed8\u51fa\u7248\u793e\u8981\u6c42\u7684\uff0c\u65e0\u6240\u8c13\u3002\u5982\u679c\u6ca1\u6709\u5fc5\u8981\uff0c\u4e3a\u4ec0\u4e48\u79d1\u6280\u6587\u7ae0\u90fd\u8981\u6c42\u5217\u51fa\u5173\u952e\u8bcd\u5462\uff1f\u5173\u952e\u8bcd\u5e94\u5f53\u662f\u53cd\u6620\u8be5\u6587\u5185\u5bb9\u6700\u4e3a\u5173\u952e\u7684\u8bcd\uff0c\u770b\u5b8c\u4e86\u5927\u4f53\u4e0a\u5c31\u53ef\u4ee5\u628a\u6587\u7ae0\u5f52\u7c7b\u5b58\u6863\uff0c\u76f8\u5f53\u4e8eindex term\u3002<\/span><\/p>\n


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

\u6253\u4e2a\u6bd4\u65b9\uff0c\u4f60\u5728\u56fe\u4e66\u9986\u548c\u6570\u636e\u5e93\u7684\u201c\u6df7\u6c8c\u7406\u8bba\u201d\u680f\u76ee\u91cc\u6ca1\u627e\u5230\u4f60\u672c\u4eba\u67d0\u7bc7\u5173\u4e8e\u6df7\u6c8c\u7406\u8bba\u7684\u6587\u7ae0\uff0c\u90a3\u662f\u56e0\u4e3a\u5916\u884c\u7684\u56fe\u4e66\u7ba1\u7406\u5458\u6ca1\u6709\u4ece\u4f60\u7684\u6587\u7ae0\u770b\u5230\u8fd9\u4e2a\u5173\u952e\u8bcd\u3002<\/span><\/p>\n


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

\u6b64\u5916\uff0c\u4e00\u4e2a\u7ec6\u8282\u662f\uff0c\u5173\u952e\u540d\u8bcd\u53ea\u9700\u5199\u5355\u6570\u3002\u4f5c\u4e3a\u5173\u952e\u8bcd\uff0c\u201csystems\u201d\u548c\u201cequations\u201d\u7b49\u590d\u6570\u540d\u8bcd\u5e76\u4e0d\u6bd4\u201csystem\u201d\u548c\u201cequation\u201d \u7b49\u5355\u6570\u540d\u8bcd\u63d0\u4f9b\u66f4\u591a\u7684\u7d22\u5f15\u4fe1\u606f\u3002<\/span><\/p>\n


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

5\uff09\u524d\u8a00\u548c\u4e3b\u4f53<\/span><\/strong><\/span><\/span><\/p>\n


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

\u524d\u8a00\uff0c\u4e5f\u79f0\u5f15\u8a00\uff0c\u662f\u4e00\u7bc7\u6587\u7ae0\u6700\u96be\u5199\u597d\u7684\u90e8\u5206\uff0c\u4f46\u662f\u5fc5\u987b\u5199\u597d\u3002<\/span><\/p>\n


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

\u524d\u8a00\u4e00\u822c\u4ece\u6240\u8bba\u95ee\u9898\u7684\u7b80\u8981\u5386\u53f2\u80cc\u666f\u8c08\u8d77\uff0c\u5f15\u51fa\u6240\u8981\u7814\u7a76\u7684\u95ee\u9898\uff0c\u8bf4\u660e\u8be5\u95ee\u9898\u7684\u610f\u4e49\u3001\u8981\u70b9\u548c\u96be\u70b9\uff0c\u56de\u987e\u524d\u4eba\u7684\u4e3b\u8981\u8d21\u732e\uff0c\u9610\u8ff0\u672c\u6587\u89e3\u51b3\u8be5\u95ee\u9898\u7684\u57fa\u672c\u601d\u8def\u548c\u5173\u952e\u6280\u672f\uff0c\u7136\u540e\u5f52\u7eb3\u51fa\u672c\u6587\u7684\u8d21\u732e\uff0c\u6700\u540e\u7b80\u5355\u52fe\u753b\u5168\u6587\u7684\u7ed3\u6784\u3002<\/span><\/p>\n


<\/p>\n

\u79d1\u6280\u6587\u7ae0\u524d\u8a00\u548c\u4e3b\u4f53\u7684\u5199\u4f5c\uff0c\u6709\u51e0\u4e2a\u5e38\u89c1\u95ee\u9898\u9700\u8981\u6ce8\u610f\u907f\u514d\uff1a<\/span><\/p>\n


<\/p>\n

5.1\uff09\u907f\u514d\u6df7\u5408\u4f7f\u7528\u7b2c\u4e00\u4eba\u79f0\u4e3b\u52a8\u8bed\u6001\u548c\u7b2c\u4e09\u4eba\u79f0\u88ab\u52a8\u8bed\u6001\u7684\u53d9\u8ff0\u3002\u4e24\u79cd\u4e66\u5199\u5f62\u5f0f\u7684\u6df7\u7528\u4f1a\u8ba9\u8bfb\u8005\u9605\u8bfb\u8d77\u6765\u6709\u4e00\u79cd\u6362\u6765\u6362\u53bb\u751a\u81f3\u662f\u626d\u6765\u626d\u53bb\u7684\u611f\u89c9\uff0c\u8bfb\u8d77\u6765\u62d7\u53e3\u4e0d\u7545\u987a\u3002\u4f8b\u5982\u4e0b\u9762\u7684\u53e5\u5b50\uff1a<\/span><\/p>\n

We study the Riemann hypothesis in this paper. A preliminary result towards its complete proof is obtained, where we derive a necessary condition. A counterexample is given to show that this condition is not sufficient.<\/span><\/p>\n


<\/p>\n

\u53ef\u4ee5\u6539\u4e3a\u7b2c\u4e00\u4eba\u79f0\u4e3b\u52a8\u8bed\u6001\u7684\u5199\u6cd5\uff1a<\/span><\/p>\n

We study the Riemann hypothesis in this paper. We obtain a preliminary result towards its complete proof, where we derive a necessary condition. We give a counterexample to show that this condition is not sufficient.<\/span><\/p>\n


<\/p>\n

\u6216\u8005\u6539\u4e3a\u7b2c\u4e09\u4eba\u79f0\u88ab\u52a8\u8bed\u6001\u7684\u5199\u6cd5\uff1a<\/span><\/p>\n

The Riemann hypothesis is studied in this paper. A preliminary result is obtained towards its complete proof, where a necessary condition is derived. A counterexample is given to show that this condition is not sufficient.<\/span><\/p>\n


<\/p>\n

\u7b2c\u4e00\u79cd\u5199\u6cd5\u5c31\u662f\u4f60\u672c\u4eba\u4e00\u76f4\u5728\u8bf4\u8bdd\uff0c\u8ba9\u8bfb\u8005\u4e00\u76f4\u8ddf\u7740\u4f60\u5411\u524d\u8d70\u3002\u7b2c\u4e8c\u79cd\u5199\u6cd5\u662f\u6bd4\u8f83\u6587\u96c5\u548c\u5ba2\u6c14\u7684\u8868\u8ff0\uff0c\u6ca1\u6709\u201c\u6211\u201d\u548c\u201c\u6211\u4eec\u201d\u51fa\u73b0\uff0c\u4e0d\u5f3a\u8c03\u81ea\u5df1\uff0c\u7b26\u5408\u4f20\u7edf\u82f1\u8bed\u79d1\u6280\u5199\u4f5c\u7684\u4e60\u60ef\u3002<\/span><\/p>\n

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

5.2\uff09\u907f\u514d\u201c\u6284\u88ad\u201d<\/span><\/span><\/p>\n


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

\u4e0d\u8981\u7167\u6284\u5176\u5b83\u6587\u7ae0<\/span>\uff08\u5305\u62ec\u81ea\u5df1\u7684\u6587\u7ae0\uff09<\/span>\u4e2d\u7684\u6587\u53e5\u548c\u6bb5\u843d\u3002\u8fd9\u5728\u4ecb\u7ecd\u4eba\u5bb6\u5de5\u4f5c\u65f6\u5c24\u5176\u8981\u6ce8\u610f\uff0c\u56e0\u4e3a\u5f88\u5bb9\u6613\u5c31\u628a\u4eba\u5bb6\u7684\u539f\u6587\u6216\u539f\u53e5\u590d\u5236\u8fc7\u6765\u3002\u6487\u5f00\u201c\u6284\u88ad\u201d\u95ee\u9898\u4e0d\u8bf4\uff0c\u4e00\u7bc7\u6587\u7ae0\u5e94\u8be5\u4ece\u5934\u5230\u5c3e\u7528\u81ea\u5df1\u7684\u8bed\u6c14\u5199\u6210\uff0c\u4e0d\u8981\u8ba9\u4eba\u5bb6\u8bfb\u8d77\u6765\u6709\u4e00\u79cd\u201c\u526a\u8d34\u62fc\u51d1\u201d\u7684\u611f\u89c9\u3002\u4e5f\u4e0d\u8981\u4ece\u81ea\u5df1\u7684\u65e7\u6587\u4e2d\u6284\u5f55\u4e00\u4e9b\u8bed\u53e5\u751a\u81f3\u6bb5\u843d\u8fc7\u6765\u3002\u8fd9\u81f3\u5c11\u8868\u660e\uff0c\u4f60\u6216\u8005\u53ea\u61c2\u4e00\u79cd\u53e5\u578b\uff0c\u6216\u8005\u53ea\u4f1a\u4e00\u79cd\u8868\u8fbe\u65b9\u5f0f\uff0c\u6216\u8005\u662f\u4e0d\u8ba4\u771f\uff0c\u6216\u8005\u5c31\u662f\u5077\u61d2\u3002\u5176\u5b9e\u628a\u4e00\u4e2a\u53e5\u5b50\u6539\u5199\u4e00\u4e0b\u5f88\u5bb9\u6613\uff0c\u4f55\u4e50\u800c\u4e0d\u4e3a\u5462\u3002<\/span><\/p>\n


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

5.3\uff09\u907f\u514d\u5199\u957f\u53e5\u5b50[5]\u3002\u8bb8\u591a\u957f\u53e5\u7684\u751f\u6210\u662f\u56e0\u4e3a\u52a0\u8fdb\u4e86\u63d2\u5165\u8bed\uff0c\u751a\u81f3\u4e0d\u53ea\u4e00\u4e2a\u63d2\u5165\u8bed\uff0c\u8bf8\u5982 which, that is, with\uff0c\u4ee5\u53ca\u7531\u5206\u8bcd\u5f15\u51fa\u7684\u4ece\u53e5\u3002\u5176\u5b9e\u5199\u7406\u5de5\u79d1\u8bba\u6587\u7684\u4e3b\u8981\u76ee\u7684\u662f\u4f20\u8fbe\u79d1\u6280\u6210\u679c\u7684\u4fe1\u606f\u800c\u4e0d\u662f\u8ba9\u8bfb\u8005\u53bb\u53cd\u590d\u54c1\u5473\u53e5\u5b50\u7684\u6587\u91c7\uff0c\u66f4\u5e94\u63d0\u5021\u591a\u5199\u77ed\u53e5\uff0c\u8ba9\u8bfb\u8005\u4e00\u76ee\u4e86\u7136\u3002\u50cf\u4e0b\u9762\u8fd9\u6837\u7684\u53e5\u5b50\u8bed\u6cd5\u662f\u6ca1\u6709\u95ee\u9898\u7684\uff0c\u4f46\u8ba9\u4eba\u8bfb\u5f97\u5f88\u7d2f\uff1a<\/span><\/p>\n


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

Let us consider a system of three nonlinear ordinary differential equations, where the nonlinearity consists of polynomial functions, which actually are quadratic functions, with only three product terms, that can generate chaos and is well known to be the Lorenz system used to approximate complex weather dynamics, useful for studying fluid motions under various heating conditions.<\/span><\/p>\n


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

\u8bfb\u8005\u4e0d\u96be\u628a\u5b83\u5206\u6210\u4e24\u53e5\u751a\u81f3\u4e09\u53e5\u8bdd\u6765\u8bf4\uff0c\u6613\u8bfb\u6613\u61c2\uff0c\u4f55\u4e50\u800c\u4e0d\u4e3a\u5462\uff1f<\/span><\/p>\n


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

5.4\uff09\u907f\u514d\u5f15\u8fdb\u4e0d\u5fc5\u8981\u7684\u5b9a\u4e49\u548c\u7b26\u53f7\u3002\u8bb8\u591a\u4f5c\u8005\u8fc7\u4e8e\u8ba4\u771f\uff0c\u5199\u79d1\u6280\u6587\u7ae0\u7279\u522b\u662f\u6570\u5b66\u6587\u7ae0\u65f6\uff0c\u5f00\u7bc7\u5c31\u90d1\u91cd\u5176\u4e8b\u5730\u7ed9\u51fa\u4e00\u8fde\u4e32\u7684\u5b9a\u4e49\u3002\u91cd\u8981\u800c\u4e14\u5728\u4e0b\u6587\u53cd\u590d\u7528\u5230\u7684\u6982\u5ff5\u9700\u8981\u9884\u5148\u5b9a\u4e49\u6e05\u695a\uff0c\u8fd9\u65e0\u53ef\u539a\u975e\u3002\u4f46\u662f\uff0c\u4e00\u4e9b\u5728\u4e0b\u6587\u5e76\u4e0d\u53cd\u590d\u4f7f\u7528\u7684\u6982\u5ff5\uff0c\u5c3d\u7ba1\u53ef\u80fd\u91cd\u8981\uff0c\u4e5f\u4e0d\u89c1\u5f97\u9700\u8981\u6761\u5217\u51fa\u6765\u3002\u5199\u8bba\u6587\u548c\u5199\u6559\u79d1\u4e66\u662f\u4e0d\u4e00\u6837\u7684\u3002\u6559\u79d1\u4e66\u9700\u8981\u53cd\u590d\u9605\u8bfb\u5e76\u8bb0\u5fc6\u5176\u4e2d\u7684\u8bb8\u591a\u5185\u5bb9\uff0c\u800c\u8bba\u6587\u5219\u5e94\u65b9\u4fbf\u8bfb\u8005\u5feb\u901f\u9605\u8bfb\u3002\u901a\u5e38\u8bfb\u8005\u4e00\u770b\u5230\u5b9a\u4e49\u5fc3\u7406\u5c31\u4e0d\u514d\u7d27\u5f20\uff0c\u62fc\u547d\u60f3\u628a\u5b83\u4eec\u8bb0\u4f4f\uff0c\u62c5\u5fc3\u5426\u5219\u6587\u7ae0\u53ef\u80fd\u8bfb\u4e0d\u4e0b\u53bb\u3002\u53ef\u662f\uff0c\u4e00\u957f\u4e32\u7684\u5b9a\u4e49\u548c\u8bb0\u53f7\u4f1a\u8ba9\u6587\u7ae0\u8bfb\u8d77\u6765\u7d2f\u800c\u65e0\u8da3\uff0c\u53cd\u800c\u59a8\u788d\u4e86\u8bfb\u8005\u5bf9\u4e3b\u9898\u5185\u5bb9\u7684\u5173\u6ce8\u548c\u601d\u8003\u3002\u5f88\u591a\u6587\u7ae0\u8bfb\u5b8c\u540e\u5e38\u5e38\u4f1a\u53d1\u73b0\u524d\u9762\u597d\u51e0\u4e2a\u5b9a\u4e49\u5176\u5b9e\u5728\u6587\u4e2d\u53ea\u51fa\u73b0\u8fc7\u4e00\u4e24\u6b21\u3002\u8fd9\u4e9b\u6982\u5ff5\u6216\u672f\u8bed\u53ef\u4ee5\u5728\u63d0\u53ca\u7684\u5730\u65b9\u518d\u52a0\u4ee5\u8bf4\u660e\u800c\u4e0d\u5fc5\u5355\u72ec\u5b9a\u4e49\u3002\u8fd9\u901a\u5e38\u5e76\u4e0d\u788d\u4e8b\uff0c\u5374\u8ba9\u6587\u7ae0\u8bfb\u8d77\u6765\u8f7b\u677e\u591a\u4e86\u3002<\/span><\/p>\n


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

5.5\uff09\u907f\u514d\u91c7\u7528\u8fc7\u591a\u7684\u7f29\u5199\u3002\u8fd9\u5728\u7269\u7406\u7c7b\u79d1\u6280\u6587\u7ae0\u7279\u522b\u5e38\u89c1\u3002\u6709\u65f6\u770b\u5230\u4e00\u7bc7\u6587\u7ae0\u5e26\u4e0a\u5341\u591a\u4e8c\u5341\u4e2a\u7f29\u5199\uff0c\u8bf8\u5982 CS\u3001SC\u3001SSC\u3001CSS \u7b49\u7b49\uff0c\u6df7\u5728\u4e00\u8d77\uff0c\u9605\u8bfb\u65f6\u9700\u8981\u53cd\u590d\u67e5\u5bf9\u524d\u6587\uff0c\u5341\u5206\u8d39\u52b2\u3002\u91c7\u7528\u7f29\u5199\u7684\u539f\u610f\u662f\u8ba9\u8bcd\u6c47\u8868\u8fbe\u7b80\u6d01\u4ece\u800c\u8ba9\u6587\u7ae0\u597d\u8bfb\u597d\u8bb0\uff0c\u4f46\u6ee5\u7528\u7684\u7ed3\u679c\u4f1a\u9002\u5f97\u5176\u53cd\u3002<\/span><\/p>\n


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

5.6\uff09\u907f\u514d\u4e0d\u5fc5\u8981\u7684\u65b9\u7a0b\u7f16\u53f7<\/span><\/p>\n


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

\u79d1\u6280\u8bba\u6587\u4e2d\u7684\u6570\u5b66\u516c\u5f0f\u6216\u65b9\u7a0b\u5f0f\u7f16\u53f7\u4ec5\u9650\u4e8e\u5728\u8be5\u6587\u7ae0\u4e2d\u4f7f\u7528\uff0c\u662f\u4e3a\u540e\u9762\u884c\u6587\u4e2d\u5f15\u8ff0\u524d\u9762\u6570\u5b66\u5f0f\u5b50\u7684\u65b9\u4fbf\u800c\u8bbe\u7acb\u3002\u5982\u679c\u4e00\u4e2a\u516c\u5f0f\u5728\u6587\u7ae0\u540e\u9762\u65e0\u9700\u5f15\u7528\u7684\u8bdd\uff0c\u5c31\u4e0d\u5fc5\u7f16\u53f7\u3002\u6709\u4e9b\u6587\u7ae0\u7bc7\u5e45\u4e0d\u957f\uff0c\u5374\u5217\u51fa\u4e00\u957f\u4e32\u7684\u516c\u5f0f\u7f16\u53f7\uff0c\u4e00\u70b9\u4e5f\u4e0d\u7b80\u6d01\uff0c\u751a\u81f3\u8ba9\u4eba\u773c\u82b1\u7f2d\u4e71\uff0c\u5b9e\u65e0\u5fc5\u8981\u3002<\/span><\/p>\n


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

5.7\uff09\u907f\u514d\u4e0d\u5fc5\u8981\u548c\u4e0d\u6070\u5f53\u7684\u81ea\u5938\u3002\u5199\u6587\u7ae0\u4e0d\u514d\u8981\u8bf4\u81ea\u5df1\u7684\u6587\u7ae0\u6bd4\u524d\u4eba\u7684\u6210\u679c\u6709\u6539\u8fdb\u6709\u63d0\u9ad8\uff0c\u56e0\u800c\u6709\u4ef7\u503c\u6709\u521b\u65b0\u3002\u8fd9\u662f\u81ea\u7136\u7684\uff0c\u4e0d\u7136\u4e3a\u4ec0\u4e48\u5199\u8fd9\u7bc7\u6587\u7ae0\u5462\uff1f\u4f46\u5e94\u6ce8\u610f\u63aa\u8f9e\u8981\u6070\u5f53\uff0c\u4e0d\u8981\u4e5f\u4e0d\u5fc5\u8fc7\u5206\u81ea\u5938\uff0c\u628a\u8bc4\u4ef7\u7559\u7ed9\u8bfb\u8005\u53bb\u8bf4\u3002\u5982\u4f55\u80af\u5b9a\u81ea\u5df1\u7684\u6210\u679c\u800c\u53c8\u80fd\u8ba9\u8bfb\u8005\u4fe1\u670d\uff0c\u8fd9\u79cd\u597d\u7684\u7b14\u6cd5\u662f\u8981\u8ba4\u771f\u659f\u914c\u548c\u63a8\u6572\u7684\u3002\u524d\u9762\u63d0\u5230[4]\uff0c\u6587\u7ae0\u6807\u9898\u548c\u6458\u8981\u4e0d\u5b9c\u6ee5\u7528\u5938\u5f20\u7684\u5b57\u773c\uff0c\u5982\u201c\u521b\u9020\u6027\u201d<\/span>\uff08innovative\uff09<\/span>\u3001\u201c\u7a81\u7834\u6027\u201d<\/span>\uff08breakthrough\uff09<\/span>\u4e4b\u7c7b\uff0c\u5728\u884c\u6587\u4e2d\u4e5f\u4e0d\u5b9c\u6ee5\u5199\u8fc7\u5206\u5f20\u626c\u7684\u53e5\u5b50\uff0c\u5982\u201cIt must be emphasized that our result is very important\u201d\u4e4b\u7c7b\u3002\u8fd9\u4e9b\u8bcd\u53e5\u5176\u5b9e\u90fd\u4e0d\u662f\u5fc5\u8981\u7684\u3002<\/span><\/p>\n


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

5.8\uff09\u907f\u514d\u5bf9\u522b\u4eba\u950b\u8292\u51cc\u5389\u7684\u8bc4\u5224\u3002\u5f88\u591a\u65f6\u5019\u4e3a\u4e86\u8bf4\u660e\u81ea\u5df1\u5199\u6587\u7ae0\u7684\u52a8\u56e0\uff0c\u5373\u6240\u8c13 motivation\uff0c\u9700\u8981\u6307\u51fa\u524d\u4eba\u7814\u7a76\u6210\u679c\u7684\u4e0d\u8db3\uff0c\u8fd9\u4e5f\u662f\u5f88\u81ea\u7136\u7684\u3002\u4e0d\u8fc7\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u7406\u5de5\u79d1\u7684\u5b66\u672f\u8bba\u6587\u57fa\u672c\u4e0a\u662f\u63a2\u8ba8\u6027\u800c\u4e0d\u662f\u7ec8\u7ed3\u6027\u7684\uff0c\u4e00\u822c\u90fd\u662f\u5173\u4e8e\u67d0\u4e2a\u95ee\u9898\u7684\u7814\u7a76\u8fc7\u7a0b\u4e2d\u7684\u8fdb\u5c55\u6027\u62a5\u544a\u3002\u56e0\u6b64\uff0c\u5076\u7136\u770b\u5230\u4e00\u4e9b\u6587\u7ae0\u7684\u7ed3\u679c\u4e0d\u591f\u5b8c\u6574\u751a\u81f3\u5b58\u5728\u67d0\u4e9b\u8c2c\u8bef\u5e76\u4e0d\u5947\u602a\u3002\u6307\u51fa\u5176\u4e2d\u7684\u95ee\u9898\u662f\u5e94\u8be5\u7684\u751a\u81f3\u662f\u5fc5\u9700\u7684\uff0c\u4f46\u76ee\u7684\u662f\u628a\u95ee\u9898\u8bf4\u6e05\u695a\uff0c\u4e0d\u662f\u53bb\u6307\u8d23\u522b\u4eba\uff0c\u56e0\u6b64\u63aa\u8f9e\u53ef\u4ee5\u6e05\u6de1\u6587\u96c5\uff0c\u8ba9\u4f5c\u8005\u548c\u8bfb\u8005\u90fd\u6b23\u7136\u63a5\u53d7\u3002\u8bf8\u5982unfortunately wrong\u3001obviously incorrect\u4e4b\u7c7b\u7528\u8bed\u6bd4\u8f83\u523a\u773c\uff0c\u5efa\u8bae\u5c3d\u91cf\u907f\u514d\u6216\u9002\u5f53\u8f6f\u5316\u3002\u5e94\u8be5\u77e5\u9053\uff0c\u4e0d\u662f\u5bf9\u4eba\u5bb6\u7684\u6279\u8bc4\u53e3\u6c14\u8d8a\u51cc\u5389\uff0c\u81ea\u5df1\u6587\u7ae0\u6c34\u5e73\u5c31\u8d8a\u9ad8\u3001\u62a5\u544a\u7684\u79d1\u7814\u6210\u679c\u5c31\u8d8a\u6709\u4ef7\u503c\u3002<\/span><\/p>\n


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

5.9\uff09\u907f\u514d\u80e1\u4e71\u5f15\u7528\u6587\u732e<\/span><\/span><\/p>\n


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

\u987b\u660e\u767d\u4e3a\u4ec0\u4e48\u8981\u5f15\u7528\u6587\u732e\uff0c\u5e94\u5c3d\u91cf\u51c6\u786e\u5b8c\u6574\u5730\u5f15\u7528\u5fc5\u8981\u548c\u91cd\u8981\u7684\u53c2\u8003\u6587\u732e\u3002\u4e0d\u8981\u8ddf\u7740\u5176\u4ed6\u6587\u7ae0\uff0c\u522b\u4eba\u5f15\u7528\u4ec0\u4e48\u4f60\u4e5f\u5f15\u7528\u4ec0\u4e48\uff0c\u7167\u6284\u7167\u642c\u3002\u9664\u4e86\u81ea\u5df1\u719f\u8bc6\u7684\u6587\u732e\u4e4b\u5916\uff0c\u5982\u6709\u53ef\u80fd\u7684\u8bdd\u628a\u5176\u4ed6\u5f15\u6587\u4e5f\u627e\u6765\u8fc7\u76ee\u4e00\u4e0b\uff0c\u907f\u514d\u4e0d\u6070\u5f53\u751a\u81f3\u662f\u9519\u8bef\u7684\u5f15\u7528\u3002\u4f8b\u5982\uff0c\u6709\u4e9b\u6587\u7ae0\u53ef\u80fd\u5df2\u6709\u52d8\u8bef\u6216\u8005\u5df2\u7ecf\u64a4\u7a3f\uff0c\u5c31\u4e0d\u8981\u95f9\u7b11\u8bdd\u53bb\u5f15\u7528\u4e86\u3002<\/span><\/p>\n


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

\u8fd8\u8981\u6ce8\u610f\uff0c\u4e0d\u8981\u5f15\u7528\u81ea\u5df1\u7684\u4f46\u4e0e\u672c\u6587\u65e0\u5173\u7684\u6587\u7ae0\u4ee5\u589e\u52a0\u5f15\u7528\u7387\u3002\u8fd9\u5c06\u4f1a\u81ea\u6211\u7559\u4e0b\u4e00\u4e2a\u4e0d\u826f\u8bb0\u5f55\u3002<\/span><\/p>\n


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

5.10\uff09\u907f\u514d\u4e66\u5199\u4e2d\u5f0f\u82f1\u8bed<\/span><\/span><\/p>\n

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

\u7531\u4e8e\u8bed\u8a00\u548c\u8bed\u6cd5\u7684\u4e0d\u540c\uff0c\u5f88\u591a\u4e2d\u6587\u7684\u8868\u8fbe\u4e60\u60ef\u5bb9\u6613\u88ab\u5e26\u5230\u82f1\u6587\u79d1\u6280\u5199\u4f5c\u4e2d\u3002\u4f8b\u5982\uff0c\u201c\u4ee4F\u4e3a\u53ef\u5fae\u51fd\u6570\uff0c\u5219\u5b83\u662f\u8fde\u7eed\u7684\u201d\u662f\u4e2d\u6587\u4e00\u4e2a\u5b8c\u6574\u53e5\u5b50\uff0c\u5bb9\u6613\u88ab\u5199\u6210\uff1a<\/span><\/p>\n


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

Let F be a differentiable function, then it is continuous.<\/span><\/p>\n


<\/p>\n

\u5728\u82f1\u6587\u91cc\uff0c\u56e0\u4e3a\u8fd9\u91cc\u6709\u4e24\u4e2a\u52a8\u8bcd\uff0clet\u548cis\uff0c\u800c\u4e14then\u53c8\u4e0d\u662f\u50cfand\u90a3\u6837\u7684\u8fde\u8bcd\uff0c\u5b83\u5e94\u8be5\u88ab\u5206\u4e3a\u4e24\u4e2a\u53e5\u5b50\uff1a<\/span>
<\/p>\n


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

Let F be a differentiable function. Then it is continuous.<\/span><\/p>\n


<\/p>\n

\u8fd9\u91cc\uff0c\u524d\u9762\u90a3\u53e5\u8bdd\u600e\u4e48\u6ca1\u6709\u4e3b\u8bed\u4e86\uff1f\u662f\u4e0d\u662f\u5e94\u8be5\u5199\u4e3a\u201cWe let F be a differential function\u201d\uff1f<\/span><\/p>\n


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

\u5728\u79d1\u6280\u6587\u7ae0\u91cc\uff0c\u7531\u4e8e\u57fa\u672c\u4e0a\u90fd\u662f\u4f5c\u8005\u81ea\u5df1\u5728\u8bf4\u8bdd\uff0c\u5e76\u4e14\u5728\u8bf4\u81ea\u5df1\u7684\u4e8b\u60c5\uff0c\u5982\u679c\u90fd\u5199\u5b8c\u6574\u53e5\u5b50\u7684\u8bdd\uff0c\u5c31\u4f1a\u51e0\u4e4e\u6bcf\u53e5\u8bdd\u90fd\u7528\u201cWe\u201d\u6216\u201cI\u201d\u6765\u5f00\u5934\uff0c\u8bf8\u5982\u201cWe do this\u201d\u548c\u201cWe do that\u201d, \u975e\u5e38\u7d2f\u8d58\u3002\u56e0\u6b64\uff0c\u5728\u79d1\u6280\u8bba\u6587\u5199\u4f5c\u4e2d\uff0c\u8bb8\u591a\u4e00\u822c\u53d9\u8ff0\u6027\u7684\u53e5\u5b50\u90fd\u628a\u4e3b\u8bed\u7701\u7565\u4e86\uff0c\u5199\u6210\u7948\u4f7f\u53e5\u3002\u4f8b\u5982\uff0c\u4e0b\u9762\u8fd9\u7c7b\u65e0\u4e3b\u8bed\u7948\u4f7f\u53e5\u578b\u662f\u5e38\u89c1\u7684\uff1a<\/span><\/p>\n


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

Consider the following problem.<\/span><\/p>\n

Assume that function F is differentiable.<\/span><\/p>\n

Integrate F from 0 to 1.<\/span><\/p>\n


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

\u5176\u5b9e\uff0c\u751f\u6d3b\u53e3\u8bed\u4e2d\u5c31\u6709\u8bb8\u591a\u65e0\u4e3b\u8bed\u7948\u4f7f\u53e5\uff0c\u5982\u201cThank you\u201d\u548c\u201cLet me see\u201d\u7b49\uff0c\u5341\u5206\u7b80\u6d01\u53c8\u4e0d\u5f3a\u8c03\u81ea\u6211\u3002<\/span><\/p>\n


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6\uff09\u7ed3\u8bba<\/span><\/strong><\/p>\n


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

\u7ed3\u8bba\u5c31\u662f\u5bf9\u6587\u7ae0\u4f5c\u4e2a\u603b\u7ed3\uff0c\u5f52\u7eb3\u672c\u6587\u7684\u4e3b\u8981\u6210\u679c\u5e76\u53d1\u8868\u4e00\u4e9b\u8bc4\u8bba\u3002\u8fd9\u90e8\u5206\u6700\u597d\u6709\u4e9b\u5b66\u672f\u8ba8\u8bba\uff0c\u6307\u51fa\u5c1a\u5b58\u5728\u7684\u548c\u5c06\u6765\u8fd8\u53ef\u4ee5\u7ee7\u7eed\u601d\u8003\u7684\u4e00\u4e24\u4e2a\u91cd\u8981\u79d1\u7814\u95ee\u9898\uff0c\u4f46\u65e0\u9700\u5c55\u5f00\u7814\u7a76\u8ba1\u5212\u548c\u6b65\u9aa4\u3002<\/span><\/p>\n


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

\u5199\u7ed3\u8bba\u65f6\u4e0d\u8981\u7b80\u5355\u5730\u628a\u6587\u7ae0\u5f00\u5934\u7684\u6458\u8981\u590d\u8ff0\u4e00\u904d\uff0c\u4e0d\u7136\u5c31\u662f\u591a\u4f59\u7684\u8bdd\uff0c\u6ca1\u6709\u65b0\u7684\u6548\u679c\u5e76\u4e14\u6d6a\u8d39\u6587\u7ae0\u7bc7\u5e45\u3002<\/span><\/p>\n


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

\u6570\u5b66\u548c\u7269\u7406Letter\u7c7b\u7684\u6587\u7ae0\u4e00\u822c\u90fd\u4e0d\u5199\u7ed3\u8bba\uff0c\u8fd9\u662f\u56e0\u4e3a\u6587\u7ae0\u8f83\u77ed\uff0c\u770b\u5b8c\u540e\u5370\u8c61\u5c1a\u6df1\uff0c\u65e0\u9700\u56de\u987e\u548c\u603b\u7ed3\u3002<\/span><\/p>\n


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7\uff09\u81f4\u8c22<\/span><\/strong><\/p>\n


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

\u6587\u7ae0\u9700\u8981\u81f4\u8c22\u79d1\u7814\u57fa\u91d1\u662f\u5468\u77e5\u7684\uff0c\u4f46\u4e0d\u8981\u7f57\u5217\u65e0\u5173\u7684\u8d44\u52a9\u9879\u76ee\u3002\u6b64\u5916\uff0c\u9664\u4e86\u611f\u8c22\u8ba4\u771f\u800c\u53c8\u6709\u5b9e\u8d28\u6027\u5efa\u8bae\u7684\u670b\u53cb\u4e4b\u5916\uff0c\u4e5f\u5e94\u8be5\u611f\u8c22\u8ba4\u771f\u800c\u53c8\u6709\u5b9e\u8d28\u6027\u5efa\u8bae\u7684\u533f\u540d\u5ba1\u7a3f\u4eba\u3002\u8fd9\u5c31\u50cf\u8def\u4eba\u5e2e\u4e86\u4f60\u7684\u5fd9\u540e\u4f60\u8bf4\u58f0\u201c\u8c22\u8c22\u201d\u4e00\u6837\uff0c\u5c3d\u7ba1\u4f60\u5e76\u4e0d\u77e5\u9053\u90a3\u4e2a\u4eba\u7684\u540d\u5b57\u3002<\/span><\/p>\n

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

8\uff09\u6587\u732e<\/span><\/strong><\/p>\n


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

\u6587\u732e\u4e00\u5b9a\u8981\u7edf\u4e00\u683c\u5f0f\u3002\u8fd9\u5e76\u4e0d\u662f\u53ef\u6709\u53ef\u65e0\u7684\u5c0f\u4e8b\uff0c\u800c\u662f\u5341\u5206\u8981\u7d27\u7684\uff0c\u662f\u79d1\u6280\u6587\u7ae0\u5370\u5237\u51fa\u7248\u7684\u4e00\u4e2a\u57fa\u672c\u8981\u6c42\u3002\u4e0d\u8981\u7b80\u5355\u5730\u628a\u6587\u732e\u4ece\u5404\u79cd\u6742\u5fd7\u6284\u8fc7\u6765\uff0c\u7136\u540e\u5806\u653e\u5728\u4e00\u8d77\u4e86\u4e8b\u3002<\/span><\/p>\n


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\u603b\u800c\u8a00\u4e4b\uff0c\u5199\u597d\u4e00\u7bc7\u79d1\u6280\u8bba\u6587\u7edd\u5bf9\u4e0d\u662f\u4e00\u4ef6\u5bb9\u6613\u7684\u4e8b\u3002<\/span><\/p>\n


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\u6700\u540e\uff0c\u7b14\u8005\u63d0\u5021\u5927\u5bb6\u591a\u5199\u77ed\u6587\u3002<\/span><\/p>\n


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\u5f88\u591a\u9ad8\u6c34\u5e73\u7684\u79d1\u6280\u8bba\u6587\u90fd\u5f88\u77ed\uff0c\u5373\u6240\u8c13\u201cshort but good\u201d\u3002\u4f8b\u5982\uff0c\u300a\u81ea\u7136\u300b\u520a\u767b\u8fc7\u591a\u7bc7\u540e\u6765\u83b7\u5f97\u8bfa\u8d1d\u5c14\u5956\u7684\u539f\u521b\u8bba\u6587\u90fd\u662f\u77ed\u5c0f\u7684\u6210\u679c\u516c\u544a\u5f0f\u7684\u77ed\u7bc7\uff0c\u5305\u62ec\u5c45\u91cc\u592b\u4eba\u7684\u5973\u513f\u548c\u5973\u5a7f1935\u5e74\u83b7\u8bfa\u8d1d\u5c14\u5316\u5b66\u5956\u7684\u5173\u952e\u6587\u7ae0\uff0c\u53ea\u6709620\u4e2a\u5355\u8bcd\u548c\u4e00\u6761\u5316\u5b66\u65b9\u7a0b\u5f0f[6]\uff1b\u6c83\u987f\u548c\u514b\u91cc\u514b1962\u5e74\u56e0DNA\u53cc\u87ba\u65cb\u7ed3\u6784\u83b7\u8bfa\u8d1d\u5c14\u533b\u5b66\u5956\u7684\u5173\u952e\u6587\u7ae0\uff0c\u53ea\u67091100\u4e2a\u5355\u8bcd\u548c\u4e00\u5e45\u56fe[7]\u3002\u7c7b\u4f3c\u7684\u4f8b\u5b50\u5f88\u591a\uff0c\u6bd4\u5982\u7eb3\u4ec0<\/span>\uff08Nash\uff09<\/span>\u83b71994\u5e74\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5b66\u5956\u7684\u201c\u535a\u5f08\u5747\u8861\u7406\u8bba\u201d\u6839\u690d\u4e8e\u4ed61950\u5e74\u5b8c\u6210\u768426\u9875\u666e\u6797\u65af\u987f\u535a\u58eb\u8bba\u6587[8]\uff0c\u5176\u4e3b\u8981\u5185\u5bb9\u4e8e\u540c\u5e74\u5728\u7f8e\u56fd\u79d1\u5b66\u9662\u9662\u62a5PNAS<\/em>\u4e0a\u53d1\u8868\u65f6\u53ea\u670928\u884c\u6587\u5b57[9]\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd8\u6709\u66f4\u77ed\u7684\u535a\u58eb\u8bba\u6587\u548c\u5960\u57fa\u6027\u5b66\u672f\u8bba\u6587\u3002\u8fd9\u4e9b\u90fd\u8868\u660e\uff0c\u4e00\u7bc7\u6587\u7ae0\u7684\u8d28\u91cf\u5e76\u4e0d\u662f\u7531\u5b83\u7684\u957f\u5ea6\u6765\u51b3\u5b9a\u7684\u3002<\/span><\/p>\n


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

[1] \u738b\u54c1\u829d\u3001\u987e\u51cc\u6587\uff0c\u201c\u5927\u5b66\u751f\u4e0d\u4f1a\u5199\u8bba\u6587\uff0c\u600e\u4e48\u7834\uff1a88.0%\u53d7\u8bbf\u8005\u8ba4\u4e3a\u5927\u5b66\u5e94\u5f00\u8bbe\u8bba\u6587\u5199\u4f5c\u8bfe\u7a0b\u201d\uff0c\u4e2d\u56fd\u9752\u5e74\u62a5\uff0c2018\u5e7411\u670801\u65e5\uff0807 \u7248\uff09\u3002\u7f51\u9875\uff1a<\/span><\/p>\n

http:\/\/zqb.cyol.com\/html\/2018-11\/01\/nw.D110000zgqnb_20181101_2-07.htm<\/span><\/p>\n

[2] Boer Deng, “Papers with shorter titles get more citations: Intriguing correlation mined from 140,000 papers,” Nature, 26 August 2015. Web:<\/span><\/p>\n

https:\/\/www.nature.com\/news\/papers-with-shorter-titles-get-more-citations-1.18246<\/span><\/p>\n

[3] Adrian Letchford, Helen Susannah Moat and Tobias Preis, “The advantage of short paper titles,” Royal Society Open Science, 1 August 2015. Web:<\/span><\/p>\n

https:\/\/royalsocietypublishing.org\/doi\/10.1098\/rsos.150266<\/span><\/p>\n

[4] Philip Ball, “\u2018Novel, amazing, innovative\u2019: positive words on the rise in science papers — Analysis suggests an increasing tendency to exaggerate and polarize results,” Nature, 14 December 2015. Web:<\/span><\/p>\n

https:\/\/www.nature.com\/news\/novel-amazing-innovative-positive-words-on-the-rise-in-science-papers-1.19024<\/span><\/p>\n

[5] Andrew Moore, “The long sentence: A disservice to science in the Internet age,” Bioessays 33: 893, 2011.<\/span><\/p>\n

[6] Fr\u00e9d\u00e9ric Joliot and Ir\u00e8ne Curie, “Artificial production of a new kind of radio-element,” Nature, 133: 201-202, 1934.<\/span><\/p>\n

[7] James D. Watson and Francis Crick, “Molecular structure of nucleic acids: A structure for Deoxyribose Nucleic Acid,” Nature, 171: 737-738, 1953.<\/span><\/p>\n

[8] John Nash, Non-cooperative Games, Ph.D. Dissertation, Princeton University, 1950.<\/span><\/p>\n

[9] John Nash, “Equilibrium points in N-person games,” Proceedings of the National Academy of Sciences, 36: 48-49, 1950.<\/span><\/p>\n


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