{"id":109827,"date":"2025-07-28T01:01:44","date_gmt":"2025-07-28T05:01:44","guid":{"rendered":"https:\/\/minzhuzhongguo.org\/?p=109827"},"modified":"2025-07-27T17:08:20","modified_gmt":"2025-07-27T21:08:20","slug":"%e6%b1%9f%e6%a3%8b%e7%94%9f%ef%bc%9a%e6%97%b6%e9%97%b4%e9%97%b4%e9%9a%94%e5%ba%94%e8%af%a5%e7%94%a8%e6%97%b6%e9%97%b4%e5%9d%90%e6%a0%87-%e6%94%b9%e5%8f%98%e9%87%8f%e7%9a%84%e7%bb%9d%e5%af%b9%e5%80%bc","status":"publish","type":"post","link":"https:\/\/minzhuzhongguo.org\/?p=109827","title":{"rendered":"\u6c5f\u68cb\u751f\uff1a\u65f6\u95f4\u95f4\u9694\u5e94\u8be5\u7528\u65f6\u95f4\u5750\u6807 \u6539\u53d8\u91cf\u7684\u7edd\u5bf9\u503c\u6765\u8868\u5f81"},"content":{"rendered":"

\u5728\u7269\u7406\u5b66\u4e2d\uff0c\u4eba\u4eec\u719f\u77e5\uff1a\u65f6\u95f4\u95f4\u9694\u662f\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\uff08\u65f6\u95f4\u5750\u6807\u589e\u91cf\uff09\u0394t\u6765\u8868\u5f81\u7684\u3002<\/p>\n

\u672c\u6587\u901a\u8fc7\u5bf9\u987a\u8ba1\u65f6\u4e0e\u5012\u8ba1\u65f6\u4e24\u79cd\u4e0d\u540c\u8ba1\u65f6\u65b9\u5f0f\u7684\u8003\u5bdf\uff0c\u63d0\u51fa\u4e00\u79cd\u65b0\u7684\u770b\u6cd5\uff0c\u8ba4\u4e3a\u5728\u987a\u8ba1\u65f6\u4e0b\uff08\u65f6\u95f4\u5750\u6807\u4e3at\uff09\uff0c\u65f6\u95f4\u95f4\u9694\u81ea\u7136\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u0394t \u6765\u8868\u5f81\uff1b\u800c\u5728\u5012\u8ba1\u65f6\u4e0b\uff08\u65f6\u95f4\u5750\u6807\u4e3a\uf074\uff09\uff0c\u5219\u5fc5\u987b\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7684\u76f8\u53cd\u6570\u2014\u0394\uf074\u6765\u8868\u5f81\u3002<\/p>\n

\u628a\u4e24\u79cd\u505a\u6cd5\u7edf\u4e00\u8d77\u6765\uff0c\u5219\u6709\uff1a\u65f6\u95f4\u95f4\u9694\u5e94\u8be5\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7684\u7edd\u5bf9\u503c\u6765\u8868\u5f81\u3002<\/p>\n

\u4e00\u3001\u4ec0\u4e48\u53eb\u65f6\u95f4\u95f4\u9694\uff1f<\/p>\n

\u901a\u5e38\u4eba\u4eec\u6240\u8bf4\u7684\u65f6\u95f4\uff0c\u5305\u542b\u201c\u65f6\u523b\u201d\u4e0e\u201c\u65f6\u95f4\u95f4\u9694\u201d\u4e24\u4e2a\u5185\u5bb9\u3002\u201c\u65f6\u523b\u201d\u662f\u6307\u67d0\u4e8b\u4ef6\u53d1\u751f\u7684\u77ac\u95f4\uff0c\u4f8b\u5982\u9ad8\u94c1\u5217\u8f66\u5728\u4e0a\u534810\u70b915\u5206\u5f00\u51fa\u3002\u201c\u65f6\u95f4\u95f4\u9694\u201d\u662f\u6307\u4e0d\u540c\u77ac\u65f6\u4e4b\u95f4\u7684\u4e00\u6bb5\u65f6\u95f4\uff0c\u7528\u6765\u8bf4\u660e\u67d0\u4e00\u4e8b\u4ef6\u6301\u7eed\u7684\u4e45\u6682\uff0c\u4f8b\u5982\u4e00\u573a\u8db3\u7403\u8e22\u4e861\u4e2a\u534a\u5c0f\u65f6\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u65f6\u523b\u662f\u8868\u793a\u4ec0\u4e48\u65f6\u5019\uff0c\u65f6\u95f4\u95f4\u9694\u662f\u8868\u793a\u67d0\u6bb5\u65f6\u95f4\u6709\u591a\u957f\u3002
\n\u4e0d\u8a00\u800c\u55bb\uff0c\u65f6\u95f4\u95f4\u9694\u4e0d\u80fd\u662f\u8d1f\u6570\uff0c\u5982\u20145\u79d2\uff0c\u201430\u5206\u949f\uff1b\u5b83\u662f\u6b63\u5b9a\u7684\uff0c\u5373\u53ea\u80fd\u53d6\u6b63\u6570\uff0c\u59825\u79d2\uff0c30\u5206\u949f\uff0c6\u5c0f\u65f6\u7b49\u7b49\u3002\u5982\u679c\u6709\u4eba\u8bf4\uff1a\u4ed6\u8d7020\u7c73\u8def\u82b1\u4e86\u20145\u79d2\u3002\u522b\u4eba\u4f1a\u4ee5\u4e3a\uff0c\u4ed6\u53ef\u80fd\u662f\u679c\u514b\u661f\u7403\u7684\u667a\u6167\u751f\u7269\u3002<\/p>\n

\u4e8c\u3001\u4ec0\u4e48\u662f\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\uff1f<\/p>\n

\u7269\u7406\u5b66\u4e2d\uff0c\u4eba\u4eec\u91c7\u7528\u53c2\u6570t\u6765\u8868\u793a\u65f6\u95f4\u5750\u6807\u3002\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u5c31\u662f\uff1a\u7528\u8f83\u665a\u65f6\u523b\u7684\u65f6\u95f4\u5750\u6807\u503c\u51cf\u53bb\u8f83\u65e9\u65f6\u523b\u7684\u65f6\u95f4\u5750\u6807\u503c\u5f97\u5230\u7684\u91cf\u3002\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7528\u7b26\u53f7\u0394t \u6765\u8868\u793a\uff0c\u8f83\u665a\u65f6\u523b\u548c\u8f83\u65e9\u65f6\u523b\u5206\u522b\u7528t\u665a\u548ct\u65e9\u6765\u8868\u793a\uff0c\u4e8e\u662f\u6709\uff1a
\n\u0394t = t\u665a\u2014t \u65e9\u00a0 (1)
\n.
\n\u4e09\u3001\u65f6\u95f4\u95f4\u9694\u4e0e\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7684\u7edd\u5bf9\u503c<\/p>\n

\u7269\u7406\u5b66\u4e2d\uff0c\u65f6\u95f4\u95f4\u9694\u7531\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u0394t \u6765\u8868\u5f81\u3002
\n1\u3001\u8fd9\u4e00\u505a\u6cd5\uff0c\u5728\u987a\u8ba1\u65f6\u4e0b\u6ca1\u5565\u95ee\u9898\u3002
\n\u8fd9\u4e2a\u6ca1\u5565\u95ee\u9898\uff0c\u5e76\u4e0d\u662f\u8bf4t\u53ea\u80fd\u53d6\u6b63\u503c\u3002\u65f6\u95f4\u5750\u6807t\u6709\u8ba1\u65f6\u96f6\u70b9\uff1at0=0 \uff1b\u6bd4\u8ba1\u65f6\u96f6\u70b9\u8f83\u665a\u7684\u65f6\u523bt\u81ea\u7136\u53d6\u6b63\u503c\uff0c\u800c\u6bd4\u8ba1\u65f6\u96f6\u70b9\u8f83\u65e9\u7684\u65f6\u523bt\u5219\u53d6\u8d1f\u503c\u3002
\n\u6ca1\u5565\u95ee\u9898\u662f\u6307\uff0c\u987a\u8ba1\u65f6\u7684\u65f6\u95f4\u5750\u6807t\u662f\u5355\u8c03\u9012\u589e\u7684\uff0c\u8f83\u665a\u65f6\u523b\u7684\u65f6\u95f4\u5750\u6807\u503ct \u665a\uff0c\u603b\u662f\u5927\u4e8e\u8f83\u65e9\u65f6\u523b\u7684\u65f6\u95f4\u5750\u6807\u503ct\u65e9\uff0c\u5373t\u665a>t\u65e9
\n\uff0c\u56e0\u800c\u53ef\u4ee5\u4fdd\u8bc1\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u0394t\u4e3a\u6b63\u503c\uff1a
\n\u0394t = t\u665a\u2014t \u65e9> 0.\u00a0 (2)
\n2\u3001\u8fd9\u4e00\u505a\u6cd5\uff0c\u5728\u5012\u8ba1\u65f6\u4e0b\u5c31\u884c\u4e0d\u901a\u4e86\u3002
\n\u5728\u5012\u8ba1\u65f6\u4e0b\uff0c\u4e0d\u59a8\u91c7\u7528\u53c2\u6570\uf074\u6765\u8868\u793a\u65f6\u95f4\u5750\u6807\u3002\u4e8e\u662f\uff0c\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u0394\uf074\u4e3a\uff1a\u8f83\u665a\u65f6\u523b\u7684\u5750\u6807\u503c\uf074\u665a\u51cf\u53bb\u8f83\u65e9\u65f6\u523b\u7684\u503c\uf074\u65e9
\n\u6240\u5f97\u5230\u7684\u91cf\uff0c\u5373
\n\u0394\uf074 = \uf074 \u665a\u2014\uf074 \u65e9 (3)
\n.\u7531\u4e8e\uf074 \u662f\u5355\u8c03\u9012\u51cf\u7684\uff0c\u5176\u8f83\u665a\u65f6\u523b\u7684\u503c\u603b\u662f\u5c0f\u4e8e\u8f83\u65e9\u65f6\u523b\u7684\u503c\uff0c\u5373\uf074\u665a< \uf074\u65e9\uff0c\u56e0\u800c\u603b\u6709
\n\u0394\uf074 = \uf074 \u665a\u2014\uf074 \u65e9<0. (4)
\n\u663e\u7136\uff0c\u53ea\u80fd\u53d6\u6b63\u503c\u7684\u65f6\u95f4\u95f4\u9694\uff0c\u5c31\u4e0d\u80fd\u518d\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u0394\uf074\u6765\u8868\u5f81\uff0c\u800c\u5e94\u6539\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7684\u76f8\u53cd\u6570 \u2014\u0394\uf074\u6765\u8868\u5f81\uff1a
\n\u2014\u0394\uf074 = \uf074 \u65e9\u2014\uf074 \u665a>0. (5)
\n3\u3001\u628a\u987a\u5012\u8ba1\u65f6\u4e24\u79cd\u65b9\u5f0f\u7efc\u5408\u8d77\u6765\u8003\u8651\uff0c\u5219\u6709\u7edf\u4e00\u8bf4\u6cd5\u5982\u4e0b\uff1a\u65f6\u95f4\u95f4\u9694\u5e94\u8be5\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7684\u7edd\u5bf9\u503c\u6765\u8868\u5f81\u3002\u5373\u5728\u987a\u8ba1\u65f6\u4e0b\uff0c\u65f6\u95f4\u95f4\u9694\u4e3a
\n|\u0394t|=\u0394t = > 0 \uff1b (6)
\n\u5728\u5012\u8ba1\u65f6\u4e0b\uff0c\u65f6\u95f4\u95f4\u9694\u4e3a
\n|\u0394\uf074 |=\u2014\u0394\uf074 >0. (7)<\/p>\n

\u56db\u3001\u987a\u5012\u8ba1\u65f6\u65b9\u5f0f\u4e0b\u7684\u901f\u5ea6\u516c\u5f0f<\/p>\n

\u4f5c\u4e3a\u6211\u4eec\u65b0\u89c1\u89e3\u7684\u4e00\u79cd\u5e94\u7528\uff0c\u6211\u4eec\u6765\u5206\u6790\u4e00\u4e0b\u8d28\u70b9\u7684\u901f\u5ea6\u516c\u5f0f\u3002\u8003\u8651\u4e00\u79cd\u7b80\u5355\u60c5\u5f62\uff1a\u5c31\u8d28\u70b9\u671dx\u8f74\u6b63\u5411\u7684\u67d0\u4e00\u76f4\u7ebf\u8fd0\u52a8\uff0c\u4e24\u4f4d\u89c2\u5bdf\u8005\u5206\u522b\u7528\u987a\u8ba1\u65f6\u548c\u5012\u8ba1\u65f6\u65b9\u5f0f\u52a0\u4ee5\u8003\u5bdf\u3002<\/p>\n

\"\"<\/p>\n

\u56fe \u8d28\u70b9\u76f4\u7ebf\u8fd0\u52a8\u793a\u610f\u56fe<\/p>\n

\u8bbe\u8d28\u70b9\u4ecex1\u51fa\u53d1\u8fd0\u52a8\u5230x2\u3002\u91c7\u7528\u987a\u8ba1\u65f6\u7684\u89c2\u5bdf\u8005\u628a\u8d28\u70b9\u51fa\u53d1\u65f6\u523b\u8bb0\u4e3at\u65e9\uff0c\u628a\u5230\u8fbe\u65f6\u523b\u8bb0\u4e3at\u665a\uff0c\u5219\u65f6\u95f4\u95f4\u9694\u4e3a
\n|\u0394t|=\u0394t = t\u665a\u2014t\u65e9> 0. (8)<\/p>\n

\u5728\u65f6\u95f4\u95f4\u9694\u0394t \u5185\uff0c\u8d28\u70b9\u7684\u4f4d\u79fb\u4e3a
\n\u0394x=x2 \u2014 x1. (9)<\/p>\n

\u4e8e\u662f\uff0c\u8d28\u70b9\u5728\u8fd9\u6bb5\u65f6\u95f4\u5185\u7684\u5e73\u5747\u901f\u5ea6\u4e3a
\nv=A x\/At.\u00a0 \u00a0(10)<\/p>\n

\u5bf9\u540c\u4e00\u8d28\u70b9\u8fd0\u52a8\uff0c\u91c7\u7528\u5012\u8ba1\u65f6\u7684\u89c2\u5bdf\u8005\u628a\u8d28\u70b9\u51fa\u53d1\u65f6\u523b\u8bb0\u4e3a\uf074\u65e9\uff0c\u628a\u5230\u8fbe\u65f6\u523b\u8bb0\u4e3a\uf074\u665a\uff0c\u5219\u65f6\u95f4\u95f4\u9694\u4e3a
\n|\u0394\uf074|=\u2014\u0394\uf074=\uf074\u65e9\u2014\uf074\u665a>0. (11)<\/p>\n

\u5728\u65f6\u95f4\u95f4\u9694\u2014\u0394\uf074\u5185\uff0c\u8d28\u70b9\u7684\u4f4d\u79fb\u4e3a\u0394x\uff1b\u8d28\u70b9\u5728\u8fd9\u6bb5\u65f6\u95f4\u5185\u7684\u5e73\u5747\u901f\u5ea6\u4e3a
\nV\u5012= \/ A x\/A \uf074 (12)
\n\u7531
\n\u2014\u0394\uf074=\u0394t, (13)
\n\u5f97\u5230
\nv\u987a= v \u5012 (14)
\n\u663e\u7136\uff0c\u8fd9\u662f\u6b63\u786e\u7684\u7ed3\u679c\u3002<\/p>\n

\u5982\u679c\u91c7\u7528\u5012\u8ba1\u65f6\u7684\u89c2\u5bdf\u8005\uff0c\u4e60\u4ee5\u4e3a\u5e38\u5730\u4ee5\u4e3a\u65f6\u95f4\u95f4\u9694\u4ecd\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u0394\uf074\u6765\u8868\u5f81\uff0c\u5219\u5c31\u4f1a\u5199\u4e0b\u5982\u4e0b\u5e73\u5747\u901f\u5ea6\u516c\u5f0f\uff1a<\/p>\n

v\u5012=Ax \/A\uf02d=Ax\u00a0 \/\u2014At=\u2014 v \u987a\u00a0 (15)<\/p>\n

\u8fd9\u6837\uff0c\u5728\u4ed6\u773c\u91cc\u5206\u660e\u662f\u671dx\u8f74\u6b63\u5411\u8fd0\u52a8\u7684\u8d28\u70b9\uff0c\u4e0a\u8ff0\u901f\u5ea6\u516c\u5f0f\u5374\u8352\u5510\u5730\u8868\u793a\uff1a\u8d28\u70b9\u662f\u671dx\u8f74\u4e4b\u8d1f\u5411\u2014\u2014x’\u65b9\u5411\u5728\u8fd0\u52a8\uff01
\n\u65e0\u7591\uff0c\u5f0f(15)\u662f\u9519\u8bef\u7684\u3002
\n\u5f0f(15)\u7684\u9519\u8bef\uff0c\u63d0\u793a\u6211\u4eec\u8981\u7279\u522b\u6ce8\u610f\uff1a\u65f6\u95f4\u53cd\u6f14\u7269\u7406\u5b66\u4e2d\u7684\u6240\u8c13\u201c\u901f\u5ea6\u53cd\u5411\u201d\uff0c\u7a76\u7adf\u662f\u4ec0\u4e48\u540d\u5802\u3002<\/p>\n

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