{"id":158,"date":"2026-08-15T13:42:03","date_gmt":"2026-08-15T05:42:03","guid":{"rendered":"http:\/\/192.168.1.219:5488\/?p=158"},"modified":"2026-08-15T13:42:05","modified_gmt":"2026-08-15T05:42:05","slug":"%e5%bc%b9%e6%80%a7","status":"publish","type":"post","link":"https:\/\/note.kazamata.uk\/index.php\/2026\/08\/15\/%e5%bc%b9%e6%80%a7\/","title":{"rendered":"\u5f39\u6027"},"content":{"rendered":"\n

\u9700\u6c42\u91cf\u6216\u4f9b\u7ed9\u91cf\u76f8\u5e94\u4e8e\u5176\u5f71\u54cd\u56e0\u7d20\u800c\u53d8\u52a8\u7684\u654f\u611f\u7a0b\u5ea6\u901a\u5e38\u662f\u7531\u5f39\u6027\u7cfb\u6570\u6765\u51b3\u5b9a\u7684<\/p>\n\n\n\n

\u5982\u679c\u4e00\u4e2a\u7ecf\u6d4e\u91cfx\u5bf9\u4e8e\u53e6\u4e00\u4e2a\u7ecf\u6d4e\u91cfy\u4ea7\u751f\u5f71\u54cd\uff0c\u90a3\u4e48\u53cd\u6620y\u76f8\u5e94\u4e8ex\u7684\u654f\u611f\u7a0b\u5ea6\u5c31\u7528y\u7684\u53d8\u52a8\u767e\u5206\u6bd4\u4e0ex\u7684\u53d8\u52a8\u767e\u5206\u6bd4\u8fdb\u884c\u6bd4\u8f83<\/p>\n\n\n\n

\u5f39\u6027\u516c\u5f0f<\/p>\n\n\n\n

\ud835\udc72<\/mi>=<\/mo>(<\/mo>\ud835\udc9a<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc9a<\/mi>0<\/mn><\/msub>)<\/mo><\/mrow>\ud835\udc9a<\/mi><\/mfrac>(<\/mo>\ud835\udc99<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc99<\/mi>0<\/mn><\/msub>)<\/mo><\/mrow>\ud835\udc99<\/mi><\/mfrac><\/mfrac><\/mrow>\\boldsymbol{K}=\\frac{\\frac{({\\boldsymbol{y}}_{1}-{\\boldsymbol{y}}_{0})}{\\boldsymbol{y}}}{\\frac{({\\boldsymbol{x}}_{1}-{\\boldsymbol{x}}_{0})}{\\boldsymbol{x}}}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u4ef7\u683c\u5f39\u6027\uff1a<\/strong><\/p>\n\n\n\n

\u4e00\u79cd\u5546\u54c1\u7684\u9700\u6c42\u91cf\u76f8\u5bf9\u53d8\u52a8\u7a0b\u5ea6\u76f8\u5e94\u4e8e\u4ef7\u683c\u76f8\u5bf9\u53d8\u52a8\u7684\u53cd\u5e94\u7a0b\u5ea6<\/strong><\/p>\n\n\n\n

\u901a\u4fd7\u800c\u8a00\u4ef7\u683c\u53d8\u5316\uff0c\u5f15\u8d77\u9700\u6c42\u7684\u5f3a\u70c8\u53d8\u5316\uff0c\u5219\u4e3a\u654f\u611f\u5ea6\u9ad8\uff0c\u4ef7\u683c\u5f39\u6027\u7cfb\u6570\u5927<\/strong><\/p>\n\n\n\n

\u4ef7\u683c\u53d8\u5316\uff0c\u5f15\u8d77\u9700\u6c42\u7684\u7f13\u6162\u53d8\u5316\u751a\u81f3\u4e0d\u53d1\u751f\u53d8\u5316\uff0c\u5219\u4e3a\u654f\u611f\u5ea6\u4f4e\uff0c\u4ef7\u683c\u5f39\u6027\u7cfb\u6570\u5c0f<\/strong><\/p>\n\n\n\n

\u9700\u6c42\u4ef7\u683c\u5f39\u6027\u7cfb\u6570\uff1a<\/strong><\/p>\n\n\n\n

\ud835\udc6c<\/mi> <\/mtext>\ud835\udc91<\/mi><\/mrow><\/msub>=<\/mo>|<\/mo>\ud835\udc78<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc78<\/mi>0<\/mn><\/msub><\/mrow>\ud835\udc78<\/mi><\/mfrac>\ud835\udc77<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc77<\/mi>0<\/mn><\/msub><\/mrow>\ud835\udc77<\/mi><\/mfrac><\/mfrac>|<\/mo><\/mrow><\/mrow>{\\boldsymbol{E}}_{\\ \\boldsymbol{p}}=\\left|\\frac{\\frac{{\\boldsymbol{Q}}_{1}-{\\boldsymbol{Q}}_{0}}{\\boldsymbol{Q}}}{\\frac{{\\boldsymbol{P}}_{1}-{\\boldsymbol{P}}_{0}}{\\boldsymbol{P}}}\\right|<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u516c\u5f0f\u4ee3\u8868\u7740<\/strong><\/p>\n\n\n\n

\u4ef7\u683c\u5f39\u6027\u7cfb\u6570=\\frac{\u9700\u6c42\u91cf\u53d8\u52a8\u7684\u767e\u5206\u6bd4}{\u4ef7\u683c\u53d8\u52a8\u7684\u767e\u5206\u6bd4}<\/p>\n\n\n\n

\u5176\u4e2d\u8981\u6c42\u4ef7\u683c\u5f39\u6027\u7cfb\u6570\u8981\u4e3a\u6b63\u6570<\/strong><\/p>\n\n\n\n

\u5f53<\/strong><\/p>\n\n\n\n

\ud835\udc6c<\/mi>\ud835\udc91<\/mi><\/msub>=<\/mo>0<\/mn><\/mrow>{\\boldsymbol{E}}_{\\boldsymbol{p}}=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u4ee3\u8868\u7740\u5b8c\u5168\u65e0\u5f39\u6027\uff0c\u4ef7\u683c\u600e\u4e48\u53d8\u52a8\u90fd\u4e0d\u4f1a\u5f15\u8d77\u9700\u6c42\u7684\u53d8\u52a8\uff0c\u6bd4\u5982\u98df\u76d0<\/strong><\/p>\n\n\n\n

\u5f53<\/strong><\/p>\n\n\n\n

0<\/mn><<\/mo>\ud835\udc6c<\/mi><\/mrow>\ud835\udc91<\/mi><\/msub><<\/mo>1<\/mn><\/mrow>{0\\lt \\boldsymbol{E}}_{\\boldsymbol{p}}\\lt 1<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u4ee3\u8868\u7740\u9700\u6c42\u7f3a\u4e4f\u5f39\u6027\uff0c\u8868\u660e\u4ef7\u683c\u53d8\u52a81%\uff0c\u9700\u6c42\u53d8\u52a8\u6027\u5c0f\u4e8e1%<\/strong><\/p>\n\n\n\n

\u5f53<\/strong> <\/p>\n\n\n\n

\ud835\udc6c<\/mi>\ud835\udc91<\/mi><\/msub>=<\/mo>1<\/mn><\/mrow>{\\boldsymbol{E}}_{\\boldsymbol{p}}=1<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u4ee3\u8868\u7740\u5355\u4f4d\u5f39\u6027\uff0c\u8868\u660e\u4ef7\u683c\u53d8\u52a81%\uff0c\u9700\u6c42\u53d8\u52a8\u4e5f\u4e3a1%<\/strong><\/p>\n\n\n\n

\u5f53<\/strong><\/p>\n\n\n\n

1<\/mn><<\/mo>\ud835\udc6c<\/mi><\/mrow>\ud835\udc91<\/mi><\/msub><<\/mo>\u221e<\/mi><\/mrow>{1\\lt \\boldsymbol{E}}_{\\boldsymbol{p}}\\lt \\infty <\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u4ee3\u8868\u7740\u9700\u6c42\u5bcc\u6709\u5f39\u6027\uff0c\u8868\u660e\u4ef7\u683c\u53d8\u52a81%\uff0c\u9700\u6c42\u53d8\u52a8\u5927\u4e8e1%<\/strong><\/p>\n\n\n\n

\u5f53<\/strong> <\/p>\n\n\n\n

\ud835\udc6c<\/mi>\ud835\udc91<\/mi><\/msub>=<\/mo>+<\/mo>\u221e<\/mi><\/mrow>{\\boldsymbol{E}}_{\\boldsymbol{p}}=+\\infty <\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u4ee3\u8868\u7740\u9700\u6c42\u4e3a\u5b8c\u5168\u5f39\u6027\uff0c\u8868\u660e\u4ef7\u683c\u53d8\u52a81%\uff0c\u9700\u6c42\u6025\u5267\u53d8\u52a8<\/strong><\/p>\n\n\n\n

\u4ef7\u683c\u5f39\u6027\u7684\u5f71\u54cd\u56e0\u7d20\uff1a<\/strong><\/p>\n\n\n\n

    \n
  1. \u5546\u54c1\u7684\u91cd\u8981\u7a0b\u5ea6\uff1a\u5546\u54c1\u8d8a\u91cd\u8981\uff0c\u4ef7\u683c\u4e0a\u5347\u540e\u6d88\u8d39\u8005\u8d8a\u4e0d\u613f\u610f\u6539\u53d8\u5176\u9700\u6c42\u91cf\uff0c\u6362\u8a00\u4e4b\u5176\u4ef7\u683c\u5f39\u6027\u7cfb\u6570\u4f4e\uff08\u5982\u7ef4\u6301\u751f\u6d3b\u7684\u91cd\u8981\u7269\u54c1\uff0c\u4f8b\u5982\u98df\u76d0\uff09<\/strong><\/li>\n\n\n\n
  2. \u5546\u54c1\u7684\u53ef\u66ff\u4ee3\u7a0b\u5ea6\uff08\u53ef\u66ff\u4ee3\u7a0b\u5ea6\u8d8a\u9ad8\uff0c\u6d88\u8d39\u8005\u5bf9\u4ef7\u683c\u53d8\u5316\u66f4\u52a0\u654f\u611f\uff0c\u56e0\u4e3a\u4ed6\u4eec\u53ef\u4ee5\u9009\u62e9\u5176\u4ed6\u5546\u54c1\u5f53\u4f5c\u66ff\u8865\uff09<\/strong><\/li>\n\n\n\n
  3. \u5546\u54c1\u7684\u6d88\u8d39\u652f\u51fa\u5360\u603b\u652f\u51fa\u7684\u6bd4\u91cd\uff0c\u652f\u51fa\u5360\u6bd4\u8d8a\u5927\u7684\u5546\u54c1\u6d88\u8d39\u8005\u66f4\u52a0\u8c28\u614e\uff0c\u5176\u4ef7\u683c\u654f\u611f\u7a0b\u5ea6\u5c31\u8d8a\u9ad8\uff0c\u4ef7\u683c\u5f39\u6027\u66f4\u5927<\/strong><\/li>\n\n\n\n
  4. \u8c03\u6574\u65f6\u95f4\u7684\u957f\u77ed<\/strong><\/li>\n<\/ol>\n\n\n\n

    \u5f27\u5f39\u6027\u7cfb\u6570\uff1a<\/strong><\/p>\n\n\n\n

    \ud835\udc6c<\/mi>\ud835\udc91<\/mi><\/msub>=<\/mo>|<\/mo>\ud835\udc78<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc78<\/mi>0<\/mn><\/msub><\/mrow>\ud835\udc78<\/mi>1<\/mn><\/msub>+<\/mo>\ud835\udc78<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac>\ud835\udc77<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc77<\/mi>0<\/mn><\/msub><\/mrow>\ud835\udc77<\/mi>1<\/mn><\/msub>+<\/mo>\ud835\udc77<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac><\/mfrac>|<\/mo><\/mrow><\/mrow>{\\boldsymbol{E}}_{\\boldsymbol{p}}=\\left|\\frac{\\frac{{\\boldsymbol{Q}}_{1}-{\\boldsymbol{Q}}_{0}}{{\\boldsymbol{Q}}_{1}+{\\boldsymbol{Q}}_{0}}}{\\frac{{\\boldsymbol{P}}_{1}-{\\boldsymbol{P}}_{0}}{{\\boldsymbol{P}}_{1}+{\\boldsymbol{P}}_{0}}}\\right|\n\n<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

    \u70b9\u5f39\u6027\u7cfb\u6570\uff1a<\/strong><\/p>\n\n\n\n

    \ud835\udc6c<\/mi>\ud835\udc91<\/mi><\/msub>=<\/mo>|<\/mo>\ud835\udc25<\/mi>\ud835\udc22<\/mi>\ud835\udc26<\/mi><\/mrow>\ud835\udeab<\/mi>\ud835\udc91<\/mi><\/mrow>\u2192<\/mo>0<\/mn><\/mrow><\/munder><\/mrow><\/mrow>\u2061<\/mo><\/mspace>\ud835\udeab<\/mi>\ud835\udc78<\/mi><\/mrow>\ud835\udc78<\/mi><\/mfrac>\ud835\udeab<\/mi>\ud835\udc77<\/mi><\/mrow>\ud835\udc77<\/mi><\/mfrac><\/mfrac>|<\/mo><\/mrow><\/mrow>{\\boldsymbol{E}}_{\\boldsymbol{p}}=\\left|\\operatorname{\\underset{\\boldsymbol{\\Delta p}\\rightarrow 0}{\\mathbf{lim}}}{\\frac{\\frac{\\boldsymbol{\\Delta Q}}{\\boldsymbol{Q}}}{\\frac{\\boldsymbol{\\Delta P}}{\\boldsymbol{P}}}}\\right|<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

    \u9700\u6c42\u7684\u6536\u5165\u5f39\u6027<\/a><\/h3>\n\n\n\n

    \u6536\u5165\u5f39\u6027\uff1a\u5728\u4e00\u5b9a\u65f6\u671f\u5185\uff0c\u6d88\u8d39\u8005\u5bf9\u67d0\u79cd\u5546\u54c1\u9700\u6c42\u91cf\u7684\u76f8\u5bf9\u53d8\u52a8\u76f8\u5e94\u4e8e\u6d88\u8d39\u8005\u6536\u5165\u53d8\u52a8\u7684\u654f\u611f\u7a0b\u5ea6<\/strong><\/p>\n\n\n\n

    \u901a\u4fd7\u800c\u8a00\u5c31\u662f\u8ba8\u8bba\u9700\u6c42\u91cf\u4e0e\u6536\u5165\u7684\u654f\u611f\u7a0b\u5ea6<\/strong><\/p>\n\n\n\n

    \u9700\u6c42\u7684\u5f39\u6027\u7cfb\u6570\uff1a<\/strong><\/p>\n\n\n\n

    \ud835\udc6c<\/mi>\ud835\udc8e<\/mi><\/msub>=<\/mo>\ud835\udc78<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc78<\/mi>0<\/mn><\/msub><\/mrow>\ud835\udc78<\/mi><\/mfrac>\ud835\udc8e<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc8e<\/mi>0<\/mn><\/msub><\/mrow>\ud835\udc8e<\/mi><\/mfrac><\/mfrac><\/mrow>{\\boldsymbol{E}}_{\\boldsymbol{m}}=\\frac{\\frac{{\\boldsymbol{Q}}_{1}-{\\boldsymbol{Q}}_{0}}{\\boldsymbol{Q}}}{\\frac{{\\boldsymbol{m}}_{1}-{\\boldsymbol{m}}_{0}}{\\boldsymbol{m}}}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

    \u516c\u5f0f\u4ee3\u8868\u7740<\/strong><\/p>\n\n\n\n

    \u9700\u6c42\u7684\u5f39\u6027\u7cfb\u6570=\\frac{\u9700\u6c42\u91cf\u53d8\u52a8\u7684\u767e\u5206\u6bd4}{\u6536\u5165\u53d8\u52a8\u7684\u767e\u5206\u6bd4}<\/p>\n\n\n\n

    \u5173\u7cfb\uff1a<\/strong><\/p>\n\n\n\n

      \n
    1. \u5546\u54c1\u4e3a\u6b63\u5e38\u54c1\u65f6\uff0c\u6d88\u8d39\u8005\u6536\u5165\u589e\u52a0\uff0c\u5176\u9700\u6c42\u91cf\u4e5f\u4f1a\u589e\u52a0\uff0c<\/strong><\/li>\n\n\n\n
    2. \u5546\u54c1\u4e3a\u4f4e\u6863\u54c1\u65f6\uff0c\u6d88\u8d39\u8005\u6536\u5165\u589e\u52a0\uff0c\u5176\u9700\u6c42\u91cf\u4f1a\u51cf\u5c11\uff0c<\/strong> <\/li>\n<\/ol>\n\n\n\n

      \u4f9b\u7ed9\u5f39\u6027<\/a><\/h3>\n\n\n\n

      \u5b9a\u4e49\uff1a\u4e00\u5b9a\u65f6\u671f\u5185\u76f8\u5e94\u4e8e\u5546\u54c1\u4ef7\u683c\u7684\u76f8\u5bf9\u53d8\u52a8\uff0c\u4e00\u79cd\u5546\u54c1\u4f9b\u5e94\u91cf\u76f8\u5bf9\u53d8\u52a8\u7684\u654f\u611f\u7a0b\u5ea6<\/strong><\/p>\n\n\n\n

      \u4f9b\u7ed9\u5f39\u6027\u516c\u5f0f\uff1a<\/strong><\/p>\n\n\n\n

      \ud835\udc6c<\/mi>=<\/mo>\ud835\udc78<\/mi>1<\/mn>\ud835\udc94<\/mi><\/msubsup>\u2212<\/mo><\/mrow><\/mtd><\/mtr>\ud835\udc78<\/mi>0<\/mn>\ud835\udc94<\/mi><\/msubsup><\/mtd><\/mtr><\/mtable>\ud835\udc78<\/mi><\/mfrac>\ud835\udc77<\/mi>1<\/mn><\/msub>\u2212<\/mo>\ud835\udc77<\/mi>0<\/mn><\/msub><\/mrow>\ud835\udc77<\/mi><\/mfrac><\/mfrac><\/mrow>\\boldsymbol{E}=\\frac{\\frac{\\begin{gathered}{\\boldsymbol{Q}}_{1}^{\\boldsymbol{s}}- \\\\ {\\boldsymbol{Q}}_{0}^{\\boldsymbol{s}}\\end{gathered}}{\\boldsymbol{Q}}}{\\frac{{\\boldsymbol{P}}_{1}-{\\boldsymbol{P}}_{0}}{\\boldsymbol{P}}}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

      \u516c\u5f0f\u4ee3\u8868\u7740\uff1a<\/strong><\/p>\n\n\n\n

      \u5f53E=0\u65f6\uff0c\u5b8c\u5168\u65e0\u5f39\u6027\u4f9b\u7ed9\u5b8c\u5168\u4e0d\u53d7\u4ef7\u683c\u7684\u5f71\u54cd\uff0c\u4f8b\u5982\u53e4\u8463<\/strong><\/p>\n\n\n\n

      \u5f530<E<1\u65f6\uff0c\u7f3a\u4e4f\u5f39\u6027\uff0c\u4ef7\u683c\u53d8\u53161%\uff0c\u4f9b\u7ed9\u53d8\u5316\u4e0d\u52301%\uff0c\u4f8b\u5982\u571f\u5730<\/strong><\/p>\n\n\n\n

      \u5f53E=1\u65f6\uff0c\u4e3a\u5355\u4f4d\u5f39\u6027\uff0c\u4ef7\u683c\u53d8\u53161%\uff0c\u4f9b\u7ed9\u53d8\u53161%\uff0c\u4f8b\u5982\u6c7d\u8f66<\/strong><\/p>\n\n\n\n

      \u5f531<E<\u221e\u65f6\uff0c\u5bcc\u6709\u5f39\u6027\uff0c\u4ef7\u683c\u53d8\u53161%\uff0c\u4f9b\u7ed9\u53d8\u5316\u8d85\u8fc71%\uff0c\u4f8b\u5982\u98df\u54c1<\/strong><\/p>\n\n\n\n

      \u5f53E=+\u221e\u65f6\uff0c\u5b8c\u5168\u5f39\u6027\u6216\u8005\u65e0\u9650\u5f39\u6027\uff0c\u4ef7\u683c\u53d8\u53161%\uff0c\u4f9b\u7ed9\u53d8\u5316\u5927\u5927\u8d85\u8fc71%\uff0c\u4f8b\u5982\u852c\u83dc<\/strong><\/p>\n\n\n\n

      \u5f71\u54cd\u4f9b\u7ed9\u5f39\u6027\u7684\u56e0\u7d20\uff1a<\/strong><\/p>\n\n\n\n

        \n
      1. \u751f\u4ea7\u8005\u8c03\u6574\u7684\u65f6\u95f4<\/strong><\/li>\n\n\n\n
      2. \u751f\u4ea7\u8005\u4f7f\u7528\u7684\u6280\u672f<\/strong><\/li>\n\n\n\n
      3. \u73b0\u6709\u751f\u4ea7\u529b\u7684\u5229\u7528\u7a0b\u5ea6<\/strong><\/li>\n<\/ol>\n\n\n\n

        \u652f\u6301\u4ef7\u683c\uff1a<\/strong><\/p>\n\n\n\n

        \u6700\u4f4e\u9650\u4ef7\uff0c\u6307\u7684\u662f\u653f\u5e9c\u4e3a\u652f\u6301\u67d0\u4ea7\u54c1\u7684\u751f\u4ea7\u800c\u5bf9\u8be5\u4ea7\u54c1\u7684\u4ef7\u683c\u89c4\u5b9a\u7684\u4e00\u4e2a\u9ad8\u4e8e\u5e02\u573a\u4ef7\u7684\u4ef7\u683c<\/strong><\/p>\n\n\n\n

        \uff08\u76f8\u5f53\u4e8e\u653f\u5e9c\u8d2d\u4e70\u4f7f\u9700\u6c42\u589e\u52a0\uff09<\/strong><\/p>\n\n\n\n

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          \n
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