{"id":20176,"date":"2020-06-26T17:26:38","date_gmt":"2020-06-26T09:26:38","guid":{"rendered":"https:\/\/swarma.org\/?p=20176"},"modified":"2020-06-26T17:26:38","modified_gmt":"2020-06-26T09:26:38","slug":"%e6%b7%b7%e6%b2%8c%e7%90%86%e8%ae%ba%e5%85%88%e9%a9%b1%e6%9d%8e%e5%a4%a9%e5%b2%a9%e5%8e%bb%e4%b8%96%ef%bc%8c%e6%9c%80%e6%97%a9%e4%b8%a5%e6%a0%bc%e5%ae%9a%e4%b9%89%e6%b7%b7%e6%b2%8c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=20176","title":{"rendered":"\u6df7\u6c8c\u7406\u8bba\u5148\u9a71\u674e\u5929\u5ca9\u53bb\u4e16\uff0c\u6700\u65e9\u4e25\u683c\u5b9a\u4e49\u201c\u6df7\u6c8c\u201d\uff0c\u63d0\u51fa\u201c\u5468\u671f\u4e09\u5373\u6df7\u6c8c\u201d"},"content":{"rendered":"<div class='wxsyncmain'>\n<section style=\"text-align: center;margin-left: 8px;margin-right: 8px;\" data-mpa-powered-by=\"yiban.io\"><img loading=\"lazy\" data-ratio=\"0.7120085015940489\"  data-type=\"png\" data-w=\"941\" height=\"auto\" style=\"white-space: normal;\" width=\"941\" src=\"\/wp-content\/uploads\/2020\/06\/wxsync-2020-06-28b370b1f401caf460e10233a1154cb6.png\"  \/><\/section>\n<section style=\"text-align: center;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;\"><span data-shimo-docs=\"[[20,&quot;\u534e\u4eba\u6570\u5b66\u7269\u7406\u5b66\u5bb6\u674e\u5929\u5ca9\uff081945-2020\uff09&quot;]]\"><\/p>\n<p line=\"3mLL\" style=\"line-height: 1.7;margin-bottom: 0pt;margin-top: 0pt;font-size: 11pt;color: #494949;\"><span style=\"color: rgb(136, 136, 136);\"><strong><span style=\"color: rgb(136, 136, 136);font-size: 13px;\">\u534e\u4eba\u6570\u5b66\u7269\u7406\u5b66\u5bb6\u674e\u5929\u5ca9\uff081945-2020\uff09<\/span><\/strong><\/span><\/p>\n<p><\/span><\/span><\/section>\n<section style=\"text-align: center;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;\">&nbsp; &nbsp; &nbsp; &nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span data-shimo-docs=\"[[20,&quot;\u6770\u51fa\u7684\u534e\u4eba\u6570\u5b66\u7269\u7406\u5b66\u5bb6\u674e\u5929\u5ca9\u6559\u6388\uff0c\u4e8e\u7f8e\u56fd\u4e1c\u90e8\u65f6\u95f46\u670825\u65e5\u4e0a\u53489\u70b9\u53bb\u4e16\uff0c\u4eab\u5e7475\u5c81\u3002\u674e\u5929\u5ca9\u662f\u5bc6\u6b47\u6839\u5927\u5b66\u6770\u51fa\u6559\u6388\uff0c\u66fe\u7ecf\u83b7\u5f97\u53e4\u6839\u6d77\u59c6\u5956\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;YnS9&quot;&quot;],[20,&quot;n&quot;,&quot;24:&quot;bPz8&quot;&quot;],[20,&quot;\u674e\u5929\u5ca9\u535a\u58eb\u5728\u6570\u5b66\u4e0e\u590d\u6742\u79d1\u5b66\u7684\u591a\u4e2a\u91cd\u8981\u9886\u57df\u4f5c\u51fa\u8fc7\u5f00\u521b\u6027\u5de5\u4f5c\u3002\u4ed6\u4e0e\u8a79\u59c6\u65af\u00b7\u7ea6\u514b\uff08James Yorke\uff09\u9996\u6b21\u5728\u6570\u5b66\u4e0a\u5b9a\u4e49\u201c\u6df7\u6c8c\u201d\u6982\u5ff5\uff1b\u4ed6\u5bf9\u4e4c\u62c9\u59c6\uff08Stanislaw Ulam\uff09\u731c\u60f3\u7684\u8bc1\u660e\u662f\u52a8\u529b\u7cfb\u7edf\u4e0d\u53d8\u6d4b\u5ea6\u8ba1\u7b97\u7406\u8bba\u4e0e\u7b97\u6cd5\u7814\u7a76\u7684\u5960\u57fa\u6027\u5de5\u4f5c\uff1b\u4ed6\u4e0e\u51ef\u6d1b\u683c\uff08R.B. Kellogg\uff09\u53ca\u7ea6\u514b\u5173\u4e8e\u8ba1\u7b97\u5e03\u52b3\u5a01\u5c14\uff08L.E.J. Brouwer\uff09\u4e0d\u52a8\u70b9\u7684\u601d\u60f3\u548c\u6570\u503c\u65b9\u6cd5\uff0c\u5f00\u8f9f\u4e86\u73b0\u4ee3\u540c\u4f26\u5ef6\u62d3\u7b97\u6cd5\u7814\u7a76\u7684\u65b0\u5929\u5730\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;bMO9&quot;&quot;],[20,&quot;n&quot;,&quot;24:&quot;5luO&quot;&quot;],[20,&quot;\u674e\u5929\u5ca9\u548c\u4ed6\u5bfc\u5e08\u8a79\u59c6\u65af\u00b7\u7ea6\u514b1975\u53d1\u8868\u4e86\u7ecf\u5178\u8bba\u6587\u300a\u5468\u671f\u4e09\u610f\u5473\u7740\u6df7\u6c8c\u300b\uff08Period Three Implies Chaos\uff09\uff0c\u7b2c\u4e00\u6b21\u5728\u52a8\u529b\u5b66\u7814\u7a76\u4e2d\u5f15\u5165\u201cChaos\u201d\u7684\u6982\u5ff5\uff0c\u63d0\u51fa\u201c\u5468\u671f\u4e09\u5373\u6df7\u6c8c\u201d\uff0c\u5f00\u521b\u4e86\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7814\u7a76\u7684\u65b0\u7eaa\u5143\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;Yjbh&quot;&quot;],[20,&quot;n&quot;,&quot;24:&quot;nGZM&quot;&quot;],[20,&quot;\u6df7\u6c8c\u73b0\u8c61\u5728\u5404\u4e2a\u9886\u57df\u5e7f\u6cdb\u5b58\u5728\uff0c\u5bf9\u5b83\u7684\u5b9a\u4e49\u6709\u591a\u79cd\uff0c\u800c\u674e-\u7ea6\u514b\u7684\u6df7\u6c8c\u5b9a\u4e49\uff0c\u662f\u5f71\u54cd\u6700\u5927\u7684\u4e00\u79cd\u3002\u8fd9\u7bc7\u8bba\u6587\u76ee\u524d\u7684\u5f15\u7528\u91cf\u5df2\u8fd15\u5343\u6b21\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;aFXP&quot;&quot;],[20,&quot;n&quot;,&quot;24:&quot;QZNW&quot;&quot;],[20,&quot;\u674e-\u7ea6\u514b\u5b9a\u7406\u63ed\u793a\u4e86\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7684\u521d\u503c\u654f\u611f\u6027\u4ee5\u53ca\u7531\u6b64\u4ea7\u751f\u7684\u89e3\u7684\u4e0d\u53ef\u9884\u6d4b\u6027\uff0c\u8fd9\u662f\u6df7\u6c8c\u73b0\u8c61\u7684\u672c\u8d28\u7279\u5f81\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;uvVp&quot;&quot;],[20,&quot;n&quot;,&quot;24:&quot;VMsr&quot;&quot;],[20,&quot;\u540c\u4e3a\u79d1\u5b66\u5148\u9a71\uff0c\u6df7\u6c8c\u7406\u8bba\u4e4b\u7236\u7231\u5fb7\u534e\u00b7\u6d1b\u4f26\u8328\uff08Edward Lorenz\uff09\u4e8e2008\u5e74\u53bb\u4e16\uff0c\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\u53d1\u73b0\u8005\u7c73\u5207\u5c14\u00b7\u8d39\u6839\u9c8d\u59c6\uff08Mitchell Feigenbaum\uff09\u4e8e2019\u5e746\u6708\u53bb\u4e16\uff0cLogistic\u6620\u5c04\u63d0\u51fa\u8005\u7f57\u4f2f\u7279\u00b7\u6885\uff08Robert May\uff09\u4e8e2020\u5e744\u6708\u53bb\u4e16\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;Y0Vy&quot;&quot;],[20,&quot;n&quot;,&quot;24:&quot;bZFF&quot;&quot;],[20,&quot;\u8fd9\u91cc\u6211\u4eec\u8f6c\u8f7d\u674e\u5929\u5ca9\u6559\u6388\u7684\u4e00\u7bc7\u56de\u5fc6\u6587\u7ae0\uff0c\u4ee5\u8868\u6000\u5ff5\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;TX7c&quot;&quot;],[20,&quot;n&quot;,&quot;24:&quot;nMk8&quot;&quot;],[20,&quot;\u6ce8\uff1a\u672c\u6587\u6574\u7406\u81ea2005\u5e74\u5e95\u53ca2006\u5e74\u5e95\u4e24\u6b21\u5728\u65b0\u7af9\u56fd\u7acb\u6e05\u534e\u5927\u5b66\u7684\u6f14\u8bb2\uff0c\u520a\u767b\u4e8e\u300a\u6578\u5b78\u50b3\u64ad\u300b31\u53774\u671f\uff0c\u7b80\u4f53\u4e2d\u6587\u7248\u6700\u65e9\u520a\u8f7d\u4e8e\u4e18\u6210\u6850\u7b49\u4e3b\u7f16\u7684\u300a\u6570\u5b66\u7684\u4eba\u6587\u300b\u7b2c17\u8f91\u3002\u5206\u8282\u548c\u5c0f\u6807\u9898\u4e3a\u7f16\u8005\u8865\u5145\u3002&quot;],[20,&quot;n&quot;,&quot;24:&quot;kA2Y&quot;&quot;]]\"><\/p>\n<p line=\"YnS9\"><span style=\"font-size: 15px;\">\u6770\u51fa\u7684\u534e\u4eba\u6570\u5b66\u7269\u7406\u5b66\u5bb6\u674e\u5929\u5ca9\u6559\u6388\uff0c\u4e8e\u7f8e\u56fd\u4e1c\u90e8\u65f6\u95f4 6 \u6708 25 \u65e5\u4e0a\u5348 9 \u70b9\u53bb\u4e16\u3002\u674e\u5929\u5ca9\u662f\u5bc6\u6b47\u6839\u5dde\u7acb\u5927\u5b66\u6770\u51fa\u6559\u6388\uff0c\u66fe\u7ecf\u83b7\u5f97\u53e4\u6839\u6d77\u59c6\u5956\u3002<\/span><\/p>\n<p line=\"bPz8\"><br  \/><\/p>\n<p line=\"bMO9\"><span style=\"font-size: 15px;\">\u674e\u5929\u5ca9\u535a\u58eb\u5728\u6570\u5b66\u4e0e\u590d\u6742\u79d1\u5b66\u7684\u591a\u4e2a\u91cd\u8981\u9886\u57df\u4f5c\u51fa\u8fc7\u5f00\u521b\u6027\u5de5\u4f5c\u3002\u4ed6\u4e0e\u8a79\u59c6\u65af\u00b7\u7ea6\u514b\uff08James Yorke\uff09\u9996\u6b21\u5728\u6570\u5b66\u4e0a\u5b9a\u4e49\u201c\u6df7\u6c8c\u201d\u6982\u5ff5\uff1b\u4ed6\u5bf9\u4e4c\u62c9\u59c6\uff08Stanislaw Ulam\uff09\u731c\u60f3\u7684\u8bc1\u660e\u662f\u52a8\u529b\u7cfb\u7edf\u4e0d\u53d8\u6d4b\u5ea6\u8ba1\u7b97\u7406\u8bba\u4e0e\u7b97\u6cd5\u7814\u7a76\u7684\u5960\u57fa\u6027\u5de5\u4f5c\uff1b\u4ed6\u4e0e\u51ef\u6d1b\u683c\uff08R.B. Kellogg\uff09\u53ca\u7ea6\u514b\u5173\u4e8e\u8ba1\u7b97\u5e03\u52b3\u5a01\u5c14\uff08L.E.J. Brouwer\uff09\u4e0d\u52a8\u70b9\u7684\u601d\u60f3\u548c\u6570\u503c\u65b9\u6cd5\uff0c\u5f00\u8f9f\u4e86\u73b0\u4ee3\u540c\u4f26\u5ef6\u62d3\u7b97\u6cd5\u7814\u7a76\u7684\u65b0\u5929\u5730\u3002<\/span><\/p>\n<p line=\"5luO\"><br  \/><\/p>\n<p line=\"Yjbh\"><span style=\"font-size: 15px;\">\u674e\u5929\u5ca9\u548c\u4ed6\u5bfc\u5e08\u8a79\u59c6\u65af\u00b7\u7ea6\u514b 1975 \u53d1\u8868\u4e86\u7ecf\u5178\u8bba\u6587\u300a\u5468\u671f\u4e09\u610f\u5473\u7740\u6df7\u6c8c\u300b\uff08Period Three Implies Chaos\uff09\uff0c\u7b2c\u4e00\u6b21\u5728\u52a8\u529b\u5b66\u7814\u7a76\u4e2d\u5f15\u5165\u201cChaos\u201d\u7684\u6982\u5ff5\uff0c\u63d0\u51fa\u201c\u5468\u671f\u4e09\u5373\u6df7\u6c8c\u201d\uff0c\u5f00\u521b\u4e86\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7814\u7a76\u7684\u65b0\u7eaa\u5143\u3002<\/span><\/p>\n<p line=\"nGZM\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/p>\n<p line=\"aFXP\"><span style=\"font-size: 15px;\">\u6df7\u6c8c\u73b0\u8c61\u5728\u5404\u4e2a\u9886\u57df\u5e7f\u6cdb\u5b58\u5728\uff0c\u5bf9\u5b83\u7684\u5b9a\u4e49\u6709\u591a\u79cd\uff0c\u800c\u674e-\u7ea6\u514b\u7684\u6df7\u6c8c\u5b9a\u4e49\uff0c\u662f\u5f71\u54cd\u6700\u5927\u7684\u4e00\u79cd\u3002\u8fd9\u7bc7\u8bba\u6587\u76ee\u524d\u7684\u5f15\u7528\u91cf\u5df2\u8fd1 5 \u5343\u6b21\u3002<\/span><\/p>\n<p line=\"QZNW\"><br  \/><\/p>\n<p line=\"uvVp\"><span style=\"font-size: 15px;\">\u674e-\u7ea6\u514b\u5b9a\u7406\u63ed\u793a\u4e86\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7684\u521d\u503c\u654f\u611f\u6027\u4ee5\u53ca\u7531\u6b64\u4ea7\u751f\u7684\u89e3\u7684\u4e0d\u53ef\u9884\u6d4b\u6027\uff0c\u8fd9\u662f\u6df7\u6c8c\u73b0\u8c61\u7684\u672c\u8d28\u7279\u5f81\u3002<\/span><\/p>\n<p line=\"uvVp\"><span style=\"font-size: 15px;\"><br  \/><\/span><\/p>\n<p line=\"Y0Vy\"><span style=\"font-size: 15px;\">\u540c\u4e3a\u79d1\u5b66\u5148\u9a71\uff0c\u6df7\u6c8c\u7406\u8bba\u4e4b\u7236\u7231\u5fb7\u534e\u00b7\u6d1b\u4f26\u8328\uff08Edward Lorenz\uff09\u4e8e 2008 \u5e74\u53bb\u4e16\uff0c\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\u53d1\u73b0\u8005\u7c73\u5207\u5c14\u00b7\u8d39\u6839\u9c8d\u59c6\uff08Mitchell Feigenbaum\uff09\u4e8e 2019 \u5e74 6 \u6708\u53bb\u4e16\uff0cLogistic \u6620\u5c04\u63d0\u51fa\u8005\u7f57\u4f2f\u7279\u00b7\u6885\uff08Robert May\uff09\u4e8e 2020 \u5e74 4 \u6708\u53bb\u4e16\u3002<\/span><\/p>\n<p line=\"bZFF\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/p>\n<section style=\"text-align: center;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;\"><img class=\"rich_pages\" data-ratio=\"0.5555555555555556\" data-s=\"300,640\"  data-type=\"png\" data-w=\"900\" style=\"text-align: center;white-space: normal;\" src=\"\/wp-content\/uploads\/2020\/06\/wxsync-2020-06-3ed33cb872133bf5d3eaa4b3ce2828d3.png\"  \/><\/span><\/section>\n<p line=\"bZFF\"><span style=\"font-size: 15px;\"><br  \/><\/span><\/p>\n<p line=\"TX7c\"><span style=\"font-size: 15px;\">\u8fd9\u91cc\u6211\u4eec\u8f6c\u8f7d\u674e\u5929\u5ca9\u6559\u6388\u7684\u4e00\u7bc7\u56de\u5fc6\u6587\u7ae0\uff0c\u4ee5\u8868\u6000\u5ff5\u3002<\/span><\/p>\n<p line=\"nMk8\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/p>\n<p line=\"kA2Y\"><span style=\"font-size: 15px;\">\u6ce8\uff1a\u672c\u6587\u6574\u7406\u81ea 2005 \u5e74\u5e95\u53ca 2006 \u5e74\u5e95\u4e24\u6b21\u5728\u65b0\u7af9\u56fd\u7acb\u6e05\u534e\u5927\u5b66\u7684\u6f14\u8bb2\uff0c\u520a\u767b\u4e8e\u300a\u6578\u5b78\u50b3\u64ad\u300b31 \u5377 4 \u671f\uff0c\u7b80\u4f53\u4e2d\u6587\u7248\u6700\u65e9\u520a\u8f7d\u4e8e\u4e18\u6210\u6850\u7b49\u4e3b\u7f16\u7684\u300a\u6570\u5b66\u7684\u4eba\u6587\u300b\u7b2c 17 \u8f91\u3002\u5206\u8282\u548c\u5c0f\u6807\u9898\u4e3a\u7f16\u8005\u8865\u5145\u3002<\/span><\/p>\n<p><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><br mpa-from-tpl=\"t\"  \/><\/section>\n<section data-mpa-template=\"t\" mpa-from-tpl=\"t\">\n<section mpa-from-tpl=\"t\">\n<section style=\"margin-top: 20px;display: flex;-webkit-box-pack: center;justify-content: center;-webkit-box-align: center;align-items: center;\" data-mid=\"t1\" mpa-from-tpl=\"t\">\n<section data-preserve-color=\"t\" style=\"min-width: 200px;min-height: 40px;border-right: 2px solid rgb(230, 230, 230);border-bottom: 2px solid rgb(230, 230, 230);padding: 0px 5px 5px 0px;\" data-mid=\"\" mpa-from-tpl=\"t\">\n<section style=\"font-size: 14px;min-width: 180px;min-height: 40px;padding: 0px 15px;border-width: 2px;border-style: solid;border-color: rgb(139, 6, 6);text-align: center;line-height: 40px;\" data-mid=\"\" mpa-from-tpl=\"t\">\n<section style=\"display: inline-block;width: 10px;height: 10px;background-color: rgb(139, 6, 6);opacity: 0.5;transform: rotate(45deg);top: -1px;left: 0px;margin-right: 15px;\" data-mid=\"\" data-contenteditable=\"false\" mpa-from-tpl=\"t\"><br  \/><\/section>\n<section data-preserve-color=\"t\" style=\"display: inline-block;color: rgb(79, 79, 79);line-height: 30px;\" data-mid=\"\" mpa-from-tpl=\"t\">\n<section data-mid=\"\" mpa-is-content=\"t\" style=\"border-color: rgb(139, 6, 6);\" mpa-from-tpl=\"t\"><strong mpa-from-tpl=\"t\"><span style=\"border-color: rgb(139, 6, 6);color: rgb(123, 12, 0);font-size: 16px;\" mpa-is-content=\"t\">\u674e\u5929\u5ca9\u300a\u56de\u9996\u6765\u65f6\u7684\u8def\u300b<\/span><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section data-mpa-template=\"t\" mpa-from-tpl=\"t\">\n<section mpa-from-tpl=\"t\">\n<section data-mid=\"t4\" style=\"margin-top: 20px;color: rgb(0, 0, 0);font-size: medium;display: flex;-webkit-box-pack: center;justify-content: center;-webkit-box-align: center;align-items: center;\" mpa-from-tpl=\"t\">\n<section data-preserve-color=\"t\" data-mid=\"\" style=\"padding-right: 30px;padding-left: 30px;min-width: 60px;text-align: center;border-bottom: 2px solid rgb(232, 230, 230);\" mpa-from-tpl=\"t\">\n<section data-mid=\"\" style=\"padding-right: 10px;padding-left: 10px;display: inline-block;font-size: 14px;color: rgb(123, 12, 0);border-bottom: 2px solid rgb(123, 12, 0);transform: translate(0px, 2px);border-top-color: rgb(123, 12, 0);border-left-color: rgb(123, 12, 0);border-right-color: rgb(123, 12, 0);\" mpa-from-tpl=\"t\"><strong mpa-from-tpl=\"t\" style=\"border-color: rgb(123, 12, 0);\"><\/p>\n<p style=\"clear: both;min-height: 1em;border-color: rgb(123, 12, 0);\"><span mpa-is-content=\"t\" style=\"font-size: 16px;border-color: rgb(123, 12, 0);\"><strong mpa-from-tpl=\"t\" mpa-is-content=\"t\" style=\"border-color: rgb(123, 12, 0);\">1. \u4fdd\u6301\u597d\u5947\u5fc3<\/strong><\/span><\/p>\n<p><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u5f53\u521d\u7b2c\u4e00\u5fd7\u613f\u8003\u8fdb\u6570\u5b66\u7cfb\uff0c\u5f53\u7136\u53f7\u79f0\u662f\u56e0\u4e3a\u5bf9\u6570\u5b66\u611f\u5174\u8da3\uff0c\u5176\u5b9e\u4e2d\u5b66\u65f6\u4ee3\u5bf9\u6570\u5b66\u7684\u6240\u8c13\u5174\u8da3\u591a\u534a\u4e5f\u53ea\u662f\u5efa\u7acb\u5728\u94bb\u7814\u548c\u89e3\u51b3\u6570\u5b66\u96be\u9898\u65f6\u6240\u5f97\u5230\u7684\u201c\u5feb\u611f\u201d\u4e0a\u5427\u3002\u6ca1\u60f3\u5230\u4e00\u8fdb\u4e86\u5927\u5b66\uff0c\u5dee\u70b9\u5c31\u88ab\u521d\u7b49\u5fae\u79ef\u5206\u91cc\u90a3\u4e9b\u83ab\u540d\u5176\u5999\u7684 \u03b5-\u03b4 \u7ed9\u903c\u75af\u4e86\u3002\u8bb0\u5f97\u90a3\u65f6\u540c\u5bdd\u5ba4\u7684\u53e6\u5916\u4e09\u4f4d\u5ba4\u53cb\u90fd\u662f\u5927\u4e00\u6570\u5b66\u7cfb\u7684\u65b0\u751f\uff0c\u6211\u4eec\u591a\u5728\u665a\u95f4 11 \u70b9\u5de6\u53f3\u5c31\u7184\u706f\u5c31\u5bdd\u3002\u4f46\u662f\u5e38\u5e38\u5728\u534a\u591c\u4e00\u4e24\u70b9\u949f\u65f6\uff0c\u53d1\u73b0\u5927\u5bb6\u90fd\u88ab\u90a3\u4e9b \u03b5-\u03b4 \u7684\u62bd\u8c61\u6982\u5ff5\u641e\u5f97\u7761\u4e0d\u7740\u89c9\u3002\u8bb0\u5f97\u6211\u9694\u58c1\u4e66\u684c\u7684\u4e00\u4f4d\u540c\u5b66\u5e38\u5e38\u5728\u6253\u8349\u7a3f\u5199\u201c\u9057\u4e66\u201d\uff0c\u5185\u5bb9\u57fa\u672c\u4e0a\u662f\u8bf4\uff1a\u4ec0\u4e48\u90fd\u641e\u4e0d\u61c2\uff0c\u4e0d\u77e5\u600e\u4e48\u529e\u597d\uff0c\u4e0d\u60f3\u6d3b\u4e0b\u53bb\u4e86\u2026\u2026\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u540e\u6765\u5230\u4e86\u7f8e\u56fd\u4ee5\u540e\u624d\u77e5\u9053\uff0c\u6211\u4eec\u90fd\u4e0d\u662f\u5929\u5b57\u7b2c\u4e00\u53f7\u7684\u7b28\u86cb\u3002\u597d\u6bd4\u8bf4\uff0c\u5728\u6211\u76ee\u524d\u4efb\u6559\u7684\u5bc6\u6b47\u6839\u5dde\u7acb\u5927\u5b66\uff0c\u7cfb\u91cc\u6839\u672c\u7981\u6b62\u5728\u4e00\u3001\u4e8c\u5e74\u7ea7\u521d\u7b49\u5fae\u79ef\u5206\u7684\u8bfe\u7a0b\u91cc\u704c\u8f93\u5b66\u751f\u6240\u8c13 \u03b5-\u03b4 \u7684\u62bd\u8c61\u6982\u5ff5\u3002\u5176\u5b9e\u5728\u725b\u987f\u3001\u83b1\u5e03\u5c3c\u8328\uff08Leibniz\uff09\u53d1\u660e\u5fae\u79ef\u5206\u65f6\uff0c\u201c\u903c\u8fd1\u201d\u3001\u201c\u6e10\u8fd1\u201d\u3001\u201c\u65e0\u7a77\u5c0f\u201d\uff08Infinitesimal\uff09\u7684\u6982\u5ff5\u5e76\u6ca1\u6709\u975e\u5e38\u4e25\u683c\u7684\u201c\u5b9a\u4e49\u201d\u3002\u4e5f\u53ea\u6709\u5230 19 \u4e16\u7eaa\u4e2d\u671f\uff0c\u6570\u5b66\u754c\u7684\u201c\u9886\u5bfc\u201d\u624d\u5f00\u59cb\u5bf9\u6240\u6709\u6570\u5b66\u6982\u5ff5\u8981\u6c42\u201c\u4e25\u683c\u5730\u5b9a\u4e49\u201d\uff08Rigorously defined\uff09\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u6bd4\u5982\u8bf4\uff0c\u8bf7\u544a\u8bc9\u6211\u5230\u5e95\u4ec0\u4e48\u662f\u201c1\u201d\uff1f\u4ec0\u4e48\u662f\u201c2\u201d\uff1f\u4e3a\u4ec0\u4e48 1+1=2\uff1f\uff08\u8bf4\u5230\u8fd9\u4e00\u70b9\uff0c\u5230\u5e95\u4ec0\u4e48\u662f\u201c+\u201d\uff1f\uff09\u82e5\u5728\u521d\u7b49\u5fae\u79ef\u5206\u5165\u95e8\u9636\u6bb5\u5c31\u8981\u7528 \u03b5-\u03b4 \u53bb\u4e25\u683c\u523b\u753b\u201c\u903c\u8fd1\u201d\u3001\u201c\u6e10\u8fd1\u201d\u3001\u201c\u65e0\u7a77\u5c0f\u201d\u7684\u62bd\u8c61\u6982\u5ff5\uff0c\u5c31\u597d\u50cf\u5728\u5c0f\u5b66\u751f\u5b66\u57fa\u672c\u7b97\u672f\u52a0\u4e58\u6cd5\u4e4b\u524d\uff0c\u8981\u6c42\u4ed6\u4eec\u5148\u4e25\u683c\u5b9a\u4e49\u4ec0\u4e48\u662f\u201c1\u201d\uff0c\u4ec0\u4e48\u662f\u201c2\u201d\u2026\u2026<strong>\u82e5\u771f\u5982\u6b64\uff0c\u5c11\u5e74\u7ef4\u7279\u5bf9\u6570\u5b66\u7684\u70e6\u607c\u80af\u5b9a\u8981\u63d0\u65e9\u53d1\u751f\u4e86\uff0c\u4e0d\u662f\u5417\uff1f<\/strong><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u4e2d\u5b66\u65f6\u4ee3\u5bf9\u6570\u5b66\u96be\u9898\u7684\u94bb\u7814\u6839\u672c\u4e0a\u548c\u6570\u5b66\u6982\u5ff5\u4e0a\u7684\u6240\u8c13\u76f4\u89c9\uff08Intuition\uff09\u6ca1\u4ec0\u4e48\u5173\u7cfb\uff0c\u56e0\u6b64\u5927\u5bb6\u597d\u50cf\u90fd\u4e25\u91cd\u5ffd\u7565\u5728\u5f15\u5165\u62bd\u8c61\u6982\u5ff5\u4e4b\u524d\uff0c\u5148\u4ecb\u7ecd\u76f4\u89c9\u7684\u91cd\u8981\u6027\u3002\u6211\u4e5f\u662f\u5230\u7f8e\u56fd\u4ee5\u540e\u624d\u77e5\u9053\uff0c\u6570\u5b66\u4e0a\u7684\u903b\u8f91\u63a8\u7406\u548c\u5bf9\u6570\u5b66\u7ed3\u6784\u6027\u7684\u8ba4\u77e5\u6709\u76f8\u5f53\u5927\u7684\u5dee\u8ddd\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8bb0\u5f97\u4e0a\u6b21\u5728\u5357\u4eac\u65f6\uff0c\u548c\u4e00\u4f4d\u5357\u4eac\u5927\u5b66\u6570\u5b66\u7cfb\u7684\u5e74\u8f7b\u6559\u6388\u5171\u8fdb\u5348\u9910\uff0c\u8fd9\u4f4d\u6559\u6388\u90a3\u65f6\u5e76\u6ca1\u6709\u7559\u8fc7\u201c\u6d0b\u201d\uff0c\u4ed6\u542c\u8bf4\u4e1c\u65b9\u5b66\u751f\u5230\u7f8e\u56fd\u5ff5\u7814\u7a76\u6240\u4e00\u3001\u4e8c\u5e74\u7ea7\u65f6\u6210\u7ee9\u591a\u534a\u6770\u51fa\uff0c\u53ef\u662f\u8fc7\u4e86\u9009\u8bfe\u671f\u5230\u7814\u7a76\u505a\u8bba\u6587\u7684\u9636\u6bb5\u5c31\u9010\u6e10\u843d\u540e\u7f8e\u56fd\u5b66\u751f\uff0c\u4e0d\u77e5\u662f\u771f\u662f\u5047\uff1f\u5176\u5b9e\u8fd9\u4f4d\u6559\u6388\u6240\u542c\u8bf4\u7684\u5927\u81f4\u6b63\u786e\u3002\u4e00\u822c\u8f83\u7528\u529f\u7684\u4e1c\u65b9\u5b66\u751f\uff0c\u5728\u56fd\u5185\u53d7\u6559\u80b2\u65f6\u5927\u90fd\u4e0b\u5f88\u5927\u5de5\u592b\u5728\u8bb0\u5fc6\u6570\u5b66\u4e0a\u7684\u903b\u8f91\u63a8\u8bba\uff1a\u8fd9\u4e00\u6b65\u4e3a\u4ec0\u4e48\u5bfc\u51fa\u4e0b\u4e00\u6b65\uff0c\u4e0b\u4e00\u6b65\u4e3a\u4ec0\u4e48\u5bfc\u51fa\u518d\u4e0b\u4e00\u6b65\u2026\u2026\u7136\u540e\u628a\u6240\u6709\u4e60\u9898\u90fd\u62ff\u6765\u94bb\u7814\u4e00\u4e0b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e00\u822c\u7684\u7b14\u8bd5\u662f\u5f88\u96be\u8003\u5012\u8fd9\u5e2e\u5b66\u751f\u7684\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u53ef\u662f\u7f8e\u56fd\u5b66\u751f\u6240\u4e0d\u540c\u7684\u662f\uff0c\u5728\u4ed6\u4eec\u65e9\u671f\u7684\u6570\u5b66\u6559\u80b2\u91cc\u5374\u5df2\u5f88\u666e\u904d\u5730\u5728\u95ee\uff1a\u8fd9\u5230\u5e95\u5728\u8bb2\u4ec0\u4e48\uff08What it says\uff09\uff1f\u4ee5\u53ca\u5b83\u4e3a\u4ec0\u4e48\u884c\u5f97\u901a\uff08Why it works\uff09\uff1f\u8fd9\u4e9b\u95ee\u9898\u5728\u7b14\u8bd5\u65f6\u51e0\u4e4e\u4e0d\u592a\u53ef\u80fd\u9047\u5230\uff0c\u4f46\u5728\u505a\u7814\u7a76\u65f6\u5374\u662f\u975e\u5e38\u975e\u5e38\u91cd\u8981\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u6211\u6709\u4e00\u4e2a\u53f0\u6e7e\u6765\u7684\u535a\u58eb\u751f\uff0c\u6709\u4e00\u6b21\u6211\u8bf7\u4ed6\u628a\u6211\u5728\u4e13\u9898\u8ba8\u8bba\u73ed\u91cc\u8bb2\u8fc7\u7684\u4e00\u7bc7\u5f88\u91cd\u8981\u3001\u5f88\u590d\u6742\u7684\u6587\u7ae0\u7528\u4ed6\u81ea\u5df1\u7684\u6570\u5b66\u8bed\u8a00\u4ed4\u7ec6\u5199\u51fa\u6765\u3002\u4ece\u4ed6\u540e\u6765\u4ea4\u6765\u7684\u62a5\u544a\u91cc\uff0c\u53ef\u4ee5\u770b\u51fa\u4ed6\u7684\u786e\u4e0b\u4e86\u5f88\u5927\u7684\u5de5\u592b\u628a\u6587\u7ae0\u4e2d\u88ab\u7701\u7565\u7684\u903b\u8f91\u7ec6\u8282\u4e25\u5bc6\u5730\u8865\u8db3\u4e86\u3002\u6211\u628a\u4ed6\u7684\u62a5\u544a\u6539\u4e86\u6539\u8fd8\u7ed9\u4ed6\u3002\u7136\u540e\u4ed6\u53c8\u4ea4\u4e86\u6765\uff0c\u6211\u53c8\u6539\u4e86\u6539\u518d\u8fd8\u7ed9\u4ed6\u3002\u4ed6\u518d\u4ea4\u6765\u65f6\uff0c\u6211\u8bf7\u4ed6\u544a\u8bc9\u6211\uff0c\u8fd9\u7bc7\u6587\u7ae0\u5230\u5e95\u5728\u5e72\u4ec0\u4e48\uff1f\u6ca1\u60f3\u5230\u4ed6\u5374\u4e00\u4e2a\u5b57\u90fd\u7b54\u4e0d\u4e0a\u6765\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u5176\u5b9e\u5728\u4e00\u822c\u7684\u6570\u5b66\u7814\u7a76\u8bba\u6587\u91cc\uff0c\u6211\u4eec\u6700\u5e38\u89c1\u7684\u662f\u4f5c\u8005\u7528\u4e00\u4e9b\u83ab\u540d\u5176\u5999\u7684\u5b9a\u4e49\u63a8\u4e9b\u6700\u4e00\u822c\u6027\u7684\u5b9a\u7406\u3002\u6211\u4eec\u82e5\u53ea\u662f\u975e\u5e38\u7528\u529b\u5730\u53bb\u4e86\u89e3\u5b83\u7684\u903b\u8f91\u63a8\u7406\uff0c\u800c\u8f7b\u6613\u5ffd\u7565\u53bb\u641e\u6e05\u695a\u4f5c\u8005\u8111\u5b50\u91cc\u5230\u5e95\u5728\u60f3\u4e9b\u4ec0\u4e48\uff0c\u90a3\u4e48\u6211\u4eec\u5bf9\u6587\u7ae0\u7684\u4e86\u89e3\u5c06\u975e\u5e38\u6709\u9650\uff0c\u5f88\u96be\u7531\u6b64\u505a\u51fa\u6770\u51fa\u7684\u5de5\u4f5c\u3002\u975e\u5e38\u9057\u61be\u7684\u662f\uff0c\u6781\u591a\u6570\u91cd\u8981 \u8bba\u6587\u7684\u4f5c\u8005\u90fd\u4e0d\u4f1a\u8f7b\u6613\u628a\u4ed6\u4eec\u8111\u5b50\u91cc\u771f\u6b63\u7684\u91cd\u70b9\u7528\u529b\u5199\u51fa\u6765\u3002\u4f60\u5fc5\u987b\u81ea\u5df1\u53bb\u95ee\u8fd9\u4e9b\u95ee\u9898\uff0c\u81ea\u5df1\u53bb\u8ffd\u5bfb\u5b83\u7684\u7b54\u6848\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8fd9\u4e00\u8def\u8fc7\u6765\uff0c\u6211\u5e38\u4e3e\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\uff0c\u6211\u5bf9\u4e00\u4e2a\u77e9\u9635\u7684\u201c\u884c\u79e9\u201d\u548c\u201c\u5217\u79e9\u201d\u4e3a\u4ec0\u4e48\u4f1a\u76f8\u7b49\u7684\u597d\u5947\u3002\u5176\u5b9e\u5728\u4efb\u4f55\u57fa\u672c\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u7684\u4e66\u91cc\uff0c\u6211\u4eec\u90fd\u53ef\u4ee5\u627e\u5230\u5b83\u4eec\u4e3a\u4ec0\u4e48\u76f8\u7b49\u7684\u8bc1\u660e\u3002\u4f46\u662f\u4ece\u90a3\u4e9b\u903b\u8f91\u63a8\u7406\u7684\u5916\u8868\uff0c\u6211\u5b9e\u5728\u770b\u4e0d\u51fa\u5b83\u4eec\u4e3a\u4ec0\u4e48\u521a\u597d\u76f8\u7b49\uff08Happen to be equal\uff09\u3002\u5728\u6211\u771f\u6b63\u4e86\u89e3\u5230\u5b83\u4eec\u4e3a\u4ec0\u4e48\u4f1a\u4e00\u6837\u7684\u8fc7\u7a0b\u4e2d\uff0c\u8fd9\u4e2a\u201c\u597d\u5947\u201d\u5374\u5e2e\u6211\u4e86\u89e3\u4e86\u8bb8\u591a\u5e7f\u4e49\u9006\u77e9\u9635\u7684\u51e0\u4f55\u610f\u4e49\u3002\u53c8\u597d\u6bd4\u8bf4\uff0c\u8c01\u4e0d\u4f1a\u77e9\u9635\u8fd0\u7b97\u91cc\u7684\u201c\u9ad8\u65af\u6d88\u53bb\u6cd5\u201d\u554a\uff1f<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u6709\u4e00\u6b21\u6211\u95ee\u53f0\u6e7e\u5357\u90e8\u5927\u5b66\u6570\u5b66\u7cfb\u7684\u4e00\u4f4d\u6559\u6388\uff08\u8fd9\u4f4d\u6559\u6388\u5728\u5927\u5b66\u5ff5\u4e66\u65f6\uff0c\u597d\u50cf\u8fd8\u8d62\u8fc7\u53f0\u6e7e\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u6bd4\u8d5b\u7684\u201c\u94f6\u724c\u201d\uff09\u9ad8\u65af\u6d88\u53bb\u6cd5\u7684\u51e0\u4f55\u610f\u4e49\u5230\u5e95\u662f\u4ec0\u4e48\uff1f\u4ed6\u8bf4\uff0c\u8fd9\u5e74\u5934\u8c01\u8981\u53bb\u60f3\u8fd9\u79cd\u95ee\u9898\uff1f\uff01\u8bed\u8a00\u7b80\u5355\u7684\u4e1c\u897f\uff08\u597d\u6bd4\u201c\u62d3\u6251\u71b5\u201d\uff09\u61c2\u4e0d\u61c2\u597d\u50cf\u4e0d\u90a3\u4e48\u91cd\u8981\u3002\u7ba1\u5b83\u61c2\u4e0d\u61c2\u4eba\u4eec\u7167\u6837\u53ef\u4ee5\u53d1\u8868SCI\u7684\u6587\u7ae0\u3002\u53ef\u662f\u9047\u5230\u8f83\u590d\u6742\u7684\u8bed\u8a00\u65f6\uff0c\u597d\u6bd4\u8fd1\u4ee3\u4ee3\u6570\u51e0\u4f55\u91cc\u7684\u57fa\u672c\u8bed\u8a00\u201c\u6982\u5f62\u201d\uff08Scheme\uff09\u3010\u4ee3\u6570\u51e0\u4f55\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u6982\u5ff5\uff0c20 \u4e16\u7eaa 50 \u5e74\u4ee3\u7531\u4e9a\u5386\u5c71\u5927\u00b7\u683c\u7f57\u6ed5\u8fea\u514b\uff08Alexandre Grothendieck\uff09\u5f15\u5165\u3011\uff0c\u82e5\u5bf9\u5b83\u6574\u4e2a\u7684\u6765\u9f99\u53bb\u8109\u7f3a\u4e4f\u4e00\u4e2a\u6574\u4f53\u6027\u7684\u7406\u89e3\uff0c\u4e00\u822c\u4eba\u6050\u6015\u8fde\u201c\u5b9a\u4e49\u201d\u90fd\u65e0\u6cd5\u8f7b\u6613\u8bb0\u5fc6\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8bb0\u5f97\u6211\u5728\u81ea\u4fee\u201c\u4ea4\u6362\u4ee3\u6570\u201d\u65f6\uff0c\u9047\u5230\u6240\u8c13\u201c\u5c40\u90e8\u73af\u201d\uff08Local ring\uff09\uff0c\u5f53\u65f6\u53ea\u662f\u597d\u5947\uff0c\u4e3a\u4ec0\u4e48\u79f0\u5b83\u4e3a\u201c\u5c40\u90e8\u73af\u201d\uff1f\u4ece\u5b83\u5b9a\u4e49\uff08\u53ea\u6709\u552f\u4e00\u7684\u4e00\u4e2a\u6700\u5927\u7406\u60f3\uff08Maximal ideal\uff09\u7684\u73af\uff09\u7684\u8868\u9762\u5b9e\u5728\u770b\u4e0d\u51fa\u51ed\u4ec0\u4e48\u79f0\u5b83\u4e3a\u201c\u5c40\u90e8\u73af\u201d\u3002\u53ef\u662f\u5728\u6211\u8bd5\u56fe\u771f\u6b63\u53bb\u4e86\u89e3\u4e3a\u4ec0\u4e48\u8981\u79f0\u5b83\u4e3a\u5c40\u90e8\u73af\u7684\u8fc7\u7a0b\u91cc\uff0c\u8fd9\u4e2a\u201c\u597d\u5947\u201d\u5374\u5e2e\u6211\u4e86\u89e3\u4e86\u8bb8\u591a\u4ee3\u6570\u51e0\u4f55\u4e0a\u7684\u6982\u5ff5\u3002\u8fd9\u4e00\u8def\u8fc7\u6765\uff0c\u8fd9\u79cd\u5bf9\u6570\u5b66\u7684\u201c\u597d\u5947\u201d\u4ee5\u53ca\u5bf9\u8fd9\u4e9b\u201c\u597d\u5947\u201d\u95ee\u9898\u7b54\u6848\u7684\u8ffd\u9010\u7684\u786e\u7ed9\u6211\u5e26\u6765\u7814\u8bfb\u6570\u5b66\u7684\u6781\u5927\u4e50\u8da3\u3002\u5728\u8fd9\u91cc\u6211\u60f3\u5f3a\u8c03\u7684\u662f\uff0c\u5bf9\u8fd9\u4e9b\u201c\u597d\u5947\u201d\u7684\u8ffd\u6c42\u6beb\u65e0\u4e89\u53d6\u5728 SCI \u7684\u671f\u520a\u4e0a\u53d1\u8868\u8bba\u6587\u7684\u610f\u56fe\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section data-mpa-template=\"t\" mpa-from-tpl=\"t\">\n<section mpa-from-tpl=\"t\">\n<p style=\"margin-right: 8px;margin-left: 8px;clear: both;min-height: 1em;color: rgb(0, 0, 0);font-size: medium;\"><br mpa-from-tpl=\"t\"  \/><\/p>\n<section data-mid=\"t4\" style=\"margin-top: 20px;color: rgb(0, 0, 0);font-size: medium;display: flex;-webkit-box-pack: center;justify-content: center;-webkit-box-align: center;align-items: center;\" mpa-from-tpl=\"t\">\n<section data-preserve-color=\"t\" data-mid=\"\" style=\"padding-right: 30px;padding-left: 30px;min-width: 60px;text-align: center;border-bottom: 2px solid rgb(232, 230, 230);\" mpa-from-tpl=\"t\">\n<section data-mid=\"\" style=\"padding-right: 10px;padding-left: 10px;display: inline-block;font-size: 14px;color: rgb(123, 12, 0);border-bottom: 2px solid rgb(123, 12, 0);transform: translate(0px, 2px);border-top-color: rgb(123, 12, 0);border-left-color: rgb(123, 12, 0);border-right-color: rgb(123, 12, 0);\" mpa-from-tpl=\"t\"><strong mpa-from-tpl=\"t\" style=\"border-color: rgb(123, 12, 0);\"><\/p>\n<p style=\"clear: both;min-height: 1em;border-color: rgb(123, 12, 0);\"><span style=\"font-size: 16px;\">2.&nbsp;\u8fdb\u5165\u9a6c\u91cc\u5170\u5927\u5b66<\/span><\/p>\n<p><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u5f53\u521d\u53bb\u9a6c\u91cc\u5170\u5927\u5b66\u5ff5\u7814\u7a76\u6240\u662f\u4e00\u4e2a\u5de7\u5408\uff0c\u9047\u5230\u540e\u6765\u7684\u6307\u5bfc\u6559\u6388\u8a79\u59c6\u65af\u00b7\u7ea6\u514b\uff08James A. Yorke\uff09\u3010\u8a79\u59c6\u65af\u00b7\u7ea6\u514b\uff0c\u4f5c\u8005\u7684\u535a\u58eb\u751f\u5bfc\u5e08\uff0c\u66fe\u4efb\u9a6c\u91cc\u5170\u5927\u5b66\u6570\u5b66\u7cfb\u4e3b\u4efb\uff0c2013\u5e74\u9000\u4f11\uff0c\u73b0\u4e3a\u8be5\u6821\u6770\u51fa\u8363\u8a89\u6559\u6388\u30021975\u5e74\uff0c\u4ed6\u548c\u4f5c\u8005\u5408\u5199\u7684\u8bba\u6587\u300a\u5468\u671f\u4e09\u5219\u6df7\u6c8c\u300b\uff08Period Three Implies Chaos\uff09\u662f\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7684\u91cd\u8981\u8bba\u6587\uff0c\u5176\u7814\u7a76\u7ed3\u679c\u662f\u6c99\u53ef\u592b\u65af\u57fa\u5b9a\u7406\uff08Sharkovskii&#8217;s theorem\uff09\u7684\u7279\u6b8a\u60c5\u51b5\u3002\u6b64\u5916\uff0c\u672c\u6587\u63d0\u5230\u7684\u6c42\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u662f\u5e08\u751f\u5408\u4f5c\u7684\u53e6\u4e00\u91cd\u8981\u6210\u679c\u3011\u66f4\u662f\u4e00\u4e2a\u6781\u5927\u7684\u5de7\u5408\u3002\u8bb0\u5f97\u7ea6\u514b\u6559\u6388\u7b2c\u4e00\u6b21\u770b\u4e86\u6211\u5f53\u521d\u5728\u6e05\u534e\u5927\u5b66\u5ff5\u4e66\u7684\u6863\u6848\u65f6\uff0c\u663e\u7136\u5403\u4e86\u4e00\u60ca\uff0c\u4ee5\u4e3a\u6211\u662f\u54ea\u8def\u201c\u9ad8\u624b\u201d\uff0c\u529f\u529b\u65e0\u6bd4\u6df1\u539a\u3002\u73b0\u5728\u56de\u60f3\u8d77\u6765\u90a3\u4e2a\u6863\u6848\u91cc\u6240\u8bb0\u5f55\u7684\u5b9e\u5728\u662f\u6709\u6781\u5927\u7684\u8bef\u5bfc\uff08Misleading\uff0c\u8fd9\u5b57\u6709\u65f6\u662f\u6307\u4eba\u201c\u6b3a\u8bc8\u201d\u7684\u793c\u8c8c\u6027\u7528\u8bcd\uff09\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u770b\u54ea\uff01\u6211\u5728\u5ff5\u5927\u4e8c\u7684\u201c\u4e09\u9ad8\u201d\u65f6\uff0c\u201c\u9ad8\u7b49\u5fae\u79ef\u5206\u201d\u7528\u7684\u662f\u963f\u6ce2\u65af\u6258\u5c14\uff08Apostol\uff09\u7684\u300a\u6570\u5b66\u5206\u6790\u300b\uff1b\u201c\u9ad8\u7b49\u51e0\u4f55\u201d\u7528\u7684\u662f\u54c8\u5c14\u83ab\u65af\uff08Halmos\uff09\u7684\u300a\u6709\u9650\u7ef4\u5411\u91cf\u7a7a\u95f4\u300b\uff1b\u201c\u9ad8\u7b49\u4ee3\u6570\u201d\u7528\u7684\u662f\u96c5\u5404\u5e03\u68ee\uff08N. Jacobson\uff09\u7684\u300a\u62bd\u8c61\u4ee3\u6570\u5b66\u300b\uff1b\u201c\u5fae\u5206\u65b9\u7a0b\u201d\u7528\u7684\u662f\u79d1\u4e01\u987f\uff08Coddington\uff09\u7684\u300a\u5e38\u5fae\u5206\u65b9\u7a0b\u5bfc\u8bba\u300b\uff1b\u5927\u4e09\u5ff5\u201c\u8fd1\u4e16\u4ee3\u6570\u201d\u65f6\uff0c\u7528\u7684\u662f\u8303\u5fb7\u74e6\u5c14\u767b\uff08Van der Waerden\uff09\u7684\u300a\u8fd1\u4e16\u4ee3\u6570\u300b\uff1b\u5ff5\u201c\u590d\u53d8\u51fd\u6570\u8bba\u201d\u7528\u7684\u662f\u963f\u5c14\u798f\u65af\uff08Ahlfors\uff09\u7684\u300a\u590d\u53d8\u51fd\u6570\u300b\u3002\u53e6\u5916\uff0c\u5927\u4e09\u8fd8\u5ff5\u4e86\u62d3\u6251\u5b66\u3001\u6570\u8bba\u3002\u5927\u56db\u5ff5\u4e86\u6cdb\u51fd\u5206\u6790\u3001\u674e\u7fa4\u3001\u5b9e\u53d8\u51fd\u6570\u8bba\uff08\u7528\u7684\u662f\u7f57\u4f0a\u767b\uff08Royden\uff09\u7684\u300a\u5b9e\u5206\u6790\u300b\uff09\u3001\u5fae\u5206\u51e0\u4f55\uff08\u7528\u7684\u662f\u5e0c\u514b\u65af\uff08Hicks\uff09\u7684\u300a\u5fae\u5206\u51e0\u4f55\u8bb2\u4e49\u300b\uff09\u3002\u8fd9\u4e9b\u8bfe\u4e0d\u4f46\u90fd\u4fee\u8fc7\uff0c\u800c\u4e14\u6210\u7ee9\u90fd\u4e0d\u4f4e\uff08\u5927\u56db\u4fee\u7684\u8bfe\u90fd\u572890\u5206\u4ee5\u4e0a\uff09\u3002\u5728\u8868\u9762\u4e0a\u770b\u6765\uff0c\u8fd9\u4e2a\u8bb0\u5f55\u7684\u786e\u662f\u76f8\u5f53\u96c4\u58ee\u4e86\uff0c\u4e0d\u662f\u5417\uff1f<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u53ef\u662f\u4eca\u5929\u628a\u90a3\u4e9b\u6559\u79d1\u4e66\u62ff\u51fa\u6765\u7ffb\u4e00\u7ffb\uff0c\u5b9e\u5728\u5f88\u96be\u60f3\u8c61\u5f53\u521d\u662f\u600e\u4e48\u6df7\u8fc7\u6765\u7684\u3002\u597d\u6bd4\u8bf4\uff0c\u963f\u5c14\u798f\u65af\u90a3\u672c\u4e66\u7684\u6c34\u5e73\u4e0d\u4f4e\uff0c\u5b83\u51b3\u4e0d\u9002\u5408\u505a\u521d\u5b66\u590d\u53d8\u51fd\u6570\u8bba\u7684\u6559\u79d1\u4e66\u3002\u8bb0\u5f97\u6211\u4eec\u5927\u4e8c\u5728\u5b66\u9ad8\u7b49\u5fae\u79ef\u5206\u65f6\uff0c\u6559\u6388\u6839\u672c\u5c31\u8df3\u8fc7\u4e86\u201c\u7ebf\u79ef\u5206\u201d\uff08\u73b0\u5728\u60f3\u6765\uff0c\u5927\u6982\u6839\u672c\u7684\u539f\u56e0\u8fd8\u5728\u4e8e\u963f\u6ce2\u65af\u6258\u5c14\u90a3\u672c\u4e66\u8fc7\u4e8e\u201c\u9ad8\u6df1\u201d\uff0c\u6559\u6388\u65e0\u6cd5\u6559\u5b8c\u4e66\u91cc\u5927\u90e8\u5206\u7684\u6750\u6599\uff09\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u53ef\u662f\u963f\u5c14\u798f\u65af\u7684\u4e66\u57fa\u672c\u4e0a\u662f\u5047\u8bbe\u8bfb\u8005\u5df2\u7ecf\u6e05\u695a\u5730\u638c\u63e1\u4e86\u6240\u8c13\u7684\u201c\u56f4\u7ebf\u79ef\u5206\u201d\uff08Contour integral\uff0c\u590d\u5e73\u9762\u4e0a\u7684\u7ebf\u79ef\u5206\uff09\u3002\u82e5\u662f\u5bf9\u56f4\u7ebf\u79ef\u5206\u90fd\u4e0d\u751a\u4e86\u89e3\uff0c\u6211\u5f88\u96be\u60f3\u8c61\u5f53\u65f6\u600e\u4e48\u53bb\u7406\u89e3\u201c\u67ef\u897f\u79ef\u5206\u5b9a\u7406\u201d\uff08Cauchy integral theorem\uff09\u3010\u4e00\u4e2a\u5173\u4e8e\u590d\u5e73\u9762\u4e0a\u5168\u7eaf\u51fd\u6570\u7684\u8def\u5f84\u79ef\u5206\u7684\u91cd\u8981\u5b9a\u7406\u3011\u3001\u201c\u6d1b\u6717\u7ea7\u6570\u201d\uff08Laurent expansion\uff09\u3010\u6d1b\u6717\u7ea7\u6570\u5305\u542b\u6b63\u8d1f\u6b21\u6570\u7684\u9879\uff0c\u65e0\u6cd5\u8868\u793a\u4e3a\u6cf0\u52d2\u7ea7\u6570\u7684\u590d\u53d8\u51fd\u6570\u53ef\u8868\u793a\u4e3a\u6d1b\u6717\u7ea7\u6570\u3011\u7b49\u57fa\u672c\u6982\u5ff5\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u90a3\u65f6\u7684\u8001\u5e08\u4eec\u597d\u50cf\u4e00\u822c\u90fd\u89c9\u5f97\uff0c\u80fd\u7528\u6108\u6df1\u7684\u6559\u79d1\u4e66\uff08\u5176\u5b9e\u6bcf\u672c\u4e66\u90fd\u53f7\u79f0\u662f\u81ea\u6210\u4e00\u4f53\u7684\uff09\uff0c\u5b66\u751f\u81ea\u7136\u5c31\u4f1a\u53d8\u5f97\u6108\u201c\u9ad8\u6863\u6b21\u201d\u5427\uff01\u5176\u5b9e\u62bd\u8c61\u6570\u5b66\u7684\u51fa\u53d1\u70b9\u591a\u534a\u8d77\u59cb\u4e8e\u5bf9\u5b9e\u9645\u95ee\u9898\u6240\u5efa\u7acb\u7684\u6570\u5b66\u6a21\u578b\u3002\u7136\u540e\u5c06\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u5f0f\u5efa\u7acb\u7406\u8bba\uff0c\u518d\u62bd\u8c61\u5316\uff0c\u5e0c\u671b\u80fd\u8986\u76d6\u66f4\u4e00\u822c\u6027\u7684\u540c\u7c7b\u95ee\u9898\u3002\u56e0\u6b64\u5728\u5b66\u4e60\u8f83\u9ad8\u6df1\u7684\u62bd\u8c61\u6570\u5b66\u7406\u8bba\u4e4b\u524d\uff0c\u591a\u591a\u5c11\u5c11\u8981\u5bf9\u6700\u539f\u59cb\u7684\u51fa\u53d1\u70b9\u548c\u5de5\u5177\u6709\u4e9b\u57fa\u672c\u7684\u8ba4\u8bc6\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8981\u4e0d\u7136\uff0c\u82e5\u662f\u4e00\u5f00\u59cb\u5c31\u641e\u4e9b\u83ab\u540d\u5176\u5999\u7684\u62bd\u8c61\u5b9a\u4e49\uff0c\u63a8\u4e9b\u83ab\u540d\u5176\u5999\u7684\u62bd\u8c61\u5b9a\u7406\uff0c\u5b66\u751f\u6839\u672c\u65e0\u6cd5\u77e5\u9053\u5230\u5e95\u662f\u5728\u5e72\u4e9b\u4ec0\u4e48\u3002\u53ef\u662f\u4e3a\u4e86\u8003\u8bd5\u8fc7\u5173\uff0c\u53ea\u597d\u8ddf\u7740\u80cc\u5b9a\u4e49\u3001\u80cc\u5b9a\u7406\u3001\u80cc\u903b\u8f91\uff0c\u4e00\u56e2\u6df7\u6218\u3002\u5bf9\u57fa\u7840\u6570\u5b66\u5b9e\u8d28\u4e0a\u7684\u8ba4\u8bc6\u771f\u662f\u5fae\u4e4e\u5176\u5fae\u3002\u6211\u4eec\u90a3\u65f6\u7684\u5b66\u4e60\u73af\u5883\u5927\u81f4\u5982\u6b64\u3002\u6240\u4ee5\u6211\u90a3\u65f6\u6863\u6848\u91cc\u7684\u8bb0\u5f55\u867d\u7136\u6781\u4e3a\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\uff0c\u4f46\u662f\u5982\u4eca\u56de\u60f3\u8d77\u6765\uff0c\u5f53\u65f6\u5b9e\u5728\u662f\u201c\u4e00\u7a8d\u4e0d\u901a\u201d\u3002\u80cc\u5b9a\u7406\u3001\u80cc\u903b\u8f91\u6700\u591a\u53ea\u80fd\u5e94\u4ed8\u8003\u8bd5\u3002\u6bd5\u4e1a\u670d\u5b8c\u5175\u5f79\u4ee5\u540e\uff0c\u7edd\u5927\u591a\u6570\u4ee5\u524d\u6240\u5b66\u90fd\u5fd8\u4e86\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\"><br  \/><\/span><\/section>\n<section data-mpa-template=\"t\" mpa-from-tpl=\"t\">\n<section mpa-from-tpl=\"t\">\n<p style=\"margin-right: 8px;margin-left: 8px;clear: both;min-height: 1em;color: rgb(0, 0, 0);font-size: medium;\"><br mpa-from-tpl=\"t\"  \/><\/p>\n<section data-mid=\"t4\" style=\"margin-top: 20px;color: rgb(0, 0, 0);display: flex;-webkit-box-pack: center;justify-content: center;-webkit-box-align: center;align-items: center;\" mpa-from-tpl=\"t\">\n<section data-preserve-color=\"t\" data-mid=\"\" style=\"padding-right: 30px;padding-left: 30px;min-width: 60px;text-align: center;border-bottom: 2px solid rgb(232, 230, 230);\" mpa-from-tpl=\"t\">\n<section data-mid=\"\" style=\"padding-right: 10px;padding-left: 10px;display: inline-block;color: rgb(123, 12, 0);border-bottom: 2px solid rgb(123, 12, 0);transform: translate(0px, 2px);border-top-color: rgb(123, 12, 0);border-left-color: rgb(123, 12, 0);border-right-color: rgb(123, 12, 0);\" mpa-from-tpl=\"t\"><strong mpa-from-tpl=\"t\" style=\"border-color: rgb(123, 12, 0);\"><\/p>\n<p style=\"clear: both;min-height: 1em;border-color: rgb(123, 12, 0);font-size: 16px;\">3. \u5e08\u4ece\u7ea6\u514b<\/p>\n<p><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8001\u5b9e\u8bf4\uff0c\u5728\u51fa\u56fd\u524d\uff0c\u6211\u771f\u60f3\u653e\u5f03\u6570\u5b66\u3002\u540e\u6765\u5728\u7f8e\u56fd\u9047\u5230\u4e86\u5bfc\u5e08\u7ea6\u514b\u6559\u6388\u3002\u4ece\u4ed6\u90a3\u91cc\uff0c\u6211\u624d\u6162\u6162\u5bf9\u5b66\u6570\u5b66\u548c\u6570\u5b66\u7814\u7a76\u6709\u4e86\u4e9b\u521d\u6b65\u7684\u8ba4\u8bc6\u3002\u8fd9\u4e9b\u8ba4\u8bc6\u5927\u5927\u5f00\u9614\u4e86\u6211\u4ee5\u540e\u5b66\u4e60\u6570\u5b66\u7684\u89c6\u91ce\u548c\u65b9\u5f0f\u3002<strong>\u6700\u91cd\u8981\u7684\u662f\uff0c\u5b66\u4e60\u201c\u9ad8\u6863\u6b21\u201d\u7684\u6570\u5b66\u7406\u8bba\uff0c\u7edd\u5bf9\u5fc5\u987b\u4ece\u5bf9\u201c\u4f4e\u6863\u6b21\u201d\u6570\u5b66\u7684\u7406\u89e3\u51fa\u53d1\u3002<\/strong><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u6211\u5e38\u5e38\u89c9\u5f97\u81ea\u5df1\u7684\u6570\u5b66\u751f\u6daf\u5b9e\u5728\u662f\u592a\u5e78\u8fd0\u4e86\u3002\u8bb0\u5f97\u90a3\u5e74\u5728\u51ef\u6d1b\u683c\uff08B. Kellogg\uff09\u6559\u6388\u6240\u5f00\u201c\u975e\u7ebf\u6027\u6570\u503c\u5206\u6790\u201d\u7684\u8bfe\u5802\u4e0a\u542c\u5230\u4ed6\u8bb2\u5173\u4e8e\u8d6b\u5e0c\uff08M. Hirsch\uff09\u7528\u5fae\u5206\u62d3\u6251\u7684\u53cd\u8bc1\u6cd5\u8bc1\u660e\u201c\u5e03\u52b3\u5a01\u5c14\uff08Brouwer\uff09\u4e0d\u52a8\u70b9\u201d\u7684\u5b58\u5728\u5b9a\u7406\u3010\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u5b9a\u7406\uff0c\u662f\u62d3\u6251\u5b66\u91cc\u4e00\u4e2a\u91cd\u8981\u5b9a\u7406\uff0c\u53ef\u5e94\u7528\u5230\u6709\u9650\u7ef4\u7a7a\u95f4\u5e76\u6784\u6210\u4e86\u4e00\u822c\u4e0d\u52a8\u70b9\u5b9a\u7406\u7684\u57fa\u77f3\u3002\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u5b9a\u7406\u5f97\u540d\u4e8e\u8377\u5170\u6570\u5b66\u5bb6\u9c81\u4f0a\u5179\u00b7\u5e03\u52b3\u5a01\u5c14\uff08L. E. J. Brouwer\uff09\u3011<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u5176\u5b9e\u6211\u89c9\u5f97\u53ea\u8981\u628a\u8d6b\u5e0c\u7684\u8bc1\u660e\u7a0d\u7a0d\u505a\u4e9b\u53d8\u52a8\uff08\u8fd9\u4e2a\u53d8\u52a8\u5927\u6982\u4e0d\u8d85\u8fc7\u539f\u6765\u8bc1\u660e\u76841%\u5427\uff01\uff09\uff0c\u5c31\u53ef\u4ee5\u8f7b\u6613\u5730\u628a\u4ed6\u7684\u53cd\u8bc1\u6cd5\uff08\u201c\u2026\u2026\u82e5\u2018\u4e0d\u52a8\u70b9\u2019\u4e0d\u5b58\u5728\uff0c\u5219\u5929\u4e0b\u4f1a\u5927\u4e71\u2026\u2026\u201d\uff09\u53d8\u6210\u4e00\u4e2a\u627e\u8fd9\u4e9b\u4e0d\u52a8\u70b9\u7684\u5b9e\u9645\u65b9\u6cd5\u3002\u540e\u6765\u548c\u5bfc\u5e08\u7ea6\u514b\u6559\u6388\u63d0\u8d77\u4e86\u6211\u7684\u770b\u6cd5\u3002\u8bb0\u5f97\u90a3\u65f6\u6446\u5728\u6211\u9762\u524d\u7684\u7814\u7a76\u8bfe\u9898\u6709\u597d\u51e0\u4e2a\uff0c\u6ca1\u60f3\u5230\u7ea6\u514b\u6559\u6388\u5374\u575a\u6301\u8981\u6211\u5168\u529b\u4ee5\u8d74\u5730\u53bb\u5b9e\u8df5\u8fd9\u4e2a\u7b97\u6cd5\u7684\u6784\u60f3\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8001\u5b9e\u8bf4\uff0c\u90a3\u65f6\u6211\u5fc3\u91cc\u6700\u4e0d\u60f3\u505a\u7684\u5c31\u662f\u8fd9\u4e2a\u95ee\u9898\u3002\u9996\u5148\uff0c\u6211\u90a3\u65f6\u6839\u672c\u4e0d\u61c2\u8ba1\u7b97\uff08\u8fde\u57fa\u672c\u7684 Fortran \u8bed\u8a00\u3010\u4e3a\u6ee1\u8db3\u6570\u503c\u8ba1\u7b97\u9700\u6c42\u800c\u53d1\u5c55\u51fa\u6765\u7684\u8ba1\u7b97\u673a\u7a0b\u5e8f\u8bed\u8a00\uff0c\u4e8e 20 \u4e16\u7eaa 50 \u5e74\u4ee3\u672b\u7531 IBM \u516c\u53f8\u5f00\u53d1\u3011\u90fd\u4e0d\u4f1a\uff09\u3002\u53e6\u5916\uff0c\u6211\u4eec\u90a3\u65f6\u5e76\u6ca1\u6709\u4ec0\u4e48\u201c\u5de5\u4f5c\u7ad9\u201d\u3001\u201c\u4e2a\u4eba\u7535\u8111\u201d\uff0c\u6240\u6709\u8ba1\u7b97\u7a0b\u5e8f\u90fd\u5fc5\u987b\u6253\u5728\u5361\u7247\u4e0a\uff08\u4e00\u884c\u4e00\u5f20\u5361\uff09\uff0c\u7136\u540e\u628a\u5b83\u4eec\u9001\u53bb\u8ba1\u7b97\u673a\u4e2d\u5fc3\uff0c\u4ed6\u4eec\u7528\u5b66\u6821\u4ec5\u6709\u7684\u4e24\u53f0\u673a\u5668\u66ff\u4f60\u8dd1\u7a0b\u5e8f\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u63a5\u4e0b\u6765\u5c31\u770b\u4f60\u7684\u8fd0\u6c14\u4e86\uff0c\u6709\u65f6\u4e8c\u5341\u5206\u949f\u4e4b\u540e\u5c31\u6709\u7ed3\u679c\uff0c\u6709\u65f6\u8981\u7b49\u4e24\u4e09\u4e2a\u5c0f\u65f6\u751a\u81f3\u66f4\u957f\u65f6\u95f4\u3002\u8fd8\u6709\u4e00\u4e2a\u4e0d\u60f3\u505a\u8fd9\u4e2a\u9898\u76ee\u7684\u7406\u7531\uff1a\u90a3\u65f6\u603b\u4ee5\u4e3a\u6570\u5b66\u7814\u7a76\u603b\u662f\u8981\u8bc1\u4e9b\u5b9a\u7406\u4ec0\u4e48\u7684\uff0c\u641e\u4e9b \u03b5-\u03b4 \u7684\u73a9\u610f\u513f\uff0c\u6211\u5bf9\u7b97\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u7684\u6784\u60f3\u5373\u4f7f\u53ef\u4ee5\u987a\u5229\u8fd0\u4f5c\uff0c\u597d\u50cf\u4e5f\u65e0\u6cd5\u63a8\u51fa\u4ec0\u4e48\u5b9a\u7406\u6765\u3002\u4e0d\u7ba1\u600e\u6837\uff0c\u5728\u6211\u4eec\u90a3\u4e2a\u5e74\u4ee3\uff0c\u597d\u50cf\u8001\u5e08\u53eb\u4f60\u505a\u4ec0\u4e48\uff0c\u4f60\u7167\u7740\u505a\u5c31\u662f\u4e86\u3002\u867d\u7136\u6211\u81ea\u5df1\u5fc3\u4e2d\u6781\u4e0d\u70ed\u8877\u8fd9\u4e2a\u9898\u76ee\uff0c\u4f46\u662f\u4ece\u91cc\u5230\u5916\u90fd\u6beb\u65e0\u6392\u65a5\u7684\u610f\u8bc6\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8bb0\u5f97\u6211\u662f\u5728 1974 \u5e74 1 \u6708\u4e2d\u5f00\u59cb\u7740\u624b\u8fd9\u4e2a\u95ee\u9898\u3002\u5173\u4e8e\u5199\u7a0b\u5e8f\uff0c\u751a\u81f3\u6253\u5361\u90fd\u53ea\u597d\u4e00\u9762\u505a\u4e00\u9762\u5b66\u3002\u6211\u51e0\u4e4e\u6bcf\u5929\u5728\u6e05\u6668 6 \u70b9\u534a\u5c31\u9001\u5361\u7247\u53bb\u8ba1\u7b97\u673a\u4e2d\u5fc3\uff0c\u7136\u540e\u662f\u7b49\u7ed3\u679c\u3001\u6539\u7a0b\u5e8f\u3001\u7b49\u7ed3\u679c\u3001\u6539\u7a0b\u5e8f\u2026\u2026\u5e38\u5e38\u5f04\u5230\u534a\u591c 12 \u70b9\u591a\u3002\u6bcf\u6b21\u7b49\u5230\u7684\u7ed3\u679c\u90fd\u56e0\u7a0b\u5e8f\u6216\u7b97\u6cd5\u7684\u9519\u8bef\uff0c\u57fa\u672c\u4e0a\u62ff\u5230\u7684\u90fd\u662f\u4e00\u5927\u6c93\u5e9f\u7eb8\u3002\u540e\u6765\uff0c\u53bb\u8ba1\u7b97\u673a\u4e2d\u5fc3\u62ff(\u6216\u7b49)\u4e00\u6c93\u5e9f\u7eb8\u597d\u50cf\u5df2\u7ecf\u53d8\u5f97\u4e60\u4ee5\u4e3a\u5e38\u4e86\u3002\u8bb0\u5f97\u662f 3 \u6708 15 \u65e5\u90a3\u5929\u65e9\u4e0a\uff0c\u6211\u5230\u8ba1\u7b97\u673a\u4e2d\u5fc3\u62ff\u5230\u7684\u7ed3\u679c\u5374\u53ea\u6709\u8584\u8584\u7684\u51e0\u9875\u3002\u8d77\u5148\u5fc3\u4e2d\u53ea\u662f\u5927\u4e3a\u7591\u60d1\uff1a\u4eca\u5929\u662f\u600e\u4e48\u56de\u4e8b\uff1f\u6ca1\u60f3\u5230\u6253\u5f00\u4e00\u770b\uff0c\u5c45\u7136\u7b97\u51fa\u201c\u4e0d\u52a8\u70b9\u201d\u6765\u4e86\uff01\u90a3\u662f\u4e2a 100 \u7ef4\u7684\u95ee\u9898\uff01<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8bf4\u5b9e\u5728\u7684\uff0c\u6211\u90a3\u65f6\u5fc3\u4e2d\u5e76\u6ca1\u6709\u5f88\u5927\u7684\u6210\u5c31\u611f\u3002\u8fd9\u5c31\u597d\u50cf\u8001\u5e08\u8981\u6211\u53bb\u626b\u5395\u6240\uff0c\u6211\u7ec8\u4e8e\u628a\u5395\u6240\u6253\u626b\u5e72\u51c0\u4e86\uff0c\u5982\u662f\u800c\u5df2\u3002\u6ca1\u60f3\u5230\uff0c\u5927\u7ea6\u5728\u4e00\u4e2a\u6708\u540e\uff0c\u7ea6\u514b\u6559\u6388\u5728\u7f8e\u56fd\u6570\u5b66\u5b66\u4f1a\u7684Notice\u3010\u5373 Notices of the American Mathematical Society\uff0c\u7f8e\u56fd\u6570\u5b66\u4f1a\u6742\u5fd7\u3011\u4e0a\u770b\u5230\u4e00\u4e2a\u5c06\u5728\u5f53\u5e746\u670826-28\u65e5\u5728\u5357\u5361\u7f57\u6765\u7eb3\u5dde\u7684\u514b\u83b1\u59c6\u68ee\u5927\u5b66\uff08Clemson University\uff09\u4e3e\u884c\u201c\u4e0d\u52a8\u70b9\u8ba1\u7b97\u53ca\u5e94\u7528\u56fd\u9645\u4f1a\u8bae\u201d\uff08International Conference on Computing Fixed Points with Applications\uff09\u7684\u6d88\u606f\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u5b8c\u5168\u51fa\u4e4e\u6211\u4eec\u610f\u6599\u4e4b\u5916\u7684\u662f\uff0c\u4ece 1967 \u5e74\u5f00\u59cb\u5c31\u6709\u4e00\u5927\u7fa4\u4eba\u5728\u7814\u7a76\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u3002\u8fd9\u4e9b\u4eba\u591a\u534a\u662f\u51fa\u81ea\u540d\u6821\u7ecf\u6d4e\u7cfb\u3001\u5546\u5b66\u9662\u3001\u4f5c\u4e1a\u7814\u7a76\u3001\u5de5\u4e1a\u5de5\u7a0b\u7b49\u7cfb\u6240\u7684\u6559\u6388\uff0c\u56e0\u4e3a\u8bb8\u591a\u7ecf\u6d4e\u5b66\u91cc\u7684\u6a21\u5f0f\u7684\u201c\u5747\u8861\u70b9\u201d\uff08Equilibrium\uff09\u90fd\u53ef\u4ee5\u7528\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u7684\u65b9\u5f0f\u6765\u8868\u8fbe\uff0c\u56e0\u6b64\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u7684\u8fd0\u7b97\u53d8\u6210\u4e86\u5b9e\u9645\u5e94\u7528\u4e0a\u7684\u4e00\u4e2a\u91cd\u8981\u5de5\u5177\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8fd9\u4e2a\u4f1a\u8bae\u663e\u7136\u9080\u8bf7\u4e86\u90a3\u4e2a\u95e8\u6d3e\u6240\u6709\u7684\u91cd\u91cf\u7ea7\u4eba\u7269\u53bb\u505a\u62a5\u544a\u3002\u7ea6\u514b\u6559\u6388\u5728\u77e5\u9053\u8fd9\u4e2a\u4f1a\u8bae\u7684\u4fe1\u606f\u4e4b\u540e\uff0c\u7acb\u523b\u6253\u4e86\u4e2a\u7535\u8bdd\u7ed9\u8fd9\u4e2a\u4f1a\u8bae\u7684\u4e3b\u529e\u4eba\u5361\u62c9\u9a6c\u5c14\u8fea\u6602\uff08S. Karamardian\uff09\uff0c\u544a\u8bc9\u4ed6\u6211\u4eec\u6709\u4e00\u4e2a\u65b0\u7684\u7b97\u6cd5\u3002\u5f53\u65f6\u5361\u62c9\u9a6c\u5c14\u8fea\u6602\u4e5f\u53ea\u662f\u534a\u4fe1\u534a\u7591\u5730\u52c9\u5f3a\u7b54\u5e94\u63d0\u4f9b\u6211\u4eec\u4e24\u5f20\u5f80\u8fd4\u514b\u83b1\u59c6\u68ee\u7684\u673a\u7968\u3002\u540e\u6765\u6211\u548c\u51ef\u6d1b\u683c\uff08Kellogg\uff09\u6559\u6388\u4e00\u8d77\u53c2\u52a0\u4e86\u90a3\u4e2a\u4f1a\u8bae\u3002\u6211\u4eec\u5728\u90a3\u91cc\u201c\u4e00\u9e23\u60ca\u4eba\u201d\u3002\u540e\u6765\u8036\u9c81\u5927\u5b66\u7ecf\u6d4e\u7cfb\u7684\u8bb2\u5ea7\u6559\u6388\u65af\u5361\u592b\uff08H. Scarf\uff0c\u4ed6\u662f\u5f53\u521d\u5728 1967 \u5e74\uff0c\u7b2c\u4e00\u4e2a\u63d0\u51fa\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u7b97 \u6cd5\u7684\uff09\u5728\u4f1a\u8bae\u8bba\u6587\u96c6\u7684\u7b80\u4ecb\u91cc\u8bf4\uff1a<\/span><\/section>\n<blockquote>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u201c\u2026\u2026\u5bf9\u4e8e\u6211\u4eec\u4e2d\u7684\u5f88\u591a\u4eba\u6765\u8bf4\uff0c\u5728\u514b\u83b1\u59c6\u68ee\u4f1a\u8bae\u4e2d\u7ed9\u6211\u4eec\u6781\u5927\u60ca\u559c\u7684\u662f\u51ef\u6d1b\u683c\u3001\u674e\u548c\u7ea6\u514b\u7684\u4e00\u7bc7\u6587\u7ae0\uff0c\u6587\u4e2d\u4ed6\u4eec\u7ed9\u51fa\u4e86\u7b2c\u4e00\u4e2a\u901a\u8fc7\u4f7f\u7528\u5fae\u5206\u62d3\u6251\u91cc\u7684\u8fde\u7eed\u6620\u5c04\u6765\u8ba1\u7b97\u4e0d\u52a8\u70b9\u7684\u65b9\u6cd5\uff0c\u800c\u4e0d\u662f\u4f7f\u7528\u6211\u4eec\u4f20\u7edf\u7684\u7ec4\u5408\u65b9\u6cd5\u3002\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u4f5c\u8005\u4eec\u540c\u6837\u7ed9\u51fa\u4e86\u4e3a\u4f55\u8d6b\u5e0c\u7684\u8bba\u8bc1\u53ef\u4ee5\u7528\u6765\u5b9a\u4e49\u4ece\u4efb\u610f\u6307\u5b9a\u7684\u8fb9\u754c\u70b9\u5230\u4e0d\u52a8\u70b9\u7684\u8def\u5f84\u2026\u2026\u201d<\/span><\/section>\n<\/blockquote>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\"><br  \/><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u9644\u5e26\u4e00\u63d0\u7684\u662f\uff0c\u6211\u4eec\u7b97\u6cd5\u4e2d\u6240\u5f15\u7528\u7684\u5fae\u5206\u62d3\u6251\u6982\u5ff5\uff0c\u540e\u6765\u5728\u89e3\u975e\u7ebf\u6027\u95ee\u9898\u6570\u503c\u8ba1\u7b97\u7684\u201c\u540c\u4f26\u7b97\u6cd5\u201d\u4e2d\u8d77\u4e86\u201c\u9769\u547d\u6027\u201d\u7684\u4f5c\u7528\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><br  \/><\/section>\n<section data-mpa-template=\"t\" mpa-from-tpl=\"t\">\n<section mpa-from-tpl=\"t\">\n<section data-mid=\"t4\" style=\"margin-top: 20px;color: rgb(0, 0, 0);display: flex;-webkit-box-pack: center;justify-content: center;-webkit-box-align: center;align-items: center;\" mpa-from-tpl=\"t\">\n<section data-preserve-color=\"t\" data-mid=\"\" style=\"padding-right: 30px;padding-left: 30px;min-width: 60px;text-align: center;border-bottom: 2px solid rgb(232, 230, 230);\" mpa-from-tpl=\"t\">\n<section data-mid=\"\" style=\"padding-right: 10px;padding-left: 10px;display: inline-block;color: rgb(123, 12, 0);border-bottom: 2px solid rgb(123, 12, 0);transform: translate(0px, 2px);border-top-color: rgb(123, 12, 0);border-left-color: rgb(123, 12, 0);border-right-color: rgb(123, 12, 0);\" mpa-from-tpl=\"t\"><strong mpa-from-tpl=\"t\" style=\"border-color: rgb(123, 12, 0);\"><\/p>\n<p style=\"clear: both;min-height: 1em;border-color: rgb(123, 12, 0);font-size: 16px;\">4.&nbsp;\u4e3a\u5c06\u6765\u7684\u5e78\u8fd0\u505a\u597d\u51c6\u5907<\/p>\n<p><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\"><br  \/><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u524d\u4e00\u9635\u5b50\uff0c\u6211\u5728\u7f8e\u56fd\u4e00\u4e2a\u671f\u520a\u4e0a\u8bfb\u5230\u4e00\u7bc7\u6210\u529f\u4f01\u4e1a\u5bb6\u9000\u4f11\u540e\u6240\u5199\u7684\u611f\u8a00\uff0c\u5176\u4e2d\u8ba9\u6211\u4e00\u76f4\u65e0\u6cd5\u5fd8\u5374\u7684\u4e00\u53e5\u8bdd\u662f\uff1a<\/span><\/section>\n<blockquote>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u201c\u2026\u2026\u4e00\u4e2a\u4eba\u5fc5\u987b\u4e3a\u6216\u5c06\u5f97\u5230\u7684\u5e78\u8fd0\u800c\u505a\u597d\u51c6\u5907\u2026\u2026\u201d<\/span><\/section>\n<\/blockquote>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\"><br  \/><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u56de\u60f3\u5f53\u521d\u6211\u5728\u6323\u624e\u662f\u5426\u7814\u7a76\u4e0d\u52a8\u70b9\u7684\u8fd0\u7b97\u65f6\uff0c\u5b9e\u5728\u6709\u5f88\u591a\u501f\u53e3\u53ef\u4ee5\u50cf\u6211\u66fe\u7ecf\u63a5\u89e6\u8fc7\u7684\u4e00\u4e9b\u5b66\u751f\u4f3c\u7684\u62d6\u5b95\u3001\u8eb2\u95ea\u3001\u9a97\u81ea\u5df1\u3001\u62d2\u7edd\u5e72\u6d3b\u2026\u2026\u82e5\u771f\u5982\u6b64\uff0c\u8fd9\u4e2a\u5929\u4e0a\u6389\u4e0b\u6765\u7684\u201c\u4e07\u5e74\u706b\u9f9f\u201d\u4e0d\u662f\u8f7b\u6613\u64e6\u8eab\u800c\u8fc7\u4e86\u5417\uff1f<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u6709\u4e00\u6b21\u548c\u7ea6\u514b\u6559\u6388\u95f2\u804a\u8d77\u5173\u4e8e\u201c\u667a\u5546\u201d\u7684\u8bdd\u9898\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u4ed6\u5e76\u4e0d\u592a\u770b\u91cd\u201c\u667a\u5546\u201d\u7684\u9ad8\u4f4e\u3002\u8bb0\u5f97\u90a3\u65f6\u4ed6\u8bf4\uff0c\u201c\u2026\u2026\u5728\u4f2f\u514b\u5229\u5927\u5b66\u7684\u4eba\u4e00\u822c\u8bf4\u6765\u6709\u9ad8\u667a\u5546\u3002\u4f46\u4f60\u5f88\u96be\u76f8\u4fe1\u4ed6\u4eec\u5728\u505a\u591a\u4e48\u7b28\u7684\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u9009\u62e9\u597d\u7684\u95ee\u9898\u4ee5\u8d85\u51fa\u4ed6\u4eec 20 \u70b9\u7684\u667a\u5546\u6253\u8d25\u4ed6\u4eec\u2026\u2026\u201d\u3002\u8fd9\u4e9b\u8bdd\u867d\u7136\u7565\u4e3a\u90aa\u95e8\uff0c\u4f46\u662f\u8fd9\u4e9b\u5e74\u6765\uff0c\u6bcf\u6b21\u9047\u5230\u8be5\u9009\u4ec0\u4e48\u7814\u7a76\u9898\u76ee\u65f6\uff0c\u603b\u662f\u60f3\u8d77\u4ed6\u7684\u8fd9\u4e9b\u8bdd\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u56de\u60f3\u5f53\u521d\u82e5\u7ed9\u6211\u4e00\u4e2a\u9009\u62e9\uff0c\u6211\u7edd\u4e0d\u4f1a\u62fc\u4e86\u547d\u53bb\u7b97\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\uff0c\u5fc3\u91cc\u771f\u6b63\u60f3\u641e\u7684\u5012\u662f\u5728\u90a3\u65f6\u504f\u5fae\u5206\u65b9\u7a0b\u9886\u57df\u91cc\u76f8\u5f53\u65f6\u9ae6\u7684\u5355\u8c03\u7b97\u5b50\uff08Monotone operator\uff09\uff0c\u90a3\u65f6\u6709\u8bb8\u591a\u77e5\u540d\u7684 \u4eba\u7269\uff08\u50cf\u662f\u54c8\u7279\u66fc\uff08Hartman\uff09\u3001\u65af\u5766\u5e15\u57fa\u4e9a\uff08Stampacchia\uff09\u3001\u660e\u8482\uff08Minty\uff09\u3001\u8001\u83b1\u6602\uff08Lion\uff09\u2026\u2026\uff09\u90fd\u5728\u7814\u7a76\u5b83\u3002\u53ef\u662f\u73b0\u5728\u770b\u6765\uff0c\u90a3\u4e2a\u65f6\u671f\u5728\u5355\u8c03\u7b97\u5b50\u9886\u57df\u91cc\u7684\u5de5\u4f5c\uff0c\u51e0\u4e4e\u6ca1\u6709\u4e00\u4e2a\u91cc\u7a0b\u7891\u6027\u7684\u6210\u679c\u80fd\u591f\u4fdd\u7559\u5230\u4eca\u5929\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u8fd9\u4e9b\u5e74\u6765\uff0c\u6211\u4e2a\u4eba\u66fe\u76f4\u63a5\u63a5\u89e6\u8fc7\u4e00\u4e9b\u6570\u5b66\u754c\u7684\u9876\u5c16\u9ad8\u624b\uff0c\u4f46\u662f\u82e5\u8c08\u5230\u5224\u65ad\u9898\u76ee\u610f\u4e49\u7684\u672c\u9886\uff0c\u6211\u7684\u5bfc\u5e08\u7ea6\u514b\u6559\u6388\u5728\u8fd9\u65b9\u9762\u7684\u529f\u529b\u7684\u786e\u6df1\u539a\uff0c\u7edd\u4e0d\u8f93\u90a3\u4e9b\u201c\u9876\u5c16\u9ad8\u624b\u201d\u3002\u8fd9\u4e5f\u8bb8\u662f\u6211\u81ea\u5df1\u6700\u5927\u7684\u5e78\u8fd0\u5427\uff01<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">&nbsp;<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u6211\u4ece\u6e05\u534e\u5927\u5b66\u6bd5\u4e1a\u5df2\u5c06\u8fd1\u56db\u5341\u5e74\u4e86\u3002\u6709\u65f6\u5e38\u5e38\u60f3\uff0c\u82e5\u662f\u91cd\u65b0\u518d\u7ed9\u6211\u4e00\u6b21\u5b66\u4e60\u7684\u673a\u4f1a\uff0c\u6211\u5c06\u600e\u4e48\u505a\u2026\u2026\u4f46\u662f<\/span><\/section>\n<blockquote>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u201c\u6ca1\u6709\u4eba\u80fd\u4f7f<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\">\u65f6\u5149\u5012\u6d41\uff0c<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\">\u8349\u539f\u518d\u7eff\uff0c<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\">\u82b1\u5349\u518d\u653e\u3002<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\">\u53ea\u6709\u5728\u5269\u4f59\u90e8\u5206\uff0c\u4e89\u53d6\u529b\u91cf\uff01\u201d<\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\">\u3010\u6458\u81ea\u4f5c\u8005\u4e2d\u5b66\u65f6\u671f\u770b\u8fc7\u7684\u4e00\u90e8\u7531\u534e\u4f26\u6bd4\u63d0\u548c\u5a1c\u59b2\u4e3d\u534e\u4e3b\u6f14\u7684\u7535\u5f71\u300a\u5929\u6daf\u4f55\u5904\u65e0\u82b3\u8349\u300b\u3002\u3011<\/section>\n<\/blockquote>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\"><br  \/><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><span style=\"font-size: 15px;\">\u6240\u4ee5\uff0c\u91cd\u65b0\u518d\u7ed9\u6211\u4e00\u6b21\u673a\u4f1a\u7684\u4e8b\u53ea\u662f\u5e7b\u60f3\u3002\u6211\u5e0c\u671b\u6211\u7684\u7ecf\u5386\u80fd\u5728\u8bf8\u4f4d\u957f\u8fdc\u7684\u6570\u5b66\u7814\u7a76\u3001\u5b66\u4e60\u3001\u751a\u81f3\u6559\u5b66\u4e0a\u8d21\u732e\u4e00\u70b9\u4ec0\u4e48\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><br  \/><\/section>\n<section data-mpa-template=\"t\" mpa-from-tpl=\"t\">\n<section mpa-from-tpl=\"t\">\n<p style=\"margin-right: 8px;margin-left: 8px;clear: both;min-height: 1em;color: rgb(0, 0, 0);font-size: medium;\"><br mpa-from-tpl=\"t\"  \/><\/p>\n<section data-mid=\"t4\" style=\"margin-top: 20px;color: rgb(0, 0, 0);display: flex;-webkit-box-pack: center;justify-content: center;-webkit-box-align: center;align-items: center;\" mpa-from-tpl=\"t\">\n<section data-preserve-color=\"t\" data-mid=\"\" style=\"padding-right: 30px;padding-left: 30px;min-width: 60px;text-align: center;border-bottom: 2px solid rgb(232, 230, 230);\" mpa-from-tpl=\"t\">\n<section data-mid=\"\" style=\"padding-right: 10px;padding-left: 10px;display: inline-block;color: rgb(123, 12, 0);border-bottom: 2px solid rgb(123, 12, 0);transform: translate(0px, 2px);border-top-color: rgb(123, 12, 0);border-left-color: rgb(123, 12, 0);border-right-color: rgb(123, 12, 0);\" mpa-from-tpl=\"t\"><strong mpa-from-tpl=\"t\" style=\"border-color: rgb(123, 12, 0);\"><\/p>\n<p style=\"clear: both;min-height: 1em;border-color: rgb(123, 12, 0);font-size: 16px;\">\u63a8\u8350\u9605\u8bfb<\/p>\n<p><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p><br mpa-from-tpl=\"t\"  \/><\/p>\n<p style=\"text-align: center;margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247501861&amp;idx=2&amp;sn=344edc5208443dbcfffeccfe6331161d&amp;chksm=e89792a8dfe01bbe35784ad44678cabcdcda28ad72d5396520f4441a3e6c1e2943223f937430&amp;scene=21#wechat_redirect\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" style=\"text-decoration: underline;\" rel=\"noopener noreferrer\"><strong><span style=\"font-size: 14px;\">\u6df7\u6c8c\u7406\u8bba | \u96c6\u667a\u767e\u79d1<\/span><\/strong><\/a><br  \/><\/p>\n<p style=\"text-align: center;margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247498129&amp;idx=1&amp;sn=87c341f58b5f936adf2708f80e9da4ea&amp;chksm=e897a31cdfe02a0aa81fab3ce46b9a98400d832bd8e9363c1b01941119e5ed708455bf34019c&amp;scene=21#wechat_redirect\" data-itemshowtype=\"11\" tab=\"innerlink\" style=\"text-decoration: underline;font-size: 14px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 14px;\"><strong>\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\u548c\u6df7\u6c8c\u7cfb\u7edf\u4e2d\u7684\u5468\u671f\u6027<\/strong><\/span><\/a><br  \/><\/p>\n<p style=\"text-align: center;margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><strong style=\"font-size: 14px;text-decoration: underline;\"><span style=\"font-size: 14px;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247500912&amp;idx=1&amp;sn=b0d03a728b049e74198b676c1c523689&amp;chksm=e8979efddfe017eb94fc1c1ea22716e3d46ec407f2b2e7fe0d288dee4a7599b923abe185126f&amp;scene=21#wechat_redirect\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 14px;text-decoration: underline;\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u6280\u672f\u5982\u4f55\u6f14\u5316\uff1a\u521b\u65b0\u80cc\u540e\u7684\u6570\u5b66\u9012\u5f52\u7ed3\u6784<\/a><\/span><\/strong><\/p>\n<p style=\"text-align: center;margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247502752&amp;idx=1&amp;sn=4ceaf4f227a4f7065b3cd256a2022552&amp;chksm=e897912ddfe0183b570a12e6b40212e33b76a95c54abe6e10afe7069acb9f6236bd39ccf8cda&amp;scene=21#wechat_redirect\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" style=\"text-decoration: underline;text-align: center;white-space: normal;\" rel=\"noopener noreferrer\"><span style=\"font-size: 14px;\"><strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n<p style=\"text-align: center;margin-left: 8px;margin-right: 8px;line-height: 1.75em;\"><br  \/><\/p>\n<section data-mpa-template=\"t\" mpa-from-tpl=\"t\" style=\"white-space: normal;\">\n<section mpa-from-tpl=\"t\">\n<section data-mpa-template-id=\"1398939\" data-mpa-color=\"null\" data-mpa-category=\"\u6536\u85cf\" mpa-from-tpl=\"t\">\n<section data-mpa-template-id=\"1345806\" data-mpa-color=\"null\" data-mpa-category=\"fav\" mpa-from-tpl=\"t\" style=\"color: rgb(0, 0, 0);font-size: medium;\">\n<hr style=\"color: rgb(51, 51, 51);font-size: 17px;letter-spacing: 0.544px;\"  \/>\n<p style=\"margin-right: 0.5em;margin-left: 0.5em;color: rgb(51, 51, 51);font-size: 17px;letter-spacing: 0.544px;text-align: center;\"><img data-ratio=\"0.9191011235955057\" data-type=\"gif\" data-w=\"445\" width=\"100%\"  style=\"letter-spacing: 0.5px;visibility: visible !important;width: 64px !important;\" src=\"\/wp-content\/uploads\/2020\/06\/wxsync-2020-06-f8813a24c65fe26cf82889d1466d1718.gif\"  \/><br mpa-from-tpl=\"t\"  \/><\/p>\n<p><br mpa-from-tpl=\"t\"  \/><\/p>\n<section data-mpa-template-id=\"5969\" data-mpa-color=\"#ffffff\" mpa-from-tpl=\"t\" style=\"margin-right: 0.5em;margin-left: 0.5em;color: rgb(51, 51, 51);font-size: 17px;letter-spacing: 0.544px;\">\n<section data-mpa-template-id=\"83535\" data-mpa-color=\"#ffffff\" mpa-from-tpl=\"t\" style=\"margin-right: 0.5em;margin-left: 0.5em;line-height: 25.6px;text-align: center;outline: none medium;\">\n<section data-mpa-template-id=\"5969\" data-mpa-color=\"#ffffff\" mpa-from-tpl=\"t\" style=\"margin-right: 0.5em;margin-left: 0.5em;line-height: 25.6px;outline: none medium;\">\n<section data-mpa-template-id=\"83535\" data-mpa-color=\"#ffffff\" mpa-from-tpl=\"t\" style=\"outline: none medium;\">\n<section data-mpa-template=\"\" mpa-from-tpl=\"t\" style=\"margin-right: 0.5em;margin-left: 0.5em;font-size: 15px;outline: none medium;\">\n<section powered-by=\"xiumi.us\" mpa-from-tpl=\"t\" style=\"line-height: 25.6px;border-color: rgb(123, 12, 0);\">\n<p style=\"margin-top: 10px;margin-bottom: 10px;padding-right: 3px;padding-left: 3px;transform: translate3d(0px, 0px, 0px);border-color: rgb(123, 12, 0);line-height: 1.5em;\"><strong mpa-from-tpl=\"t\"><span style=\"font-size: 12px;color: rgb(136, 136, 136);\">\u96c6\u667a\u4ff1\u4e50\u90e8QQ\u7fa4\uff5c877391004<\/span><\/strong><\/p>\n<p style=\"margin-top: 10px;margin-bottom: 10px;padding-right: 3px;padding-left: 3px;transform: translate3d(0px, 0px, 0px);border-color: rgb(123, 12, 0);line-height: 1.5em;\"><strong mpa-from-tpl=\"t\"><span style=\"font-size: 12px;color: rgb(136, 136, 136);\">\u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org<br mpa-from-tpl=\"t\"  \/><\/span><\/strong><\/p>\n<section data-mpa-template-id=\"5969\" data-mpa-color=\"#ffffff\" mpa-from-tpl=\"t\" style=\"margin-right: 0.5em;margin-left: 0.5em;outline: none medium;\">\n<h1 style=\"margin-top: 10px;margin-bottom: 10px;line-height: 1.75em;\"><strong mpa-from-tpl=\"t\" style=\"font-size: 14px;white-space: pre-wrap;color: rgb(0, 112, 192);line-height: 25.6px;\"><strong mpa-from-tpl=\"t\" style=\"line-height: 28px;white-space: normal;color: rgb(61, 170, 214);font-size: 20px;\"><span style=\"font-size: 14px;color: rgb(136, 136, 136);\"><span style=\"color: rgb(255, 76, 0);\">\u25c6&nbsp;<\/span><span style=\"color: rgb(0, 128, 255);\">\u25c6&nbsp;<\/span><span style=\"color: rgb(61, 170, 214);\">\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n<p style=\"margin-right: 0.5em;margin-left: 0.5em;font-size: 19px;color: rgb(71, 193, 168);line-height: 23.2727px;\"><span style=\"color: rgb(123, 12, 0);\"><strong mpa-from-tpl=\"t\"><span style=\"font-size: 14px;\">\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n<p style=\"margin-right: 0.5em;margin-left: 0.5em;font-size: 19px;color: rgb(71, 193, 168);line-height: 23.2727px;\"><br  \/><\/p>\n<p style=\"margin-right: 0.5em;margin-left: 0.5em;font-size: 19px;color: rgb(71, 193, 168);line-height: 23.2727px;\"><span style=\"color: rgb(0, 0, 0);\"><strong mpa-from-tpl=\"t\"><span style=\"font-size: 14px;\">\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n<section mpa-from-tpl=\"t\" style=\"margin-right: 0.5em;margin-left: 0.5em;font-size: 14px;color: rgb(71, 193, 168);line-height: 20px;\">\n<p style=\"margin: 5px auto;padding: 10px;width: 180px;border-width: 2px;border-style: dashed;border-color: rgb(132, 132, 132);line-height: normal;\"><img data-copyright=\"0\" data-cropselx1=\"0\" data-cropselx2=\"156\" data-cropsely1=\"0\" data-cropsely2=\"156\" data-ratio=\"1\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"1125\"  style=\"visibility: visible !important;width: 156px !important;\" src=\"\/wp-content\/uploads\/2020\/06\/wxsync-2020-06-8d63ba433b859b930f684933c607651c.jpeg\"  \/><\/p>\n<\/section>\n<p><span style=\"font-size: 14px;\">\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p style=\"white-space: normal;\"><br mpa-from-tpl=\"t\"  \/><\/p>\n<p style=\"white-space: normal;font-size: 15px;font-weight: 700;letter-spacing: 0.544px;text-align: center;\"><br  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