{"id":600,"date":"2022-08-23T08:11:52","date_gmt":"2022-08-23T00:11:52","guid":{"rendered":"https:\/\/damakey.com\/?p=600"},"modified":"2023-05-24T16:05:28","modified_gmt":"2023-05-24T08:05:28","slug":"%e6%98%af%e6%b9%8a%e5%b7%a7%e9%82%84%e6%98%af%e6%a9%9f%e7%8e%87","status":"publish","type":"post","link":"https:\/\/damakey.com\/?p=600","title":{"rendered":"\u662f\u6e4a\u5de7\u9084\u662f\u6a5f\u7387"},"content":{"rendered":"

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\u4e00\u500b\u73ed\u7d1a\u8981\u81f3\u5c11\u591a\u5c11\u4eba\uff0c\u6709\u4eba\u751f\u65e5\u76f8\u540c\u7684\u6a5f\u7387\u624d\u53ef\u4ee5\u8d85\u904e<\/span>50%<\/span>\uff1f<\/span><\/p>\n

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\u9019\u662f\u6578\u5b78\u5bb6\u7406\u5bdf·\u7c73\u6fa4\u65af<\/span>(Richard von Mises<\/span>\uff0c<\/span>1883-1953)<\/span>\u9996\u5148\u63d0\u51fa\u4f86\u7684\u6709\u8da3\u554f\u984c\u3002<\/span><\/p>\n

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\u7b54\u6848\u662f<\/span>23<\/span>\u4eba\u3002\u662f\u4e0d\u662f\u6bd4\u4f60\u60f3\u50cf\u4e2d\u7684\u5c0f\u5f88\u591a\uff1f<\/span><\/p>\n

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\u89e3\uff1a<\/span><\/p>\n

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\u5047\u8a2d<\/span>p(N)<\/span>\u662f<\/span>N<\/span>\u500b\u4eba\u4e2d\uff0c\u6bcf\u4e00\u500b\u4eba\u751f\u65e5\u7686\u4e0d\u540c\u7684\u6a5f\u7387\u3002<\/span>(<\/span>\u6240\u4ee5\uff0c<\/span>1-p(N)<\/span>\u5c31\u662f\u81f3\u5c11\u6709\u4e00\u5c0d<\/span>(2<\/span>\u500b\u4eba<\/span>)<\/span>\u751f\u65e5\u662f\u76f8\u540c\u7684\u6a5f\u7387<\/span>)<\/span><\/p>\n

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N=2<\/span>\u3002<\/span>p(2)=<\/span>\u7b2c<\/span>1<\/span>\u500b\u4eba\u5728<\/span>365<\/span>\u5929\u4e2d\u67d0\u4e00\u5929\u751f\u65e5\u7684\u6a5f\u7387<\/span>* <\/span>\u7b2c<\/span>2<\/span>\u500b\u4eba\u5728\u7b2c<\/span>1<\/span>\u500b\u4eba\u751f\u65e5\u4e4b\u5916\u7684<\/span>364<\/span>\u5929\u4e2d\u4efb\u4e00\u5929\u751f\u65e5\u7684\u6a5f\u7387<\/span>=(365\/365)*(364\/365)<\/span><\/p>\n

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N=3<\/span>\u3002<\/span>p(3)= <\/span>\u7b2c<\/span>1<\/span>\u500b\u4eba\u5728<\/span>365<\/span>\u5929\u4e2d\u67d0\u4e00\u5929\u751f\u65e5\u7684\u6a5f\u7387<\/span>* <\/span>\u7b2c<\/span>2<\/span>\u500b\u4eba\u5728\u7b2c<\/span>1<\/span>\u500b\u4eba\u751f\u65e5\u4e4b\u5916\u7684<\/span>364<\/span>\u5929\u4e2d\u4efb\u4e00\u5929\u751f\u65e5\u7684\u6a5f\u7387<\/span>* <\/span>\u7b2c<\/span>3<\/span>\u500b\u4eba\u5728\u7b2c<\/span>1<\/span>\u500b\u4eba\u548c\u7b2c<\/span>2<\/span>\u500b\u4eba\u751f\u65e5\u4e4b\u5916\u7684<\/span>363<\/span>\u5929\u4e2d\u4efb\u4e00\u5929\u751f\u65e5\u7684\u6a5f\u7387<\/span>= (365\/365)*(364\/365)*(363\/365)<\/span><\/p>\n

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……<\/span><\/p>\n

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N=23<\/span>\u3002<\/span>p(23)=  <\/span>(365\/365)*(364\/365)*(363\/365)*…*(343\/365)=0.4927<\/span><\/p>\n

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1-p(23)<\/span>\u5c31\u662f\u81f3\u5c11\u6709\u4e00\u5c0d<\/span>(2<\/span>\u500b\u4eba<\/span>)<\/span>\u751f\u65e5\u662f\u76f8\u540c\u7684\u6a5f\u7387<\/span>=0.5073 <\/span><\/p>\n

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\u6240\u4ee5\u5728\u4e00\u500b\u7fa4\u9ad4\u4e2d\u8981\u767c\u73fe\u6709\u4eba\u7684\u751f\u65e5\u76f8\u540c\uff0c\u53ea\u8981\u4eba\u6578\u5920\u591a\u800c\u4e14\u4e0d\u7528\u592a\u591a\uff0c\u53ea\u8981\u8d85\u904e<\/span>23<\/span>\u4eba\uff0c\u6a5f\u7387\u5c31\u8d85<\/span>50%<\/span>\u4e86\u5462\uff01<\/span><\/p>\n

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\u5982\u679c\u628a\u751f\u65e5\u76f8\u540c\uff0c\u6539\u6210\u8eab\u4efd\u5b57\u865f\u5f8c<\/span>4<\/span>\u78bc\u76f8\u540c\u7684\u6a5f\u7387\uff0c\u53ea\u8981\u628a<\/span>365<\/span>\u63db\u6210<\/span>9999<\/span>\u5c31\u53ef\u4ee5\u4e86\u3002<\/span><\/p>\n

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1-p(118)>50%<\/span>\u3002\u53ea\u8981\u7fa4\u9ad4\u5927\u5230<\/span>118<\/span>\u4eba\uff0c\u90a3\u9ebc\u6709\u4eba\u7684\u8eab\u4efd\u8b49\u865f\u5f8c<\/span>4<\/span>\u78bc\u76f8\u540c\u7684\u6a5f\u7387\u5c31\u5927\u65bc<\/span>50%<\/span>\u4e86\u3002<\/span><\/p>\n

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\u6211\u5011\u76f8\u4fe1\u7684\u5076\u7136\uff0c\u5176\u5be6\u5f88\u591a\u662f\u7d71\u8a08\u6a5f\u7387\u7684\u5fc5\u7136\u5462\uff01<\/span><\/p>\n

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\u4f46\u662f\uff0c\u5982\u679c\u8aaa\u662f\u6211\u5728\u7db2\u8def\u4e0a\u8a8d\u8b58\u7684\u670b\u53cb\uff0c\u548c\u6211\u662f\u540c\u5e74\u540c\u6708\u540c\u65e5\u751f\u7684\u6a5f\u7387\u5462\uff1f<\/span><\/p>\n

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\u5148\u8003\u616e\u540c\u6708\u540c\u65e5\u751f\u7684\u60c5\u5f62\u3002\u5982\u679c\u6211\u7684\u751f\u65e5\u662f\u67d0\u4e00\u5929\uff0c\u8b6c\u5982\u4e03\u6708\u4e00\u65e5\uff0c\u90a3\u9ebc\u6211\u5176\u4ed6\u7684\u670b\u53cb\uff0c\u5982\u679c\u90fd\u548c\u6211\u4e0d\u540c\u4e00\u5929\u751f\u65e5\uff0c\u6bcf\u500b\u4eba\u7684\u6a5f\u7387\u5c31<\/span>364\/365<\/span>\uff0c\u5982\u679c\u6211\u6709<\/span>N<\/span>\u500b\u670b\u53cb\uff0c\u90a3\u6211\u8ddf\u4ed6\u5011\u6bcf\u4e00\u500b\u4eba\u751f\u65e5\u90fd\u4e0d\u540c\u7684\u6a5f\u7387\u5c31<\/span>(364\/365)^N<\/span>\u3002<\/span><\/p>\n

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(364\/365)^252.65=50% <\/span>\u3002\u610f\u601d\u662f\u8aaa\u53ea\u8981\u6211\u8a8d\u8b58\u9ad8\u9054<\/span>253<\/span>\u4f4d\u670b\u53cb\uff0c\u90a3\u9ebc\u6709\u4eba\u8ddf\u6211\u751f\u65e5\u7684\u6a5f\u6703\u5c31\u6703\u5927\u65bc<\/span>50%<\/span>\u3002<\/span>(1-(364\/365)^253>50%)<\/span>\u3002<\/span><\/p>\n

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\u90a3\u9ebc\uff0c\u5982\u679c\u52a0\u4e0a\u5e74\u5ea6\u7684\u8003\u616e\u5462\uff1f\u70ba\u4e86\u7c21\u5316\u554f\u984c\uff0c\u5047\u8a2d\u5e74\u7d00\u8207\u6211\u76f8\u5dee\u5728<\/span>10<\/span>\u6b72\u4e4b\u5167\uff0c\u90a3\u8003\u616e\u7684\u5929\u6578\u70ba\u52a0\u6e1b<\/span>3650<\/span>\u65e5\uff0c\u8981\u78b0\u4e0a\u4e00\u4f4d\u540c\u5e74\u540c\u6708\u540c\u65e5\u751f\u7684\u4eba\uff0c\u5c31\u662f<\/span>(1-(7299\/7300)^5,105>50%)<\/span>\u3002\u5fc5\u9808\u8a8d\u8b58\u8d85\u904e<\/span>5,105<\/span>\uff0c\u5982\u679c\u5728<\/span>5<\/span>\u5e74\u5167\uff0c\u610f\u601d\u6bcf\u5929<\/span>3<\/span>\u500b\u4eba\uff0c\u52e4\u5feb\u4e00\u9ede\uff0c\u4f3c\u4e4e\u662f\u6709\u53ef\u80fd\u3002\u4f46\u662f\u4e26\u4e0d\u6703\u6bcf\u6b21\u90fd\u6703\u8ac7\u5230\u751f\u65e5\uff0c\u5982\u679c\u6bcf<\/span>100<\/span>\u6b21\u5c0d\u8a71\u624d\u6709<\/span>1<\/span>\u6b21\uff0c\u90a3\u9ebc\u4ee3\u8868\u6211\u5fc5\u9808\u9047\u898b<\/span>510,500<\/span>\u500b\u4eba\uff0c\u9019\u5c31\u883b\u96e3\u7684\u3002<\/span><\/p>\n

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\u6240\u4ee5\uff0c\u78b0\u4e0a\u540c\u5e74\u540c\u6708\u540c\u65e5\u751f\u7684\u4eba\uff0c\u540c\u73ed\u540c\u5b78\u5bb9\u6613\uff0c\u4f46\u662f\u5982\u679c\u662f\u7db2\u8def\u4e0a\u4e0d\u540c\u5e74\u5ea6\u7684\u670b\u53cb\uff0c\u5c31\u76f8\u5c0d\u96e3\u5f97\u591a\u4e86\u3002<\/span><\/p>\n

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\u53e6\u5916\u4e00\u500b\u6709\u8da3\u7684\u547d\u984c\uff0c\u662f\u6cd5\u570b\u6578\u5b78\u5bb6\u57c3\u7c73\u723e·\u535a\u96f7\u723e<\/span>(Émile Borel, 1871-1956)<\/span>\u63d0\u51fa\u4f86\u7684\uff1a\u300c\u5982\u679c\u7d66\u5b9a\u8db3\u5920\u7684\u6642\u9593\uff0c\u4e00\u96bb\u7334\u5b50\u53ef\u4ee5\u5728\u9375\u76e4\u4e0a\u96a8\u6a5f\u6572\u51fa\u838e\u58eb\u6bd4\u4e9e\u5168\u96c6\u3002\u300d<\/span><\/p>\n

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\u4ec0\u9ebc\uff1f\uff01<\/span><\/p>\n

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\u70ba\u4e86\u63a2\u8a0e\u65b9\u4fbf\uff0c\u6211\u5011\u5148\u5047\u8a2d\u7334\u5b50\u8981\u6253\u7684\u662f\u9019\u9ebc\u4e00\u53e5\u8a71\uff1a<\/span>shall I compare thee to a summer’s day<\/span>\uff1f\u7334\u5b50\u80fd\u5920\u96a8\u6a5f\u7528<\/span>26<\/span>\u500b\u5b57\u6bcd\u7684\u9375\u76e4\u6572\u51fa\u4f86\u7684\u6a5f\u7387\u662f\u591a\u5c11\uff1f<\/span><\/p>\n

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\u5148\u8a66\u7b97\u6572\u51fa<\/span>shall<\/span>\u9019<\/span>5<\/span>\u500b\u5b57\u6bcd\u7684\u6a5f\u7387\uff0c\u5047\u8a2d\u6bcf\u6b21\u6572\u4ec0\u9ebc\u5b57\u6bcd\u4e4b\u9593\u662f\u7368\u7acb\u7684\uff0c\u6572\u5c0d<\/span>shall<\/span>\u9019<\/span>5<\/span>\u500b\u5b57\u6bcd\u7684\u6a5f\u7387\u662f<\/span>(1\/26)^5<\/span>\uff0c\u90a3\u6c92\u6709\u6572\u5c0d\u7684\u6a5f\u7387\u5c31\u662f\uff1a<\/span><\/p>\n

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1-(1\/26)^5=0.99999991573<\/span>\uff0c\u4e5f\u5c31\u662f\u8aaa\u5e7e\u4e4e\u4e0d\u53ef\u80fd\u5c0d\uff0c\u9019\u548c\u6211\u5011\u7684\u76f4\u89ba\u4e00\u81f4\uff0c\u4e00\u6b21\u8981\u6572\u5c0d\u7684\u6a5f\u6703\u5fae\u4e4e\u5176\u5fae\u3002<\/span><\/p>\n

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\u4e0d\u904e\u56e0\u70ba\u6211\u5011\u7d66\u7334\u5b50\u300c\u8db3\u5920\u591a\u6b21\u300d\u7684\u5617\u8a66\uff0c\u5047\u8a2d\u662f<\/span>N<\/span>\u6b21\u7684\u5617\u8a66\uff0c\u90a3\u9ebc\u6c92\u6709\u6572\u5c0d\u7684\u6a5f\u7387\u8b8a\u6210\uff1a<\/span><\/p>\n

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(1-(1\/26)^5)^N<\/span><\/p>\n

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N=8,235,542 <\/span>\u7684\u6642\u5019\uff0c<\/span>1-(1-(1\/26)^5)^N>50%<\/span>\uff0c\u6703\u6709<\/span>50%<\/span>\u7684\u6a5f\u7387\u8499\u51fa\u300c<\/span>shall<\/span>\u300d\u9019\u500b\u5b57\u3002<\/span><\/p>\n

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\u9019\u5728\u5bc6\u78bc\u7684\u4fdd\u8b77\u7a0b\u5ea6\u65b9\u9762\uff0c\u6709\u5f88\u5927\u7684\u5553\u767c\u3002\u5c0d\u65bc\u96fb\u8166\u4f86\u8aaa\uff0c\u8a66\u4e0a<\/span>8,235,542<\/span>\u6b21\u4e26\u975e\u96e3\u4e8b\u3002\u7531<\/span>5<\/span>\u500b\u5b57\u6bcd\u7d44\u6210\u7684\u5bc6\u78bc\uff0c\u7834\u89e3\u4e26\u975e\u96e3\u4e8b\u3002\u6240\u4ee5\uff0c\u4e00\u822c\u6703\u8981\u6c42\u52a0\u4e0a\u5927\u5c0f\u5beb\u3001\u6578\u5b57\u751a\u81f3\u7279\u6b8a\u7b26\u865f\uff0c\u5c31\u662f\u70ba\u4e86\u589e\u52a0\u7834\u89e3\u7684\u96e3\u5ea6<\/span>(<\/span>\u5448\u73fe\u6307\u6578\u589e\u9577<\/span>)<\/span>\u3002<\/span><\/p>\n

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\u9019\u4e5f\u662f\u70ba\u4ec0\u9ebc\u6cd5\u570b\u6578\u5b78\u5bb6\u57c3\u7c73\u723e·\u535a\u96f7\u723e\u6703\u8aaa\uff0c\u300c\u5982\u679c\u7d66\u5b9a\u8db3\u5920\u7684\u6642\u9593\uff0c\u4e00\u96bb\u7334\u5b50\u53ef\u4ee5\u5728\u9375\u76e4\u4e0a\u96a8\u6a5f\u6572\u51fa\u838e\u58eb\u6bd4\u4e9e\u5168\u96c6\u3002\u300d\u4ee5\u73fe\u4ee3\u7684\u8a9e\u5f59\u4f86\u8b1b\uff0c\u6240\u8b02\u8db3\u5920\u7684\u6642\u9593\uff0c\u5176\u5be6\u5c31\u662f\u96fb\u8166\u7684\u901f\u5ea6\u3002\u9019\u4e5f\u662f\u70ba\u4ec0\u9ebc\u6709\u4eba\u6703\u64d4\u5fc3\u91cf\u5b50\u96fb\u8166\u7684\u901f\u5ea6\uff0c\u5c07\u53ef\u80fd\u662f\u73fe\u5728\u8d85\u7d1a\u96fb\u8166\u901f\u5ea6\u7684<\/span>100<\/span>\u5146\u500d<\/span>(10^14=100,000,000,000,000<\/span>\u500d<\/span>)<\/span>\uff0c\u90a3\u9ebc\u73fe\u884c\u7684\u5f88\u591a\u7684\u52a0\u5bc6\u65b9\u6cd5\u5c07\u4e0d\u518d\u53ef\u9760\u4e86\u3002<\/span><\/p>\n

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\u6700\u5f8c\u518d\u4f86\u601d\u8003\u4e00\u500b\u554f\u984c\uff1a\u4e00\u4f4d\u7d93\u5e38\u5728\u4e0d\u540c\u57ce\u5e02\u9593\u65c5\u884c\u7684\u79c1\u52df\u57fa\u91d1\u5973\u57f7\u884c\u9577\uff0c\u5728\u829d\u52a0\u54e5\u53eb\u4e86\u4e00\u8f1b\u8a08\u7a0b\u8eca\uff0c\u4e09\u5e74\u5f8c\uff0c\u5979\u5728\u9081\u963f\u5bc6\u53eb\u5230\u4e00\u6a23\u7684\u8a08\u7a0b\u8eca\u4e26\u767c\u73fe\u548c\u829d\u52a0\u54e5\u662f\u540c\u4e00\u4f4d\u53f8\u6a5f\u7684\u6a5f\u7387\u662f\u591a\u5c11\u3002<\/span><\/p>\n

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\u9996\u5148\u4f30\u8a08\u8a08\u7a0b\u53f8\u6a5f\u5f9e\u829d\u52a0\u54e5\u9077\u79fb\u5230\u9081\u963f\u5bc6\u7684\u6a5f\u7387\u3002<\/span><\/p>\n

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\u829d\u52a0\u54e5\u6709<\/span>15,327<\/span>\u540d\u8a08\u7a0b\u8eca\u53f8\u6a5f\uff0c\u9081\u963f\u5bc6\u5927\u7d04<\/span>5000<\/span>\u540d\uff0c\u4f46\u662f\u6211\u5011\u7121\u6cd5\u77e5\u6709\u591a\u5c11\u829d\u52a0\u54e5\u7684\u53f8\u6a5f\u6703\u642c\u53bb\u9081\u963f\u5bc6\u3002<\/span>2014<\/span>\u5e74\uff0c\u829d\u52a0\u54e5\u4eba\u53e3\u70ba<\/span>2,722,389<\/span>\uff0c\u9077\u51fa<\/span>95,000<\/span>\uff0c\u4e5f\u5c31\u662f\u6bcf\u5e74<\/span>29<\/span>\u5206\u4e4b<\/span>1<\/span>\u3002\u5982\u679c\u5047\u8a2d\u8a08\u7a0b\u8eca\u53f8\u6a5f\u9077\u51fa\u7387\u76f8\u540c\uff0c\u90a3\u9ebc\u4e09\u5e74\u5167\u5c31\u6709<\/span>529<\/span>\u4f4d\u9077\u5f80\u4ed6\u8655\u3002\u829d\u52a0\u54e5\u662f\u7f8e\u570b\u7b2c<\/span>3<\/span>\u5927\u57ce\uff0c\u9081\u963f\u5bc6\u662f\u7b2c<\/span>44<\/span>\u4f4d\uff0c\u6211\u5011\u96e3\u4ee5\u731c\u6e2c\u829d\u52a0\u54e5\u7684\u53f8\u6a5f\u9077\u5f80\u4f55\u8655\uff0c\u4f46\u4f9d\u7167\u7f8e\u570b\u71b1\u9580\u79fb\u5c45\u57ce\u5e02\u6392\u884c\uff0c\u9081\u963f\u5bc6\u540d\u5217\u7b2c<\/span>40<\/span>\u4f4d\uff0c\u56e0\u6b64\u6211\u5011\u53ef\u4ee5\u5047\u8a2d\u829d\u52a0\u54e5\u53f8\u6a5f\u9077\u5f80\u9081\u963f\u5bc6\u7684\u4eba\u6578\u5f88\u5c11\uff0c\u6216\u8a31\u4ecb\u65bc<\/span>20<\/span>\u5230<\/span>40<\/span>\u4e4b\u9593\uff0c\u90a3\u9ebc\u9019\u4f4d\u5973\u57f7\u884c\u9577\u6514\u5230\u540c\u4e00\u4f4d\u53f8\u6a5f\u7684\u6bd4\u7387\u5c31\u662f\u4ecb\u65bc<\/span>20\/15,327<\/span>\u548c<\/span>40\/15,327<\/span>\u4e4b\u9593\u3002\u6a5f\u7387\u662f<\/span>0.13%-0.26%<\/span>\u4e4b\u9593\uff0c\u770b\u4f86\u4e26\u4e0d\u662f\u4e0d\u53ef\u80fd\uff0c\u53ea\u662f\u6a5f\u7387\u883b\u4f4e\u7684\u3002<\/span><\/p>\n

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\u7576\u7136\uff0c\u9019\u5176\u4e2d\u7684\u4e00\u4e9b\u5047\u8a2d\u6703\u9762\u81e8\u8003\u9a57\u3002\u8b6c\u5982\uff0c\u8a08\u7a0b\u8eca\u53f8\u6a5f\u96e3\u9053\u4e0d\u6703\u56e0\u70ba\u5c0d\u4e00\u500b\u5730\u5340\u6bd4\u8f03\u719f\u6089\uff0c\u800c\u8b8a\u5f97\u66f4\u5b89\u571f\u91cd\u9077\u55ce\uff1f\u5982\u679c\u662f\uff0c\u90a3\u9ebc\u6703\u518d\u78b0\u4e0a\u7684\u6a5f\u7387\u5c31\u8981\u518d\u6253\u500b\u6298\u6263\uff0c\u4f46\u662f\u6a5f\u7387\u5927\u5c0f\u7684\u7d1a\u91cf\u5c31\u662f\u5728\u767e\u5206\u4e4b\u96f6\u9ede\u591a\uff0c\u539f\u4f86\u7684\u6578\u5b57\u4e5f\u6709\u53c3\u8003\u7684\u50f9\u503c\u3002<\/span><\/p>\n

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\u6700\u5f8c\uff0c\u7d66\u5927\u5bb6\u4e00\u500b\u503c\u5f97\u601d\u8003\u7684\u554f\u984c\uff0c\u5728\u516c\u53f8\u7684\u96fb\u68af\u88cf\u6703\u78b0\u5230\u5927\u8001\u95c6\u7684\u6a5f\u7387\u6709\u591a\u5c11\uff1f\u5927\u5bb6\u53ef\u4ee5\u7528\u5404\u7a2e\u5047\u8a2d\u53bb\u63a8\u7b97\uff0c\u53ef\u662f\uff0c\u70ba\u4ec0\u9ebc\u8981\u7b97\u9019\u4e00\u984c\u5462\uff1f\u4e0d\u5982\u5148\u60f3\u597d\uff0c\u600e\u9ebc\u8ddf\u5927\u8001\u95c6\u6253\u62db\u547c\uff0c\u5982\u679c\u4ed6\u554f\u8d77\u4ec0\u9ebc\uff0c\u8981\u600e\u6a23\u56de\u61c9\u624d\u597d\u7559\u4e0b\u826f\u597d\u7684\u5370\u8c61\u5427\uff01<\/span><\/p>\n

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\u5728\u516c\u53f8\u78b0\u5230\u5927\u8001\u95c6\u7684\u6a5f\u7387\u5982\u679c\u4e0d\u9ad8\uff0c\u4e0d\u4ee3\u8868\u5b83\u4e0d\u6703\u767c\u751f\uff1b\u800c\u4e14\u5f80\u5f80\u5728\u6211\u5011\u4e0d\u9810\u671f\u7684\u6642\u5019\u53ef\u80fd\u6703\u767c\u751f\uff0c\u90a3\u5c31\u662f\u83ab\u975e\u5b9a\u5f8b\u3002\u5927\u5bb6\u8981\u597d\u597d\u628a\u63e1\uff0c\u62cd\u500b\u99ac\u5c41\uff0c\u7686\u5927\u6b61\u559c\uff0c\u4e5f\u4e0d\u6789\u82b1\u6642\u9593\u7814\u7a76\u6a5f\u7387\u4e00\u5834\u3002<\/span><\/p>\n

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*<\/span>\uff1a\u300a\u662f\u6e4a\u5de7\u9084\u662f\u6a5f\u7387\u300b\uff0c\u7d04\u745f\u592b·\u99ac\u7956\u723e<\/span>  <\/span>Joseph Mazur <\/span>\u8457\uff0c\u738b\u79cb\u6708<\/span><\/p>\n

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2022\/8\/22 <\/span>\u662f\u6e4a\u5de7\u9084\u662f\u6a5f\u7387<\/span> Damakey<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

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