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Zahl\u62ff\u4e0b\u3002<\/p>\n<p>\u56db\u7ef4\u53ca\u4ee5\u4e0a\uff0c\u81f3\u4eca\u6ca1\u4eba\u8bc1\u51fa\u6765\u3002<\/p>\n<p>OpenAI\u8fd9\u6b21\u516c\u5f00\u7684\u4e24\u7bc7\u624b\u7a3f\uff0c\u5206\u522b\u5904\u7406\u4e86\u6302\u8c37\u95ee\u9898\u7684\u4e24\u4e2a\u7248\u672c\u3002<\/p>\n<p>\u7b2c\u4e00\u7bc7\uff1a\u4e09\u7ef4\u6302\u8c37\u6781\u5927\u51fd\u6570\u731c\u60f3<\/p>\n<p>\u4f9d\u7136\u662f\u4e09\u7ef4\uff0c\u4f46\u9898\u76ee\u6362\u6210\u4e86\u66f4\u96be\u7684\u7248\u672c\u3002<\/p>\n<p>\u53ef\u4ee5\u5148\u628a\u5b83\u60f3\u6210\u4e00\u4e2a\u300c\u7ba1\u5b50\u91cd\u53e0\u63a7\u5236\u300d\u95ee\u9898\uff1a\u628a\u8bb8\u591a\u6839\u7ec6\u957f\u7684\u7ba1\u5b50\u653e\u8fdb\u4e09\u7ef4\u7a7a\u95f4\uff0c\u6bcf\u6839\u7ba1\u5b50\u4ee3\u8868\u9488\u7684\u4e00\u4e2a\u65b9\u5411\u3002<\/p>\n<p>\u25b3OpenAI\u516c\u5f00\u7684\u4e09\u7ef4\u6302\u8c37\u6781\u5927\u51fd\u6570\u731c\u60f3\u8bba\u6587\u9996\u9875<\/p>\n<p>\u6570\u5b66\u5bb6\u8981\u7814\u7a76\u7684\u662f\uff0c\u5f53\u8fd9\u4e9b\u7ba1\u5b50\u671d\u5411\u5404\u4e0d\u76f8\u540c\u7684\u65b9\u5411\u65f6\uff0c\u5b83\u4eec\u80fd\u91cd\u53e0\u5230\u4ec0\u4e48\u7a0b\u5ea6\uff0c\u53c8\u80fd\u5426\u7528\u4e00\u4e2a\u7edf\u4e00\u7684\u4f30\u8ba1\u63a7\u5236\u8fd9\u79cd\u91cd\u53e0\u3002<\/p>\n<p>\u738b\u8679\u548cZahl\u8bc1\u660e\u7684\u662f\u300c\u96c6\u5408\u7248\u300d\uff0c\u7814\u7a76\u7684\u662f\u8fd9\u4e9b\u9488\u5806\u5728\u4e00\u8d77\u81f3\u5c11\u5360\u591a\u5927\u5730\u65b9\u3002<\/p>\n<p>\u800cOpenAI\u8bc1\u660e\u7684\u300c\u6781\u5927\u51fd\u6570\u7248\u300d\u5219\u7814\u7a76\u5f97\u66f4\u52a0\u7ec6\u81f4\uff1a<\/p>\n<p>\u628a\u6bcf\u6839\u9488\u52a0\u7c97\u6210\u4e00\u6839\u7ec6\u7ba1\u5b50\uff0c\u5047\u8bbe\u6bcf\u6839\u7ba1\u5b50\u91cc\u53ea\u6709\u4e00\u90e8\u5206\u662f\u300c\u5b9e\u5fc3\u300d\u7684\uff0c\u6bd4\u4f8b\u8bb0\u4f5c\u03bb\u3002\u6240\u6709\u5b9e\u5fc3\u90e8\u5206\u5e76\u5728\u4e00\u8d77\uff0c\u4f53\u79ef\u80fd\u4e0d\u80fd\u4fdd\u8bc1\u4e0d\u5c0f\u4e8e\u03bb\u00b3\u8fd9\u4e2a\u91cf\u7ea7\uff1f<\/p>\n<p>\u03bb\u8d8a\u5c0f\uff0c\u7ba1\u5b50\u8d8a\u7a7a\uff0c\u8d8a\u96be\u63a7\u5236\u3002\u96c6\u5408\u7248\u53ea\u9700\u8981\u4e00\u4e2a\u6bd4\u8f83\u5bbd\u677e\u7684\u03bb\u7684\u5e42\u6b21\u5c31\u591f\u4e86\uff0c\u6781\u5927\u51fd\u6570\u7248\u5219\u8981\u6c42\u8fd9\u4e2a\u5e42\u6b21\u6070\u597d\u662f3\u3002<\/p>\n<p>\u8fd9\u4e00\u70b9\u5728OpenAI\u8bba\u6587\u7684\u5f15\u8a00\u91cc\u4e5f\u660e\u786e\u5199\u51fa\uff1a\u738b\u8679\u548cZahl\u7684\u5b9a\u7406\u7ed9\u51fa\u7684\u662f\u03bb\u7684K(\u03b5)\u6b21\u65b9\uff0c\u300c\u6362\u6210\u03bb\u00b3\u7684\u9700\u8981\u300d\u5728\u4ed6\u4eec\u5b9a\u7406\u4e4b\u540e\u5c31\u5df2\u7ecf\u88ab\u660e\u786e\u63d0\u51fa\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u662f\u738b\u8679\u548cZahl\u7559\u4e0b\u7684\u4e0b\u4e00\u6b65\u3002\u800cOpenAI\u8fd9\u7bc797\u9875\u7684\u8bba\u6587\uff0c\u58f0\u79f0\u628a\u8fd9\u4e00\u6b65\u89e3\u51b3\u4e86\u3002<\/p>\n<p>\u8fd9\u4e3a\u4ec0\u4e48\u91cd\u8981\uff1f\u56e0\u4e3a\u6302\u8c37\u6781\u5927\u51fd\u6570\u628a\u300c\u5404\u79cd\u65b9\u5411\u7684\u7ec6\u7ba1\u5982\u4f55\u6324\u5728\u4e00\u8d77\u300d\u53d8\u6210\u4e86\u53ef\u8ba1\u7b97\u7684\u5206\u6790\u95ee\u9898\u3002<\/p>\n<p>\u5b83\u4e0e\u5085\u91cc\u53f6\u5206\u6790\u4e2d\u7684\u4e00\u4e9b\u6838\u5fc3\u731c\u60f3\u76f8\u8fde\uff0c\u4e5f\u957f\u671f\u88ab\u8ba4\u4e3a\u662f\u7406\u89e3\u6ce2\u3001\u9891\u7387\u548c\u7a7a\u95f4\u96c6\u4e2d\u73b0\u8c61\u7684\u91cd\u8981\u5de5\u5177\u3002<\/p>\n<p>1971\u5e74\uff0cFefferman\u5c31\u662f\u7528\u6302\u8c37\u96c6\u5408\u6784\u9020\u53cd\u4f8b\uff0c\u8bc1\u660e\u4e86\u9ad8\u7ef4\u7684\u7403\u4e58\u5b50\u9664L\u00b2\u5916\u90fd\u4e0d\u6709\u754c\u3002\u6b64\u540e\u6302\u8c37\u95ee\u9898\u5c31\u548c\u5085\u91cc\u53f6\u9650\u5236\u731c\u60f3\u3001Bochner-Riesz\u731c\u60f3\u7d27\u7d27\u8054\u7cfb\u5728\u4e86\u4e00\u8d77\u3002<\/p>\n<p>\u7b2c\u4e8c\u7bc7\uff1a\u56db\u7ef4\u6302\u8c37\u96c6\u7684Hausdorff\u7ef4\u6570<\/p>\n<p>\u56db\u7ef4\u8fd9\u8fb9\uff0c\u4eba\u7c7b\u6b64\u524d\u7684\u8fdb\u5ea6\u662f\u8fd9\u6837\u7684\uff1a<\/p>\n<p>1995\u5e74\uff0cWolff\u7528\u300c\u53d1\u5237\u300d\u65b9\u6cd5\u8bc1\u5230\u7ef4\u6570\u81f3\u5c113\uff1b<\/p>\n<p>\u540e\u6765Guth\u548cZahl\u7528\u591a\u9879\u5f0f\u65b9\u6cd5\u63a8\u52303+1\/40\uff0c\u5927\u7ea63.025\uff1b<\/p>\n<p>2019\u5e74\uff0cKatz\u548cZahl\u7528\u300c\u5e73\u9762\u5237\u300d\u63a8\u52303.059\uff1b<\/p>\n<p>\u4e4b\u540e\u7684\u8fdb\u5c55\uff0c\u57fa\u672c\u90fd\u5728\u5c0f\u6570\u70b9\u540e\u7b2c\u4e8c\u4e09\u4f4d\u4e0a\u632a\u52a8\u3002<\/p>\n<p>\u800cOpenAI\u8fd9\u7bc7175\u9875\u7684\u8bba\u6587\uff0c\u58f0\u79f0\u76f4\u63a5\u8bc1\u52304\u3002<\/p>\n<p>\u25b3OpenAI\u516c\u5f00\u7684\u56db\u7ef4\u6302\u8c37\u96c6Hausdorff\u7ef4\u6570\u731c\u60f3\u8bba\u6587\u9996\u9875<\/p>\n<p>\u56db\u7ef4\u96be\u5728\u54ea\uff1fGuth\u5728\u7efc\u8ff0\u91cc\u6307\u51fa\uff0c\u738b\u8679\u548cZahl\u4e09\u7ef4\u8bc1\u660e\u91cc\u7684\u5173\u952e\u5b9a\u7406\uff0c\u642c\u5230\u56db\u7ef4\u5c31\u4e0d\u6210\u7acb\u4e86\u30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Zahl\u5173\u4e8e\u4e09\u7ef4\u6302\u8c37\u96c6\u731c\u60f3\u7684\u8bba\u6587<\/p>\n<p>Nets 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