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\"11160933788-1_u_1.jpg\"\/<\/p>\n

\u3010\u51dd\u805a\u614b\u7269\u7406\u5b78\u3011\uff08\u4e0a\u5377\uff09<\/span><\/strong><\/p>\n

<\/span><\/strong><\/p>\n

\u5167\u5bb9\u7c21\u4ecb<\/span><\/strong><\/p>\n

\u4e0a\u5377\u4ee5\u7d9c\u89bd\u958b\u982d\uff0c\u63a5\u4e0b\u4f86\u662f\u524d\u56db\u7de8\u3002 \u7b2c\u4e00\u7de8\u51dd\u805a\u7269\u8cea\u7684\u7d50\u69cb\uff0c\u8ad6\u8ff0\u6676\u614b\u7269\u8cea\u7684\u7d50\u69cb\u5c0d\u7a31\u6027\u548c\u69cb\u7bc9\u539f\u7406\uff0c\u4e26\u5ef6\u4f38\u81f3\u6676\u9ad4\u4e4b\u5916\uff0c\u6d89\u53ca\u5230\u5408\u91d1\u3001\u73bb\u7483\u3001\u6db2\u6676\u548c\u805a\u5408\u7269\u7b49\uff0c\u4ee5\u53ca\u975e\u5747\u8cea\u7269\u8cea\uff1b \u7b2c\u4e8c\u7de8\u5404\u7a2e\u7269\u8cea\u7d50\u69cb\u4e2d\u6ce2\u7684\u884c\u70ba\uff0c\u5f9e\u8ad6\u8ff0\u9031\u671f\u7d50\u69cb\u4e2d\u6ce2\u7684\u50b3\u64ad\u51fa\u767c\uff0c\u5206\u5225\u52a0\u4e0a\u51c6\u9031\u671f\u6027\u3001\u8868\u9762\u548c\u96dc\u8cea\uff0c\u4ee5\u53ca\u7121\u5e8f\u5e36\u4f86\u7684\u5f71\u97ff\uff0c\u7279\u5225\u5f37\u8abf\u4e86\u4e0d\u540c\u7d50\u69cb\u548c\u689d\u4ef6\u4e0b\u96fb\u5b50\u7684\u52d5\u529b\u5b78\u548c\u8f38\u904b\u6027\u8cea\uff1b \u7b2c\u4e09\u7de8\u9375\u3001\u80fd\u5e36\u53ca\u5176\u5b83\uff0c\u570d\u7e5e\u96fb\u5b50\u7d50\u69cb\u9019\u4e00\u91cd\u8981\u4e3b\u984c\uff0c\u5206\u5225\u8ad6\u8ff0\u4e86\u5728\u4e0d\u540c\u5834\u5408\u4e0b\u9375\u548c\u80fd\u5e36\u9014\u5f91\u7684\u6709\u6548\u6027\uff0c\u4ee5\u53ca\u5728\u8655\u7406\u5f3a\u95dc\u806f\u96fb\u5b50\u7cfb\u7d71\u6642\u7684\u5c40\u9650\u6027\uff0c\u4e5f\u6307\u51fa\u4e86\u53ef\u80fd\u7684\u6539\u9032\u65b9\u6848\uff0c\u9032\u800c\u5c0d\u7d0d\u7c73\u7d50\u69cb\u7684\u96fb\u5b50\u6027\u8cea\u9032\u884c\u4e86\u8ad6\u8ff0\uff1b \u7b2c\u56db\u7de8\u76f8\u8b8a\u548c\u6709\u5e8f\u76f8\uff0c\u9996\u5148\u5229\u7528\u552f\u8c61\u7684Landau\u7406\u8ad6\uff0c\u7a81\u51fa\u5c0d\u7a31\u6027\u7834\u7f3a\u9019\u4e00\u8988\u5fc3\u6982\u5ff5\uff0c\u70ba\u5404\u7a2e\u4e0d\u540c\u7684\u76f8\u8b8a\u985e\u578b\u5efa\u7acb\u4e86\u7d71\u4e00\u7684\u7406\u8ad6\u6846\u67b6\uff0c\u9032\u800c\u5206\u5225\u8ad6\u8ff0\u4e86\u7d50\u69cb\u76f8\u8b8a\u3001\u78c1\u6709\u5e8f\u76f8\u8b8a\u548c\u8d85\u5c0e\u8d85\u6d41\u76f8\u8b8a\uff0c\u517c\u9867\u5230\u5b8f\u89c0\u548c\u5fae\u89c0\u7684\u63cf\u8ff0\uff0c\u6700\u5f8c\u8003\u5bdf\u4e86\u8207\u66f4\u5ee3\u7fa9\u7684\u904d\u6b77\u6027\u7834\u7f3a\u6709\u95dc\u7684\u76f8<\/p>\n

\u672c\u66f8\u65e2\u662f\u7814\u7a76\u751f\u5de5\u4f5c\u8fa6\u516c\u5ba4\u7684\u7814\u7a76\u751f\u6559\u5b78\u7528\u66f8\uff0c\u9069\u5408\u65bc\u51dd\u805a\u614b\u7269\u7406\u5b78\u548c\u6750\u6599\u79d1\u5b78\u7b49\u5c08\u696d\u7684\u7814\u7a76\u751f\u4f5c\u70ba\u6559\u6750\uff0c\u4e5f\u662f\u666e\u901a\u9ad8\u7b49\u6559\u80b2\u9ede\u6559\u6750\uff0c\u9069\u5408\u65bc\u4f5c\u70ba\u9ad8\u6821\u7269\u7406\u985e\u5c08\u696d\u9ad8\u5e74\u7d1a\u5927\u5b78\u751f\u9078\u4fee\u201c\u51dd\u805a\u614b\u7269\u7406\u5b78\u201d\u8ab2\u7a0b\u7684\u6559\u6750\uff1b \u7576\u7136\uff0c\u4ea6\u53ef\u4f9b\u5f9e\u4e8b\u76f8\u95dc\u9818\u57df\u7814\u7a76\u7684\u79d1\u5b78\u5de5\u4f5c\u8005\u53c3\u6537\u3002<\/p>\n

\u76ee\u9304<\/span><\/strong><\/p>\n

\u7d9c\u89bd<\/p>\n

0.1\u7269\u8cea\u4e16\u754c\u7684\u5c64\u6b21\u5316<\/p>\n

0.1.1 20\u4e16\u7d00\u7684\u7269\u7406\u5b78<\/p>\n

0.1.2\u7c21\u55ae\u6027\u8207\u8907\u96dc\u6027<\/p>\n

0.1.3\u5c64\u5c55\u73fe\u8c61<\/p>\n

0.2\u51dd\u805a\u614b\u7269\u7406\u5b78\u7684\u7bc4\u570d<\/p>\n

0.2.1\u7406\u8ad6\u65b9\u6cd5\uff1a\u91cf\u5b50\u529b\u5b78\u8207\u7d93\u5178\u7269\u7406<\/p>\n

0.2.2\u51dd\u805a\u73fe\u8c61<\/p>\n

0.2.3\u6709\u5e8f\u5316<\/p>\n

0.3\u51dd\u805a\u614b\u7269\u7406\u5b78\u7684\u6b77\u53f2\u900f\u8996\u8207\u6982\u5ff5\u6846\u67b6<\/p>\n

0.3.1\u56fa\u9ad4\u7269\u7406\u5b78\u7684\u7bc4\u5f0f<\/p>\n

0.3.2\u9375\u8207\u80fd\u5e36\u2014\u2014\u5f9e\u55ae\u96fb\u5b50\u8fd1\u4f3c\u8d70\u5411\u95dc\u806f\u96fb\u5b50\u614b<\/p>\n

0.3.3\u5408\u4f5c\u73fe\u8c61\u53ca\u5176\u5b83<\/p>\n

0.3.4\u51dd\u805a\u614b\u7269\u7406\u5b78\u7684\u7bc4\u5f0f<\/p>\n

\u53c3\u8003\u6587\u737b<\/p>\n

\u7b2c\u4e00\u7de8\u51dd\u805a\u7269\u8cea\u7684\u7d50\u69cb<\/p>\n

\u7b2c\u4e00\u7ae0\u7d50\u69cb\u7684\u5c0d\u7a31\u6027<\/p>\n

1.1\u95dc\u65bc\u5c0d\u7a31\u6027\u7684\u57fa\u672c\u6982\u5ff5<\/p>\n

1.1.1\u5c0d\u7a31\u53ca\u5c0d\u7a31\u64cd\u4f5c<\/p>\n

1.1.2\u5c0d\u7a31\u5143\u7d20\u7684\u7d44\u5408\u5b9a\u7406<\/p>\n

1.1.3\u5c0d\u7a31\u7fa4<\/p>\n

1.1.4\u5c0d\u7a31\u7fa4\u7684\u8868\u793a<\/p>\n

1.2\u6709\u9650\u7d50\u69cb\u8207\u9ede\u7fa4<\/p>\n

1.2.1\u5c0d\u7a31\u8ef8\u7684\u7d44\u5408\u898f\u5247<\/p>\n

1.2.2\u8ff4\u5708\u7fa4\u8207\u4e8c\u9762\u9ad4\u7fa4<\/p>\n

1.2.3\u6b63\u591a\u9762\u9ad4\u8207\u7acb\u65b9\u9ede\u7fa4<\/p>\n

1.3\u9031\u671f\u7d50\u69cb\u548c\u7a7a\u9593\u7fa4<\/p>\n

1.3.1\u9031\u671f\u7d50\u69cb\u548c\u6676\u683c<\/p>\n

1.3.2 Bravais\u683c<\/p>\n

1.3.3\u7a7a\u9593\u7fa4<\/p>\n

1.3.4\u6676\u9ad4\u7d50\u69cb\u7684\u63cf\u8ff0<\/p>\n

1.4\u7269\u8cea\u7d50\u69cb\u548c\u5176Fourier\u8b8a\u63db<\/p>\n

1.4.1\u666e\u904d\u60c5\u5f62<\/p>\n

1.4.2\u5012\u683c<\/p>\n

1.4.3\u9031\u671f\u7d50\u69cb\u7684Fourier\u8b8a\u63db<\/p>\n

1.5\u5ee3\u7fa9\u5c0d\u7a31\u6027<\/p>\n

1.5.1\u9ad8\u7dad\u7a7a\u9593\u7fa4<\/p>\n

1.5.2\u8272\u7fa4<\/p>\n

1.5.3\u5012\u7a7a\u9593\u7684\u5c0d\u7a31\u6027<\/p>\n

1.5.4\u5c0d\u7a31\u6027\u7684\u5176\u5b83\u63a8\u5ee3<\/p>\n

\u53c3\u8003\u6587\u737b<\/p>\n

\u7b2c\u4e8c\u7ae0\u6676\u614b\u7d50\u69cb\u53ca\u5176\u69cb\u7bc9\u539f\u7406<\/p>\n

2.1\u5806\u7a4d\u7d50\u69cb\u8207\u76f8\u95dc\u554f\u984c<\/p>\n

2.1.1\u4e8c\u7dad\u7a7a\u9593\u7684\u62fc\u780c\u3001\u5806\u7a4d\u548c\u8986\u84cb<\/p>\n

2.1.2\u4e09\u7dad\u7a7a\u9593\u7684\u5806\u7a4d\u548c\u8986\u84cb<\/p>\n

2.1.3\u7d50\u69cb\u4e2d\u7684\u7a7a\u9699\u548c\u76f8\u95dc\u554f\u984c<\/p>\n

2.2\u9375\u9023\u7d50\u69cb\u548c\u76f8\u95dc\u554f\u984c<\/p>\n

2.2.1\u9375\u9023\u7d50\u69cb<\/p>\n

2.2.2\u6c27\u5316\u7269\u7684\u7d50\u69cb<\/p>\n

2.2.3\u7d50\u69cb\u65cf<\/p>\n

2.3\u66f2\u9762\u8207\u66f2\u7387<\/p>\n

2.3.1\u66f2\u9762\u7684\u66f2\u7387<\/p>\n

2.3.2 Euler\u516c\u5f0f\u8207Gauss\u2014Bonnet\u516c\u5f0f<\/p>\n

2.3.3\u7766\u9762\u6982\u8ff0<\/p>\n

2.3.4 Fuller\u70ef\u548c\u76f8\u95dc\u7684\u7d50\u69cb<\/p>\n

2.4\u51c6\u9031\u671f\u7d50\u69cb<\/p>\n

2.4.1\u7121\u7406\u6578\u8207\u51c6\u9031\u671f\u51fd\u6578<\/p>\n

2.4.2\u4e00\u7dad\u51c6\u9031\u671f\u7d50\u69cb<\/p>\n

2.4.3\u4e8c\u7dad\u9031\u671f\u7d50\u69cb\u7684\u6295\u5f71<\/p>\n

2.4.4\u4e8c\u7dad\u51c6\u9031\u671f\u7d50\u69cb<\/p>\n

2.4.5\u4e09\u7dad\u51c6\u9031\u671f\u7d50\u69cb<\/p>\n

2.4.6\u57fa\u672c\u6982\u5ff5\u7684\u8a0e\u8ad6<\/p>\n

\u53c3\u8003\u6587\u737b<\/p>\n

\u7b2c\u4e09\u7ae0\u6676\u614b\u4e4b\u5916<\/p>\n

\u7b2c\u56db\u7ae0\u975e\u5747\u8cea\u7d50\u69cb<\/p>\n

\u7b2c\u4e8c\u7de8\u5404\u7a2e\u7269\u8cea\u7d50\u69cb\u4e2d\u6ce2\u7684\u884c\u70ba<\/p>\n

\u7b2c\u4e94\u7ae0\u9031\u671f\u548c\u51c6\u9031\u671f\u7d50\u69cb\u4e2d\u6ce2\u7684\u50b3\u64ad<\/p>\n

\u7b2c\u516d\u7ae0Bloch\u96fb\u5b50\u52d5\u529b\u5b78<\/p>\n

\u7b2c\u4e03\u7ae0\u8868\u9762\u548c\u96dc\u8cea\u6548\u61c9<\/p>\n

\u7b2c\u516b\u7ae0\u8f38\u904b\u6027\u8cea<\/p>\n

\u7b2c\u4e5d\u7ae0\u7121\u5e8f\u7cfb\u7d71\u4e2d\u7684\u6ce2\u7684\u5b9a\u57df\u5316<\/p>\n

\u7b2c\u5341\u7ae0\u4ecb\u89c0\u91cf\u5b50\u8f38\u904b<\/p>\n

\u7b2c\u4e09\u7de8\u9375\u3001\u80fd\u5e36\u53ca\u5176\u5b83<\/p>\n

\u7b2c\u5341\u4e00\u7ae0\u9375\u9014\u5f91<\/p>\n

\u7b2c\u5341\u4e8c\u7ae0\u80fd\u5e36\u9014\u5f91<\/p>\n

\u7b2c\u5341\u4e09\u7ae0\u95dc\u806f\u96fb\u5b50\u614b<\/p>\n

\u7b2c\u5341\u56db\u7ae0\u91cf\u5b50\u9650\u5236\u7d0d\u7c73\u7d50\u69cb<\/p>\n

\u7b2c\u56db\u7de8\u76f8\u8b8a\u548c\u6709\u5e8f\u76f8<\/p>\n

\u7b2c\u5341\u4e94\u7ae0Landau\u76f8\u8b8a\u7406\u8ad6<\/p>\n

\u7b2c\u5341\u516d\u7ae0\u6676\u9ad4\u3001\u51c6\u6676\u548c\u6db2\u6676<\/p>\n

\u7b2c\u5341\u4e03\u7ae0\u9435\u78c1\u9ad4\u3001\u53cd\u9435\u78c1\u9ad4\u548c\u4e9e\u9435\u78c1\u9ad4<\/p>\n

\u7b2c\u5341\u516b\u7ae0\u8d85\u6d41\u9ad4\u8207\u8d85\u5c0e\u9ad4<\/p>\n

\u7b2c\u5341\u4e5d\u7ae0\u904d\u6b77\u6027\u7834\u7f3a<\/p>\n

——————————————————————————–<\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

\u3010\u51dd\u805a\u614b\u7269\u7406\u5b78\u3011\uff08\u4e0b\u5377\uff09<\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

<\/p>\n

\u5167\u5bb9\u7c21\u4ecb<\/span><\/strong><\/p>\n

\u63a5\u4e0a\u5377\u7684\u524d\u56db\u7de8\u4e4b\u5f8c\uff0c\u4e0b\u5377\u62ec\u5f8c\u56db\u7de8. \u7b2c\u4e94\u7de8\u70ba\u81e8\u754c\u73fe\u8c61\uff0c\u5f9e\u5206\u6790\u6f32\u843d\u548c\u95dc\u806f\u51fa\u767c\uff0c\u8ad6\u8ff0\u4e86\u51dd\u805a\u7269\u8cea\u4e2d\u7531\u6eab\u5ea6\u3001\u5e7e\u4f55\u53c3\u6578\u3001\u6642\u9593\u548c\u71b1\u7269\u7406\u91cf\u8abf\u63a7\u7684\u5404\u985e\u81e8\u754c\u73fe\u8c61\uff0c\u5f37\u8abf\u4e86\u6a19\u5ea6\u7406\u8ad6\u548c\u91cd\u6b63\u5316\u7fa4\u65b9\u6cd5\uff1b \u7b2c\u516d\u7de8\u70ba\u5143\u6fc0\u767c\uff0c\u9996\u5148\u7d66\u51fa\u4e86\u5143\u6fc0\u767c\u7684\u4e00\u822c\u7279\u5fb5\u3001\u5206\u985e\u539f\u5247\u548c\u5834\u8ad6\u63cf\u8ff0\uff0c\u7136\u5f8c\u5206\u5225\u8ad6\u8ff0\u4e86\u8207\u539f\u5b50\u4f4d\u79fb\u6709\u95dc\u7684\u632f\u52d5\u6fc0\u767c\uff0c\u8207\u81ea\u65cb\u9032\u52d5\u806f\u7cfb\u7684\u81ea\u65cb\u6fc0\u767c\uff0c\u8207\u96fb\u5b50\u76f8\u4e92\u4f5c\u7528\u95dc\u806f\u7684\u96fb\u5b50\u6fc0\u767c\uff0c\u4ee5\u53ca\u4f86\u81ea\u4e0d\u540c\u985e\u578b\u6fc0\u767c\u4e4b\u9593\u8026\u5408\u7684\u8026\u5408\u578b\u6fc0\u767c\uff1b \u7b2c\u4e03\u7de8\u70ba\u7e54\u69cb\u548c\u62d3\u64b2\u7f3a\u9677\uff0c\u5f9e\u5ee3\u7fa9\u5f48\u6027\u548c\u6d41\u9ad4\u52d5\u529b\u5b78\u51fa\u767c\uff0c\u8ad6\u8ff0\u4e86\u6676\u9ad4\u3001\u6db2\u6676\u3001\u9435\u78c1\u9ad4\u548c\u8d85\u5c0e\u9ad4\u4e2d\u7f3a\u9677\u7684\u62d3\u64b2\u548c\u5e7e\u4f55\u6027\u8cea\uff0c\u7d50\u69cb\u548c\u80fd\u91cf\u5b78\uff0c\u529b\u5b78\u548c\u7269\u7406\u6027\u8cea\uff0c\u4ee5\u53ca\u6709\u7f3a\u9677\u4ecb\u5165\u7684\u76f8\u8b8a\uff1b \u7b2c\u516b\u7de8\u70ba\u8d85\u51fa\u5e73\u8861\u614b\uff0c\u4e00\u65b9\u9762\u5728\u50b3\u7d71\u7684\u51dd\u805a\u7269\u8cea\u7bc4\u570d\u5167\uff0c\u63a2\u8a0e\u4e86\u8207\u6210\u6838\u3001\u5931\u7a69\u5206\u89e3\u548c\u7587\u58c1\u5f62\u6210\u6709\u95dc\u7684\u76f8\u8b8a\u52d5\u529b\u5b78\uff0c\u4ee5\u53ca\u5f9e\u529b\u5b78\u3001\u5e7e\u4f55\u548c\u80fd\u91cf\u89d2\u5ea6\u5206\u6790\u4e86\u6676\u9ad4\u751f\u9577\u548c\u5f62\u8c8c\u5b78\uff0c\u53e6\u4e00\u65b9\u9762\u8003\u616e\u5728\u9060\u96e2\u5e73\u8861\u5340\uff0c\u5f9e\u5931\u7a69\u8d70\u5411\u6df7\u6c8c\uff0c\u76f4\u81f3\u6e4d\u6d41\u554f\u984c\uff0c\u4ee5\u53ca\u5f37\u8abf\u51dd\u805a\u614b\u7269\u7406\u5b78\u57fa\u672c\u6982\u5ff5\u7684\u958b\u62d3\u6f5c\u529b\uff0c\u8868\u73fe\u51fa\u5728\u5730\u9707\u3001 \u751f\u7269\u7b49\u8207\u8907\u96dc\u6027\u6709\u95dc\u7684\u5b78\u79d1\u4e2d\u7684\u61c9\u7528<\/p>\n

\u672c\u66f8\u9ad4\u7cfb\u7cbe\u5be9\u3001\u8996\u91ce\u958b\u95ca\u3001\u8ad6\u8ff0\u878d\u8cab\u3001\u5167\u5bb9\u65b0\u7a4e\uff0c\u5c0d\u65bc\u5f9e\u4e8b\u51dd\u805a\u614b\u7269\u7406\u5b78\u53ca\u76f8\u95dc\u5b78\u79d1\u7684\u7814\u7a76\u5de5\u4f5c\u8005\u662f\u4e00\u672c\u5bcc\u6709\u555f\u767c\u6027\u4e14\u4fbf\u65bc\u95b1\u8b80\u7684\u79d1\u5b78\u8ad6\u8457\uff0c\u4e5f\u53ef\u4ee5\u4f5c\u70ba\u653b\u8b80\u51dd\u805a\u614b\u7269\u7406\u5b78\u8207\u76f8\u95dc\u5b78\u79d1\u5b78\u4f4d\u7684\u7814\u7a76\u751f\u7684\u5165\u9580\u53c3\u8003\u66f8.<\/p>\n

\u76ee\u9304<\/span><\/strong><\/p>\n

\u7b2c\u4e94\u7de8\u81e8\u754c\u73fe\u8c61<\/p>\n

\u7b2c\u4e8c\u5341\u7ae0\u6f32\u843d\u3001\u95dc\u806f\u548c\u8017\u6563<\/p>\n

20.1\u6982\u7387\u5206\u4f48<\/p>\n

20.1.1GaUSS\u5206\u4f48<\/p>\n

20.1.2\u5e42\u5f8b\u5206\u4f48\u548c\u5176\u5b83Ga.USS\u5206\u4f48<\/p>\n

20.2\u7d71\u8a08\u7269\u7406\u5b78\u4e2d\u7684\u6f32\u843d\u548c\u95dc\u806f<\/p>\n

20.2.1\u7269\u7406\u91cf\u7684\u6f32\u843d<\/p>\n

20.2.2Poisson\u516c\u5f0f<\/p>\n

20.2.3\u95dc\u806f\u51fd\u6578<\/p>\n

20.2.4\u6f32\u843d\u7684\u7a7a\u9593\u95dc\u806f\u6027<\/p>\n

20.2.5\u6f32\u843d\u7684\u6642\u9593\u95dc\u806f\u6027<\/p>\n

20.3\u96a8\u6a5f\u904e\u7a0b<\/p>\n

20.3.1Bron\u904b\u52d5\u7406\u8ad6\u548c\u64f4\u6563\u65b9\u7a0b<\/p>\n

20.3.2Levy\u98db\u884c\u7406\u8ad6\u548c\u53cd\u5e38\u64f4\u6563<\/p>\n

20.3.3Langevin\u65b9\u7a0b<\/p>\n

20.3.4\u4e3b\u65b9\u7a0b<\/p>\n

20.3.5Fokker-Planck\u65b9\u7a0b<\/p>\n

20.4\u52d5\u529b\u5b78\u97ff\u61c9<\/p>\n

20.4.1\u7dda\u6027\u97ff\u61c9<\/p>\n

20.4.2Onsager\u5012\u6613\u95dc\u4fc2<\/p>\n

20.4.3\u5ee3\u7fa9\u6975\u5316\u7387<\/p>\n

20.4.4\u6f32\u843d\u8017\u6563\u5b9a\u7406<\/p>\n

20.4.5Nyquist\u516c\u5f0f<\/p>\n

20.5\u91cf\u5b50\u6f32\u843d<\/p>\n

20.5.1\u91cf\u5b50\u7c21\u4e26\u6c23\u9ad4\u7684\u6f32\u843d<\/p>\n

20.5.2\u6f32\u843d\u7684\u91cf\u5b50\u529b\u5b78\u8655\u7406<\/p>\n

20.5.3\u91cf\u5b50\u81ea\u65cb\u7684\u6f32\u843d<\/p>\n

\u53c3\u8003\u6587\u737b<\/p>\n

\u7b2c\u4e8c\u5341\u4e00\u7ae0\u71b1\u81e8\u754c\u73fe\u8c61<\/p>\n

21.1\u81e8\u754c\u9ede\u5340\u57df<\/p>\n

21.1.1\u81e8\u754c\u884c\u70ba<\/p>\n

21.1.2\u81e8\u754c\u6307\u6578<\/p>\n

21.1.3\u6a19\u5ea6\u5f8b<\/p>\n

21.2\u5e73\u5747\u5834\u63cf\u8ff0<\/p>\n

21.2.1Ising\u7cfb\u7d71\u7684\u95dc\u806f\u51fd\u6578<\/p>\n

21.2.2\u95dc\u806f\u51fd\u6578\u7684\u5e73\u5747\u5834\u7d50\u679c<\/p>\n

21.2.3\u504f\u96e2\u5e73\u5747\u5834\u7406\u8ad6<\/p>\n

21.2.4\u5e73\u5747\u5834\u7406\u8ad6\u7684\u6709\u6548\u7bc4\u570d<\/p>\n

21.3\u6a19\u5ea6\u7406\u8ad6<\/p>\n

21.3.1\u81ea\u7531\u80fd\u7684\u9f4a\u6b21\u6027<\/p>\n

21.3.2\u95dc\u806f\u51fd\u6578\u7684\u6a19\u5ea6\u8b8a\u63db<\/p>\n

21.3.3\u6709\u9650\u5c3a\u5bf8\u6a19\u5ea6<\/p>\n

21.4\u5be6\u7a7a\u9593\u91cd\u6b63\u5316\u7fa4\u65b9\u6cd5<\/p>\n

21.4.1\u53c3\u91cf\u91cd\u6b63\u5316<\/p>\n

21.4.2\u914d\u5206\u51fd\u6578\u8207\u81ea\u7531\u80fd<\/p>\n

21.4.3\u4e09\u89d2\u6676\u683c\u4e0a\u7684Ising\u81ea\u65cb<\/p>\n

21.5\u52d5\u91cf\u7a7a\u9593\u91cd\u6b63\u5316\u7fa4\u65b9\u6cd5<\/p>\n

21.5.1\u81ea\u65cb\u8b8a\u6578\u9023\u7e8c\u5316<\/p>\n

21.5.2Gauss\u6a21\u578b<\/p>\n

21.5.3\u52d5\u91cf\u7a7a\u9593\u4e2d\u7684\u6a19\u5ea6\u8b8a\u63db<\/p>\n

21.5.4\u52d5\u91cf\u7a7a\u9593\u7684\u91cd\u6b63\u5316\u8655\u7406<\/p>\n

\u53c3\u8003\u6587\u737b<\/p>\n

\u7b2c\u4e8c\u5341\u4e8c\u7ae0\u5ee3\u7fa9\u7684\u81e8\u754c\u73fe\u8c61<\/p>\n

22.1\u666e\u9069\u6027\u53ca\u5176\u610f\u7fa9<\/p>\n

22.1.1\u666e\u9069\u985e<\/p>\n

22.1_ 2n-\u5411\u91cf\u6a21\u578b<\/p>\n

22.1.3\u805a\u5408\u7269\u7d71\u8a08\u7684\u78c1\u985e\u6bd4<\/p>\n

22.1.4Potts\u6a21\u578b<\/p>\n

22.1.5\u51dd\u81a0\u548c\u6ef2\u6d41<\/p>\n

22.2\u5f9e\u6ef2\u6d41\u5230\u805a\u5408\u7269<\/p>\n

22.2.1\u5e7e\u4f55\u81e8\u754c\u9ede<\/p>\n

22.2.2\u6b63\u65b9\u6676\u683c\u4e0a\u7684\u6ef2\u6d41\u96c6\u5718<\/p>\n

22.2.3\u81ea\u56de\u907f\u884c\u8d70\u548c\u805a\u5408\u7269\u69cb\u8c61<\/p>\n

22.2.4\u5ea7\u4e00\u9375\u6ef2\u6d41\u548c\u6eb6\u81a0\u4e00\u51dd\u81a0\u8f49\u8b8a<\/p>\n

\u2026\u2026<\/p>\n

\u7b2c\u516d\u7de8\u5143\u6fc0\u767c<\/p>\n

\u7b2c\u4e03\u7de8\u7e54\u69cb\u548c\u62d3\u64b2\u7f3a\u9677<\/p>\n

\u7b2c\u516b\u7de8\u8d85\u51fa\u5e73\u8861\u614b<\/p>\n

<\/p>\n

<\/span><\/strong><\/p>\n

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