{"id":53054,"date":"2014-05-13T15:23:45","date_gmt":"2014-05-13T07:23:45","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=53054"},"modified":"2021-10-06T16:18:30","modified_gmt":"2021-10-06T08:18:30","slug":"%e6%94%b9%e8%ae%8a%e6%ad%b7%e5%8f%b2%e9%80%b2%e7%a8%8b%e7%9a%8417%e5%80%8b%e6%96%b9%e7%a8%8b%e5%bc%8f","status":"publish","type":"post","link":"http:\/\/localhost\/%e6%94%b9%e8%ae%8a%e6%ad%b7%e5%8f%b2%e9%80%b2%e7%a8%8b%e7%9a%8417%e5%80%8b%e6%96%b9%e7%a8%8b%e5%bc%8f\/","title":{"rendered":"\u6539\u8b8a\u6b77\u53f2\u9032\u7a0b\u768417\u500b\u65b9\u7a0b\u5f0f"},"content":{"rendered":"

\u6539\u8b8a\u6b77\u53f2\u9032\u7a0b\u768417\u500b\u65b9\u7a0b\u5f0f<\/strong><\/span>
\n\u81fa\u5317\u5e02\u7acb\u7b2c\u4e00\u5973\u5b50\u9ad8\u7d1a\u4e2d\u5b78\u8607\u4fca\u9d3b\u8001\u5e2b\u7de8\u8b6f\/\u570b\u7acb\u81fa\u7063\u5927\u5b78\u7269\u7406\u7cfb\u738b\u540d\u5112\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/strong><\/span><\/p>\n

\u7de8\u8b6f\u4f86\u6e90\uff1a<\/span>The 17 Equations That Changed The Course Of History<\/a><\/strong><\/p>\n

\u6578\u5b78\u570d\u7e5e\u5728\u6211\u5011\u56db\u5468\uff0c\u5b83\u5728\u8a31\u591a\u65b9\u9762\u578b\u5851(shaped)\u6211\u5011\u5c0d\u9019\u500b\u4e16\u754c\u7684\u7406\u89e3\u3002<\/p>\n

2013\u5e74\uff0c\u8eab\u70ba\u6578\u5b78\u5bb6\uff0c\u4e5f\u662f\u79d1\u666e\u4f5c\u8005\u7684\u4f0a\u6069\uff0e\u53f2\u90fd\u83ef(Ian Stewart)\u51fa\u7248\u4e86\u300a\u6539\u8b8a\u4e16\u754c\u768417\u500b\u65b9\u7a0b\u5f0f\u300b(The 17 Equations that Changed the World)\u4e00\u66f8\u3002\u8fd1\u4f86\uff0c\u6211\u5011\u5728Dr. Paul Coxon\u7684Twitter (\u7531\u6578\u5b78\u8f14\u5c0e\u8001\u5e2b\uff0c\u4e5f\u662f\u90e8\u843d\u5ba2\u7684Larry Phillips\u6240\u8a3b\u518a)\u4e0a\u767c\u73fe\u9019\u500b\u4ed6\u6458\u9304\u66f8\u4e2d\u65b9\u7a0b\u5f0f\u6240\u6210\u7684\u7c21\u4fbf\u8868\u683c\uff1a<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

\u00a0\u6539\u8b8a\u4e16\u754c\u7684 17 \u500b\u65b9\u7a0b\u5f0f<\/p>\n

\u4f0a\u6069\\(\\cdot\\)\u53f2\u90fd\u83ef<\/p>\n<\/th>\n<\/tr>\n

\u00a01.<\/td>\n\u7562\u6c0f\u5b9a\u7406
\nPythagoras’s Theorem<\/td>\n		\\(a^2+b^2=c^2\\)<\/td>\n\u7562\u9054\u54e5\u62c9\u65af(Pythagoras)
\n\u516c\u5143\u524d 530 \u5e74<\/td>\n<\/tr>\n
\u00a02.<\/td>\n\u5c0d\u6578
\nLogarithms<\/td>\n		\\(\\log xy=\\log x+\\log y\\)<\/td>\n\u7d0d\u76ae\u723e(John Napier)
\n1610 \u5e74<\/td>\n<\/tr>\n
3.<\/td>\n\u5fae\u7a4d\u5206
\nCalculus<\/td>\n		\\(\\displaystyle\\frac{\\mathrm{d}f}{\\mathrm{d}t}=\\lim_{h\\to 0}\\frac{f(t+h)-f(t)}{h}\\)<\/td>\n\u00a0\u725b\u9813(Newton)
\n1668 \u5e74<\/td>\n<\/tr>\n
4.<\/td>\n\u842c\u6709\u5f15\u529b\u5b9a\u5f8b
\nLaw of Gravity<\/td>\n		\\(\\displaystyle F=G\\frac{m_1m_2}{r^2}\\)<\/td>\n\u725b\u9813(Newton)
\n1687 \u5e74<\/td>\n<\/tr>\n
5.<\/td>\n-1 \u7684\u5e73\u65b9\u6839
\nThe Square Root of Minus One<\/td>\n		\\(i^2=-1\\)<\/td>\n\u6b50\u62c9(Euler)
\n1750 \u5e74<\/td>\n<\/tr>\n
6.<\/td>\n\u6b50\u62c9\u7684\u591a\u9762\u9ad4\u516c\u5f0f
\nEuler’s Formula for Polyhedra<\/td>\n		\\(V-E+F=2\\)<\/td>\n\u6b50\u62c9(Euler)
\n1751 \u5e74<\/td>\n<\/tr>\n
7.<\/td>\n\u5e38\u614b\u5206\u5e03
\nNormal Distribution<\/td>\n		\\(\\displaystyle \\Phi(x)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}\\)<\/td>\n\u9ad8\u65af(C. F. Gauss)
\n1810 \u5e74<\/td>\n<\/tr>\n
8.<\/td>\n\u6ce2\u52d5\u65b9\u7a0b\u5f0f
\nWave Equation<\/td>\n		\\(\\displaystyle \\frac{\\partial^2 u}{\\partial t^2}=c^2\\frac{\\partial^2 u}{\\partial x^2}\\)<\/td>\n\u9054\u6717\u8c9d\u723e(J. d’Almbert)
\n1746 \u5e74<\/td>\n<\/tr>\n
9.<\/td>\n\u5085\u5229\u8449\u8b8a\u63db
\nFourier Transform<\/td>\n		\\(\\displaystyle\\overline{f}(\\omega)=\\int^\\infty_{-\\infty}f(x)e^{-2\\pi ix\\omega}\\mathrm{d}x\\)<\/td>\n\u5085\u5229\u8449(J. Fourier)
\n1822 \u5e74<\/td>\n<\/tr>\n
10.<\/td>\n\u7d0d\u7dad-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u5f0f
\nNavier-Stokes Equations<\/td>\n		\\(\\displaystyle\\rho(\\frac{\\partial v}{\\partial t}+v\\cdot \\triangledown v)=-\\triangledown p+\\triangledown \\cdot T+f\\)<\/td>\n\u7d0d\u7dad(C. Navier)\uff0c\u65af\u6258\u514b\u65af(G. Stokes)
\n1845 \u5e74<\/td>\n<\/tr>\n
11.<\/td>\n\u99ac\u514b\u58eb\u5a01\u65b9\u7a0b\u7d44
\nMaxwell’s Equations<\/td>\n		\\(\\displaystyle\\triangledown\\cdot E=\\frac{\\rho}{\\varepsilon_0}\\\\\\triangledown\\cdot B=0\\\\\\displaystyle\\triangledown\\times E=-\\frac{\\partial B}{\\partial t}\\\\\\displaystyle\\triangledown\\times B=\\mu_0(J+\\varepsilon_0\\frac{\\partial E}{\\partial t})\\)<\/td>\n\u99ac\u514b\u58eb\u5a01(J. C. Maxwell)
\n1865 \u5e74<\/td>\n<\/tr>\n
12.<\/td>\n\u71b1\u529b\u5b78\u7b2c\u4e8c\u5b9a\u5f8b
\nSecond Law of Thermodynamics<\/td>\n		\\(\\mathrm{d}S\\ge 0~(S=k\\cdot \\log W)\\)<\/td>\n\u6ce2\u8332\u66fc(L. Boltzmann)
\n1874 \u5e74<\/td>\n<\/tr>\n
13.<\/td>\n\u76f8\u5c0d\u8ad6
\nRelativity<\/td>\n		\\(E=mc^2\\)<\/td>\n\u611b\u56e0\u65af\u5766(Einstein)
\n1905 \u5e74<\/td>\n<\/tr>\n
14.<\/td>\n\u859b\u4e01\u683c\u65b9\u7a0b\u5f0f
\nSchrodinger’s Equation<\/td>\n		\\(\\displaystyle i\\hbar\\frac{\\partial}{\\partial t}\\Psi=\\hat{H}\\Psi\\)<\/td>\n\u859b\u4e01\u683c(E. Schrodinger)
\n1927 \u5e74<\/td>\n<\/tr>\n
15.<\/td>\n\u8cc7\u8a0a\u7406\u8ad6
\nInformation Theory<\/td>\n		\\(H=-\\sum_xp(x)\\log p(x)\\)<\/td>\n\u590f\u8fb2(C. Shannon)
\n1949 \u5e74<\/td>\n<\/tr>\n
16.<\/td>\n\u6df7\u6c8c\u7406\u8ad6
\nChaos Theory<\/td>\n		\\(x_{t+1}=kx_t(1-x_t)\\)<\/td>\n\u6885(Robert May)
\n1975 \u5e74<\/td>\n<\/tr>\n
17.<\/td>\n\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f
\nBlack-Scholes Equation<\/td>\n		\\(\\displaystyle\\frac{1}{2}\\sigma^2S^2\\frac{\\partial^2V}{\\partial S^2}+rS\\frac{\\partial V}{\\partial S}+\\frac{\\partial V}{\\partial t}-rV=0\\)<\/td>\n\u5e03\u840a\u514b(F. Black)\uff0c\u4f11\u65af(M. Scholes)
\n1990 \u5e74<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

(\u539f\u6587\u4e2d\u932f\u8aa4\u5747\u5df2\u70ba\u4f5c\u8005\u8207\u8cac\u4efb\u7de8\u8f2f\u66f4\u6b63\u3002)<\/p>\n

\u5c0d\u65bc\u9019\u4e9b\u5851\u9020\u6578\u5b78\u53ca\u4eba\u985e\u6b77\u53f2\u7684\u7f8e\u5999\u65b9\u7a0b\u5f0f\uff0c\u4e0b\u9762\u6709\u66f4\u591a\u7684\u4ecb\u7d39\uff1a<\/strong><\/p>\n

\"a1\"<\/a>1.\u7562\u6c0f\u5b9a\u7406<\/strong><\/span>\uff1a\u9019\u500b\u5b9a\u7406\u662f\u6211\u5011\u7406\u89e3\u5e7e\u4f55\u7684\u57fa\u790e\u3002\u5b83\u63cf\u8ff0\u5e73\u9762\u4e0a\u4e00\u500b\u76f4\u89d2\u4e09\u89d2\u5f62\u4e09\u908a\u4e4b\u9593\u7684\u95dc\u4fc2\uff1a\u5169\u500b\u77ed\u908a(\\(a\\) \u548c \\(b\\))\u5e73\u65b9\u76f8\u52a0\uff0c\u53ef\u4ee5\u5f97\u5230\u9577\u908a(\\(c\\))\u7684\u5e73\u65b9\u3002<\/p>\n

\u5728\u67d0\u4e9b\u65b9\u9762\uff0c\u9019\u500b\u95dc\u4fc2\u78ba\u5be6\u5c07\u6211\u5011\u719f\u77e5\u7684\u5e73\u9762\u6b50\u6c0f\u5e7e\u4f55\u548c\u66f2\u9762\u7684\u975e\u6b50\u5e7e\u4f55\u5206\u958b\u4f86\u3002\u4f8b\u5982\uff0c\u756b\u5728\u7403\u9762\u4e0a\u7684\u76f4\u89d2\u4e09\u89d2\u5f62\u5c31\u4e0d\u7528\u9075\u5b88\u7562\u6c0f\u5b9a\u7406\u3002<\/p>\n

2. \u5c0d\u6578<\/strong><\/span>\uff1a\u5c0d\u6578(\u51fd\u6578)\u662f\u6307\u6578\u51fd\u6578\u7684\u53cd\u51fd\u6578\u3002\u4e00\u500b\u7279\u5b9a\u5e95\u6578\u7684\u5c0d\u6578\uff0c\u544a\u8a34\u4f60\u7528\u9019\u500b\u5e95\u6578\u4f86\u8868\u793a\u9019\u500b\u6578\u6240\u9700\u8981\u7684\u6307\u6578(power)\u3002\u8b6c\u5982 \\(10^0=1\\)\uff0c\u6240\u4ee5\u5e95\u6578\u70ba \\(10\\) \u7684 \\(1\\) \u4e4b\u5c0d\u6578 \\(\\log 1=0\\)\uff1b\\(10^1=10\\)\uff0c\u6240\u4ee5 \\(\\log 10=1\\)\uff1b\\(10^2=100\\)\uff0c\u6240\u4ee5 \\(\\log 100=2\\)\u3002<\/p>\n

\u65b9\u7a0b\u5f0f \\(\\log ab=\\log a+\\log b\\)\uff0c\u5c55\u793a\u5c0d\u6578\u6700\u6709\u7528\u7684\u61c9\u7528\uff1a\u5c07\u4e58\u6cd5\u8b8a\u6210\u52a0\u6cd5\u3002\u4e00\u76f4\u5230\u8a08\u7b97\u6a5f\u767c\u5c55\u4e4b\u524d\uff0c\u9019\u662f\u5feb\u901f\u9032\u884c\u5927\u6578\u5b57\u76f8\u4e58\u6700\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u5927\u5927\u5730\u52a0\u5feb\u5728\u7269\u7406\u3001\u5929\u6587\uff0c\u4ee5\u53ca\u5de5\u7a0b\u4e0a\u7684\u8a08\u7b97\u3002<\/p>\n

3. \u5fae\u7a4d\u5206<\/strong><\/span>\uff1a\u9019\u88cf\u7d66\u7684\u516c\u5f0f\u662f\u5fae\u7a4d\u5206\u4e0a\u5c0e\u6578\u7684\u5b9a\u7fa9\uff0c\u5c0e\u6578\u662f\u8861\u91cf\u5169\u500b\u91cf\u4e4b\u9593\u8b8a\u5316\u95dc\u4fc2\u7684\u6bd4\u7387\u3002\u6bd4\u65b9\u8aaa\uff0c\u6211\u5011\u8003\u616e\u901f\u5ea6\uff0c\u9019\u662f\u4f4d\u7f6e\u5c0d\u6642\u9593\u7684\u5c0e\u6578 \u2500 \u5047\u5982\u4f60\u6bcf\u5c0f\u6642\u7528 \\(3\\) \u82f1\u91cc\u7684\u901f\u5ea6\u884c\u8d70\uff0c\u8868\u793a\u4f60\u4ee5\u6bcf\u500b\u5c0f\u6642 \\(3\\) \u82f1\u91cc\u6539\u8b8a\u4f60\u7684\u4f4d\u7f6e\u3002<\/p>\n

\u4e00\u822c\u800c\u8a00\uff0c\u591a\u6578\u79d1\u5b78\u5bb6\u6709\u8208\u8da3\u7684\u662f\u77ad\u89e3\u4e8b\u7269\u5982\u4f55\u6539\u8b8a\uff0c\u5c0e\u6578\u548c\u7a4d\u5206 \u2500 \u5fae\u7a4d\u5206\u53e6\u4e00\u500b\u57fa\u790e \u2500 \u6b63\u662f\u6578\u5b78\u5bb6\u8207\u79d1\u5b78\u5bb6\u7406\u89e3\u8b8a\u5316\u7684\u95dc\u9375\u3002<\/p>\n

4. \u842c\u6709\u5f15\u529b\u5b9a\u5f8b<\/strong><\/span>\uff1a\u725b\u9813\u7684\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u63cf\u8ff0\u5169\u500b\u7269\u9ad4\u9593\u7684\u5438\u5f15\u529b \\(F\\)\uff0c\u7531\u5e38\u6578 \\(G\\)\u3001\u5169\u7269\u9ad4\u7684\u8cea\u91cf \\(m_1\\) \u548c \\(m_2\\)\uff0c\u4ee5\u53ca\u5169\u7269\u9ad4\u4e4b\u9593\u7684\u8ddd\u96e2 \\(r\\) \u800c\u6c7a\u5b9a\u3002\u725b\u9813\u7684\u5b9a\u5f8b\u662f\u79d1\u5b78\u53f2\u975e\u5e38\u51fa\u8272\u7684\u90e8\u4efd \u2500 \u5b83\u5e7e\u4e4e\u5b8c\u7f8e\u5730\u89e3\u91cb\u884c\u661f\u70ba\u4f55\u4f9d\u7167\u4ed6\u5011\u6240\u9075\u5faa\u7684\u65b9\u5f0f\u79fb\u52d5\u3002\u540c\u6a23\u51fa\u8272\u7684\u662f\u5b83\u7684\u666e\u904d\u6027 \u2500 \u4e0d\u53ea\u662f\u9069\u7528\u65bc\u5730\u7403\u4e0a\u7684\u91cd\u529b\u5982\u4f55\u4f5c\u7528\uff0c\u6216\u662f\u5728\u6211\u5011\u7684\u592a\u967d\u7cfb\uff0c\u4e5f\u5305\u62ec\u5b87\u5b99\u7684\u4efb\u4f55\u89d2\u843d\u3002<\/p>\n

\u725b\u9813\u7684\u5f15\u529b\u6709\u6548\u7dad\u6301\u4e86200\u5e74\uff0c\u76f4\u5230\u88ab\u611b\u56e0\u65af\u5766\u7684\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u53d6\u4ee3\u70ba\u6b62\u3002<\/p>\n

5.\u00a0\\(-1\\) \u7684\u5e73\u65b9\u6839<\/strong><\/span>\uff1a\u6578\u5b78\u5bb6\u7e3d\u662f\u5728\u64f4\u5c55\u6578\u5b57\u5230\u5e95\u662f\u4ec0\u9ebc\u7684\u6982\u5ff5\uff0c\u5f9e\u81ea\u7136\u6578\uff0c\u5230\u8ca0\u6578\u3001\u5206\u6578\u3001\u548c\u5be6\u6578\u3002\\(-1\\) \u7684\u5e73\u65b9\u6839(\u7d93\u5e38\u88ab\u5beb\u4f5c \\(i\\))\uff0c\u5b8c\u6210\u9019\u500b\u904e\u7a0b\uff0c\u4e26\u4e14\u5f15\u51fa\u8907\u6578\u3002<\/p>\n

\u5728\u6578\u5b78\u4e0a\uff0c\u8907\u6578\u662f\u975e\u5e38\u512a\u96c5\u7684\u3002\u4ee3\u6578\u80fd\u5b8c\u7f8e\u4f9d\u5faa\u6211\u5011\u6240\u8981\u7684\u65b9\u5f0f\u904b\u4f5c \u2500 \u4efb\u4f55\u65b9\u7a0b\u5f0f\u90fd\u6709\u8907\u6578\u89e3\uff0c\u4e0d\u4e00\u5b9a\u6709\u5be6\u6578\u89e3\uff1a\u50cf \\(x^2+4=0\\) \u6c92\u6709\u5be6\u6578\u89e3\uff0c\u4f46\u5b83\u6709\u5169\u500b\u8907\u6578\u7684\u89e3\uff1a\\(\\pm 2i\\)\u3002\u5fae\u7a4d\u5206\u53ef\u4ee5\u64f4\u5c55\u5230\u8907\u6578\uff0c\u7d93\u7531\u9019\u9ebc\u505a\uff0c\u6211\u5011\u767c\u73fe\u9019\u4e9b\u6578\u5b57\u4e00\u4e9b\u9a5a\u4eba\u7684\u5c0d\u7a31\u6027\u548c\u6027\u8cea\uff0c\u9019\u4e9b\u6027\u8cea\u4f7f\u5f97\u8907\u6578\u5728\u96fb\u8def\u548c\u4fe1\u865f\u8655\u7406\u4e0a\u8b8a\u5f97\u4e0d\u53ef\u6216\u7f3a\u3002<\/p>\n

\"a2\"<\/a>

\u6b63\u65b9\u9ad4<\/p><\/div>\n

6. \u6b50\u62c9\u7684\u591a\u9762\u9ad4\u516c\u5f0f<\/strong><\/span>\uff1a\u591a\u9762\u9ad4\u662f\u591a\u908a\u5f62\u4e09\u7dad\u7684\u7248\u672c\uff0c\u50cf\u7acb\u65b9\u9ad4\u5c31\u662f\u5176\u4e2d\u4e00\u500b\u4f8b\u5b50\u3002\u591a\u9762\u9ad4\u7684\u89d2\u843d\u5c31\u7a31\u70ba\u9802\u9ede\uff0c\u9023\u63a5\u9802\u9ede\u7684\u7dda\u6bb5\u7a31\u70ba\u908a\uff0c\u8986\u84cb\u5b83\u7684\u591a\u908a\u5f62\u5c31\u7a31\u70ba\u9762\u3002\u4e00\u500b\u7acb\u65b9\u9ad4\u6709 \\(8\\) \u500b\u9802\u9ede\uff0c\\(12\\) \u689d\u908a\uff0c\u548c \\(6\\) \u500b\u9762\u3002\u5018\u82e5\u5c07\u9802\u9ede\u6578\u548c\u9762\u6578\u52a0\u8d77\u4f86\uff0c\u518d\u6e1b\u53bb\u908a\u6578\uff0c\u5f97\u5230 \\(8+6-12=2\\)\u3002\u6b50\u62c9\u7684\u516c\u5f0f\u6307\u51fa\uff0c\u53ea\u8981\u4f60\u7684\u591a\u9762\u9ad4\u662f\u826f\u614b\u7684(well behaved)\uff0c\u5c07\u9802\u9ede\u6578\u548c\u9762\u6578\u76f8\u52a0\uff0c\u518d\u6e1b\u53bb\u908a\u6578\uff0c\u4f60\u7e3d\u6703\u5f97\u5230 \\(2\\)\u3002\u7121\u8ad6\u4f60\u7684\u591a\u9762\u9ad4\u6709 \\(4\\)\u3001\\(8\\)\u3001\\(12\\)\u3001\\(20\\) \u6216\u662f\u4efb\u610f\u9762\u6578\uff0c\u90fd\u5c07\u70ba\u771f\u3002<\/p>\n

\u6b50\u62c9\u7684\u767c\u73fe\u662f\u73fe\u5728\u88ab\u7a31\u70ba\u62d3\u6a38\u4e0d\u8b8a\u91cf\u7684\u6700\u521d\u4f8b\u5b50\u4e4b\u4e00 \u2500 \u540c\u985e\u5f62\u72c0\u6240\u5171\u4eab\u7684\u67d0\u4e9b\u6578\u5b57\u548c\u6027\u8cea\u5f7c\u6b64\u90fd\u76f8\u4f3c\u3002\u826f\u614b\u7684\u591a\u9762\u9ad4\u90fd\u6709 \\(V+F-1=2\\)\u3002\u9019\u500b\u767c\u73fe\uff0c\u9023\u540c\u6b50\u62c9\u54e5\u5c3c\u65af\u5821\u4e03\u6a4b\u554f\u984c(the Bridges of Konigsburg Problem)\u7684\u89e3\u6cd5\uff0c\u4e00\u8d77\u70ba\u73fe\u4ee3\u7269\u7406\u5b78\u4e0d\u53ef\u6216\u7f3a\u7684\u6578\u5b78\u5206\u652f\u62d3\u6a38\u5b78\u7684\u767c\u5c55\u92ea\u597d\u9053\u8def\u3002<\/p>\n

7.\u5e38\u614b\u5206\u5e03<\/strong><\/span>\uff1a\u6709\u8457\u719f\u77e5\u9418\u5f62\u66f2\u7dda\u5716\u5f62\u7684\u5e38\u614b\u6a5f\u7387\u5206\u5e03\uff0c\u5728\u7d71\u8a08\u5b78\u4e2d\u7121\u8655\u4e0d\u5728\u3002\u7269\u7406\u3001\u751f\u7269\u4ee5\u53ca\u793e\u6703\u79d1\u5b78\u4e0a\u7d93\u5e38\u904b\u7528\u5e38\u614b\u5206\u5e03\u4f86\u6a21\u5f0f\u5316\u5404\u7a2e\u6027\u8cea\uff0c\u539f\u56e0\u4e4b\u4e00\u662f\u5e38\u614b\u66f2\u7dda\u53ef\u4ee5\u7528\u4f86\u63cf\u8ff0\u5927\u91cf\u7368\u7acb\u904e\u7a0b(independent processes)\u7684\u884c\u70ba\u3002<\/p>\n

\"a3\"<\/a>

\u5e38\u614b\u5206\u5e03<\/p><\/div>\n

8.\u6ce2\u52d5\u65b9\u7a0b\u5f0f<\/strong><\/span>\uff1a\u9019\u662f\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\uff0c\u898f\u7bc4\u6ce2\u51fd\u6578\u5c0d\u6642\u9593\u8207\u7a7a\u9593\u8b8a\u6578\u7684\u4e8c\u6b21\u5fae\u5206\u7684\u65b9\u7a0b\u5f0f\uff0c\u5176\u4e2d \\(c\\)\u00a0<\/i>\u4ee3\u8868\u6ce2\u7684\u50b3\u905e\u901f\u7387\u3002\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u53ef\u63cf\u8ff0\u6ce2\u7684\u884c\u70ba \u5982\u632f\u52d5\u7684\u5409\u4ed6\u5f26\uff0c\u77f3\u584a\u4e1f\u51fa\u5f8c\u6c60\u5858\u7522\u751f\u7684\u6f23\u6f2a\uff0c\u767d\u71be\u71c8\u6ce1\u7522\u751f\u7684\u5149\u7b49\u3002\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u96d6\u7136\u53ea\u662f\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\u5f0f\uff0c\u89e3\u6c7a\u9019\u500b\u65b9\u7a0b\u6240\u767c\u5c55\u51fa\u7684\u6280\u5de7\u958b\u555f\u4e86\u7406\u89e3\u5176\u4ed6\u5fae\u5206\u65b9\u7a0b\u7684\u5927\u9580\u3002<\/p>\n

9. \u5085\u7acb\u8449\u8b8a\u63db<\/strong><\/span>\uff1a\u60f3\u8981\u7406\u89e3\u8907\u96dc\u7684\u6ce2\u52d5\u7d50\u69cb\uff0c\u50cf\u662f\u4eba\u7684\u8aaa\u8a71\uff0c\u5085\u7acb\u8449\u8b8a\u63db\u662f\u4e0d\u53ef\u7f3a\u5c11\u7684\u3002\u7d66\u5b9a\u4e00\u500b\u8907\u96dc\u3001\u51cc\u4e82\u7684\u6ce2\u52d5\u7d50\u69cb\uff0c\u4f8b\u5982\u4eba\u7684\u8ac7\u8a71\u9304\u97f3\uff0c\u5085\u7acb\u8449\u8b8a\u63db\u5141\u8a31\u6211\u5011\u5c07\u9019\u51cc\u4e82\u7684\u7d50\u69cb\u5206\u89e3\u6210\u4e00\u4e9b\u7c21\u55ae\u6ce2\u7684\u5408\u6210\uff0c\u5927\u5927\u5730\u7c21\u5316\u5206\u6790\u7684\u5de5\u4f5c\u3002<\/p>\n

\u5085\u7acb\u8449\u8b8a\u63db\u662f\u73fe\u4ee3\u4fe1\u865f\u8655\u7406\u548c\u5206\u6790\uff0c\u4ee5\u53ca\u6578\u64da\u58d3\u7e2e\u7684\u6838\u5fc3\u3002<\/p>\n

10. \u7d0d\u7dad-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u5f0f<\/strong><\/span>\uff1a\u548c\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u76f8\u540c\uff0c\u9019\u4e5f\u662f\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\u3002\u7d0d\u7dad-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u5f0f\u63cf\u8ff0\u6d41\u9ad4\u7684\u884c\u70ba \u2500 \u6c34\u5728\u7ba1\u9053\u7684\u6d41\u52d5\uff0c\u7a7a\u6c23\u6d41\u904e\u6a5f\u7ffc\uff0c\u6216\u662f\u7159\u5f9e\u9ede\u71c3\u7684\u9999\u7159\u4e0a\u5347\u8d77\u3002\u5118\u7ba1\u5229\u7528\u96fb\u8166\u6a21\u64ec\u6d41\u9ad4\u904b\u52d5\uff0c\u6211\u5011\u53ef\u4ee5\u5f97\u5230\u7d0d\u7dad-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u5f0f\u6975\u4f73\u7684\u8fd1\u4f3c\u89e3\uff0c\u4f46\u80fd\u5426\u69cb\u9020\u51fa\u9019\u500b\u65b9\u7a0b\u5f0f\u6578\u5b78\u7684\u7cbe\u78ba\u89e3\uff0c\u4ecd\u7136\u662f\u5f85\u89e3\u7684\u554f\u984c(\u6709\u767e\u842c\u7f8e\u5143\u734e\u91d1)\u3002<\/p>\n

11.\u99ac\u514b\u58eb\u5a01\u65b9\u7a0b\u7d44<\/strong><\/span>\uff1a\u9019\u662f\u7531\u56db\u500b\u63cf\u8ff0\u96fb\\((E)\\)\u8207\u78c1\\((H)\\)\u7684\u884c\u70ba\u548c\u95dc\u4fc2\u4e4b\u5fae\u5206\u65b9\u7a0b\u6240\u7d44\u6210\u7684\u65b9\u7a0b\u7d44\u3002\u99ac\u514b\u58eb\u5a01\u65b9\u7a0b\u7d44\u4e4b\u65bc\u53e4\u5178\u96fb\u78c1\u5b78\uff0c\u5982\u540c\u725b\u9813\u7684\u904b\u52d5\u5b9a\u5f8b\u548c\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u4e4b\u65bc\u53e4\u5178\u529b\u5b78 \u2500 \u4ed6\u5011\u662f\u6211\u5011\u89e3\u91cb\u96fb\u78c1\u5b78\u5728\u65e5\u5e38\u5c3a\u5ea6\u4e0b\u5982\u4f55\u4f5c\u7528\u7684\u57fa\u790e\u3002\u5982\u8981\u63a8\u5ee3\u5230\u539f\u5b50\u7684\u5c3a\u5ea6\uff0c\u5c31\u6709\u8cf4\u91cf\u5b50\u529b\u5b78\u7684\u4fee\u6b63\uff0c\u9019\u9580\u5b78\u554f\u7a31\u70ba\u91cf\u5b50\u96fb\u52d5\u529b\u5b78\u3002\u6e05\u695a\u7684\u662f\uff0c\u9019\u4e9b\u512a\u7f8e\u7684\u99ac\u514b\u58eb\u5a01\u65b9\u7a0b\u5f0f\u662f\u5728\u4eba\u985e\u5c3a\u5ea6\u4e0b\uff0c\u96fb\u78c1\u5b78\u4ee5\u53ca\u5149\u5b78\u2500\u5149\u5373\u96fb\u78c1\u6ce2\u2500\u80fd\u5920\u88ab\u826f\u597d\u63cf\u8ff0\u7684\u8fd1\u4f3c\u65b9\u7a0b\u7d44\u3002<\/p>\n

12. \u71b1\u529b\u5b78\u7b2c\u4e8c\u5b9a\u5f8b<\/strong><\/span>\uff1a\u5728\u4e00\u500b\u5c01\u9589\u7684\u7cfb\u7d71\u4e2d\uff0c\u71b5\\((S)\\)\u7e3d\u662f\u4fdd\u6301\u7a69\u5b9a\u6216\u9010\u6f38\u589e\u52a0\uff0c\u800c\u6ce2\u8332\u66fc\u5beb\u4e0b\u7684\u65b9\u7a0b\u5f0f\u66f4\u8ce6\u4e88\u4e86\u71b5\u7d71\u8a08\u7684\u610f\u7fa9\u3002\u7c21\u55ae\u5730\u8aaa\uff0c\u71b1\u529b\u5b78\u7684\u71b5\u662f\u5ea6\u91cf\u4e00\u500b\u7cfb\u7d71\u7684\u7d0a\u4e82\u7a0b\u5ea6\u3002\u4e00\u500b\u958b\u59cb\u6642\u6709\u5e8f\uff0c\u4f46\u4e0d\u5e73\u8861\u7684\u7cfb\u7d71 \u2500 \u4f8b\u5982\uff0c\u9760\u8fd1\u5bd2\u51b7\u5340\u57df\u7684\u71b1\u9ede\u5340\u57df \u2500 \u7e3d\u662f\u8da8\u5411\u5e73\u8861\u7684\u7d0a\u4e82\u72c0\u614b\uff0c\u71b1\u6703\u5f9e\u71b1\u5340\u6d41\u5411\u51b7\u5340\uff0c\u76f4\u5230\u5747\u52fb\u5206\u4f48\u70ba\u6b62\u3002\u5927\u591a\u6578\u7684\u7269\u7406\u904e\u7a0b\u90fd\u662f\u4e0d\u53ef\u9006\u7684 \u2500 \u4ea6\u5373\u5b87\u5b99\u7684\u71b5\u6703\u4e00\u76f4\u8b8a\u5927\uff0c\u9019\u96b1\u542b\u4e86\u6642\u9593\u662f\u6709\u65b9\u5411\u6027\u7684\u3002\u4f8b\u5982\u6211\u5011\u5c07\u51b0\u584a\u653e\u5165\u4e00\u676f\u71b1\u5496\u5561\u4e2d\uff0c\u6211\u5011\u7e3d\u662f\u770b\u5230\u51b0\u584a\u878d\u5316\uff0c\u537b\u672a\u66fe\u898b\u904e\u4e00\u676f\u5496\u5561\u751f\u51fa\u51b0\u584a\u800c\u5496\u5561\u81ea\u5df1\u8b8a\u71b1\u3002<\/p>\n

13. \u76f8\u5c0d\u8ad6<\/strong><\/span>\uff1a\u611b\u56e0\u65af\u5766\u7528\u72f9\u7fa9\u548c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u5f9e\u6839\u672c\u4e0a\u6539\u8b8a\u4e86\u7269\u7406\u7684\u9032\u7a0b\uff0c\u7d93\u5178\u7684\u65b9\u7a0b\u5f0f \\(E=mc^2\\) \u8aaa\u660e\u8cea\u91cf\u8207\u80fd\u91cf\u7684\u8f49\u63db\u95dc\u4fc2\u3002\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u5f15\u9032\u5149\u5728\u771f\u7a7a\u4e2d\u7684\u901f\u5ea6\u662f\u56fa\u5b9a\u4e0d\u8b8a\u7684\uff0c\u4ee5\u53ca\u4e0d\u540c\u901f\u5ea6\u79fb\u52d5\u7684\u4eba\u5c0d\u6642\u9593\u6d41\u901d\u53ca\u7a7a\u9593\u8ddd\u96e2\u611f\u53d7\u4e26\u4e0d\u76f8\u540c\u7684\u6982\u5ff5\u3002\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u5247\u8a8d\u70ba\u91cd\u529b\u662f\u6642\u9593\u8207\u7a7a\u9593\u672c\u8eab\u7684\u5f4e\u66f2\u548c\u647a\u758a\uff0c\u81ea\u725b\u9813\u7684\u5b9a\u5f8b\u4ee5\u4f86\uff0c\u9019\u662f\u6211\u5011\u5c0d\u91cd\u529b\u7684\u7406\u89e3\u9996\u6b21\u5de8\u5927\u7684\u6539\u8b8a\uff0c\u5c0d\u65bc\u6211\u5011\u4e86\u89e3\u5b87\u5b99\u7684\u8d77\u6e90\u3001\u69cb\u9020\uff0c\u548c\u6700\u7d42\u7d50\u5c40\uff0c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u3002<\/p>\n

14. \u859b\u4e01\u683c\u65b9\u7a0b\u5f0f<\/strong><\/span>\uff1a\u9019\u662f\u5728\u91cf\u5b50\u529b\u5b78\u4e0a\u6700\u4e3b\u8981\u7684\u65b9\u7a0b\u5f0f\uff0c\u5982\u540c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u5728\u6700\u5927\u5c3a\u5ea6\u4e0a\u8aaa\u660e\u6211\u5011\u7684\u5b87\u5b99\uff0c\u9019\u500b\u65b9\u7a0b\u5247\u662f\u652f\u914d\u539f\u5b50\u548c\u6b21\u539f\u5b50\u7c92\u5b50\u7684\u884c\u70ba\u3002<\/p>\n

\u73fe\u4ee3\u91cf\u5b50\u529b\u5b78\u662f\u6b77\u53f2\u4e0a\u975e\u5e38\u6210\u529f\u7684\u79d1\u5b78\u7406\u8ad6 \u2500 \u6240\u6709\u6211\u5011\u505a\u7684\u5be6\u9a57\u7d50\u679c\u90fd\u548c\u91cf\u5b50\u529b\u5b78\u7684\u9810\u6e2c\u5b8c\u5168\u4e00\u81f4\u3002\u6700\u73fe\u4ee3\u7684\u6280\u8853\u4e5f\u9700\u8981\u91cf\u5b50\u529b\u5b78\uff0c\u8209\u51e1\u6838\u80fd\u3001\u8087\u57fa\u65bc\u534a\u5c0e\u9ad4\u7684\u96fb\u8166\uff0c\u4ee5\u53ca\u96f7\u5c04\u7b49\u90fd\u5efa\u7acb\u5728\u91cf\u5b50\u73fe\u8c61\u4e0a\u3002<\/p>\n

15.\u8cc7\u8a0a\u7406\u8ad6<\/strong><\/span>\uff1a\u9019\u88cf\u7d66\u51fa\u7684\u65b9\u7a0b\u5f0f\u662f\u70ba\u4e86\u590f\u8fb2\u8cc7\u8a0a\u71b5(Shannon information entropy)\u3002\u5982\u540c\u524d\u8ff0\uff0c\u71b1\u529b\u5b78\u7684\u71b5\u662f\u5c0d\u7d0a\u4e82\u7684\u4e00\u7a2e\u5ea6\u91cf\uff0c\u9019\u88cf\u6307\u7684\u662f\u5c0d\u8a0a\u606f\u8cc7\u8a0a\u91cf\u7684\u5ea6\u91cf \u2500 \u4e00\u672c\u66f8\uff0c\u4e00\u5f35\u7db2\u8def\u4e0a\u5bc4\u9001\u7684JPEG\u5716\u7247\uff0c\u6216\u662f\u4efb\u4f55\u53ef\u7528\u7b26\u865f\u8868\u793a\u7684\u4e8b\u7269\u3002\u8a0a\u606f\u7684\u590f\u8fb2\u71b5\u8aaa\u7684\u662f\u5728\u4e0d\u6f0f\u5931\u5167\u5bb9\u7684\u60c5\u5f62\u4e0b\uff0c\u8a0a\u606f\u53ef\u4ee5\u88ab\u58d3\u7e2e\u591a\u5c11\u7684\u4e0b\u9650\u3002<\/p>\n

\u590f\u8fb2\u7684\u71b5\u5ea6\u91cf\u5f15\u8d77\u8cc7\u8a0a\u7406\u8ad6\u7684\u6578\u5b78\u7814\u7a76\uff0c\u4ed6\u7684\u6210\u679c\u662f\u4eca\u65e5\u6211\u5011\u5982\u4f55\u5728\u7db2\u8def\u4e0a\u6e9d\u901a\u7684\u6838\u5fc3\u3002<\/p>\n

16.\u6df7\u6c8c\u7406\u8ad6<\/strong><\/span>\uff1a\u9019\u500b\u65b9\u7a0b\u5f0f\u662f\u6885\u7684\u4e8c\u6b21\u591a\u9805\u5f0f\u6620\u5c04(May\u2019s logistic map)\uff0c\u5b83\u63cf\u8ff0\u4e00\u7a2e\u901a\u904e\u6642\u9593\u6f14\u8b8a\u7684\u904e\u7a0b \u2500\\(x\\) \u7684\u4e0b\u4e00\u500b\u6642\u9593\u4e16\u4ee3 \\(x_{t+1}\\)\u2500 \u7531\u65b9\u7a0b\u5f0f\u7684\u53f3\u908a\u7d66\u51fa\uff0c\u4f9d\u8cf4 \\(x\\) \u76ee\u524d\u7684\u4e16\u4ee3 \\(x_t\\)\u3002\\(k\\) \u662f\u4e00\u500b\u9078\u64c7\u7684\u5e38\u6578\uff0c\u5c0d\u65bc\u67d0\u4e9b \\(k\\) \u503c\uff0c\u6620\u5c04\u6703\u986f\u793a\u6df7\u6c8c\u7684\u884c\u70ba\uff1a\u5982\u679c\u5f9e\u67d0\u4e9b\u7279\u6b8a\u7684\u521d\u59cb\u503c \\(x\\) \u958b\u59cb\uff0c\u904e\u7a0b\u5c07\u6f14\u5316\u51fa\u4e00\u7a2e\u7d50\u679c\uff0c\u5982\u679c\u7531\u5176\u4ed6\u7684\u521d\u59cb\u503c\u958b\u59cb\uff0c\u751a\u81f3\u975e\u5e38\u975e\u5e38\u9760\u8fd1\u7b2c\u4e00\u500b\u503c\uff0c\u904e\u7a0b\u5c07\u6f14\u5316\u51fa\u5b8c\u5168\u4e0d\u540c\u7684\u7d50\u679c\u3002\u6211\u5011\u6240\u898b\u7684\u6df7\u6c8c\u884c\u70ba \u2500 \u5c0d\u521d\u59cb\u689d\u4ef6\u975e\u5e38\u654f\u611f \u2500 \u5728\u8a31\u591a\u9818\u57df\u90fd\u662f\u5982\u6b64\u3002\u5929\u6c23\u662f\u500b\u5178\u578b\u7684\u4f8b\u5b50 \u2500\u5927\u6c23\u689d\u4ef6\u7684\u4e00\u500b\u5fae\u5c0f\u6539\u8b8a\u53ef\u4ee5\u5c0e\u81f4\u5e7e\u5929\u5f8c\u5b8c\u5168\u4e0d\u540c\u7684\u5929\u6c23\u7cfb\u7d71\uff0c\u9019\u500b\u6982\u5ff5\u6700\u5e38\u63d0\u53ca\u7684\u8aaa\u6cd5\u5c31\u662f\u300c\u8774\u8776\u6548\u61c9\u300d\u3002<\/p>\n

17.\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f<\/strong><\/span>\uff1a\u53e6\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\uff0c\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f\u63cf\u8ff0\u91d1\u878d\u5c08\u5bb6\u548c\u5546\u4eba\u5982\u4f55\u627e\u5230\u884d\u751f\u6027\u5546\u54c1\u7684\u50f9\u683c\u3002\u884d\u751f\u6027\u5546\u54c1 \u2500 \u57fa\u65bc\u67d0\u4e9b\u6f5b\u5728\u8cc7\u7522\u7684\u91d1\u878d\u5546\u54c1\uff0c\u4f8b\u5982\u80a1\u7968 \u2500 \u4e00\u500b\u73fe\u4ee3\u91d1\u878d\u9ad4\u7cfb\u7684\u4e3b\u8981\u90e8\u4efd\u3002<\/p>\n

\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f\u5141\u8a31\u91d1\u878d\u5c08\u5bb6\u5229\u7528\u884d\u751f\u6027\u5546\u54c1\u7684\u7279\u6027\u548c\u6f5b\u5728\u8cc7\u7522\u4f86\u8a08\u7b97\u9019\u4e9b\u91d1\u878d\u5546\u54c1\u7684\u50f9\u503c\u3002<\/p>\n

\"a4\"<\/a>

\u9019\u4e9b\u662f\u829d\u52a0\u54e5\u671f\u4ea4\u6240\u6a19\u6e96\u666e\u723e500\u6307\u6578\u7684\u4ea4\u6613\u54e1\uff0c\u4f60\u4e0d\u6703\u767c\u73fe\u6709\u4eba\u6c92\u807d\u904e\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f\u3002<\/p><\/div>\n

—<\/p>\n

\u672c\u6587\u7531\u81fa\u7063\u5927\u5b78\u79d1\u5b78\u6559\u80b2\u767c\u5c55\u4e2d\u5fc3\u7d04\u7a3f\u7de8\u8b6f\u3002<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

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