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機械学習に役立つ数学

Cb18c19223700dd8185fef0d88435fe4?s=47 Kimikazu Kato
November 14, 2018

 機械学習に役立つ数学

2018/11/14 みんなのPython勉強会の発表資料です。

主に本の宣伝と、ラグランジュ未定乗数法の解説です。

Cb18c19223700dd8185fef0d88435fe4?s=128

Kimikazu Kato

November 14, 2018
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  1. ػցֶशʹ໾ཱͭ਺ֶ 2018/11/14 Ճ౻ެҰ ΈΜͳͷPythonษڧձ

  2. ࠓ೔ͷ಺༰ • ࣗݾ঺հ • ຊͷએ఻ • ཪ࿩ɾۤ࿑࿩ • ਺ཧ࠷దԽͱͦͷཧղͷͨΊͷ਺ֶ •

    ओʹϥάϥϯδϡະఆ৐਺๏ • ຊʹؚ·ΕΔ͜ͱɺؚ·Εͳ͍͜ͱ
  3. ࣗݾ঺հ Ճ౻ެҰʢ͔ͱ͏͖Έ͔ͣʣ ॴଐɿγϧόʔΤοάɾςΫϊϩδʔʢגʣ ത࢜ʢ৘ใཧ޻ֶʣ ʢम࢜·Ͱ͸਺ֶʣ झຯɿےτϨ Twitter: @hamukazu ࢓ࣄɿϨίϝϯσʔγϣϯγεςϜʹؔ͢Δݚڀ։ൃ ஶॻ

  4. એ఻ ಛ௃ɿ ɾπʔϧͷ࢖͍ํͰ͸ͳ͘ػցֶशΞϧΰϦζϜͷ࢓૊ΈΛղઆͨ͠ຊ ɾPythonͷجຊ΍ɺΞϧΰϦζϜͷཧղʹඞཁͳ਺ֶ͔Βղઆ http://bit.ly/mlessence

  5. ࣥචͷഎܠ • େਓͷ਺ֶษڧ΍Γ௚͠ϒʔϜ͕དྷͯΔ͔΋͠Εͳ͍ • ͦͷυϥΠϒཁૉͷҰͭͱͳ͍ͬͯΔͷ͕ػցֶशɾਓ޻ ஌ೳ • ݸਓతʹ΋ɺษڧ͍ͨ͠ͷͰͲ͏͢Ε͹ʁͱ͍͏૬ஊ͕͋ͬ ͨΓ •

    ػցֶशͷཧ࿦తͳઆ໌͸ɺϕΠζ౷ܭͳͲͷ؍఺͔Βͷ ॻ੶͕ଟ͘ɺ਺ཧ࠷దԽ͔ΒͷΞϓϩʔν͸͋·Γͳ͍
  6. ํ਑ • Ͱ͖Δ͚ͩʮඞཁͳ͜ͱ͸શͯॻ͍ͯ͋ΔʯΛΊͨ͟͠ • ࣌ؒత੍໿Ͱඞͣ͠΋ୡ੒Ͱ͖ͯͳ͍͕… • ਺ֶ͸ɺʮূ໌ʯΑΓ΋ʮઆ໌ʯΛॏࢹ • ௿࣍ݩͷέʔεΛ؍࡯͠ɺߴ࣍ݩͷ৔߹͸ূ໌ͤͣʹೲಘͯ͠΋Β͏ •

    ূ໌͠ͳͯ͘΋ɺఆཧͷओு͸ਖ਼֬ʹ • ਺ֶͱ਺஋ܭࢉͷઆ໌Λ׬શʹ෼཭ • ͢΂ͯʹαϯϓϧίʔυΛ͚ͭΔ
  7. ۤ࿑࿩ • ͳ͔ͳ͔ಈ͔ͳ͍αϯϓϧίʔυʢΪϦΪϦ·Ͱσόοάʣ • ਺ࣜͷσόοάͷ೉͠͞ • ਺ࣜʹ׳Εͯͳ͍ฤूऀ • ਤͷ४උͷେม͞

  8. None
  9. ۤ࿑ͷࠟ੻

  10. ਺ཧ࠷దԽͱ͸ ༩͑ΒΕ੍ͨ໿ͷ΋ͱͷ༩͑ΒΕͨؔ਺Λ࠷খԽʢ·ͨ͸࠷ େԽʣ͢Δͱ͍͏໰୊ x2 + xy + y2 + 2x

    + 4y <latexit sha1_base64="G4C6fxrFwI495oKxSmWNZiJhiHQ=">AAAB+XicbZDLSgMxFIbP1Futt1GXuggWQSiUmSLosujGZQv2Au1YMmnahmYyQ5IpHYa+iRsXirh143O4c+ejmF4W2nog5OP/zyEnvx9xprTjfFmZtfWNza3sdm5nd2//wD48qqswloTWSMhD2fSxopwJWtNMc9qMJMWBz2nDH95O/caISsVCca+TiHoB7gvWYwRrI3Vse/xQKoyTQmKu0rhwmXTsvFN0ZoVWwV1Avnz6Uf0GgErH/mx3QxIHVGjCsVIt14m0l2KpGeF0kmvHikaYDHGftgwKHFDlpbPNJ+jcKF3UC6U5QqOZ+nsixYFSSeCbzgDrgVr2puJ/XivWvWsvZSKKNRVk/lAv5kiHaBoD6jJJieaJAUwkM7siMsASE23CypkQ3OUvr0K9VHQNV00aNzCvLJzAGVyAC1dQhjuoQA0IjOARnuHFSq0n69V6m7dmrMXMMfwp6/0HpHeUkQ==</latexit> <latexit sha1_base64="0VLOn/OcbEm4Bc1VZd2AwfGlSO8=">AAAB+XicbZDLSgMxFIbPeK31NupSkWARhEKZKYIui25ctmAv0I4lk2ba0MyFJFM6DF36Fm5cKOLWTZ/Dnc/gS5heFtp6IOTj/88hJ78bcSaVZX0ZK6tr6xubma3s9s7u3r55cFiTYSwIrZKQh6LhYkk5C2hVMcVpIxIU+y6ndbd/O/HrAyokC4N7lUTU8XE3YB4jWGmpbZrDh2J+mOQTfRWH+cukbeasgjUttAz2HHKlk3Hl+/F0XG6bn61OSGKfBopwLGXTtiLlpFgoRjgdZVuxpBEmfdylTY0B9ql00unmI3SulQ7yQqFPoNBU/T2RYl/KxHd1p49VTy56E/E/rxkr79pJWRDFigZk9pAXc6RCNIkBdZigRPFEAyaC6V0R6WGBidJhZXUI9uKXl6FWLNiaKzqNG5hVBo7hDC7AhisowR2UoQoEBvAEL/BqpMaz8Wa8z1pXjPnMEfwp4+MHgryV9w==</latexit> <latexit sha1_base64="0VLOn/OcbEm4Bc1VZd2AwfGlSO8=">AAAB+XicbZDLSgMxFIbPeK31NupSkWARhEKZKYIui25ctmAv0I4lk2ba0MyFJFM6DF36Fm5cKOLWTZ/Dnc/gS5heFtp6IOTj/88hJ78bcSaVZX0ZK6tr6xubma3s9s7u3r55cFiTYSwIrZKQh6LhYkk5C2hVMcVpIxIU+y6ndbd/O/HrAyokC4N7lUTU8XE3YB4jWGmpbZrDh2J+mOQTfRWH+cukbeasgjUttAz2HHKlk3Hl+/F0XG6bn61OSGKfBopwLGXTtiLlpFgoRjgdZVuxpBEmfdylTY0B9ql00unmI3SulQ7yQqFPoNBU/T2RYl/KxHd1p49VTy56E/E/rxkr79pJWRDFigZk9pAXc6RCNIkBdZigRPFEAyaC6V0R6WGBidJhZXUI9uKXl6FWLNiaKzqNG5hVBo7hDC7AhisowR2UoQoEBvAEL/BqpMaz8Wa8z1pXjPnMEfwp4+MHgryV9w==</latexit> <latexit sha1_base64="3YwNdNiYMFSWdPltxu7RfpfdQUY=">AAAB+XicbZDLSgMxFIbP1Futt1GXboJFEAplpgi6LLpxWcFeoB1LJs20oZnMkGRKh6Fv4saFIm59E3e+jWk7C209EPLx/+eQk9+POVPacb6twsbm1vZOcbe0t39weGQfn7RUlEhCmyTikez4WFHOBG1qpjntxJLi0Oe07Y/v5n57QqVikXjUaUy9EA8FCxjB2kh9254+1SrTtJKaqzatXKV9u+xUnUWhdXBzKENejb791RtEJAmp0IRjpbquE2svw1Izwums1EsUjTEZ4yHtGhQ4pMrLFpvP0IVRBiiIpDlCo4X6eyLDoVJp6JvOEOuRWvXm4n9eN9HBjZcxESeaCrJ8KEg40hGax4AGTFKieWoAE8nMroiMsMREm7BKJgR39cvr0KpVXcMPTrl+m8dRhDM4h0tw4RrqcA8NaAKBCTzDK7xZmfVivVsfy9aClc+cwp+yPn8AlH2STA==</latexit> x + y = 0 <latexit sha1_base64="7/EnbG619G+dyndXMk7ryXe7N50=">AAAB7HicbZDLSgMxFIbPeK31VnWpi2ARBKHMuNGNUHTjsgWnLbRDyaSZNjTJDElGHIY+gxsXirj1GXwOd+58FNPLQlt/CHz85xxyzh8mnGnjul/O0vLK6tp6YaO4ubW9s1va22/oOFWE+iTmsWqFWFPOJPUNM5y2EkWxCDlthsObcb15T5VmsbwzWUIDgfuSRYxgYy3/4Sy7crulsltxJ0KL4M2gXD36qH8DQK1b+uz0YpIKKg3hWOu25yYmyLEyjHA6KnZSTRNMhrhP2xYlFlQH+WTZETqxTg9FsbJPGjRxf0/kWGididB2CmwGer42Nv+rtVMTXQY5k0lqqCTTj6KUIxOj8eWoxxQlhmcWMFHM7orIACtMjM2naEPw5k9ehMZ5xbNct2lcw1QFOIRjOAUPLqAKt1ADHwgweIRneHGk8+S8Om/T1iVnNnMAf+S8/wAqEpB2</latexit> <latexit sha1_base64="d50r2+C94qjmMxhh95DV8I3TZnM=">AAAB7HicbZDLSsNAFIZP6q3WW9WlIoNFEISSuNGNUHTjsgXTFtpQJtNJO3QyCTMTMYQuXbtxoYhbn6HP4c5n8CWcXhba+sPAx3/OYc75/ZgzpW37y8otLa+sruXXCxubW9s7xd29uooSSahLIh7Jpo8V5UxQVzPNaTOWFIc+pw1/cDOuN+6pVCwSdzqNqRfinmABI1gby304S6/sTrFkl+2J0CI4MyhVDke178ejUbVT/Gx3I5KEVGjCsVItx461l2GpGeF0WGgnisaYDHCPtgwKHFLlZZNlh+jEOF0URNI8odHE/T2R4VCpNPRNZ4h1X83XxuZ/tVaig0svYyJONBVk+lGQcKQjNL4cdZmkRPPUACaSmV0R6WOJiTb5FEwIzvzJi1A/LzuGayaNa5gqDwdwDKfgwAVU4Baq4AIBBk/wAq+WsJ6tN+t92pqzZjP78EfWxw8IV5Hc</latexit> <latexit sha1_base64="d50r2+C94qjmMxhh95DV8I3TZnM=">AAAB7HicbZDLSsNAFIZP6q3WW9WlIoNFEISSuNGNUHTjsgXTFtpQJtNJO3QyCTMTMYQuXbtxoYhbn6HP4c5n8CWcXhba+sPAx3/OYc75/ZgzpW37y8otLa+sruXXCxubW9s7xd29uooSSahLIh7Jpo8V5UxQVzPNaTOWFIc+pw1/cDOuN+6pVCwSdzqNqRfinmABI1gby304S6/sTrFkl+2J0CI4MyhVDke178ejUbVT/Gx3I5KEVGjCsVItx461l2GpGeF0WGgnisaYDHCPtgwKHFLlZZNlh+jEOF0URNI8odHE/T2R4VCpNPRNZ4h1X83XxuZ/tVaig0svYyJONBVk+lGQcKQjNL4cdZmkRPPUACaSmV0R6WOJiTb5FEwIzvzJi1A/LzuGayaNa5gqDwdwDKfgwAVU4Baq4AIBBk/wAq+WsJ6tN+t92pqzZjP78EfWxw8IV5Hc</latexit> <latexit sha1_base64="IjsygNkVUs3wQ0OAiraJ0gLonbA=">AAAB7HicbZBNS8NAEIYn9avWr6pHL4tFEISSeNGLUPTisYKphTaUzXbTLt1swu5EDKW/wYsHRbz6g7z5b9y2OWjrCwsP78ywM2+YSmHQdb+d0srq2vpGebOytb2zu1fdP2iZJNOM+yyRiW6H1HApFPdRoOTtVHMah5I/hKObaf3hkWsjEnWPecqDmA6UiASjaC3/6Sy/cnvVmlt3ZyLL4BVQg0LNXvWr209YFnOFTFJjOp6bYjCmGgWTfFLpZoanlI3ogHcsKhpzE4xny07IiXX6JEq0fQrJzP09MaaxMXkc2s6Y4tAs1qbmf7VOhtFlMBYqzZArNv8oyiTBhEwvJ32hOUOZW6BMC7srYUOqKUObT8WG4C2evAyt87pn+c6tNa6LOMpwBMdwCh5cQANuoQk+MBDwDK/w5ijnxXl3PuatJaeYOYQ/cj5/ABoYjjE=</latexit> Minimize Subject to ྫɿ ←໨తؔ਺ ←੍໿ࣜ
  11. ػցֶशͱ਺ཧ࠷దԽ • ػցֶशͷΞϧΰϦζϜ͸ɺ਺ཧ࠷దԽʹؼண͞ΕΔ͜ͱ ͕ଟ͍ • ݫີͳ࠷దղΛಘΑ͏͢Δ͜ͱΑΓʮ࠷దղʹۙͮ͘ʯ ͜ͱ͕େࣄͳ͜ͱ΋

  12. ஫ҙɿ ҎԼͷ਺ֶతઆ໌͸ࡶͳͱ͜Ζ΋͋Δͷ ͰɺదٓʮػցֶशͷΤοηϯεʯࢀর

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    x <latexit sha1_base64="PEl+uLprXdRtMgMSVACkfin0Kps=">AAAB6HicbZC7SwNBEMbnfMbzFbW0WQyCVbiz0UYM2lgmYB6QhLC3mUvW7O0du3tiOAL2NhaK2PrP2Nv537h5FJr4wcKP75thZyZIBNfG876dpeWV1bX13Ia7ubW9s5vf26/pOFUMqywWsWoEVKPgEquGG4GNRCGNAoH1YHA9zuv3qDSP5a0ZJtiOaE/ykDNqrFV56OQLXtGbiCyCP4PC5ad78QgA5U7+q9WNWRqhNExQrZu+l5h2RpXhTODIbaUaE8oGtIdNi5JGqNvZZNARObZOl4Sxsk8aMnF/d2Q00noYBbYyoqav57Ox+V/WTE143s64TFKDkk0/ClNBTEzGW5MuV8iMGFqgTHE7K2F9qigz9jauPYI/v/Ii1E6LvuWKVyhdwVQ5OIQjOAEfzqAEN1CGKjBAeIIXeHXunGfnzXmfli45s54D+CPn4wdUQo7F</latexit> <latexit 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sha1_base64="tsSciFPHdBi5a2pNHakW48E5+20=">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</latexit> <latexit sha1_base64="L0Ni2yZd9xeYuv3H4eWpj6xCLes=">AAACEnicbVA7T8MwGHTKq5RXgJHFokK0QlQJCyxIFSyMRaIPqYkix3Uaq3YS2Q5qFeU3sPBXWBhAiJWJjX+D22aAwkmWT3ffJ/vOTxiVyrK+jNLS8srqWnm9srG5tb1j7u51ZJwKTNo4ZrHo+UgSRiPSVlQx0ksEQdxnpOuPrqd+954ISePoTk0S4nI0jGhAMVJa8sx6cFwb1y8dRrmXhY6KoZVDJxAIZ0FtfBLWT/VVz7Mw98yq1bBmgH+JXZAqKNDyzE9nEOOUk0hhhqTs21ai3AwJRTEjecVJJUkQHqEh6WsaIU6km80i5fBIKwMYxEKfSMGZ+nMjQ1zKCff1JEcqlIveVPzP66cquHAzGiWpIhGePxSkDOrk037ggAqCFZtogrCg+q8Qh0j3oXSLFV2CvRj5L+mcNWzNb61q86qoowwOwCGoARucgya4AS3QBhg8gCfwAl6NR+PZeDPe56Mlo9jZB79gfHwD1FicTg==</latexit> f0(x) = 0 <latexit sha1_base64="xE50bmjX93j26KL9Sb/c0ZysP5Q=">AAAB7nicbZDLSgMxFIbP1Futt6pLN6FFrAhlxo1uhKIblxXsBdqhZNIzbWgmMyQZsZQ+hBsXiujS53Hn25heFtr6Q+DjP+eQc/4gEVwb1/12Miura+sb2c3c1vbO7l5+/6Cu41QxrLFYxKoZUI2CS6wZbgQ2E4U0CgQ2gsHNpN54QKV5LO/NMEE/oj3JQ86osVYjPCk9nl65nXzRLbtTkWXw5lCsFNpnHwBQ7eS/2t2YpRFKwwTVuuW5ifFHVBnOBI5z7VRjQtmA9rBlUdIItT+arjsmx9bpkjBW9klDpu7viRGNtB5Gge2MqOnrxdrE/K/WSk146Y+4TFKDks0+ClNBTEwmt5MuV8iMGFqgTHG7K2F9qigzNqGcDcFbPHkZ6udlz/KdTeMaZsrCERSgBB5cQAVuoQo1YDCAJ3iBVydxnp03533WmnHmM4fwR87nD9CHkAg=</latexit> <latexit sha1_base64="29SGNpY38W8p1zAhk9kgCIuPZFY=">AAAB7nicbZDLSgMxFIZPvNZ6q7p0E1rEilBm3OhGKLpxWcFeoB1KJs20oZnMkGTEYehDCOJCEbc+j7u+jelloa0/BD7+cw455/djwbVxnDFaWV1b39jMbeW3d3b39gsHhw0dJYqyOo1EpFo+0UxwyeqGG8FasWIk9AVr+sPbSb35yJTmkXwwacy8kPQlDzglxlrN4LT8dHbtdAslp+JMhZfBnUOpWuycv4yraa1b+O70IpqETBoqiNZt14mNlxFlOBVslO8kmsWEDkmftS1KEjLtZdN1R/jEOj0cRMo+afDU/T2RkVDrNPRtZ0jMQC/WJuZ/tXZigisv4zJODJN09lGQCGwiPLkd97hi1IjUAqGK210xHRBFqLEJ5W0I7uLJy9C4qLiW720aNzBTDo6hCGVw4RKqcAc1qAOFITzDG7yjGL2iD/Q5a11B85kj+CP09QPZ8ZGO</latexit> <latexit sha1_base64="29SGNpY38W8p1zAhk9kgCIuPZFY=">AAAB7nicbZDLSgMxFIZPvNZ6q7p0E1rEilBm3OhGKLpxWcFeoB1KJs20oZnMkGTEYehDCOJCEbc+j7u+jelloa0/BD7+cw455/djwbVxnDFaWV1b39jMbeW3d3b39gsHhw0dJYqyOo1EpFo+0UxwyeqGG8FasWIk9AVr+sPbSb35yJTmkXwwacy8kPQlDzglxlrN4LT8dHbtdAslp+JMhZfBnUOpWuycv4yraa1b+O70IpqETBoqiNZt14mNlxFlOBVslO8kmsWEDkmftS1KEjLtZdN1R/jEOj0cRMo+afDU/T2RkVDrNPRtZ0jMQC/WJuZ/tXZigisv4zJODJN09lGQCGwiPLkd97hi1IjUAqGK210xHRBFqLEJ5W0I7uLJy9C4qLiW720aNzBTDo6hCGVw4RKqcAc1qAOFITzDG7yjGL2iD/Q5a11B85kj+CP09QPZ8ZGO</latexit> <latexit sha1_base64="qTgnIS+7mWYVgMtScwoTZ1vad4Y=">AAAB7nicbZA9SwNBEIbn/IzxK2ppsxjE2IQ7G22EoI1lBPMByRH2NnPJkr29Y3dPDEd+hI2FIrb+Hjv/jZvkCk18YeHhnRl25g0SwbVx3W9nZXVtfWOzsFXc3tnd2y8dHDZ1nCqGDRaLWLUDqlFwiQ3DjcB2opBGgcBWMLqd1luPqDSP5YMZJ+hHdCB5yBk11mqFZ5Wn82u3Vyq7VXcmsgxeDmXIVe+Vvrr9mKURSsME1brjuYnxM6oMZwInxW6qMaFsRAfYsShphNrPZutOyKl1+iSMlX3SkJn7eyKjkdbjKLCdETVDvVibmv/VOqkJr/yMyyQ1KNn8ozAVxMRkejvpc4XMiLEFyhS3uxI2pIoyYxMq2hC8xZOXoXlR9Szfu+XaTR5HAY7hBCrgwSXU4A7q0AAGI3iGV3hzEufFeXc+5q0rTj5zBH/kfP4AvgiOfw==</latexit> Λղ͚͹ۃ஋ʢۃେ஋orۃখ஋ʣΛٻΊΒΕΔʢ͔΋͠Εͳ͍ʣ x + h <latexit sha1_base64="n9L7Zf+BFTgXbfOO04PsBnsrmbM=">AAAB6nicbZDLSgMxFIbP1Ftbb1WXboJFEIQy40aXRTcuK9oLtEPNpJk2NJMZkjNiGfoIblwoxa1P5M63Mb0stPWHwMd/ziHn/EEihUHX/XZya+sbm1v5QnF7Z3dvv3Rw2DBxqhmvs1jGuhVQw6VQvI4CJW8lmtMokLwZDG+m9eYT10bE6gFHCfcj2lciFIyite6fzwfdUtmtuDORVfAWUK4WkskjANS6pa9OL2ZpxBUySY1pe26CfkY1Cib5uNhJDU8oG9I+b1tUNOLGz2arjsmpdXokjLV9CsnM/T2R0ciYURTYzojiwCzXpuZ/tXaK4ZWfCZWkyBWbfxSmkmBMpneTntCcoRxZoEwLuythA6opQ5tO0YbgLZ+8Co2Limf5zqZxDXPl4RhO4Aw8uIQq3EIN6sCgDy/wBu+OdF6difMxb805i5kj+CPn8wdYrI9R</latexit> <latexit sha1_base64="0B1f8WpnyC23Pg3aZ+MLF6U01rA=">AAAB6nicbZC7SgNBFIbPek3iLWppMxgEQQi7NloGbSwjmgsmS5idzCZDZmeXmbOSEPIINhZKsLX3Xex8Gp1cCk38YeDjP+cw5/xBIoVB1/1yVlbX1jc2M9nc1vbO7l5+/6Bq4lQzXmGxjHU9oIZLoXgFBUpeTzSnUSB5LehdT+q1R66NiNU9DhLuR7SjRCgYRWvd9c+6rXzBLbpTkWXw5lAoZZPxw0f/u9zKfzbbMUsjrpBJakzDcxP0h1SjYJKPcs3U8ISyHu3whkVFI2784XTVETmxTpuEsbZPIZm6vyeGNDJmEAW2M6LYNYu1iflfrZFieOkPhUpS5IrNPgpTSTAmk7tJW2jOUA4sUKaF3ZWwLtWUoU0nZ0PwFk9ehup50bN8a9O4gpkycATHcAoeXEAJbqAMFWDQgSd4gVdHOs/O2Hmbta4485lD+CPn/QcvPZFx</latexit> <latexit sha1_base64="0B1f8WpnyC23Pg3aZ+MLF6U01rA=">AAAB6nicbZC7SgNBFIbPek3iLWppMxgEQQi7NloGbSwjmgsmS5idzCZDZmeXmbOSEPIINhZKsLX3Xex8Gp1cCk38YeDjP+cw5/xBIoVB1/1yVlbX1jc2M9nc1vbO7l5+/6Bq4lQzXmGxjHU9oIZLoXgFBUpeTzSnUSB5LehdT+q1R66NiNU9DhLuR7SjRCgYRWvd9c+6rXzBLbpTkWXw5lAoZZPxw0f/u9zKfzbbMUsjrpBJakzDcxP0h1SjYJKPcs3U8ISyHu3whkVFI2784XTVETmxTpuEsbZPIZm6vyeGNDJmEAW2M6LYNYu1iflfrZFieOkPhUpS5IrNPgpTSTAmk7tJW2jOUA4sUKaF3ZWwLtWUoU0nZ0PwFk9ehup50bN8a9O4gpkycATHcAoeXEAJbqAMFWDQgSd4gVdHOs/O2Hmbta4485lD+CPn/QcvPZFx</latexit> <latexit sha1_base64="5huoM78eKumjjRIUvpUTFq5Gs5Y=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tFEISSeKnHohePFe0HtKFstpN26WYTdjdiCf0JXjwo4tVf5M1/47bNQVtfWHh4Z4adeYNEcG1c99sprK1vbG4Vt0s7u3v7B+XDo5aOU8WwyWIRq05ANQousWm4EdhJFNIoENgOxjezevsRleaxfDCTBP2IDiUPOaPGWvdPF6N+ueJW3bnIKng5VCBXo1/+6g1ilkYoDRNU667nJsbPqDKcCZyWeqnGhLIxHWLXoqQRaj+brzolZ9YZkDBW9klD5u7viYxGWk+iwHZG1Iz0cm1m/lfrpia88jMuk9SgZIuPwlQQE5PZ3WTAFTIjJhYoU9zuStiIKsqMTadkQ/CWT16F1mXVs3znVurXeRxFOIFTOAcPalCHW2hAExgM4Rle4c0Rzovz7nwsWgtOPnMMf+R8/gAOyo2f</latexit> df dx (x) <latexit sha1_base64="5/jbm4uwBOEdNqILBrRvj+ZexH4=">AAAB+XicbZC7TsMwFIZPyq2UW4CRxaJCKkuVsNCxgoWxSPQitVHlOE5r1XEi26laRXkTFgYQYuVFEBsTr4J7GaDllyx9+s85Ose/n3CmtON8WYWNza3tneJuaW//4PDIPj5pqTiVhDZJzGPZ8bGinAna1Exz2kkkxZHPadsf3c7q7TGVisXiQU8T6kV4IFjICNbG6tt2L5SYZEGYZ8Ekr0wu+3bZqTpzoXVwl1Cu174/EAA0+vZnL4hJGlGhCcdKdV0n0V6GpWaE07zUSxVNMBnhAe0aFDiiysvml+fowjgBCmNpntBo7v6eyHCk1DTyTWeE9VCt1mbmf7VuqsOalzGRpJoKslgUphzpGM1iQAGTlGg+NYCJZOZWRIbYRKFNWCUTgrv65XVoXVVdw/cmjRtYqAhncA4VcOEa6nAHDWgCgTE8wjO8WJn1ZL1ab4vWgrWcOYU/st5/ALLpleU=</latexit> <latexit sha1_base64="/zhiinwp2bBmjgpaCIXjAqapJ0k=">AAAB+XicbZDLSsNAFIZP6q3WW9SFiJtgEeqmJG7ssujGZQV7gTaUyWTSDp1MwsyktIS8iRsXirj1RcSdbtz6GE4vC239YeDjP+dwzvxezKhUtv1h5FZW19Y38puFre2d3T1z/6Aho0RgUscRi0TLQ5IwykldUcVIKxYEhR4jTW9wPak3h0RIGvE7NY6JG6IepwHFSGmra5qdQCCc+kGW+qOsNDrvmkW7bE9lLYMzh2K18vV29Pl9XOua7x0/wklIuMIMSdl27Fi5KRKKYkayQieRJEZ4gHqkrZGjkEg3nV6eWWfa8a0gEvpxZU3d3xMpCqUch57uDJHqy8XaxPyv1k5UUHFTyuNEEY5ni4KEWSqyJjFYPhUEKzbWgLCg+lYL95GOQumwCjoEZ/HLy9C4KDuab3UaVzBTHk7gFErgwCVU4QZqUAcMQ7iHR3gyUuPBeDZeZq05Yz5zCH9kvP4AIlGXtw==</latexit> <latexit sha1_base64="/zhiinwp2bBmjgpaCIXjAqapJ0k=">AAAB+XicbZDLSsNAFIZP6q3WW9SFiJtgEeqmJG7ssujGZQV7gTaUyWTSDp1MwsyktIS8iRsXirj1RcSdbtz6GE4vC239YeDjP+dwzvxezKhUtv1h5FZW19Y38puFre2d3T1z/6Aho0RgUscRi0TLQ5IwykldUcVIKxYEhR4jTW9wPak3h0RIGvE7NY6JG6IepwHFSGmra5qdQCCc+kGW+qOsNDrvmkW7bE9lLYMzh2K18vV29Pl9XOua7x0/wklIuMIMSdl27Fi5KRKKYkayQieRJEZ4gHqkrZGjkEg3nV6eWWfa8a0gEvpxZU3d3xMpCqUch57uDJHqy8XaxPyv1k5UUHFTyuNEEY5ni4KEWSqyJjFYPhUEKzbWgLCg+lYL95GOQumwCjoEZ/HLy9C4KDuab3UaVzBTHk7gFErgwCVU4QZqUAcMQ7iHR3gyUuPBeDZeZq05Yz5zCH9kvP4AIlGXtw==</latexit> <latexit sha1_base64="7jfeONZ8Fcza2gH7AwTnH5711cw=">AAAB+XicbZC7TsMwFIZPyq2UW4CRxaJCKkuVsJSxgoWxSPQitVHlOE5r1XEi26laRXkTFgYQYuVN2Hgb3DYDtPySpU//OUfn+PcTzpR2nG+rtLW9s7tX3q8cHB4dn9inZx0Vp5LQNol5LHs+VpQzQduaaU57iaQ48jnt+pP7Rb07pVKxWDzpeUK9CI8ECxnB2lhD2x6EEpMsCPMsmOW12fXQrjp1Zym0CW4BVSjUGtpfgyAmaUSFJhwr1XedRHsZlpoRTvPKIFU0wWSCR7RvUOCIKi9bXp6jK+MEKIyleUKjpft7IsORUvPIN50R1mO1XluY/9X6qQ5vvYyJJNVUkNWiMOVIx2gRAwqYpETzuQFMJDO3IjLGJgptwqqYENz1L29C56buGn50qs27Io4yXMAl1MCFBjThAVrQBgJTeIZXeLMy68V6tz5WrSWrmDmHP7I+fwCfHpOe</latexit> ·ͨ͸
  14. (f(x) + g(x))0 = f0(x) + g0(x) (kf(x))0 = kf0(x)

    (f(x)g(x))0 = f0(x)g(x) + f(x)g0(x) (xn)0 = nxn 1 <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">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</latexit> <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">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</latexit> <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">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</latexit> <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">AAACeHicbVFNSwMxEM2u3/Wr6tFLsGpbxLIrgl4E0YtHBatCt5ZsmrSh2eySzErL0t/gf/PmD/Hiyey2oFUHMjzeezNJZsJECgOe9+64c/MLi0vLK6XVtfWNzfLW9oOJU01Zk8Yy1k8hMUwKxZogQLKnRDMShZI9hoPrXH98YdqIWN3DKGHtiPSU4IISsFSn/BpIxqHGa8P6Uc+mQIteH+rVwwteLbg8B0FpYhvwGcuAz6i5+E+PnDoqtBn38Fl9GxUePmfq2B93yhWv4RWB/wJ/CipoGred8lvQjWkaMQVUEmNavpdAOyMaBJVsXApSwxJCB6THWhYqEjHTzorBjfGBZbqYx9oeBbhgf1ZkJDJmFIXWGRHom99aTv6ntVLg5+1MqCQFpujkIp5KDDHOt4C7QjMKcmQBoVrYt2LaJ5pQsLsq2SH4v7/8FzycNHyL704rl1fTcSyjXbSHashHZ+gS3aBb1EQUfTi7zr5z4Hy62K269YnVdaY1O2gm3JMvNHu3vQ==</latexit> x5 + 3x3 4x2 0 = x5 0 + 3 x3 0 4 x2 0 = 5x4 + 3 ⇥ 3x2 4 ⇥ 2x = 5x4 + 9x2 8x <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">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</latexit> <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">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</latexit> <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">AAACcnicbVHLTuMwFHXCO8OjgNiAxHioeAlaJW0RsEBCzGaWIFFAatrKcZ3WwnnIvkGpKj6A32PHV7DhA3BKCsPjSpaOzznX1z72YsEV2PaTYY6NT0xOTc9Yv2bn5hcKi0tXKkokZXUaiUjeeEQxwUNWBw6C3cSSkcAT7Nq7/Zvp13dMKh6Fl9CPWTMg3ZD7nBLQVLvw4Armw07aOtirpq1qqZa2Kq7k3R7sbm+dWO/qiNurjqjqiLJKtRH33uq61tbJQdqqaT/wgCmsT69o49umkn4YjjPhKLXahaJdtoeFvwMnB0WU13m78Oh2IpoELAQqiFINx46hOSASOBXs3nITxWJCb0mXNTQMiZ7cHAwju8ebmulgP5J6hYCH7P8dAxIo1Q887QwI9NRXLSN/0hoJ+EfNAQ/jBFhI3wb5icAQ4Sx/3OGSURB9DQiVXN8V0x6RhIL+pSwE5+uTv4OrStnR+KJWPD3L45hGa2gD7SAHHaJT9A+dozqi6NlYMdaN38aLuWr+MfPsTCPvWUafytx/Baysthg=</latexit> <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">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</latexit> ॏཁެࣜ ܭࢉྫ
  15. ภඍ෼ f(x1, x2, . . . , xn) <latexit sha1_base64="8rqCZP6ZEBcqPaAjcv1l5qvT46Y=">AAAB/nicbZDLSsNAFIZP6q3WW1RcuQktQsVSkm50WXTjsoK9QBPCZDpph04mYWYiLaHgo+jGhSJufQ53vo3Ty0Jbfxj4+M85nDN/kDAqlW1/G7m19Y3Nrfx2YWd3b//APDxqyTgVmDRxzGLRCZAkjHLSVFQx0kkEQVHASDsY3kzr7QciJI35vRonxItQn9OQYqS05ZsnYXnkO5WRX6u4rBcrqZGf+2bJrtozWavgLKBUL7oXTwDQ8M0vtxfjNCJcYYak7Dp2orwMCUUxI5OCm0qSIDxEfdLVyFFEpJfNzp9YZ9rpWWEs9OPKmrm/JzIUSTmOAt0ZITWQy7Wp+V+tm6rwyssoT1JFOJ4vClNmqdiaZmH1qCBYsbEGhAXVt1p4gATCSidW0CE4y19ehVat6mi+02lcw1x5OIUilMGBS6jDLTSgCRgyeIZXeDMejRfj3fiYt+aMxcwx/JHx+QObrZYV</latexit>

    <latexit sha1_base64="HIJM1yxuMYM13umGdVqtNkwzBkQ=">AAAB/nicbZDLSsNAFIYn9VbrLSqu3AwtQsVSkm50WXTjsoK9QBPCZDJph04mYWYiDaHgQ/gCblwo4tbncNe3cXpZaPWHgY//nMM58/sJo1JZ1tQorK1vbG4Vt0s7u3v7B+bhUUfGqcCkjWMWi56PJGGUk7aiipFeIgiKfEa6/uhmVu8+ECFpzO9VlhA3QgNOQ4qR0pZnnoTVsWfXxl6j5rAgVlIjP/fMilW35oJ/wV5CpVl2Lp6mzazlmV9OEOM0IlxhhqTs21ai3BwJRTEjk5KTSpIgPEID0tfIUUSkm8/Pn8Az7QQwjIV+XMG5+3MiR5GUWeTrzgipoVytzcz/av1UhVduTnmSKsLxYlGYMqhiOMsCBlQQrFimAWFB9a0QD5FAWOnESjoEe/XLf6HTqNua73Qa12ChIjgFZVAFNrgETXALWqANMMjBM3gFb8aj8WK8Gx+L1oKxnDkGv2R8fgOlF5eb</latexit> <latexit sha1_base64="HIJM1yxuMYM13umGdVqtNkwzBkQ=">AAAB/nicbZDLSsNAFIYn9VbrLSqu3AwtQsVSkm50WXTjsoK9QBPCZDJph04mYWYiDaHgQ/gCblwo4tbncNe3cXpZaPWHgY//nMM58/sJo1JZ1tQorK1vbG4Vt0s7u3v7B+bhUUfGqcCkjWMWi56PJGGUk7aiipFeIgiKfEa6/uhmVu8+ECFpzO9VlhA3QgNOQ4qR0pZnnoTVsWfXxl6j5rAgVlIjP/fMilW35oJ/wV5CpVl2Lp6mzazlmV9OEOM0IlxhhqTs21ai3BwJRTEjk5KTSpIgPEID0tfIUUSkm8/Pn8Az7QQwjIV+XMG5+3MiR5GUWeTrzgipoVytzcz/av1UhVduTnmSKsLxYlGYMqhiOMsCBlQQrFimAWFB9a0QD5FAWOnESjoEe/XLf6HTqNua73Qa12ChIjgFZVAFNrgETXALWqANMMjBM3gFb8aj8WK8Gx+L1oKxnDkGv2R8fgOlF5eb</latexit> <latexit sha1_base64="KgOcFDJRysl1jVJtNCTz1Yp5MOw=">AAAB/nicbZDLSsNAFIYnXmu9RcWVm8EiVCgl6UaXRTcuK9gLtCFMppN26GQSZk6kJRR8FTcuFHHrc7jzbZy2WWjrDwMf/zmHc+YPEsE1OM63tba+sbm1Xdgp7u7tHxzaR8ctHaeKsiaNRaw6AdFMcMmawEGwTqIYiQLB2sHodlZvPzKleSwfYJIwLyIDyUNOCRjLt0/D8th3K2O/VumJfgzaoLz07ZJTdebCq+DmUEK5Gr791evHNI2YBCqI1l3XScDLiAJOBZsWe6lmCaEjMmBdg5JETHvZ/PwpvjBOH4exMk8Cnru/JzISaT2JAtMZERjq5drM/K/WTSG89jIukxSYpItFYSowxHiWBe5zxSiIiQFCFTe3YjokilAwiRVNCO7yl1ehVau6hu+dUv0mj6OAztA5KiMXXaE6ukMN1EQUZegZvaI368l6sd6tj0XrmpXPnKA/sj5/AIkulIw=</latexit> xi <latexit 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sha1_base64="GapjA6AsxCZZbhtaL0a90SW8Isc=">AAACCHicbZC7TsMwFIZPuJZyCzAyYFEhMVUJC4wVLIxFohepiSLHdVqrjhPZDqKKOrLwKiwMIMTKI7DxNjhtJKDllyx9+s85ts8fppwp7Thf1tLyyuraemWjurm1vbNr7+23VZJJQlsk4YnshlhRzgRtaaY57aaS4jjktBOOrop6545KxRJxq8cp9WM8ECxiBGtjBfaRF0lMci/FUjPMUTT54fuATQK75tSdqdAiuCXUoFQzsD+9fkKymApNOFaq5zqp9vPiSsLppOpliqaYjPCA9gwKHFPl59NFJujEOH0UJdIcodHU/T2R41ipcRyazhjroZqvFeZ/tV6mows/ZyLNNBVk9lCUcaQTVKSC+kxSovnYACaSmb8iMsQmGW2yq5oQ3PmVF6F9VncN3zi1xmUZRwUO4RhOwYVzaMA1NKEFBB7gCV7g1Xq0nq03633WumSVMwfwR9bHN3wEmj0=</latexit> ଟม਺ؔ਺ ͰɺɹɹҎ֎ͷม਺Λ͢΂ͯఆ਺ͩͱࢥͬͯ Ͱඍ෼ͨ͠΋ͷΛ xi <latexit sha1_base64="NMjPkaUHU7F0iA+Cy75ZeZeohSA=">AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6Nl0MYyQXOBZImzk7PJkNnZZWZWDEsewcZCEVufyM7GZ3FyKTTxh4GP/5zDnPMHieDauO6Xk1tZXVvfyG8WtrZ3dveK+wcNHaeKYZ3FIlatgGoUXGLdcCOwlSikUSCwGQyvJ/XmAyrNY3lnRgn6Ee1LHnJGjbVuH7u8Wyy5ZXcqsgzeHEqVo9r3PQBUu8XPTi9maYTSMEG1bntuYvyMKsOZwHGhk2pMKBvSPrYtShqh9rPpqmNyap0eCWNlnzRk6v6eyGik9SgKbGdEzUAv1ibmf7V2asJLP+MySQ1KNvsoTAUxMZncTXpcITNiZIEyxe2uhA2ooszYdAo2BG/x5GVonJc9yzWbxhXMlIdjOIEz8OACKnADVagDgz48wQu8OsJ5dt6c91lrzpnPHMIfOR8/7eqPuQ==</latexit> <latexit sha1_base64="ACkR23ag2e52OsMJU+NT7B1ozDw=">AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6NliI1lguYCSQizk7PJkNnZZWZWDEsewcZCEVtb38InsLPxWZxcCk38YeDjP+cw5/x+LLg2rvvlZFZW19Y3spu5re2d3b38/kFdR4liWGORiFTTpxoFl1gz3Ahsxgpp6Ats+MOrSb1xh0rzSN6aUYydkPYlDzijxlo3913ezRfcojsVWQZvDoXSUfWbv5c/Kt38Z7sXsSREaZigWrc8NzadlCrDmcBxrp1ojCkb0j62LEoaou6k01XH5NQ6PRJEyj5pyNT9PZHSUOtR6NvOkJqBXqxNzP9qrcQEl52UyzgxKNnsoyARxERkcjfpcYXMiJEFyhS3uxI2oIoyY9PJ2RC8xZOXoX5e9CxXbRplmCkLx3ACZ+DBBZTgGipQAwZ9eIAneHaE8+i8OK+z1owznzmEP3LefgA/OpF1</latexit> <latexit sha1_base64="ACkR23ag2e52OsMJU+NT7B1ozDw=">AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6NliI1lguYCSQizk7PJkNnZZWZWDEsewcZCEVtb38InsLPxWZxcCk38YeDjP+cw5/x+LLg2rvvlZFZW19Y3spu5re2d3b38/kFdR4liWGORiFTTpxoFl1gz3Ahsxgpp6Ats+MOrSb1xh0rzSN6aUYydkPYlDzijxlo3913ezRfcojsVWQZvDoXSUfWbv5c/Kt38Z7sXsSREaZigWrc8NzadlCrDmcBxrp1ojCkb0j62LEoaou6k01XH5NQ6PRJEyj5pyNT9PZHSUOtR6NvOkJqBXqxNzP9qrcQEl52UyzgxKNnsoyARxERkcjfpcYXMiJEFyhS3uxI2oIoyY9PJ2RC8xZOXoX5e9CxXbRplmCkLx3ACZ+DBBZTgGipQAwZ9eIAneHaE8+i8OK+z1owznzmEP3LefgA/OpF1</latexit> <latexit sha1_base64="OUNp3RlaSerf75yoPZY4PdrPiTI=">AAAB6nicbZBNT8JAEIan+IX4hXr0spGYeCKtFz0SvXjEaIEEGrJdtrBhu212p0bS8BO8eNAYr/4ib/4bF+hBwTfZ5Mk7M9mZN0ylMOi6305pbX1jc6u8XdnZ3ds/qB4etUySacZ9lshEd0JquBSK+yhQ8k6qOY1Dydvh+GZWbz9ybUSiHnCS8iCmQyUiwSha6/6pL/rVmlt35yKr4BVQg0LNfvWrN0hYFnOFTFJjup6bYpBTjYJJPq30MsNTysZ0yLsWFY25CfL5qlNyZp0BiRJtn0Iyd39P5DQ2ZhKHtjOmODLLtZn5X62bYXQV5EKlGXLFFh9FmSSYkNndZCA0ZygnFijTwu5K2IhqytCmU7EheMsnr0Lrou5ZvnNrjesijjKcwCmcgweX0IBbaIIPDIbwDK/w5kjnxXl3PhatJaeYOYY/cj5/AF9SjdQ=</latexit> ͱॻ͘ f(x, y) = x2 + xy + y3 + 3y <latexit sha1_base64="aYSoPFu8khV7xM03VrDzr0+wlcg=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA==</latexit> <latexit sha1_base64="aYSoPFu8khV7xM03VrDzr0+wlcg=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA==</latexit> <latexit sha1_base64="aYSoPFu8khV7xM03VrDzr0+wlcg=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA==</latexit> <latexit sha1_base64="aYSoPFu8khV7xM03VrDzr0+wlcg=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA==</latexit> @f @x = 2x + y <latexit sha1_base64="5dn85xRoxIiOcC7bjxyT3736lb4=">AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2</latexit> <latexit sha1_base64="5dn85xRoxIiOcC7bjxyT3736lb4=">AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2</latexit> <latexit sha1_base64="5dn85xRoxIiOcC7bjxyT3736lb4=">AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2</latexit> <latexit sha1_base64="5dn85xRoxIiOcC7bjxyT3736lb4=">AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2</latexit> @f @y = x + 3y2 + 3 <latexit sha1_base64="TUX4kB7/rNi+/s6kKHxUBUURYYM=">AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg==</latexit> <latexit sha1_base64="TUX4kB7/rNi+/s6kKHxUBUURYYM=">AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg==</latexit> <latexit sha1_base64="TUX4kB7/rNi+/s6kKHxUBUURYYM=">AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg==</latexit> <latexit sha1_base64="TUX4kB7/rNi+/s6kKHxUBUURYYM=">AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg==</latexit> ܭࢉྫɿ ͷͱ͖
  16. ޯ഑ rf = 0 B B B B @ @f

    @x1 @f @x2 . . . @f @xn 1 C C C C A <latexit sha1_base64="hC1lFOa7kcTq/yfZde0vM408z4g=">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</latexit> <latexit sha1_base64="LJSyuN+lgRu5CL2m4nWlo9jmyBc=">AAACfnichVFNT+MwEHWyfIavwh65GCoQAgEJF7igRcuFI0gUkJqqmjiTYtVxLNtBVFF/xv6C/THcuaz2t3DBbRHfgpEsPb15M288kyjBjQ3D/57/Y2x8YnJqOpiZnZtfqC0uXZii1AwbrBCFvkrAoOASG5ZbgVdKI+SJwMukezzIX96gNryQ57ansJVDR/KMM7COatf+xBISATSjh0GcYIfLSuVgNb/tB3GmgVWxAm05CJr1X/BtO+rH8deKvaHiJi2s+U4qnRnK9Nm6XauHO+Ew6EcQPYH6r7vgUP39F5y2a/dxWrAyR2mZAGOaUahsqxoYMIGue2lQAetCB5sOSsjRtKrh+vp0zTEpzQrtnrR0yL6uqCA3ppcnTunmuzbvcwPys1yztNlBq+JSlRYlGxllpaC2oINb0JRrZFb0HACmuZuVsmtwe7LuYoFbQvT+yx/Bxd5O5PBZWD/6TUYxRZbJKtkgEdknR+SEnJIGYeTBW/E2vS2f+Ov+tr87kvreU81P8ib8g0f/4caT</latexit> <latexit sha1_base64="LJSyuN+lgRu5CL2m4nWlo9jmyBc=">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</latexit> <latexit sha1_base64="f4YMgJx/+UhxtJVbH1guIFy0GUY=">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</latexit> Λޯ഑ͱݺͿ rf = 0 <latexit sha1_base64="i6wBboO4NG7nVj5mfWggrqQGqKg=">AAAB8XicbZC7SgNBFIbPxluMt6ilFoNBsAq7NtoIQRvLBMwFkyWcncwmQ2Znl5lZISx5CxsLRWx9AZ/Dzs5HcXIpNPGHgY//nMOc8weJ4Nq47peTW1ldW9/Ibxa2tnd294r7Bw0dp4qyOo1FrFoBaia4ZHXDjWCtRDGMAsGawfBmUm8+MKV5LO/MKGF+hH3JQ07RWOu+IzEQSMIrt1ssuWV3KrIM3hxKleOP2jcAVLvFz04vpmnEpKECtW57bmL8DJXhVLBxoZNqliAdYp+1LUqMmPaz6cZjcmqdHgljZZ80ZOr+nsgw0noUBbYzQjPQi7WJ+V+tnZrw0s+4TFLDJJ19FKaCmJhMzic9rhg1YmQBqeJ2V0IHqJAaG1LBhuAtnrwMjfOyZ7lm07iGmfJwBCdwBh5cQAVuoQp1oCDhEZ7hxdHOk/PqvM1ac8585hD+yHn/AZ0Xkmw=</latexit> <latexit sha1_base64="EBcZz4Qhcz2fIBuwKjfgLbxt5lw=">AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS</latexit> <latexit sha1_base64="EBcZz4Qhcz2fIBuwKjfgLbxt5lw=">AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS</latexit> <latexit sha1_base64="2jek3adgZlMoxExh2C8HvCm+H1s=">AAAB8XicbZBNS8NAEIYn9avWr6hHL4tF8FQSL3oRil48VrAf2IYy2W7apZtN2N0IJfRfePGgiFf/jTf/jds2B219YeHhnRl25g1TwbXxvG+ntLa+sblV3q7s7O7tH7iHRy2dZIqyJk1Eojohaia4ZE3DjWCdVDGMQ8Ha4fh2Vm8/MaV5Ih/MJGVBjEPJI07RWOuxJzEUSKJrr+9WvZo3F1kFv4AqFGr03a/eIKFZzKShArXu+l5qghyV4VSwaaWXaZYiHeOQdS1KjJkO8vnGU3JmnQGJEmWfNGTu/p7IMdZ6Eoe2M0Yz0su1mflfrZuZ6CrIuUwzwyRdfBRlgpiEzM4nA64YNWJiAanidldCR6iQGhtSxYbgL5+8Cq2Lmm/53qvWb4o4ynACp3AOPlxCHe6gAU2gIOEZXuHN0c6L8+58LFpLTjFzDH/kfP4AjR2QJw==</latexit> ͱ͓͘ͱɺۃ஋ΛٻΊΒΕΔʢ͔΋͠Εͳ͍ʣ
  17. ޯ഑ͷزԿతੑ࣭ f(x, y) (x0, y0) f(x0, y0) = a rf(x0,

    y0) f(x, y) = a ͳΊΒ͔ͳ2ม਺ؔ਺ ʹ͓͍ͯ ͱ͢Δɻ (x0, y0) ఺ ʹ͓͚Δޯ഑ ͸ɺۂઢ ͷ f(x, y) = a ఺ ʹ͓͚Δ઀ઢͱਨ௚Ͱ͋Γɺ͔ͭ f(x, y)͕େ͖͘ ͳΔํ޲Λ޲͍͍ͯΔ rf(x0, y0) f(x, y) খ f(x, y) େ ͜ͷɹɹɹɹɹΛ఺ɹɹɹʹ͓͚Δ๏ઢϕΫτϧͱݺͿ (x0, y0) rf(x0, y0)
  18. ޯ഑߱Լ๏ xk+1 = xk ↵rf(xk) rf(xk) ߋ৽ࣜɿ rf ɹɹͷํ޲ʹগ͠ਐΉͱؔ਺ͷ஋͸ খ͘͞ͳΔͩΖ͏ͱ͍͏ߟ͑ํ

    ྫɿ f(x, y) = 5x2 6xy + 3y2 + 6x 6y Λ࠷খԽ ͜ͷ఺ઢ͕౳ߴઢʢf=Ұఆͷઢʣ ౳ߴઢʹ͍ͭͯߟ͑Δ͜ͱ͕ɺ͜ΕҎ߱ͱͯ΋େࣄʂ
  19. ϥάϥϯδϡະఆ৐਺๏ f(x, y) <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit

    sha1_base64="ck8pdC+ekZH4nUmSP+ZG7r8lEyk=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odOn4MoA7ncAFXEMIN3MEDdKALAhJ4hXdv4r15H6uuat66tDP4I+/zBzjGijg=</latexit> <latexit sha1_base64="4QsSB70Qi04m97dQBnmQWme8VIM=">AAAB4nicbZBLSwMxFIXv1FetVatbN8EiVJAy40aXghuXFewD2qFk0jttbCYZkow4lP4HNy4U8Ue589+YPhbaeiDwcU5C7j1RKrixvv/tFTY2t7Z3irulvfL+wWHlqNwyKtMMm0wJpTsRNSi4xKblVmAn1UiTSGA7Gt/O8vYTasOVfLB5imFCh5LHnFHrrFZce77Iz/uVql/35yLrECyhCks1+pWv3kCxLEFpmaDGdAM/teGEasuZwGmplxlMKRvTIXYdSpqgCSfzaafkzDkDEivtjrRk7v5+MaGJMXkSuZsJtSOzms3M/7JuZuPrcMJlmlmUbPFRnAliFZmtTgZcI7Mid0CZ5m5WwkZUU2ZdQSVXQrC68jq0LuuB43sfinACp1CDAK7gBu6gAU1g8Agv8AbvnvJevY9FXQVv2dsx/JH3+QOOXY0y</latexit> <latexit sha1_base64="4QsSB70Qi04m97dQBnmQWme8VIM=">AAAB4nicbZBLSwMxFIXv1FetVatbN8EiVJAy40aXghuXFewD2qFk0jttbCYZkow4lP4HNy4U8Ue589+YPhbaeiDwcU5C7j1RKrixvv/tFTY2t7Z3irulvfL+wWHlqNwyKtMMm0wJpTsRNSi4xKblVmAn1UiTSGA7Gt/O8vYTasOVfLB5imFCh5LHnFHrrFZce77Iz/uVql/35yLrECyhCks1+pWv3kCxLEFpmaDGdAM/teGEasuZwGmplxlMKRvTIXYdSpqgCSfzaafkzDkDEivtjrRk7v5+MaGJMXkSuZsJtSOzms3M/7JuZuPrcMJlmlmUbPFRnAliFZmtTgZcI7Mid0CZ5m5WwkZUU2ZdQSVXQrC68jq0LuuB43sfinACp1CDAK7gBu6gAU1g8Agv8AbvnvJevY9FXQVv2dsx/JH3+QOOXY0y</latexit> <latexit sha1_base64="MRUYAfazeX61kQ75Tpd5BxgO8xc=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAy040ui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprK1vbG4Vt0s7u3v7B+XDo7aWiSK0RSSXqhtgTTkTtGWY4bQbK4qjgNNOMLmZ1TuPVGkmxb1JY+pHeCRYyAg21mqH1aeL9HxQrrg1dy60Cl4OFcjVHJS/+kNJkogKQzjWuue5sfEzrAwjnE5L/UTTGJMJHtGeRYEjqv1svu0UnVlniEKp7BMGzd3fExmOtE6jwHZG2Iz1cm1m/lfrJSa88jMm4sRQQRYfhQlHRqLZ6WjIFCWGpxYwUczuisgYK0yMDahkQ/CWT16Fdr3mWb5zK43rPI4inMApVMGDS2jALTShBQQe4Ble4c2Rzovz7nwsWgtOPnMMf+R8/gCx946G</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> g(x, y) = 0 <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> L(x, y, ) = f(x, y) + g(x, y) <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> Minimize Subject to ͜ΕΛղ͘ʹ͸ ͱ͓͍ͯ Λղ͚͹Α͍ rL = 0 <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit> <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit> <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit> <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit>
  20. rf = rg <latexit sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> <latexit sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> <latexit sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> <latexit

    sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> g = 0 <latexit 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sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit 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  21. ϥάϥϯδϡະఆ৐਺๏ ʢෆ౳੍ࣜ໿ʣ f(x, y) <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit>

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sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> Minimize Subject to ͜ΕΛղ͘ʹ͸ ͱ͓͍ͯ Λղ͚͹Α͍ rL(x, y) = 0 g(x, y) = 0 0 g(x, y)  0 <latexit sha1_base64="7tfacI2uug9E43APNemx/WkaVYQ=">AAACMHicbZDLSgMxFIYz9VbrbdSlm2CxVJAyI4JuhKILXbioYC/QKeVMmrahmcyYZMRS+khufBTdKCji1qcw03ahbQ8Efr7/HE7O70ecKe0471ZqYXFpeSW9mllb39jcsrd3KiqMJaFlEvJQ1nxQlDNBy5ppTmuRpBD4nFb93mXiVx+oVCwUd7of0UYAHcHajIA2qGlfeQJ8Dvgm/3jUP8ydO56X8biZbwHuzGE5r0PvcULGrgE8AU076xScUeFZ4U5EFk2q1LRfvFZI4oAKTTgoVXedSDcGIDUjnA4zXqxoBKQHHVo3UkBAVWMwOniIDwxp4XYozRMaj+jfiQEESvUD33QGoLtq2kvgPK8e6/ZZY8BEFGsqyHhRO+ZYhzhJD7eYpETzvhFAJDN/xaQLEog2GWdMCO70ybOiclxwjb49yRYvJnGk0R7aR3nkolNURNeohMqIoCf0ij7Qp/VsvVlf1ve4NWVNZnbRv7J+fgETTaS4</latexit> <latexit sha1_base64="7tfacI2uug9E43APNemx/WkaVYQ=">AAACMHicbZDLSgMxFIYz9VbrbdSlm2CxVJAyI4JuhKILXbioYC/QKeVMmrahmcyYZMRS+khufBTdKCji1qcw03ahbQ8Efr7/HE7O70ecKe0471ZqYXFpeSW9mllb39jcsrd3KiqMJaFlEvJQ1nxQlDNBy5ppTmuRpBD4nFb93mXiVx+oVCwUd7of0UYAHcHajIA2qGlfeQJ8Dvgm/3jUP8ydO56X8biZbwHuzGE5r0PvcULGrgE8AU076xScUeFZ4U5EFk2q1LRfvFZI4oAKTTgoVXedSDcGIDUjnA4zXqxoBKQHHVo3UkBAVWMwOniIDwxp4XYozRMaj+jfiQEESvUD33QGoLtq2kvgPK8e6/ZZY8BEFGsqyHhRO+ZYhzhJD7eYpETzvhFAJDN/xaQLEog2GWdMCO70ybOiclxwjb49yRYvJnGk0R7aR3nkolNURNeohMqIoCf0ij7Qp/VsvVlf1ve4NWVNZnbRv7J+fgETTaS4</latexit> <latexit sha1_base64="7tfacI2uug9E43APNemx/WkaVYQ=">AAACMHicbZDLSgMxFIYz9VbrbdSlm2CxVJAyI4JuhKILXbioYC/QKeVMmrahmcyYZMRS+khufBTdKCji1qcw03ahbQ8Efr7/HE7O70ecKe0471ZqYXFpeSW9mllb39jcsrd3KiqMJaFlEvJQ1nxQlDNBy5ppTmuRpBD4nFb93mXiVx+oVCwUd7of0UYAHcHajIA2qGlfeQJ8Dvgm/3jUP8ydO56X8biZbwHuzGE5r0PvcULGrgE8AU076xScUeFZ4U5EFk2q1LRfvFZI4oAKTTgoVXedSDcGIDUjnA4zXqxoBKQHHVo3UkBAVWMwOniIDwxp4XYozRMaj+jfiQEESvUD33QGoLtq2kvgPK8e6/ZZY8BEFGsqyHhRO+ZYhzhJD7eYpETzvhFAJDN/xaQLEog2GWdMCO70ybOiclxwjb49yRYvJnGk0R7aR3nkolNURNeohMqIoCf0ij7Qp/VsvVlf1ve4NWVNZnbRv7J+fgETTaS4</latexit> <latexit sha1_base64="7tfacI2uug9E43APNemx/WkaVYQ=">AAACMHicbZDLSgMxFIYz9VbrbdSlm2CxVJAyI4JuhKILXbioYC/QKeVMmrahmcyYZMRS+khufBTdKCji1qcw03ahbQ8Efr7/HE7O70ecKe0471ZqYXFpeSW9mllb39jcsrd3KiqMJaFlEvJQ1nxQlDNBy5ppTmuRpBD4nFb93mXiVx+oVCwUd7of0UYAHcHajIA2qGlfeQJ8Dvgm/3jUP8ydO56X8biZbwHuzGE5r0PvcULGrgE8AU076xScUeFZ4U5EFk2q1LRfvFZI4oAKTTgoVXedSDcGIDUjnA4zXqxoBKQHHVo3UkBAVWMwOniIDwxp4XYozRMaj+jfiQEESvUD33QGoLtq2kvgPK8e6/ZZY8BEFGsqyHhRO+ZYhzhJD7eYpETzvhFAJDN/xaQLEog2GWdMCO70ybOiclxwjb49yRYvJnGk0R7aR3nkolNURNeohMqIoCf0ij7Qp/VsvVlf1ve4NWVNZnbRv7J+fgETTaS4</latexit> g(x, y)  0 <latexit sha1_base64="7mEvOU7tLUi6pu4Q3K5IsSySj8I=">AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ==</latexit> <latexit sha1_base64="7mEvOU7tLUi6pu4Q3K5IsSySj8I=">AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ==</latexit> <latexit sha1_base64="7mEvOU7tLUi6pu4Q3K5IsSySj8I=">AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ==</latexit> <latexit sha1_base64="7mEvOU7tLUi6pu4Q3K5IsSySj8I=">AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ==</latexit> KKT৚݅ͱݺ͹ΕΔ
  22. f(x, y) = 5x2 + 6xy + 5y2 26x 26y

    g(x, y) = x2 + y2 4 <latexit sha1_base64="CektuUOH/dH2InAkhA3RtnTClWU=">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</latexit> <latexit sha1_base64="CektuUOH/dH2InAkhA3RtnTClWU=">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</latexit> <latexit sha1_base64="CektuUOH/dH2InAkhA3RtnTClWU=">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</latexit> <latexit sha1_base64="CektuUOH/dH2InAkhA3RtnTClWU=">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</latexit> ྫɿ f(x, y) = 5x2 + 6xy + 5y2 16x 16y g(x, y) = x2 + y2 4 <latexit sha1_base64="islkD36VSVCHFNtfd61NT+2+m44=">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</latexit> <latexit sha1_base64="islkD36VSVCHFNtfd61NT+2+m44=">AAACI3icbVDLSgMxFM34rPU16tJNsCiV2jJT2iqCUHTjsoJ9QFtLJs20oZkHSUZmKP0XN/6KGxdKcePCfzFtR9DWCwkn55zLzT2Wz6iQhvGpLS2vrK6tJzaSm1vbO7v63n5NeAHHpIo95vGGhQRh1CVVSSUjDZ8T5FiM1K3BzUSvPxIuqOfey8gnbQf1XGpTjKSiOvqlnQ7PotOTK1gMH/IwA0thpO5ipB5ZaJZCmDVLUauV7P34lC2j1Gyho6eMnDEtuAjMGKRAXJWOPm51PRw4xJWYISGapuHL9hBxSTEjo2QrEMRHeIB6pKmgixwi2sPpjiN4rJgutD2ujivhlP3dMUSOEJFjKaeDZF/MaxPyP60ZSPuiPaSuH0ji4tkgO2BQenASGOxSTrBkkQIIc6r+CnEfcYSlijWpQjDnV14EtXzOVPiukCpfx3EkwCE4AmlggnNQBregAqoAgyfwAt7Au/asvWpj7WNmXdLingPwp7Svb1X1ne4=</latexit> <latexit sha1_base64="islkD36VSVCHFNtfd61NT+2+m44=">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</latexit> <latexit sha1_base64="islkD36VSVCHFNtfd61NT+2+m44=">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</latexit> rf = rg <latexit sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> <latexit sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> <latexit sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> <latexit sha1_base64="fxL7LYTqUqBdKCy5QW8uS39coLI=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL</latexit> g = 0 <latexit sha1_base64="0s7QBn8W1fYtDKGnA1TBLznmNnQ=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfQiFL14rGhtoQ1ls92kSzebsDsRSuhP8OJBEa/+Im/+G7dtDtr6wsLDOzPszBukUhh03W+ntLK6tr5R3qxsbe/s7lX3Dx5NkmnGWyyRie4E1HApFG+hQMk7qeY0DiRvB6Obab39xLURiXrAccr9mEZKhIJRtNZ9dOX2qzW37s5ElsEroAaFmv3qV2+QsCzmCpmkxnQ9N0U/pxoFk3xS6WWGp5SNaMS7FhWNufHz2aoTcmKdAQkTbZ9CMnN/T+Q0NmYcB7Yzpjg0i7Wp+V+tm2F46edCpRlyxeYfhZkkmJDp3WQgNGcoxxYo08LuStiQasrQplOxIXiLJy/D41nds3x3XmtcF3GU4QiO4RQ8uIAG3EITWsAggmd4hTdHOi/Ou/Mxby05xcwh/JHz+QO8j41s</latexit> <latexit sha1_base64="0s7QBn8W1fYtDKGnA1TBLznmNnQ=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfQiFL14rGhtoQ1ls92kSzebsDsRSuhP8OJBEa/+Im/+G7dtDtr6wsLDOzPszBukUhh03W+ntLK6tr5R3qxsbe/s7lX3Dx5NkmnGWyyRie4E1HApFG+hQMk7qeY0DiRvB6Obab39xLURiXrAccr9mEZKhIJRtNZ9dOX2qzW37s5ElsEroAaFmv3qV2+QsCzmCpmkxnQ9N0U/pxoFk3xS6WWGp5SNaMS7FhWNufHz2aoTcmKdAQkTbZ9CMnN/T+Q0NmYcB7Yzpjg0i7Wp+V+tm2F46edCpRlyxeYfhZkkmJDp3WQgNGcoxxYo08LuStiQasrQplOxIXiLJy/D41nds3x3XmtcF3GU4QiO4RQ8uIAG3EITWsAggmd4hTdHOi/Ou/Mxby05xcwh/JHz+QO8j41s</latexit> <latexit sha1_base64="0s7QBn8W1fYtDKGnA1TBLznmNnQ=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfQiFL14rGhtoQ1ls92kSzebsDsRSuhP8OJBEa/+Im/+G7dtDtr6wsLDOzPszBukUhh03W+ntLK6tr5R3qxsbe/s7lX3Dx5NkmnGWyyRie4E1HApFG+hQMk7qeY0DiRvB6Obab39xLURiXrAccr9mEZKhIJRtNZ9dOX2qzW37s5ElsEroAaFmv3qV2+QsCzmCpmkxnQ9N0U/pxoFk3xS6WWGp5SNaMS7FhWNufHz2aoTcmKdAQkTbZ9CMnN/T+Q0NmYcB7Yzpjg0i7Wp+V+tm2F46edCpRlyxeYfhZkkmJDp3WQgNGcoxxYo08LuStiQasrQplOxIXiLJy/D41nds3x3XmtcF3GU4QiO4RQ8uIAG3EITWsAggmd4hTdHOi/Ou/Mxby05xcwh/JHz+QO8j41s</latexit> <latexit sha1_base64="0s7QBn8W1fYtDKGnA1TBLznmNnQ=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfQiFL14rGhtoQ1ls92kSzebsDsRSuhP8OJBEa/+Im/+G7dtDtr6wsLDOzPszBukUhh03W+ntLK6tr5R3qxsbe/s7lX3Dx5NkmnGWyyRie4E1HApFG+hQMk7qeY0DiRvB6Obab39xLURiXrAccr9mEZKhIJRtNZ9dOX2qzW37s5ElsEroAaFmv3qV2+QsCzmCpmkxnQ9N0U/pxoFk3xS6WWGp5SNaMS7FhWNufHz2aoTcmKdAQkTbZ9CMnN/T+Q0NmYcB7Yzpjg0i7Wp+V+tm2F46edCpRlyxeYfhZkkmJDp3WQgNGcoxxYo08LuStiQasrQplOxIXiLJy/D41nds3x3XmtcF3GU4QiO4RQ8uIAG3EITWsAggmd4hTdHOi/Ou/Mxby05xcwh/JHz+QO8j41s</latexit> rf = 0 <latexit sha1_base64="i6wBboO4NG7nVj5mfWggrqQGqKg=">AAAB8XicbZC7SgNBFIbPxluMt6ilFoNBsAq7NtoIQRvLBMwFkyWcncwmQ2Znl5lZISx5CxsLRWx9AZ/Dzs5HcXIpNPGHgY//nMOc8weJ4Nq47peTW1ldW9/Ibxa2tnd294r7Bw0dp4qyOo1FrFoBaia4ZHXDjWCtRDGMAsGawfBmUm8+MKV5LO/MKGF+hH3JQ07RWOu+IzEQSMIrt1ssuWV3KrIM3hxKleOP2jcAVLvFz04vpmnEpKECtW57bmL8DJXhVLBxoZNqliAdYp+1LUqMmPaz6cZjcmqdHgljZZ80ZOr+nsgw0noUBbYzQjPQi7WJ+V+tnZrw0s+4TFLDJJ19FKaCmJhMzic9rhg1YmQBqeJ2V0IHqJAaG1LBhuAtnrwMjfOyZ7lm07iGmfJwBCdwBh5cQAVuoQp1oCDhEZ7hxdHOk/PqvM1ac8585hD+yHn/AZ0Xkmw=</latexit> <latexit sha1_base64="EBcZz4Qhcz2fIBuwKjfgLbxt5lw=">AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS</latexit> <latexit sha1_base64="EBcZz4Qhcz2fIBuwKjfgLbxt5lw=">AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS</latexit> <latexit sha1_base64="2jek3adgZlMoxExh2C8HvCm+H1s=">AAAB8XicbZBNS8NAEIYn9avWr6hHL4tF8FQSL3oRil48VrAf2IYy2W7apZtN2N0IJfRfePGgiFf/jTf/jds2B219YeHhnRl25g1TwbXxvG+ntLa+sblV3q7s7O7tH7iHRy2dZIqyJk1Eojohaia4ZE3DjWCdVDGMQ8Ha4fh2Vm8/MaV5Ih/MJGVBjEPJI07RWOuxJzEUSKJrr+9WvZo3F1kFv4AqFGr03a/eIKFZzKShArXu+l5qghyV4VSwaaWXaZYiHeOQdS1KjJkO8vnGU3JmnQGJEmWfNGTu/p7IMdZ6Eoe2M0Yz0su1mflfrZuZ6CrIuUwzwyRdfBRlgpiEzM4nA64YNWJiAanidldCR6iQGhtSxYbgL5+8Cq2Lmm/53qvWb4o4ynACp3AOPlxCHe6gAU2gIOEZXuHN0c6L8+58LFpLTjFzDH/kfP4AjR2QJw==</latexit> ͜Ε͸ͭ·ΓɹɹɹɹɹɹͰɹɹɹɹͱ͓͍ͨ΋ͷ ౳੍ࣜ໿ͷ৔߹ͱಉ͡ ౳ࣜͳ͠ͷ৔߹ͱಉ͡ ͜ͷͱ͖͸ rL = 0 <latexit sha1_base64="iM/VzOztCjwZV4pCLgkkIAz6vAE=">AAAB8nicbZC7SgNBFIbPxltcb1FLm8EgWIVdG22CQRsLiwjmApslzE5mkyGzM8vMrBCWgC9hY6GIre9hb+fbOLkUmvjDwMf/n8Occ6KUM20879sprKyurW8UN92t7Z3dvdL+QVPLTBHaIJJL1Y6wppwJ2jDMcNpOFcVJxGkrGl5P8tYDVZpJcW9GKQ0T3BcsZgQbawUdgSOO0S2qet1S2at4U6Fl8OdQvvx0q48AUO+Wvjo9SbKECkM41jrwvdSEOVaGEU7HbifTNMVkiPs0sChwQnWYT0ceoxPr9FAslX3CoKn7uyPHidajJLKVCTYDvZhNzP+yIDPxRZgzkWaGCjL7KM44MhJN9kc9pigxfGQBE8XsrIgMsMLE2Cu59gj+4srL0Dyr+JbvvHLtCmYqwhEcwyn4cA41uIE6NICAhCd4gVfHOM/Om/M+Ky04855D+CPn4wctRJIE</latexit> <latexit sha1_base64="htYnnZ9nWIXl56ReRGgc2tDkWME=">AAAB8nicbZC7SgNBFIZnvcb1FrW0GQyCVdi10SYYtLGwiGAusFnC2clsMmR2ZpmZFcKSx7CxUCSt72FvI76Nk0uhiT8MfPz/Ocw5J0o508bzvp2V1bX1jc3Clru9s7u3Xzw4bGiZKULrRHKpWhFoypmgdcMMp61UUUgiTpvR4GaSNx+p0kyKBzNMaZhAT7CYETDWCtoCIg74Dle8TrHklb2p8DL4cyhdfbiVdPzl1jrFz3ZXkiyhwhAOWge+l5owB2UY4XTktjNNUyAD6NHAooCE6jCfjjzCp9bp4lgq+4TBU/d3Rw6J1sMkspUJmL5ezCbmf1mQmfgyzJlIM0MFmX0UZxwbiSf74y5TlBg+tABEMTsrJn1QQIy9kmuP4C+uvAyN87Jv+d4rVa/RTAV0jE7QGfLRBaqiW1RDdUSQRE/oBb06xnl23pzxrHTFmfccoT9y3n8AHtOTeA==</latexit> <latexit sha1_base64="htYnnZ9nWIXl56ReRGgc2tDkWME=">AAAB8nicbZC7SgNBFIZnvcb1FrW0GQyCVdi10SYYtLGwiGAusFnC2clsMmR2ZpmZFcKSx7CxUCSt72FvI76Nk0uhiT8MfPz/Ocw5J0o508bzvp2V1bX1jc3Clru9s7u3Xzw4bGiZKULrRHKpWhFoypmgdcMMp61UUUgiTpvR4GaSNx+p0kyKBzNMaZhAT7CYETDWCtoCIg74Dle8TrHklb2p8DL4cyhdfbiVdPzl1jrFz3ZXkiyhwhAOWge+l5owB2UY4XTktjNNUyAD6NHAooCE6jCfjjzCp9bp4lgq+4TBU/d3Rw6J1sMkspUJmL5ezCbmf1mQmfgyzJlIM0MFmX0UZxwbiSf74y5TlBg+tABEMTsrJn1QQIy9kmuP4C+uvAyN87Jv+d4rVa/RTAV0jE7QGfLRBaqiW1RDdUSQRE/oBb06xnl23pzxrHTFmfccoT9y3n8AHtOTeA==</latexit> <latexit sha1_base64="vHdVqjZLWZUxMqnttv1xzXqxFc0=">AAAB8nicbZA9SwNBEIb34leMX1FLm8UgWIU7G22EoI2FRQTzAZcjzG32kiV7e8funBCO/AwbC0Vs/TV2/hs3yRWa+MLCwzsz7MwbplIYdN1vp7S2vrG5Vd6u7Ozu7R9UD4/aJsk04y2WyER3QzBcCsVbKFDybqo5xKHknXB8O6t3nrg2IlGPOEl5EMNQiUgwQGv5PQWhBHpPr91+tebW3bnoKngF1EihZr/61RskLIu5QibBGN9zUwxy0CiY5NNKLzM8BTaGIfctKoi5CfL5ylN6Zp0BjRJtn0I6d39P5BAbM4lD2xkDjsxybWb+V/MzjK6CXKg0Q67Y4qMokxQTOrufDoTmDOXEAjAt7K6UjUADQ5tSxYbgLZ+8Cu2Lumf5wa01boo4yuSEnJJz4pFL0iB3pElahJGEPJNX8uag8+K8Ox+L1pJTzByTP3I+fwC9/ZA3</latexit> = 0 <latexit sha1_base64="jeiI02Rq7/ywr2rF7d1BirpJ5h4=">AAAB8XicbZDLSgMxFIbP1Fsdb1WXboJFcFUybnRTLLpxWcFesB1KJpNpQzOZIckIZSj4EG5cKOLWB3HvzrcxvSy09YfAx/+fQ845QSq4Nhh/O4WV1bX1jeKmu7W9s7tX2j9o6iRTlDVoIhLVDohmgkvWMNwI1k4VI3EgWCsYXk/y1gNTmifyzoxS5sekL3nEKTHWuu8KWxoSVMW9UhlX8FRoGbw5lC8/3eojANR7pa9umNAsZtJQQbTueDg1fk6U4VSwsdvNNEsJHZI+61iUJGbaz6cTj9GJdUIUJco+adDU/d2Rk1jrURzYypiYgV7MJuZ/WScz0YWfc5lmhkk6+yjKBDIJmqyPQq4YNWJkgVDF7ayIDogi1NgjufYI3uLKy9A8q3iWb3G5dgUzFeEIjuEUPDiHGtxAHRpAQcITvMCro51n5815n5UWnHnPIfyR8/ED+AyR8Q==</latexit> <latexit sha1_base64="tg2zSoWEiWXCOxO/b1TrdqIBfNc=">AAAB8XicbZDLSgMxFIbPeK3jrerSTbAIrkrGjW6KRTcuK9gLtkPJZDJtaCYzJBmhDH0LNy4U0aUP4t6N+Daml4W2/hD4+P9zyDknSAXXBuNvZ2l5ZXVtvbDhbm5t7+wW9/YbOskUZXWaiES1AqKZ4JLVDTeCtVLFSBwI1gwGV+O8ec+U5om8NcOU+THpSR5xSoy17jrCloYEVXC3WMJlPBFaBG8GpYsPt5K+fbm1bvGzEyY0i5k0VBCt2x5OjZ8TZTgVbOR2Ms1SQgekx9oWJYmZ9vPJxCN0bJ0QRYmyTxo0cX935CTWehgHtjImpq/ns7H5X9bOTHTu51ymmWGSTj+KMoFMgsbro5ArRo0YWiBUcTsron2iCDX2SK49gje/8iI0Tsue5Rtcql7CVAU4hCM4AQ/OoArXUIM6UJDwAE/w7Gjn0XlxXqelS86s5wD+yHn/Aembk2U=</latexit> <latexit 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sha1_base64="HR2nCncxyfdvMybsJoq2Go0LhGw=">AAAB8XicbVDLSsNAFL2pr1pfVZduBovgqiRudCMU3bisYB/YhjKZ3LRDJ5MwMxFK6F+4caGIW//GnX/jtM1CWw8MHM45l7n3BKng2rjut1NaW9/Y3CpvV3Z29/YPqodHbZ1kimGLJSJR3YBqFFxiy3AjsJsqpHEgsBOMb2d+5wmV5ol8MJMU/ZgOJY84o8ZKj31hoyEl1+6gWnPr7hxklXgFqUGB5qD61Q8TlsUoDRNU657npsbPqTKcCZxW+pnGlLIxHWLPUklj1H4+33hKzqwSkihR9klD5urviZzGWk/iwCZjakZ62ZuJ/3m9zERXfs5lmhmUbPFRlAliEjI7n4RcITNiYgllittdCRtRRZmxJVVsCd7yyaukfVH3LL93a42boo4ynMApnIMHl9CAO2hCCxhIeIZXeHO08+K8Ox+LaMkpZo7hD5zPH4jUkCQ=</latexit> g = 0 <latexit sha1_base64="ffdDQeaqsv3rSozPzRPee7IEHl4=">AAAB6nicbZC7SgNBFIbPxluMt6ilFoNBsAq7NtoIQRvLBM0FkiXMTs5uhszOLjOzQgh5BBsLRWx9CJ/Dzs5HcXIpNPGHgY//nMOc8wep4Nq47peTW1ldW9/Ibxa2tnd294r7Bw2dZIphnSUiUa2AahRcYt1wI7CVKqRxILAZDG4m9eYDKs0TeW+GKfoxjSQPOaPGWnfRldstltyyOxVZBm8OpcrxR+0bAKrd4menl7AsRmmYoFq3PTc1/ogqw5nAcaGTaUwpG9AI2xYljVH7o+mqY3JqnR4JE2WfNGTq/p4Y0VjrYRzYzpiavl6sTcz/au3MhJf+iMs0MyjZ7KMwE8QkZHI36XGFzIihBcoUt7sS1qeKMmPTKdgQvMWTl6FxXvYs12wa1zBTHo7gBM7AgwuowC1UoQ4MIniEZ3hxhPPkvDpvs9acM585hD9y3n8Ay0mPrQ==</latexit> <latexit 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sha1_base64="cva5URaKFeDx8RDzzznkZOxN6Ps=">AAAB6nicbZDLSgMxFIbPeK31VnWpSLAIrsqMG90IRTcuW7QXaIeSSTPT0CQzJBmhDF26dONCEbc+RJ/Dnc/gS5heFtr6Q+DjP+eQc/4g4Uwb1/1ylpZXVtfWcxv5za3tnd3C3n5dx6kitEZiHqtmgDXlTNKaYYbTZqIoFgGnjaB/M643HqjSLJb3ZpBQX+BIspARbKx1F125nULRLbkToUXwZlAsH42q34/Ho0qn8NnuxiQVVBrCsdYtz02Mn2FlGOF0mG+nmiaY9HFEWxYlFlT72WTVITq1TheFsbJPGjRxf09kWGg9EIHtFNj09HxtbP5Xa6UmvPQzJpPUUEmmH4UpRyZG47tRlylKDB9YwEQxuysiPawwMTadvA3Bmz95EernJc9y1aZxDVPl4BBO4Aw8uIAy3EIFakAggid4gVeHO8/Om/M+bV1yZjMH8EfOxw+pjpET</latexit> <latexit sha1_base64="J66Zi7zKQjHsVDRT4is+4Cv31r8=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSL3oRil48VrQf0Iay2W7SpZtN2J0IJfQnePGgiFd/kTf/jds2B219YeHhnRl25g1SKQy67rdTWlvf2Nwqb1d2dvf2D6qHR22TZJrxFktkorsBNVwKxVsoUPJuqjmNA8k7wfh2Vu88cW1Eoh5xknI/ppESoWAUrfUQXbuDas2tu3ORVfAKqEGh5qD61R8mLIu5QiapMT3PTdHPqUbBJJ9W+pnhKWVjGvGeRUVjbvx8vuqUnFlnSMJE26eQzN3fEzmNjZnEge2MKY7Mcm1m/lfrZRhe+blQaYZcscVHYSYJJmR2NxkKzRnKiQXKtLC7EjaimjK06VRsCN7yyavQvqh7lu/dWuOmiKMMJ3AK5+DBJTTgDprQAgYRPMMrvDnSeXHenY9Fa8kpZo7hj5zPH7tPjWg=</latexit> g < 0 <latexit sha1_base64="/zfVho932OlaCSYlY7+PV8swEZc=">AAAB6nicbZC7SgNBFIbPxluMt6ilFoNBsAq7NlpYBG0sEzQXSJYwOzm7GTI7u8zMCiHkEWwsFLH1IXwOOzsfxcml0MQfBj7+cw5zzh+kgmvjul9ObmV1bX0jv1nY2t7Z3SvuHzR0kimGdZaIRLUCqlFwiXXDjcBWqpDGgcBmMLiZ1JsPqDRP5L0ZpujHNJI85Iwaa91FV263WHLL7lRkGbw5lCrHH7VvAKh2i5+dXsKyGKVhgmrd9tzU+COqDGcCx4VOpjGlbEAjbFuUNEbtj6arjsmpdXokTJR90pCp+3tiRGOth3FgO2Nq+nqxNjH/q7UzE176Iy7TzKBks4/CTBCTkMndpMcVMiOGFihT3O5KWJ8qyoxNp2BD8BZPXobGedmzXLNpXMNMeTiCEzgDDy6gArdQhTowiOARnuHFEc6T8+q8zVpzznzmEP7Ief8BycSPrA==</latexit> <latexit sha1_base64="E9b/+ysbSAdnGhGkei4aKvzgqoQ=">AAAB6nicbZC7SgNBFIbPeo3xFrVUZDAIVmHXRguLoI1lguYCyRJmJ7ObITOzy8ysEJaUljYWitj6EHkOO5/Bl3ByKTTxh4GP/5zDnPMHCWfauO6Xs7S8srq2ntvIb25t7+wW9vbrOk4VoTUS81g1A6wpZ5LWDDOcNhNFsQg4bQT9m3G98UCVZrG8N4OE+gJHkoWMYGOtu+jK7RSKbsmdCC2CN4Ni+WhU/X48HlU6hc92NyapoNIQjrVueW5i/Awrwwinw3w71TTBpI8j2rIosaDazyarDtGpdboojJV90qCJ+3siw0LrgQhsp8Cmp+drY/O/Wis14aWfMZmkhkoy/ShMOTIxGt+NukxRYvjAAiaK2V0R6WGFibHp5G0I3vzJi1A/L3mWqzaNa5gqB4dwAmfgwQWU4RYqUAMCETzBC7w63Hl23pz3aeuSM5s5gD9yPn4AqAmREg==</latexit> <latexit sha1_base64="E9b/+ysbSAdnGhGkei4aKvzgqoQ=">AAAB6nicbZC7SgNBFIbPeo3xFrVUZDAIVmHXRguLoI1lguYCyRJmJ7ObITOzy8ysEJaUljYWitj6EHkOO5/Bl3ByKTTxh4GP/5zDnPMHCWfauO6Xs7S8srq2ntvIb25t7+wW9vbrOk4VoTUS81g1A6wpZ5LWDDOcNhNFsQg4bQT9m3G98UCVZrG8N4OE+gJHkoWMYGOtu+jK7RSKbsmdCC2CN4Ni+WhU/X48HlU6hc92NyapoNIQjrVueW5i/Awrwwinw3w71TTBpI8j2rIosaDazyarDtGpdboojJV90qCJ+3siw0LrgQhsp8Cmp+drY/O/Wis14aWfMZmkhkoy/ShMOTIxGt+NukxRYvjAAiaK2V0R6WGFibHp5G0I3vzJi1A/L3mWqzaNa5gqB4dwAmfgwQWU4RYqUAMCETzBC7w63Hl23pz3aeuSM5s5gD9yPn4AqAmREg==</latexit> <latexit sha1_base64="+Q7bJxmOMGD6oarcDbHqUcjPNcU=">AAAB6nicbZA9T8MwEIYv5auUrwIji0WFxFQlLDAwVLAwFkE/pDaqHNdJrTpOZF+Qqqg/gYUBhFj5RWz8G9w2A7S8kqVH793Jd2+QSmHQdb+d0tr6xuZWebuys7u3f1A9PGqbJNOMt1giE90NqOFSKN5CgZJ3U81pHEjeCca3s3rniWsjEvWIk5T7MY2UCAWjaK2H6NodVGtu3Z2LrIJXQA0KNQfVr/4wYVnMFTJJjel5bop+TjUKJvm00s8MTykb04j3LCoac+Pn81Wn5Mw6QxIm2j6FZO7+nshpbMwkDmxnTHFklmsz879aL8Pwys+FSjPkii0+CjNJMCGzu8lQaM5QTixQpoXdlbAR1ZShTadiQ/CWT16F9kXds3zv1ho3RRxlOIFTOAcPLqEBd9CEFjCI4Ble4c2Rzovz7nwsWktOMXMMf+R8/gC5yo1n</latexit> ͜Ε͸ͭ·ΓKKT৚݅ Ͱ͋Γɺ ͔ͭ ͔ͭ ͱͳΔ఺Λ୳ͤ͹Α͍ ( ( ) ) ·ͨ͸
  23. Ԡ༻ྫ • αϙʔτϕΫλϚγϯʢSVMʣ • ৄࡉ͸ʮػցֶशͷΤοηϯεʯࢀর

  24. ݁࿦ • ਺ֶͳΜͯͰ͖ͳͯ͘΋σʔλαΠΤϯςΟετͱͯ͠΍ͬ ͍͚ͯΔ • Ͱ΋਺ֶΛָ͠΋͏ • ຊങͬͯͶὑ