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鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�(gu贸)400澶氭墍楂樼瓑闄㈡牎鎷涙敹纰╁＋銆佸崥澹爺绌剁敓鍏ュ(xu茅)鑰冭│姝峰勾鑰冪爺鐪熼銆佽€冨崥鐪熼銆佺瓟妗堬紝閮ㄥ垎瀛�(xu茅)鏍℃洿鏂拌嚦2012骞�锛�2013骞�锛涘潎鎻愪緵鏀惰不(f猫i)涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛�(di菐n)鎿娾€�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛�(di菐n)鎿娾€�鑰冨崥瑭﹀嵎搴�(k霉)鈥� 涓嬭級
婀栧崡甯寖澶у(xu茅)纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│鑷懡椤岃€冭│澶х侗
鑰冭│绉戠洰浠ｇ⒓锛歔寰�(f霉)瑭︾鐩甝 鑰冭│绉戠洰鍚嶇ū锛氫笘鐣屽湴鐞�
涓€銆佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲�(g貌u)
1)瑭﹀嵎鎴愮妇(j墨)鍙婅€冭│鏅�(sh铆)闁擄細
鏈│鍗锋豢鍒嗙偤 100 鍒�锛岃€冭│鏅�(sh铆)闁撶偤 180 鍒嗛悩銆�
2)绛旈鏂瑰紡锛氶枆鍗�銆佺瓎瑭�
3)瑭﹀嵎鍏�(n猫i)瀹圭祼(ji茅)妲�(g貌u)
锛堜竴锛夊瑙€椤岄儴鍒� 40%
锛堜簩锛変富瑙€椤岄儴鍒� 60%
4)椤屽瀷绲�(ji茅)妲�(g貌u)
a: 鍠爡(xi脿ng)閬告搰椤�锛�20 灏忛锛屾瘡灏忛 1 鍒嗭紝鍏� 20 鍒�
b: 璁€鍦栫躬鍦栭锛�2 灏忛锛屾瘡灏忛 10 鍒�锛屽叡 20 鍒�
c: 鍟忕瓟椤岋紝5 灏忛锛屾瘡灏忛 6 鍒嗭紝鍏� 30 鍒�
d锛氱稖鍚堥锛�2 灏忛锛屾瘡灏忛 15 鍒�锛屽叡 30 鍒�
浜�銆佽€冭│鍏�(n猫i)瀹硅垏鑰冭│瑕佹眰
绗竴绔� 鍏ㄧ悆鍦拌〃褰㈡厠(t脿i)鑸囧叏鐞冩埃鍊�
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 鍏ㄧ悆鍦拌〃褰㈡厠(t脿i)
锛�2锛� 鍏ㄧ悆姘ｅ€欏付鍜屾埃鍊欏瀷
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻″叏鐞冩捣闄稿垎甯冨ぇ鍕�(sh矛)锛岀悊瑙ｅ湴琛ㄥ舰鎱�(t脿i)婕斿寲
锛�2锛夋帉鎻″叏鐞冩埃鍊欏付鍜屾埃鍊欏瀷浠ュ強涓栫晫姘ｅ€欑殑鍒嗗竷瑕�(gu墨)寰�
绗簩绔� 鍏ㄧ悆闄稿湴鑷劧甯剁殑鍩烘湰鏍煎眬鍙婂叾鐞嗚珫鐮旂┒
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 闄稿湴鑷劧甯剁殑褰㈡垚鑸囧垎甯�
锛�2锛夎嚜鐒跺湴鐞嗙挵(hu谩n)澧冪殑鏁村樊鐞嗚珫鍜屽湴鍩熷垎鐣�
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻￠櫢鍦拌嚜鐒跺付鍒嗗竷鍙婄壒寰�锛岀悊瑙ｈ嚜鐒跺付鐨勬紨鍖栭亷绋�
锛�2锛夌悊瑙ｈ嚜鐒跺湴鐞嗙挵(hu谩n)澧冪殑鏁撮珨鎬у拰宸暟鎬�锛屾帉鎻¤嚜鐒跺湴鐞嗙挵(hu谩n)澧冪殑鍦板煙鍒嗙暟
绗笁绔� 缍�(j墨ng)婵�(j矛)鍏ㄧ悆鍖栬垏鍗€(q奴)鍩熺稉(j墨ng)婵�(j矛)涓€楂斿寲
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛夌稉(j墨ng)婵�(j矛)鍏ㄧ悆鍖栵紝鐣�(d膩ng)浠ｄ笘鐣岀稉(j墨ng)婵�(j矛)鐨勫湴鐞嗘牸灞€
锛�2锛夊崁(q奴)鍩熺稉(j墨ng)婵�(j矛)涓€楂斿寲鐨勭悊璜栬垏瀵�(sh铆)韪�
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻＄稉(j墨ng)婵�(j矛)鍏ㄧ悆鍖栫殑鍏�(n猫i)娑�锛岀悊瑙ｅ垎鏋愮稉(j墨ng)婵�(j矛)鍏ㄧ悆鍖栫殑鐧�(f膩)灞曡定鍕�(sh矛)
锛�2锛夌悊瑙ｄ笘鐣岀稉(j墨ng)婵�(j矛)鐧�(f膩)灞曠殑涓嶅钩琛℃€т互鍙婄暥(d膩ng)鍓嶄笘鐣岀稉(j墨ng)婵�(j矛)鏍煎眬
锛�3锛夋帉鎻″崁(q奴)鍩熺稉(j墨ng)婵�(j矛)涓€楂斿寲鐨勬蹇靛強鍏跺惈缇┿€佷簡瑙ｅ崁(q奴)鍩熺稉(j墨ng)婵�(j矛)涓€楂斿寲鐨勭祫绻旈鍨�
绗洓绔� 浜炴床
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锛�1锛� 浜炴床鑷劧鍦扮悊姒傝堪锛屼簽娲茬殑灞呮皯鑸囧湅(gu贸)瀹�
锛�2锛� 鏃ユ湰
锛�3锛� 瑗夸簽鍖楅潪
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻′簽娲蹭綅缃€侀潰绌嶅拰澶ч櫢杓粨
锛�2锛夌啛绶存帉鎻′簽娲插湴褰㈠拰浜炴床姘ｅ€欑殑鐗瑰緛銆佸垎鍗€(q奴)绛�
锛�3锛夌悊瑙ｄ簽娲茬殑浜哄彛銆佹皯鏃�銆佽獮(y菙)瑷€鍙婂畻鏁欙紝骞惰兘鐞嗚В鍒嗘瀽浜炴床鍦扮罚闂�(gu膩n)绯诲晱椤�
锛�4锛夌啛绶存帉鎻℃棩鏈湴鐞嗕綅缃�銆佽嚜鐒剁挵(hu谩n)澧冪壒榛�(di菐n)鍙婂叾鎰忕京锛屾帉鎻℃埌(zh脿n)鍚庢棩鏈稉(j墨ng)婵�(j矛)鐧�(f膩)灞�
鐨勫熀鏈壒寰佷互鍙婃棩鏈埌(zh脿n)鍚庣稉(j墨ng)婵�(j矛)楂橀€熺櫦(f膩)灞曠殑鍘熷洜
锛�5锛夌啛绶存帉鎻¤タ浜炲寳闈炲湴鐞嗕綅缃拰鑷劧鐠�(hu谩n)澧冪壒寰�锛岀悊瑙ｈタ浜炲寳闈炰汉鏂囩櫦(f膩)灞曞拰绀�
鏈�(hu矛)绲�(ji茅)妲�(g貌u)鐗瑰緛锛屾帉鎻¤タ浜炲寳闈炵殑鐭虫补缍�(j墨ng)婵�(j矛)銆�
绗簲绔� 姝愭床
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锛�1锛� 姝愭床鑷劧鍦扮悊
锛�2锛� 姝愭床浜烘枃鍦扮悊
锛�3锛� 姝愮洘
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锛�1锛夌啛绶存帉鎻℃瓙娲插湴鐞嗕綅缃�銆佸湴褰�銆佹埃鍊欍€佹按鏂�銆佺う鐢�(ch菐n)绛夎嚜鐒剁壒寰�
锛�2锛夌悊瑙ｆ瓙娲茬殑鍦�(gu贸)瀹躲€佷汉鍙�銆佹皯鏃忋€佺ó鏃忓拰瑾�(y菙)瑷€锛屼互鍙婃瓙娲茬櫦(f膩)灞曠殑绀炬渻(hu矛)娣垫簮
锛�3锛変簡瑙ｆ瓙娲蹭竴楂斿寲鐨勬绋嬶紝鎺屾彙姝愮洘涓昏鐢�(ch菐n)妤�(y猫)閮ㄩ杸鐨勭櫦(f膩)灞曞拰甯冨眬锛屾帉鎻℃瓙鐩�
杈�(n贸ng)妤�(y猫)鐧�(f膩)灞曞強鍏跺皥闁€鍖栥€�
绗叚绔� 闈炴床
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 闈炴床鑷劧鍦扮悊
锛�2锛� 闈炴床浜烘枃鍦扮悊
锛�3锛� 闈炴床鍦扮悊鍒嗗崁(q奴)
鑰冭│瑕佹眰锛�
锛�1锛夌啛绶存帉鎻￠潪娲插湴鐞嗕綅缃�銆佸ぇ闄歌吉寤�銆佽嚜鐒跺湴鐞嗙壒寰佹サ鍏跺湴鐞嗘剰缇╋紝鐞嗚В闈�
娲茶睈瀵岀殑绀︾敘(ch菐n)璩囨簮锛�
锛�2锛変簡瑙ｉ潪娲叉鍙茬櫦(f膩)灞曞拰鏀挎不鍦板湒婕旇畩锛屼互鍙婇潪娲蹭汉鍙ｃ€佺ó鏃�銆佹皯鏃忓拰瀹楁暀锛�
鎺屾彙闈炴床杈�(n贸ng)妤�(y猫)鍜屽伐绀︽キ(y猫)鐨勭壒寰�
锛�3锛夋帉鎻℃澅闈炪€佷腑闈�銆佽タ闈�銆佸崡闈炵殑鍩烘湰鐗瑰緛
绗竷绔� 鍖楃編娲�
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 鍖楃編娲茶嚜鐒跺湴鐞�
锛�2锛� 缇庡湅(gu贸)
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻″寳缇庢床鍦扮悊浣嶇疆銆佸湴褰�銆佹埃鍊欍€佹渤娴�銆佹箹娉婄瓑鑷劧鍦扮悊鐗瑰緛锛�
锛�2锛夌悊瑙ｇ編鍦�(gu贸)浣嶇疆鑸囬牁(l菒ng)鍦熺祫鎴�锛屾帉鎻＄編鍦�(gu贸)鐨勮嚜鐒跺湴鐞嗙壒寰佸拰鑷劧璩囨簮妲�(g貌u)鎴�锛屾帉
鎻＄編鍦�(gu贸)缍�(j墨ng)婵�(j矛)鐗瑰緛锛�
绗叓绔� 鍗楃編娲�
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 鍗楃編娲茶嚜鐒跺湴鐞�
锛�2锛� 鍗楃編娲蹭汉鏂囧湴鐞�
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻″崡缇庢床鍦扮悊浣嶇疆銆佸湴褰㈠湴璨屻€佹埃鍊欓鍨嬭垏鍒嗗竷銆佹按绯诲強涓昏绀︾敘(ch菐n)锛�
锛�2锛夌悊瑙ｅ崡缇庢床姝峰彶娣垫簮鍜屼汉鏂囪儗鏅�锛�
锛�3锛夋帉鎻″崡缇庢床缍�(j墨ng)婵�(j矛)鐧�(f膩)灞曞拰鐢�(ch菐n)妤�(y猫)甯冨眬锛�
绗節绔� 澶ф磱娲�
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锛�1锛� 澶ф磱娲叉杩�
锛�2锛� 婢冲ぇ鍒╀簽
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锛�1锛夋帉鎻″ぇ娲嬫床鐨勫湴鐞嗚寖鍦嶄互鍙婂ぇ娲嬫床鑷劧鍦扮悊鐠�(hu谩n)澧冪殑鍩烘湰鐗归粸(di菐n)
锛�2锛変簡瑙ｅぇ娲嬫床鐨勫眳姘戝拰鍦�(gu贸)瀹�
锛�3锛夌啛绶存帉鎻℃境澶у埄浜炰綅缃�銆侀潰绌�銆佸ぇ闄歌吉寤撲互鍙婄崹(d煤)鐗圭殑鑷劧鐠�(hu谩n)澧冪壒寰侊紝鎺屾彙
婢冲ぇ鍒╀簽缍�(j墨ng)婵�(j矛)鐧�(f膩)灞曠壒寰�
涓�銆佸弮鑰冩浉鐩�
妤婇潚灞便€侀煋鏉�銆佷竵鍥涗繚涓荤法锛屻€婁笘鐣屽湴鐞嗐€�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2004 骞�
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鍙冭€冩ǎ鏈� 1
脳脳脳脳骞寸ⅸ澹爺绌剁敓鍏ュ(xu茅)鑰冭│鑷懡椤岃€冭│澶х侗
鑰冭│绉戠洰浠ｇ⒓锛歔333] 鑰冭│绉戠洰鍚嶇ū锛氭暀鑲茬稖鍚�
涓€銆佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲�(g貌u)
1)瑭﹀嵎鎴愮妇(j墨)鍙婅€冭│鏅�(sh铆)闁�
鏈│鍗锋豢鍒嗙偤 150 鍒�锛岃€冭│鏅�(sh铆)闁撶偤 180 鍒嗛悩銆�
2)绛旈鏂瑰紡
绛旈鏂瑰紡鐐洪枆鍗�銆佺瓎瑭�銆�
3)瑭﹀嵎鍏�(n猫i)瀹圭祼(ji茅)妲�(g貌u)
鍚勯儴鍒嗗収(n猫i)瀹规墍鍗犲垎鍊肩偤锛�
鏁欒偛瀛�(xu茅)鍘熺悊 绱� 60 鍒�
涓湅(gu贸)鏁欒偛鍙� 绱� 30 鍒�
澶栧湅(gu贸)鏁欒偛鍙� 绱� 30 鍒�
鏁欒偛蹇冪悊瀛�(xu茅) 绱� 30 鍒�
4)椤屽瀷绲�(ji茅)妲�(g貌u)
鍚嶈瑙ｉ噵椤岋細6 灏忛锛屾瘡灏忛 5 鍒�锛屽叡 30 鍒�
绨�(ji菐n)绛旈锛� 4 灏忛锛屾瘡灏忛 10 鍒�锛屽叡 40 鍒�
鍒嗘瀽璜栬堪椤岋細4 灏忛锛屾瘡灏忛 20 鍒�锛屽叡 80 鍒�
浜�銆佽€冭│鍏�(n猫i)瀹硅垏鑰冭│瑕佹眰
鏁欒偛瀛�(xu茅)鍘熺悊
鑰冭│鐩(bi膩o)锛�
1銆佺郴绲�(t菕ng)鎺屾彙鏁欒偛瀛�(xu茅)鍘熺悊鐨勫熀绀�(ch菙)鐭ヨ瓨(sh铆)銆佸熀鏈蹇�銆佸熀鏈悊璜栧拰鐝�(xi脿n)浠ｆ暀鑲茶蹇点€�
2銆佺悊瑙ｆ暀瀛�(xu茅)銆佸痉鑲�銆佺鐞嗙瓑鏁欒偛娲诲嫊(d貌ng)鐨勪换鍕�(w霉)銆侀亷绋�銆佸師鍓囧拰鏂规硶銆�
3銆佽兘閬�(y霉n)鐢ㄦ暀鑲茬殑鍩烘湰鐞嗚珫鍜岀従(xi脿n)浠ｆ暀鑲茬悊蹇典締鍒嗘瀽鍜岃В姹烘暀鑲茬殑鐝�(xi脿n)瀵�(sh铆)鍟忛銆�
鑰冭│鍏�(n猫i)瀹癸細
涓€銆佹暀鑲插(xu茅)姒傝堪
锛堜竴锛夋暀鑲插(xu茅)鐨勫皪(du矛)璞″拰浠诲嫏(w霉)
鏁欒偛瀛�(xu茅)鐨勭爺绌跺皪(du矛)璞℃槸鏁欒偛鐝�(xi脿n)璞″拰鏁欒偛鍟忛锛涙暀鑲插(xu茅)鐨勪换鍕�(w霉)鏄彮绀烘暀鑲茶(gu墨)寰�锛�
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锛堝洓锛夋暀鑲叉蹇电殑鐣屽畾
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锛堜簩锛夋暀鑲茬殑绀炬渻(hu矛)鍔熻兘
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锛堜簩锛夋暀鑲茬洰鐨勭殑鐞嗚珫鍩虹(ch菙)
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锛堝洓锛夊痉鑲查€斿緫鑸囨柟娉�
1銆佸痉鑲查€斿緫
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2銆佸痉鑲叉柟娉�
瑾湇銆佹妯�銆侀崨鐓夈€佷慨椁�(y菐ng)銆侀櫠鍐�銆佺崕(ji菐ng)鎳茬瓑鏂规硶鐨勬兜缇╁拰瑕佹眰銆�
鍗佷竴銆佺彮涓讳换
锛堜竴锛夌彮涓讳换宸ヤ綔姒傝堪
鐝富浠诲伐浣滅殑鎰忕京鑸囦换鍕�(w霉)锛涚彮涓讳换绱犺唱(zh矛)鐨勮姹�銆�
锛堜簩锛夌彮闆嗛珨鐨勫煿椁�(y菐ng)
鐝泦楂旂殑鏁欒偛鍔熻兘锛涚彮闆嗛珨鑸囧(xu茅)鐢熺兢楂旓紱闆嗛珨鐨勭櫦(f膩)灞曢殠娈�锛涘煿椁�(y菐ng)闆嗛珨鐨勬柟娉�
锛堜笁锛夌彮涓讳换宸ヤ綔鐨勫収(n猫i)瀹瑰拰鏂规硶
浜嗚В鍜岀爺绌跺(xu茅)鐢燂紱鏁欏皫(d菐o)瀛�(xu茅)鐢熷(xu茅)濂藉姛瑾�锛涚祫绻旂彮鏈�(hu矛)娲诲嫊(d貌ng)锛涚祫绻旇澶栨椿鍕�(d貌ng)銆佹牎澶�
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鍗佷簩銆佹暀甯�
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1銆佹暀甯嫗鍕�(d貌ng)鐨勭壒榛�(di菐n)
鏁欏斧鍕炲嫊(d貌ng)鐨勫京(f霉)闆滄€э紱鏁欏斧鍕炲嫊(d貌ng)鐨勭ず鑼冩€�锛涙暀甯嫗鍕�(d貌ng)鐨勫壍(chu脿ng)閫犳€э紱鏁欏斧鍕炲嫊(d貌ng)鐨勫皥
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2銆佹暀甯嫗鍕�(d貌ng)鐨勫児(ji脿)鍊�
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3銆佹暀甯殑娆�(qu谩n)鍒╄垏缇╁嫏(w霉)
4銆佹暀甯伔妤�(y猫)鐨勮鑹叉壆婕�
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涓�銆佷富瑕佸弮鑰冩浉
鐜嬮亾淇�銆侀儹鏂囧畨涓荤法锛氥€婃暀鑲插(xu茅)銆嬶紝浜烘皯鏁欒偛鍑虹増绀� 2009 骞�銆�
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1) 瑭﹀嵎鎴愮妇(j墨)鍙婅€冭│鏅�(sh铆)闁�
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鍑芥暩(sh霉)鐨勬€ц唱(zh矛)
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｅ嚱鏁�(sh霉)鐨勬蹇�锛屾帉鎻″嚱鏁�(sh霉)鐨勮〃绀烘硶锛屾渻(hu矛)寤虹珛鎳�(y墨ng)鐢ㄥ晱椤岀殑鍑芥暩(sh霉)闂�(gu膩n)绯�.
锛�2锛変簡瑙ｅ嚱鏁�(sh霉)鐨勬湁鐣屾€�銆佸柈瑾�(di脿o)鎬�銆佸懆鏈熸€у拰濂囧伓鎬э紟
锛�3锛夌悊瑙ｅ京(f霉)鍚堝嚱鏁�(sh霉)鍙婂垎娈靛嚱鏁�(sh霉)鐨勬蹇�锛屼簡瑙ｅ弽鍑芥暩(sh霉)鍙婇毐鍑芥暩(sh霉)鐨勬蹇碉紟
锛�4锛夋帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦栧舰锛屼簡瑙ｅ垵绛夊嚱鏁�(sh霉)鐨勬蹇�.
锛�5锛夌悊瑙ｆサ闄愮殑姒傚康锛岀悊瑙ｅ嚱鏁�(sh霉)宸︽サ闄愯垏鍙虫サ闄愮殑姒傚康浠ュ強鍑芥暩(sh霉)妤甸檺瀛樺湪鑸�
宸�銆佸彸妤甸檺涔嬮枔鐨勯棞(gu膩n)绯伙紟
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闄愭眰妤甸檺鐨勬柟娉曪紟
锛�8锛夌悊瑙ｇ劇绐皬閲�銆佺劇绐ぇ閲忕殑姒傚康锛屾帉鎻＄劇绐皬閲忕殑姣旇純鏂规硶锛屾渻(hu矛)鐢ㄧ瓑鍍�(ji脿)
鐒＄灏忛噺姹傛サ闄愶紟
锛�9锛夌悊瑙ｅ嚱鏁�(sh霉)閫ｇ簩(x霉)鎬х殑姒傚康锛堝惈宸﹂€ｇ簩(x霉)鑸囧彸閫ｇ簩(x霉)锛�锛屾渻(hu矛)鍒ゅ垾鍑芥暩(sh霉)闁撴柗榛�(di菐n)鐨勯
鍨嬶紟
锛�10锛変簡瑙ｉ€ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍜屽垵绛夊嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬э紝鐞嗚В闁夊崁(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€�
璩�(zh矛)锛堟湁鐣屾€�銆佹渶澶у€煎拰鏈€灏忓€煎畾鐞嗐€佷粙鍊煎畾鐞嗭級锛屽苟鏈�(hu矛)鎳�(y墨ng)鐢ㄩ€欎簺鎬ц唱(zh矛)锛�
2銆佷竴鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)
鑰冭│鍏�(n猫i)瀹�
灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑姒傚康 灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇╁拰鐗╃悊鎰忕京 鍑芥暩(sh霉)鐨勫彲灏�(d菐o)鎬ц垏閫ｇ簩(x霉)鎬�
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灏�(d菐o)鏁�(sh霉) 寰�(f霉)鍚堝嚱鏁�(sh霉)銆佸弽鍑芥暩(sh霉)銆侀毐鍑芥暩(sh霉)浠ュ強鍙冩暩(sh霉)鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)鐨勫井鍒嗘硶 楂橀殠灏�(d菐o)
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鍑芥暩(sh霉)鐨勬渶澶у€艰垏鏈€灏忓€� 寮у井鍒� 鏇茬巼鐨勬蹇� 鏇茬巼鍦撹垏鏇茬巼鍗婂緫
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｅ皫(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑姒傚康锛岀悊瑙ｅ皫(d菐o)鏁�(sh霉)鑸囧井鍒嗙殑闂�(gu膩n)绯�锛岀悊瑙ｅ皫(d菐o)鏁�(sh霉)鐨勫咕浣曟剰
缇╋紝鏈�(hu矛)姹傚钩闈㈡洸绶氱殑鍒囩窔鏂圭▼鍜屾硶绶氭柟绋�锛屼簡瑙ｅ皫(d菐o)鏁�(sh霉)鐨勭墿鐞嗘剰缇�锛屾渻(hu矛)鐢ㄥ皫(d菐o)鏁�(sh霉)鎻忚堪
涓€浜涚墿鐞嗛噺锛岀悊瑙ｅ嚱鏁�(sh霉)鐨勫彲灏�(d菐o)鎬ц垏閫ｇ簩(x霉)鎬т箣闁撶殑闂�(gu膩n)绯伙紟
锛�2锛夋帉鎻″皫(d菐o)鏁�(sh霉)鐨勫洓鍓囬亱(y霉n)绠楁硶鍓囧拰寰�(f霉)鍚堝嚱鏁�(sh霉)鐨勬眰灏�(d菐o)娉曞墖锛屾帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)
鐨勫皫(d菐o)鏁�(sh霉)鍏紡锛庝簡瑙ｅ井鍒嗙殑鍥涘墖閬�(y霉n)绠楁硶鍓囧拰涓€闅庡井鍒嗗舰寮忕殑涓嶈畩鎬�锛屾渻(hu矛)姹傚嚱鏁�(sh霉)鐨勫井
鍒嗭紟
锛�3锛変簡瑙ｉ珮闅庡皫(d菐o)鏁�(sh霉)鐨勬蹇�锛屾渻(hu矛)姹傜啊(ji菐n)鍠嚱鏁�(sh霉)鐨勯珮闅庡皫(d菐o)鏁�(sh霉)锛�
锛�4锛夋渻(hu矛)姹傚垎娈靛嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛屾渻(hu矛)姹傞毐鍑芥暩(sh霉)鍜岀敱鍙冩暩(sh霉)鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)浠ュ強鍙�
鍑芥暩(sh霉)鐨勫皫(d菐o)鏁�(sh霉).
锛�5锛夌悊瑙ｅ苟鏈�(hu矛)鐢ㄧ緟鐖�(Rolle)瀹氱悊銆佹媺鏍兼湕鏃�(Lagrange)涓€煎畾鐞嗗拰娉板嫆
(Taylor)瀹氱悊锛屼簡瑙ｅ苟鏈�(hu矛)鐢ㄦ煰瑗�(Cauchy)涓€煎畾鐞嗭紟
锛�6锛夋帉鎻＄敤娲涘繀閬�(d谩)娉曞墖姹傛湭瀹氬紡妤甸檺鐨勬柟娉曪紟
锛�7锛夌悊瑙ｅ嚱鏁�(sh霉)鐨勬サ鍊兼蹇�锛屾帉鎻＄敤灏�(d菐o)鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鐨勫柈瑾�(di脿o)鎬у拰姹傚嚱鏁�(sh霉)妤靛€肩殑
鏂规硶锛屾帉鎻″嚱鏁�(sh霉)鏈€澶у€煎拰鏈€灏忓€肩殑姹傛硶鍙婂叾鎳�(y墨ng)鐢紟
锛�8锛夋渻(hu矛)鐢ㄥ皫(d菐o)鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鍦栧舰鐨勫嚬鍑告€э紙娉細鍦ㄥ崁(q奴)闁�( , )a b 鍏�(n猫i)锛岃ō(sh猫)鍑芥暩(sh霉) ( )f x 鍏�
鏈変簩闅庡皫(d菐o)鏁�(sh霉)銆傜暥(d膩ng) ( ) 0f x?? ? 鏅�(sh铆)锛� ( )f x 鐨勫湒褰㈡槸鍑圭殑锛涚暥(d膩ng) ( ) 0f x?? ? 鏅�(sh铆)锛� ( )f x 鐨勫湒褰�
鏄嚫鐨勶級锛屾渻(hu矛)姹傚嚱鏁�(sh霉)鍦栧舰鐨勬嫄榛�(di菐n)浠ュ強姘村钩銆侀墰鐩村拰鏂滄几杩戠窔锛屾渻(hu矛)鎻忕躬鍑芥暩(sh霉)鐨勫湒褰紟
锛�9锛変簡瑙ｆ洸鐜�銆佹洸鐜囧湏鑸囨洸鐜囧崐寰戠殑姒傚康锛屾渻(hu矛)瑷�(j矛)绠楁洸鐜囧拰鏇茬巼鍗婂緫锛�
3銆佷竴鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
鑰冭│鍏�(n猫i)瀹�
鍘熷嚱鏁�(sh霉)鍜屼笉瀹氱⿳鍒嗙殑姒傚康 涓嶅畾绌嶅垎鐨勫熀鏈€ц唱(zh矛) 鍩烘湰绌嶅垎鍏紡 瀹氱⿳鍒�
鐨勬蹇靛拰鍩烘湰鎬ц唱(zh矛) 瀹氱⿳鍒嗕腑鍊煎畾鐞� 绌嶅垎涓婇檺鐨勫嚱鏁�(sh霉)鍙婂叾灏�(d菐o)鏁�(sh霉) 鐗涢爴-钀婂竷灏�
鑼紙Newton-Leibniz锛夊叕寮� 涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬彌鍏冪⿳鍒嗘硶鑸囧垎閮ㄧ⿳鍒嗘硶 鏈�
鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鐨勬湁鐞嗗紡鍜岀啊(ji菐n)鍠劇鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒� 鍙嶅父锛堝唬缇╋級绌嶅垎 瀹氱⿳鍒�
鐨勬噳(y墨ng)鐢�
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｅ師鍑芥暩(sh霉)鐨勬蹇�锛岀悊瑙ｄ笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑姒傚康锛�
锛�2锛夋帉鎻′笉瀹氱⿳鍒嗙殑鍩烘湰鍏紡锛屾帉鎻′笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婂畾绌嶅垎涓�
鍊煎畾鐞嗭紝鎺屾彙鎻涘厓绌嶅垎娉曡垏鍒嗛儴绌嶅垎娉曪紟
锛�3锛夋渻(hu矛)姹傛湁鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鏈夌悊寮忓拰绨�(ji菐n)鍠劇鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒嗭紟
锛�4锛夌悊瑙ｇ⿳鍒嗕笂闄愮殑鍑芥暩(sh霉)锛屾渻(hu矛)姹傚畠鐨勫皫(d菐o)鏁�(sh霉)锛屾帉鎻＄墰闋�-钀婂竷灏艰尐鍏紡锛�
锛�5锛変簡瑙ｅ弽甯哥⿳鍒嗙殑姒傚康锛屾渻(hu矛)瑷�(j矛)绠楀弽甯哥⿳鍒嗭紟
锛�6锛夋帉鎻＄敤瀹氱⿳鍒嗚〃閬�(d谩)鍜岃▓(j矛)绠椾竴浜涘咕浣曢噺鑸囩墿鐞嗛噺锛堝钩闈㈠湒褰㈢殑闈㈢⿳銆佸钩
闈㈡洸绶氱殑寮ч暦(zh菐ng)銆佹棆杞�(zhu菐n)楂旂殑楂旂⿳鍙婂伌(c猫)闈㈢⿳銆佸钩琛屾埅闈㈤潰绌嶇偤宸茬煡鐨勭珛楂旈珨绌�銆佸姛銆�
寮曞姏銆佸鍔涖€佽唱(zh矛)蹇�銆佸舰蹇冪瓑锛夊強鍑芥暩(sh霉)鐨勫钩鍧囧€硷紟
4銆佸悜閲忎唬鏁�(sh霉)鍜岀┖闁撹В鏋愬咕浣�
鑰冭│鍏�(n猫i)瀹�
鍚戦噺鐨勬蹇� 鍚戦噺鐨勭窔鎬ч亱(y霉n)绠� 鍚戦噺鐨勬暩(sh霉)閲忕⿳鍜屽悜閲忕⿳ 鍚戦噺鐨勬贩鍚堢⿳
鍏╁悜閲忓瀭鐩�銆佸钩琛岀殑姊濅欢 鍏╁悜閲忕殑澶捐 鍚戦噺鐨勫潗妯�(bi膩o)琛ㄩ仈(d谩)寮忓強鍏堕亱(y霉n)绠� 鍠綅鍚�
閲� 鏂瑰悜鏁�(sh霉)鑸囨柟鍚戜綑寮� 鏇查潰鏂圭▼鍜岀┖闁撴洸绶氭柟绋嬬殑姒傚康 骞抽潰鏂圭▼ 鐩寸窔鏂�
绋� 骞抽潰鑸囧钩闈�銆佸钩闈㈣垏鐩寸窔銆佺洿绶氳垏鐩寸窔鐨勫ぞ瑙掍互鍙婂钩琛屻€佸瀭鐩寸殑姊濅欢 榛�(di菐n)鍒�
骞抽潰鍜岄粸(di菐n)鍒扮洿绶氱殑璺濋洟 鐞冮潰 鏌遍潰 鏃嬭綁(zhu菐n)鏇查潰 甯哥敤鐨勪簩娆℃洸闈㈡柟绋嬪強鍏跺湒
褰� 绌洪枔鏇茬窔鐨勫弮鏁�(sh霉)鏂圭▼鍜屼竴鑸柟绋� 绌洪枔鏇茬窔鍦ㄥ潗妯�(bi膩o)闈笂鐨勬姇褰辨洸绶氭柟绋�
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｇ┖闁撶洿瑙掑潗妯�(bi膩o)绯�锛岀悊瑙ｅ悜閲忕殑姒傚康鍙婂叾琛ㄧず.
锛�2锛夋帉鎻″悜閲忕殑閬�(y霉n)绠楋紙绶氭€ч亱(y霉n)绠椼€佹暩(sh霉)閲忕⿳銆佸悜閲忕⿳銆佹贩鍚堢⿳锛�锛屼簡瑙ｅ叐鍊�(g猫)
鍚戦噺鍨傜洿銆佸钩琛岀殑姊濅欢.
锛�3锛夌悊瑙ｅ柈浣嶅悜閲�銆佹柟鍚戞暩(sh霉)鑸囨柟鍚戜綑寮�銆佸悜閲忕殑鍧愭(bi膩o)琛ㄩ仈(d谩)寮忥紝鎺屾彙鐢ㄥ潗妯�(bi膩o)
琛ㄩ仈(d谩)寮忛€�(j矛n)琛屽悜閲忛亱(y霉n)绠楃殑鏂规硶.
锛�4锛夋帉鎻″钩闈㈡柟绋嬪拰鐩寸窔鏂圭▼鍙婂叾姹傛硶.
锛�5锛夋渻(hu矛)姹傚钩闈㈣垏骞抽潰銆佸钩闈㈣垏鐩寸窔銆佺洿绶氳垏鐩寸窔涔嬮枔鐨勫ぞ瑙�锛屽苟鏈�(hu矛)鍒╃敤骞�
闈�銆佺洿绶氱殑鐩镐簰闂�(gu膩n)绯伙紙骞宠銆佸瀭鐩�銆佺浉浜ょ瓑锛夎В姹烘湁闂�(gu膩n)鍟忛.
锛�6锛夋渻(hu矛)姹傞粸(di菐n)鍒扮洿绶氫互鍙婇粸(di菐n)鍒板钩闈㈢殑璺濋洟.
锛�7锛変簡瑙ｆ洸闈㈡柟绋嬪拰绌洪枔鏇茬窔鏂圭▼鐨勬蹇�.
锛�8锛変簡瑙ｅ父鐢ㄤ簩娆℃洸闈㈢殑鏂圭▼鍙婂叾鍦栧舰锛屾渻(hu矛)姹傜啊(ji菐n)鍠殑鏌遍潰鍜屾棆杞�(zhu菐n)鏇查潰鐨勬柟
绋�.
锛�9锛変簡瑙ｇ┖闁撴洸绶氱殑鍙冩暩(sh霉)鏂圭▼鍜屼竴鑸柟绋�.浜嗚В绌洪枔鏇茬窔鍦ㄥ潗妯�(bi膩o)骞抽潰涓婄殑鎶�
褰憋紝骞舵渻(hu矛)姹傝┎鎶曞奖鏇茬窔鐨勬柟绋�.
5銆佸鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)
鑰冭│鍏�(n猫i)瀹�
澶氬厓鍑芥暩(sh霉)鐨勬蹇� 浜屽厓鍑芥暩(sh霉)鐨勫咕浣曟剰缇� 浜屽厓鍑芥暩(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)鐨勬蹇� 鏈�
鐣岄枆鍗€(q奴)鍩熶笂澶氬厓閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛) 澶氬厓鍑芥暩(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉)鍜屽叏寰垎 鍏ㄥ井鍒嗗瓨鍦ㄧ殑
蹇呰姊濅欢鍜屽厖鍒嗘浠� 澶氬厓寰�(f霉)鍚堝嚱鏁�(sh霉)銆侀毐鍑芥暩(sh霉)鐨勬眰灏�(d菐o)娉� 浜岄殠鍋忓皫(d菐o)鏁�(sh霉) 鏂瑰悜?q奴)顫�?sh霉)
鍜屾搴� 绌洪枔鏇茬窔鐨勫垏绶氬拰娉曞钩闈� 鏇查潰鐨勫垏骞抽潰鍜屾硶绶� 浜屽厓鍑芥暩(sh霉)鐨勪簩闅庢嘲
鍕掑叕寮� 澶氬厓鍑芥暩(sh霉)鐨勬サ鍊煎拰姊濅欢妤靛€� 澶氬厓鍑芥暩(sh霉)鐨勬渶澶у€�銆佹渶灏忓€煎強鍏剁啊(ji菐n)鍠噳(y墨ng)鐢�
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｅ鍏冨嚱鏁�(sh霉)鐨勬蹇碉紝鐞嗚В浜屽厓鍑芥暩(sh霉)鐨勫咕浣曟剰缇�.
锛�2锛変簡瑙ｄ簩鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)鐨勬蹇典互鍙婃湁鐣岄枆鍗€(q奴)鍩熶笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛).
锛�3锛夌悊瑙ｅ鍏冨嚱鏁�(sh霉)鍋忓皫(d菐o)鏁�(sh霉)鍜屽叏寰垎鐨勬蹇�锛屾渻(hu矛)姹傚叏寰垎锛屼簡瑙ｅ叏寰垎瀛樺湪
鐨勫繀瑕佹浠跺拰鍏呭垎姊濅欢锛屼簡瑙ｅ叏寰垎褰㈠紡鐨勪笉璁婃€�.
锛�4锛夌悊瑙ｆ柟鍚�?q奴)顫�?sh霉)鑸囨搴︾殑姒傚康锛屽苟鎺屾彙鍏惰▓(j矛)绠楁柟娉�.
锛�5锛夋帉鎻″鍏冨京(f霉)鍚堝嚱鏁�(sh霉)涓€闅�銆佷簩闅庡亸灏�(d菐o)鏁�(sh霉)鐨勬眰娉�.
锛�6锛変簡瑙ｉ毐鍑芥暩(sh霉)瀛樺湪瀹氱悊锛屾渻(hu矛)姹傚鍏冮毐鍑芥暩(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉).
锛�7锛変簡瑙ｇ┖闁撴洸绶氱殑鍒囩窔鍜屾硶骞抽潰鍙婃洸闈㈢殑鍒囧钩闈㈠拰娉曠窔鐨勬蹇�锛屾渻(hu矛)姹傚畠
鍊戠殑鏂圭▼.
锛�8锛変簡瑙ｄ簩鍏冨嚱鏁�(sh霉)鐨勪簩闅庢嘲鍕掑叕寮�.
锛�9锛夌悊瑙ｅ鍏冨嚱鏁�(sh霉)妤靛€煎拰姊濅欢妤靛€肩殑姒傚康锛屾帉鎻″鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑蹇呰
姊濅欢锛屼簡瑙ｄ簩鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑鍏呭垎姊濅欢锛屾渻(hu矛)姹備簩鍏冨嚱鏁�(sh霉)鐨勬サ鍊硷紝鏈�(hu矛)鐢ㄦ媺鏍兼湕鏃�
涔樻暩(sh霉)娉曟眰姊濅欢妤靛€�锛屾渻(hu矛)姹傜啊(ji菐n)鍠鍏冨嚱鏁�(sh霉)鐨勬渶澶у€煎拰鏈€灏忓€�锛屽苟鏈�(hu矛)瑙ｆ焙涓€浜涚啊(ji菐n)鍠殑
鎳�(y墨ng)鐢ㄥ晱椤�.
6銆佸鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
鑰冭│鍏�(n猫i)瀹�
浜岄噸绌嶅垎鑸囦笁閲嶇⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)銆佽▓(j矛)绠楀拰鎳�(y墨ng)鐢� 鍏╅鏇茬窔绌嶅垎鐨勬蹇点€佹€�
璩�(zh矛)鍙婅▓(j矛)绠� 鍏╅鏇茬窔绌嶅垎鐨勯棞(gu膩n)绯� 鏍兼灄锛圙reen锛夊叕寮� 骞抽潰鏇茬窔绌嶅垎鑸囪矾寰戠劇
闂�(gu膩n)鐨勬浠� 浜屽厓鍑芥暩(sh霉)鍏ㄥ井鍒嗙殑鍘熷嚱鏁�(sh霉) 鍏╅鏇查潰绌嶅垎鐨勬蹇�銆佹€ц唱(zh矛)鍙婅▓(j矛)绠� 鍏╅
鏇查潰绌嶅垎鐨勯棞(gu膩n)绯� 楂樻柉锛圙auss锛夊叕寮� 鏂墭鍏嬫柉锛圫tokes)鍏紡 鏁ｅ害銆佹棆搴︾殑
姒傚康鍙婅▓(j矛)绠� 鏇茬窔绌嶅垎鍜屾洸闈㈢⿳鍒嗙殑鎳�(y墨ng)鐢�
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｄ簩閲嶇⿳鍒嗐€佷笁閲嶇⿳鍒嗙殑姒傚康锛屼簡瑙ｉ噸绌嶅垎鐨勬€ц唱(zh矛)锛屼簡瑙ｄ簩閲嶇⿳鍒�
鐨勪腑鍊煎畾鐞�.
锛�2锛夋帉鎻′簩閲嶇⿳鍒嗙殑瑷�(j矛)绠楁柟娉曪紙鐩磋鍧愭(bi膩o)銆佹サ鍧愭(bi膩o)锛�锛屾渻(hu矛)瑷�(j矛)绠椾笁閲嶇⿳鍒嗭紙鐩�
瑙掑潗妯�(bi膩o)銆佹煴闈㈠潗妯�(bi膩o)銆佺悆闈㈠潗妯�(bi膩o)锛�.
锛�3锛夌悊瑙ｅ叐椤炴洸绶氱⿳鍒嗙殑姒傚康锛屼簡瑙ｅ叐椤炴洸绶氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婂叐椤炴洸绶氱⿳鍒�
鐨勯棞(gu膩n)绯�.
锛�4锛夋帉鎻¤▓(j矛)绠楀叐椤炴洸绶氱⿳鍒嗙殑鏂规硶.
锛�5锛夋帉鎻℃牸鏋楀叕寮忓苟鏈�(hu矛)閬�(y霉n)鐢ㄥ钩闈㈡洸绶氱⿳鍒嗚垏璺緫鐒￠棞(gu膩n)鐨勬浠�锛屾渻(hu矛)姹備簩鍏冨嚱
鏁�(sh霉)鍏ㄥ井鍒嗙殑鍘熷嚱鏁�(sh霉).
锛�6锛変簡瑙ｅ叐椤炴洸闈㈢⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)鍙婂叐椤炴洸闈㈢⿳鍒嗙殑闂�(gu膩n)绯�锛屾帉鎻¤▓(j矛)绠楀叐
椤炴洸闈㈢⿳鍒嗙殑鏂规硶锛屾帉鎻＄敤楂樻柉鍏紡瑷�(j矛)绠楁洸闈㈢⿳鍒嗙殑鏂规硶锛屽苟鏈�(hu矛)鐢ㄦ柉鎵樺厠鏂叕寮�
瑷�(j矛)绠楁洸绶氱⿳鍒�.
锛�7锛変簡瑙ｆ暎搴﹁垏鏃嬪害鐨勬蹇碉紝骞舵渻(hu矛)瑷�(j矛)绠�.
锛�8锛夋渻(hu矛)鐢ㄩ噸绌嶅垎銆佹洸绶氱⿳鍒嗗強鏇查潰绌嶅垎姹備竴浜涘咕浣曢噺鑸囩墿鐞嗛噺锛堝钩闈㈠湒褰�
鐨勯潰绌嶃€侀珨绌�銆佹洸闈㈤潰绌嶃€佸姬闀�(zh菐ng)銆佽唱(zh矛)閲�銆佽唱(zh矛)蹇�銆併€佸舰蹇�銆佽綁(zhu菐n)鍕�(d貌ng)鎱ｉ噺銆佸紩鍔�銆佸姛鍙�
娴侀噺绛夛級.
7銆佺劇绐礆(j铆)鏁�(sh霉)
鑰冭│鍏�(n猫i)瀹�
甯告暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁ｇ殑姒傚康 鏀舵杺绱�(j铆)鏁�(sh霉)鐨勫拰鐨勬蹇� 绱�(j铆)鏁�(sh霉)鐨勫熀鏈€ц唱(zh矛)
鑸囨敹鏂傜殑蹇呰姊濅欢 骞句綍绱�(j铆)鏁�(sh霉)鑸� p
绱�(j铆)鏁�(sh霉)鍙婂叾鏀舵杺鎬� 姝ｉ爡(xi脿ng)绱�(j铆)鏁�(sh霉)鏀舵杺鎬х殑鍒ゅ垾娉�
浜ら尟(cu貌)绱�(j铆)鏁�(sh霉)鑸囪悐甯冨凹鑼ㄥ畾鐞� 浠绘剰闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勭禃灏�(du矛)鏀舵杺鑸囨浠舵敹鏂� 鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨�
鏀舵杺鍩熻垏鍜屽嚱鏁�(sh霉)鐨勬蹇� 鍐礆(j铆)鏁�(sh霉)鍙婂叾鏀舵杺鍗婂緫銆佹敹鏂傚崁(q奴)闁擄紙鎸囬枊鍗€(q奴)闁擄級鍜屾敹鏂傚煙
鍐礆(j铆)鏁�(sh霉)鐨勫拰鍑芥暩(sh霉) 鍐礆(j铆)鏁�(sh霉)鍦ㄥ叾鏀舵杺鍗€(q奴)闁撳収(n猫i)鐨勫熀鏈€ц唱(zh矛) 绨�(ji菐n)鍠啰绱�(j铆)鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勬眰
娉� 鍒濈瓑鍑芥暩(sh霉)鐨勫啰绱�(j铆)鏁�(sh霉)灞曢枊寮� 鍑芥暩(sh霉)鐨勫倕閲岃憠锛團ourier锛夌郴鏁�(sh霉)鑸囧倕閲岃憠绱�(j铆)鏁�(sh霉) 鐙�
鍒╁厠闆凤紙Dirichlet锛夊畾鐞� 鍑芥暩(sh霉)鍦╗ , ]l l?
涓婄殑鍌呴噷钁夌礆(j铆)鏁�(sh霉) 鍑芥暩(sh霉)鍦╗0, ]l
涓婄殑姝ｅ鸡绱�(j铆)
鏁�(sh霉)鍜屼綑寮︾礆(j铆)鏁�(sh霉)
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｅ父鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鏀舵杺銆佺櫦(f膩)鏁ｄ互鍙婃敹鏂傜礆(j铆)鏁�(sh霉)鐨勫拰鐨勬蹇�锛屾帉鎻＄礆(j铆)鏁�(sh霉)鐨勫熀
鏈€ц唱(zh矛)鍙婃敹鏂傜殑蹇呰姊濅欢.
锛�2锛夋帉鎻″咕浣曠礆(j铆)鏁�(sh霉)鑸� p 绱�(j铆)鏁�(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁ｇ殑姊濅欢.
锛�3锛夋帉鎻℃闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鏀舵杺鎬х殑姣旇純鍒ゅ垾娉曞拰姣斿€煎垽鍒ユ硶锛屾渻(hu矛)鐢ㄦ牴鍊煎垽鍒ユ硶.
锛�4锛夋帉鎻′氦閷�(cu貌)绱�(j铆)鏁�(sh霉)鐨勮悐甯冨凹鑼ㄥ垽鍒ユ硶.
锛�5锛変簡瑙ｄ换鎰忛爡(xi脿ng)绱�(j铆)鏁�(sh霉)绲曞皪(du矛)鏀舵杺鑸囨浠舵敹鏂傜殑姒傚康浠ュ強绲曞皪(du矛)鏀舵杺鑸囨敹鏂傜殑闂�(gu膩n)
绯�.
锛�6锛変簡瑙ｅ嚱鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬敹鏂傚煙鍙婂拰鍑芥暩(sh霉)鐨勬蹇�.
锛�7锛夌悊瑙ｅ啰绱�(j铆)鏁�(sh霉)鏀舵杺鍗婂緫鐨勬蹇�銆佸苟鎺屾彙鍐礆(j铆)鏁�(sh霉)鐨勬敹鏂傚崐寰戙€佹敹鏂傚崁(q奴)闁撳強
鏀舵杺鍩熺殑姹傛硶.
锛�8锛変簡瑙ｅ啰绱�(j铆)鏁�(sh霉)鍦ㄥ叾鏀舵杺鍗€(q奴)闁撳収(n猫i)鐨勫熀鏈€ц唱(zh矛)锛堝拰鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬�銆侀€愰爡(xi脿ng)姹傚皫(d菐o)
鍜岄€愰爡(xi脿ng)绌嶅垎锛�锛屾渻(hu矛)姹備竴浜涘啰绱�(j铆)鏁�(sh霉)鍦ㄦ敹鏂傚崁(q奴)闁撳収(n猫i)鐨勫拰鍑芥暩(sh霉)锛屽苟鏈�(hu矛)鐢辨姹傚嚭鏌愪簺鏁�(sh霉)闋�(xi脿ng)
绱�(j铆)鏁�(sh霉)鐨勫拰.
锛�9锛変簡瑙ｅ嚱鏁�(sh霉)灞曢枊鐐烘嘲鍕掔礆(j铆)鏁�(sh霉)鐨勫厖鍒嗗繀瑕佹浠�.
锛�10锛夋帉鎻�
x
e 锛宻in x 锛宑os x 锛宭n(1 )x? 鍙�(1 )x
?
?
鐨勯亥鍏嬪嫗鏋楋紙Maclaurin锛夊睍闁�
寮�锛屾渻(hu矛)鐢ㄥ畠鍊戝皣涓€浜涚啊(ji菐n)鍠嚱鏁�(sh霉)闁撴帴灞曢枊鐐哄啰绱�(j铆)鏁�(sh霉).
锛�11锛変簡瑙ｅ倕閲岃憠绱�(j铆)鏁�(sh霉)鐨勬蹇靛拰鐙勫埄鍏嬮浄鏀舵杺瀹氱悊锛屾渻(hu矛)灏囧畾缇╁湪[ , ]l l? 涓婄殑
鍑芥暩(sh霉)灞曢枊鐐哄倕閲岃憠绱�(j铆)鏁�(sh霉)锛屾渻(hu矛)灏囧畾缇╁湪[0, ]l 涓婄殑鍑芥暩(sh霉)灞曢枊鐐烘寮︾礆(j铆)鏁�(sh霉)鑸囦綑寮︾礆(j铆)鏁�(sh霉)锛�
鏈�(hu矛)瀵嚭鍌呴噷钁夌礆(j铆)鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勮〃閬�(d谩)寮�.
8銆佸父寰垎鏂圭▼
鑰冭│鍏�(n猫i)瀹�
甯稿井鍒嗘柟绋嬬殑鍩烘湰姒傚康 璁婇噺鍙垎闆㈢殑寰垎鏂圭▼ 榻婃寰垎鏂圭▼ 涓€闅庣窔
鎬у井鍒嗘柟绋� 浼姫鍒� 锛圔ernoulli锛夋柟绋� 鍏ㄥ井鍒嗘柟绋� 鍙敤绨�(ji菐n)鍠殑璁婇噺浠ｆ彌姹�
瑙ｇ殑鏌愪簺寰垎鏂圭▼ 鍙檷闅庣殑楂橀殠寰垎鏂圭▼ 绶氭€у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)鍙婅В鐨勭祼(ji茅)
妲�(g貌u)瀹氱悊 浜岄殠甯哥郴鏁�(sh霉)榻婃绶氭€у井鍒嗘柟绋� 楂樹簬浜岄殠鐨勬煇浜涘父绯绘暩(sh霉)榻婃绶氭€у井鍒�
鏂圭▼ 绨�(ji菐n)鍠殑浜岄殠甯哥郴鏁�(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋� 姝愭媺锛圗uler锛夋柟绋� 寰垎鏂圭▼鐨�
绨�(ji菐n)鍠噳(y墨ng)鐢�
鑰冭│瑕佹眰
锛�1锛変簡瑙ｅ井鍒嗘柟绋嬪強鍏堕殠銆佽В銆侀€氳В銆佸垵濮嬫浠跺拰鐗硅В绛夋蹇�.
锛�2锛夋帉鎻¤畩閲忓彲鍒嗛洟鐨勫井鍒嗘柟绋嬪強涓€闅庣窔鎬у井鍒嗘柟绋嬬殑瑙ｆ硶锛�
锛�3锛夋渻(hu矛)瑙ｉ綂娆″井鍒嗘柟绋嬨€佷集鍔埄鏂圭▼鍜屽叏寰垎鏂圭▼锛屾渻(hu矛)鐢ㄧ啊(ji菐n)鍠殑璁婇噺浠ｆ彌
瑙ｆ煇浜涘井鍒嗘柟绋嬶紟
锛�4锛夋渻(hu矛)鐢ㄩ檷闅庢硶瑙ｄ笅鍒楀舰寮忕殑寰垎鏂圭▼锛�
( )
( ), ( , )
n
y f x y f x y?? ?? ? 鍜� ( , )y f y y?? ?? 锛�
锛�5锛夌悊瑙ｇ窔鎬у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)鍙婅В鐨勭祼(ji茅)妲�(g貌u)锛�
锛�6锛夋帉鎻′簩闅庡父绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋嬬殑瑙ｆ硶锛屽苟鏈�(hu矛)瑙ｆ煇浜涢珮浜庝簩闅庣殑甯�
绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋�.
锛�7锛夋渻(hu矛)瑙ｈ嚜鐢遍爡(xi脿ng)鐐哄闋�(xi脿ng)寮忋€佹寚鏁�(sh霉)鍑芥暩(sh霉)銆佹寮﹀嚱鏁�(sh霉)銆佷綑寮﹀嚱鏁�(sh霉)浠ュ強瀹冨€戠殑鍜�
鑸囩⿳鐨勪簩闅庡父绯绘暩(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋嬶紟
锛�8锛夋渻(hu矛)瑙ｆ瓙鎷夋柟绋嬶紟
锛�9锛夋渻(hu矛)鐢ㄥ井鍒嗘柟绋嬭В姹轰竴浜涚啊(ji菐n)鍠殑鎳�(y墨ng)鐢ㄥ晱椤岋紟
锛堜簩锛夌窔鎬т唬鏁�(sh霉)
1銆佽鍒楀紡
鑰冭│鍏�(n猫i)瀹�
顥ヮ棩琛屽垪寮忕殑姒傚康鍜屽熀鏈€ц唱(zh矛) 琛屽垪寮忔寜琛岋紙鍒楋級灞曢枊瀹氱悊
鑰冭│瑕佹眰
锛�1锛変簡瑙ｈ鍒楀紡鐨勬蹇�锛屾帉鎻¤鍒楀紡鐨勬€ц唱(zh矛)锛�
锛�2锛夋渻(hu矛)鎳�(y墨ng)鐢ㄨ鍒楀紡鐨勬€ц唱(zh矛)鍜岃鍒楀紡鎸夎锛堝垪锛夊睍闁嬪畾鐞嗚▓(j矛)绠楄鍒楀紡锛�
2銆佺煩闄�
鑰冭│鍏�(n猫i)瀹�
顥ヮ棩顥ョ煩闄ｇ殑姒傚康 鐭╅櫍鐨勭窔鎬ч亱(y霉n)绠� 鐭╅櫍鐨勪箻娉� 鏂归櫍鐨勫啰 鏂归櫍涔樼⿳鐨勮
鍒楀紡 鐭╅櫍鐨勮綁(zhu菐n)缃� 閫嗙煩闄ｇ殑姒傚康鍜屾€ц唱(zh矛) 鐭╅櫍鍙€嗙殑鍏呭垎蹇呰姊濅欢 浼撮毃鐭�
闄� 鐭╅櫍鐨勫垵绛夎畩鎻� 鍒濈瓑鐭╅櫍 鐭╅櫍鐨勭З 鐭╅櫍鐨勭瓑鍍�(ji脿) 鍒嗗鐭╅櫍鍙婂叾閬�(y霉n)
绠�
鑰冭│瑕佹眰
顥ワ紙1锛夌悊瑙ｇ煩闄ｇ殑姒傚康锛屼簡瑙ｅ柈浣嶇煩闄�銆佹暩(sh霉)閲忕煩闄�銆佸皪(du矛)瑙掔煩闄ｃ€佷笁瑙掔煩闄�銆佸皪(du矛)
绋辩煩闄ｅ拰鍙嶅皪(du矛)绋辩煩闄ｄ互鍙婂畠鍊戠殑鎬ц唱(zh矛)锛�
锛�2锛夋帉鎻＄煩闄ｇ殑绶氭€ч亱(y霉n)绠椼€佷箻娉�銆佽綁(zhu菐n)缃互鍙婂畠鍊戠殑閬�(y霉n)绠楄(gu墨)寰�锛屼簡瑙ｆ柟闄ｇ殑鍐�
鑸囨柟闄ｄ箻绌嶇殑琛屽垪寮忕殑鎬ц唱(zh矛).
锛�3锛夌悊瑙ｉ€嗙煩闄ｇ殑姒傚康锛屾帉鎻￠€嗙煩闄ｇ殑鎬ц唱(zh矛)浠ュ強鐭╅櫍鍙€嗙殑鍏呭垎蹇呰姊濅欢锛�
鐞嗚В浼撮毃鐭╅櫍鐨勬蹇�锛屾渻(hu矛)鐢ㄤ即闅ㄧ煩闄ｆ眰閫嗙煩闄ｏ紟
锛�4锛夌悊瑙ｇ煩闄ｅ垵绛夎畩鎻涚殑姒傚康锛屼簡瑙ｅ垵绛夌煩闄ｇ殑鎬ц唱(zh矛)鍜岀煩闄ｇ瓑鍍�(ji脿)鐨勬蹇碉紝鐞�
瑙ｇ煩闄ｇ殑绉╃殑姒傚康锛屾帉鎻＄敤鍒濈瓑璁婃彌姹傜煩闄ｇ殑绉╁拰閫嗙煩闄ｇ殑鏂规硶锛�
锛�5锛変簡瑙ｅ垎濉婄煩闄ｅ強鍏堕亱(y霉n)绠楋紟
3銆佸悜閲�
鑰冭│鍏�(n猫i)瀹�
鍚戦噺鐨勬蹇� 鍚戦噺鐨勭窔鎬х祫鍚堣垏绶氭€ц〃绀� 鍚戦噺绲勭殑绶氭€х浉闂�(gu膩n)鑸囩窔鎬х劇闂�(gu膩n)
鍚戦噺绲勭殑妤靛ぇ绶氭€х劇闂�(gu膩n)绲� 绛夊児(ji脿)鍚戦噺绲� 鍚戦噺绲勭殑绉� 鍚戦噺绲勭殑绉╄垏鐭╅櫍鐨勭З
涔嬮枔鐨勯棞(gu膩n)绯� 鍚戦噺绌洪枔鍙婂叾鐩搁棞(gu膩n)姒傚康 n 缍悜閲忕┖闁撶殑鍩鸿畩鎻涘拰鍧愭(bi膩o)璁婃彌 閬�
娓＄煩闄� 鍚戦噺鐨勫収(n猫i)绌� 绶氭€х劇闂�(gu膩n)鍚戦噺绲勭殑姝ｄ氦瑕�(gu墨)鑼冨寲鏂规硶 瑕�(gu墨)鑼冩浜ゅ熀 姝ｄ氦
鐭╅櫍鍙婂叾鎬ц唱(zh矛)
鑰冭│瑕佹眰
锛�1锛夌悊瑙� n 缍悜閲�銆佸悜閲忕殑绶氭€х祫鍚堣垏绶氭€ц〃绀虹殑姒傚康锛�
锛�2锛夌悊瑙ｅ悜閲忕祫绶氭€х浉闂�(gu膩n)銆佺窔鎬х劇闂�(gu膩n)鐨勬蹇碉紝鎺屾彙鍚戦噺绲勭窔鎬х浉闂�(gu膩n)銆佺窔鎬�
鐒￠棞(gu膩n)鐨勬湁闂�(gu膩n)鎬ц唱(zh矛)鍙婂垽鍒ユ硶锛�
锛�3锛夌悊瑙ｅ悜閲忕祫鐨勬サ澶х窔鎬х劇闂�(gu膩n)绲勫拰鍚戦噺绲勭殑绉╃殑姒傚康锛屾渻(hu矛)姹傚悜閲忕祫鐨勬サ
澶х窔鎬х劇闂�(gu膩n)绲勫強绉╋紟
锛�4锛夌悊瑙ｅ悜閲忕祫绛夊児(ji脿)鐨勬蹇碉紝鐞嗚В鐭╅櫍鐨勭З鑸囧叾琛�(鍒�)鍚戦噺绲勭殑绉╀箣闁撶殑
闂�(gu膩n)绯�.
锛�5锛変簡瑙� n 缍悜閲忕┖闁�銆佸瓙绌洪枔銆佸熀搴�銆佺董鏁�(sh霉)銆佸潗妯�(bi膩o)绛夋蹇碉紟
锛�6锛変簡瑙ｅ熀璁婃彌鍜屽潗妯�(bi膩o)璁婃彌鍏紡锛屾渻(hu矛)姹傞亷娓＄煩闄ｏ紟
锛�7锛変簡瑙ｅ収(n猫i)绌嶇殑姒傚康锛屾帉鎻＄窔鎬х劇闂�(gu膩n)鍚戦噺绲勬浜よ(gu墨)鑼冨寲鐨勬柦瀵嗙壒锛圫chmidt锛�
鏂规硶锛�
锛�8锛変簡瑙ｈ(gu墨)鑼冩浜ゅ熀銆佹浜ょ煩闄ｇ殑姒傚康浠ュ強瀹冨€戠殑鎬ц唱(zh矛)
4銆佺窔鎬ф柟绋嬬祫
鑰冭│鍏�(n猫i)瀹�:
绶氭€ф柟绋嬬祫鐨勫厠钀婂锛圕ramer锛夋硶鍓� 榻婃绶氭€ф柟绋嬬祫鏈夐潪闆惰В鐨勫厖鍒嗗繀瑕�
姊濅欢 闈為綂娆＄窔鎬ф柟绋嬬祫鏈夎В鐨勫厖鍒嗗繀瑕佹浠� 绶氭€ф柟绋嬬祫瑙ｇ殑鎬ц唱(zh矛)鍜岃В鐨勭祼(ji茅)
妲�(g貌u) 榻婃绶氭€ф柟绋嬬祫鐨勫熀绀�(ch菙)瑙ｇ郴鍜岄€氳В 瑙ｇ┖闁� 闈為綂娆＄窔鎬ф柟绋嬬祫鐨勯€氳В
鑰冭│瑕佹眰
锛�1锛夋渻(hu矛)鐢ㄥ厠钀婂娉曞墖锛�
锛�2锛夌悊瑙ｉ綂娆＄窔鎬ф柟绋嬬祫鏈夐潪闆惰В鐨勫厖鍒嗗繀瑕佹浠跺強闈為綂娆＄窔鎬ф柟绋嬬祫鏈�
瑙ｇ殑鍏呭垎蹇呰姊濅欢锛�
锛�3锛夌悊瑙ｉ綂娆＄窔鎬ф柟绋嬬祫鐨勫熀绀�(ch菙)瑙ｇ郴銆侀€氳В鍙婅В绌洪枔鐨勬蹇碉紝鎺屾彙榻婃绶�
鎬ф柟绋嬬祫鐨勫熀绀�(ch菙)瑙ｇ郴鍜岄€氳В鐨勬眰娉�.
锛�4锛夌悊瑙ｉ潪榻婃绶氭€ф柟绋嬬祫瑙ｇ殑绲�(ji茅)妲�(g貌u)鍙婇€氳В鐨勬蹇碉紟
锛�5锛夋帉鎻＄敤鍒濈瓑琛岃畩鎻涙眰瑙ｇ窔鎬ф柟绋嬬祫鐨勬柟娉曪紟
5銆佺煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺
鑰冭│鍏�(n猫i)瀹�:
鐭╅櫍鐨勭壒寰佸€煎拰鐗瑰緛鍚戦噺鐨勬蹇�銆佹€ц唱(zh矛) 鐩镐技璁婃彌銆佺浉浼肩煩闄ｇ殑姒傚康鍙婃€ц唱(zh矛)
鐭╅櫍鍙浉浼煎皪(du矛)瑙掑寲鐨勫厖鍒嗗繀瑕佹浠跺強鐩镐技灏�(du矛)瑙掔煩闄� 瀵�(sh铆)灏�(du矛)绋辩煩闄ｇ殑鐗瑰緛鍊�銆佺壒寰�
鍚戦噺鍙婂叾鐩镐技灏�(du矛)瑙掔煩闄�
鑰冭│瑕佹眰:
锛�1锛夌悊瑙ｇ煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺鐨勬蹇靛強鎬ц唱(zh矛)锛屾渻(hu矛)姹傜煩闄ｇ殑鐗瑰緛鍊煎拰鐗�
寰佸悜閲�.
锛�2锛夌悊瑙ｇ浉浼肩煩闄ｇ殑姒傚康銆佹€ц唱(zh矛)鍙婄煩闄ｅ彲鐩镐技灏�(du矛)瑙掑寲鐨勫厖鍒嗗繀瑕佹浠�锛屾帉
鎻″皣鐭╅櫍鍖栫偤鐩镐技灏�(du矛)瑙掔煩闄ｇ殑鏂规硶.
锛�3锛夋帉鎻″(sh铆)灏�(du矛)绋辩煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺鐨勬€ц唱(zh矛)锛�
6銆佷簩娆″瀷
鑰冭│鍏�(n猫i)瀹�
浜屾鍨嬪強鍏剁煩闄ｈ〃绀� 鍚堝悓璁婃彌鑸囧悎鍚岀煩闄� 浜屾鍨嬬殑绉� 鎱ｆ€у畾鐞� 浜屾鍨�
鐨勬(bi膩o)婧�(zh菙n)褰㈠拰瑕�(gu墨)鑼冨舰 鐢ㄦ浜よ畩鎻涘拰閰嶆柟娉曞寲浜屾鍨嬬偤妯�(bi膩o)婧�(zh菙n)褰� 浜屾鍨嬪強鍏剁煩闄ｇ殑
姝ｅ畾鎬�
鑰冭│瑕佹眰
锛�1锛夋帉鎻′簩娆″瀷鍙婂叾鐭╅櫍琛ㄧず锛屼簡瑙ｄ簩娆″瀷绉╃殑姒傚康锛屼簡瑙ｅ悎鍚岃畩鎻涜垏鍚�
鍚岀煩闄ｇ殑姒傚康锛屼簡瑙ｄ簩娆″瀷鐨勬(bi膩o)婧�(zh菙n)褰�銆佽(gu墨)鑼冨舰鐨勬蹇典互鍙婃叄鎬у畾鐞嗭紟
锛�2锛夋帉鎻＄敤姝ｄ氦璁婃彌鍖栦簩娆″瀷鐐烘(bi膩o)婧�(zh菙n)褰㈢殑鏂规硶锛屾渻(hu矛)鐢ㄩ厤鏂规硶鍖栦簩娆″瀷鐐烘(bi膩o)
婧�(zh菙n)褰紟
锛�3锛夌悊瑙ｆ瀹氫簩娆″瀷銆佹瀹氱煩闄ｇ殑姒傚康锛屽苟鎺屾彙鍏跺垽鍒ユ硶锛�
涓夈€佸弮鑰冩浉鐩�
[1] 鍚屾繜(j矛)澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯荤法. 楂樼瓑鏁�(sh霉)瀛�(xu茅)锛堢鍏増锛�. 楂樼瓑鏁欒偛鍑虹増绀�, 2007
[2] 鏌存儬鏂�, 瀹椾簯鍗�. 绶氭€т唬鏁�(sh霉). 楂樼瓑鏁欒偛鍑虹増绀�, 2011
鍏嶈铂(z茅)鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘�锛岃珛(q菒ng)鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€�(g猫)浜鸿榛�(di菐n)锛岃垏鏈恫(w菐ng)绔欑劇闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊(sh铆)锛屽皪(du矛)鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹�銆佹枃瀛楃殑鐪熷(sh铆)鎬�銆佸畬鏁存€с€佸強鏅�(sh铆)鎬ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛(q菒ng)璁€鑰呭儏浣滃弮鑰冿紝骞惰珛(q菒ng)鑷鏍稿(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
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鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
