2021骞�瑗垮寳甯寖澶у(xu茅)纰╁＋鐮旂┒鐢熸嫑鐢熻€冭│澶х侗        
纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│
缍滃悎鑰冭│锛堣繎涓栦唬鏁�(sh霉)銆佹硾鍑藉垎鏋愩€佸父寰垎鏂圭▼銆佽В鏋愬咕浣曪級绉戠洰澶х侗
 (绉戠洰浠ｇ⒓锛�945)    

瀛�(xu茅)闄㈠悕绋�(钃嬬珷)锛�    鏁�(sh霉)瀛�(xu茅)鑸囩当(t菕ng)瑷�(j矛)瀛�(xu茅)闄�     
瀛�(xu茅)闄㈣矤(f霉)璨�(z茅)浜�(绨藉瓧)锛�                         
绶�  鍒�  鏅�(sh铆)  闁擄細  2019骞� 7 鏈�3 鏃�     鏁�(sh霉)瀛�(xu茅)缍滃悎鑰冭│锛堣繎涓栦唬鏁�(sh霉)銆佹硾鍑藉垎鏋愩€佸父寰垎鏂圭▼銆佽В鏋愬咕浣曪級绉戠洰澶х侗
 (绉戠洰浠ｇ⒓锛�945)   鏈杸鑰冭│鍖呭惈鍥涢杸瑾茬▼锛氳繎涓栦唬鏁�(sh霉)銆佹硾鍑藉垎鏋�銆佸父寰垎鏂圭▼銆佽В鏋愬咕浣�锛岀附鍒嗙偤100鍒�锛屽叾涓繎涓栦唬鏁�(sh霉)鍜屾硾鍑藉垎鏋愬垎鍒ュ崰20鍒嗗埌25鍒�锛岃В鏋愬咕浣曞強甯稿井鍒嗘柟绋嬪垎鍒ュ崰25鍒�30鍒�銆傝繎涓栦唬鏁�(sh霉)     绗竴绔�  鍩烘湰姒傚康
    鑰冭│瑕侀粸(di菐n)锛�
    瑕佽畵瀛�(xu茅)鐢熸帉鎻′竴浜涘熀鏈蹇碉細浠ｆ暩(sh霉)閬�(y霉n)绠椼€佺祼(ji茅)鍚堝緥銆佷氦鎻涘緥銆佸垎閰嶅緥銆佸悓鎱�(t脿i)鑸囧悓妲�(g貌u)銆佺瓑鍍�(ji脿)闂�(gu膩n)绯昏垏闆嗗悎鍒嗛鐨勫畾缇�锛涚悊瑙ｇ祼(ji茅)鍚堝緥銆佷氦鎻涘緥銆佸垎閰嶅緥鐨勪綔鐢ㄤ互鍙婂悓鎱�(t脿i)婊垮皠淇濇寔绲�(ji茅)鍚堝緥銆佷氦鎻涘緥銆佸垎閰嶅緥閫欎簺鏁�(sh霉)瀛�(xu茅)浜嬪(sh铆)锛涚啛绶存噳(y墨ng)鐢ㄧ瓑鍍�(ji脿)闂�(gu膩n)绯昏垏闆嗗悎鍒嗛鍙互鐩镐簰姹哄畾閫欎竴绲�(ji茅)璜�銆�
    鑰冭│鍏�(n猫i)瀹癸細
    绗竴绡€(ji茅)  浠ｆ暩(sh霉)閬�(y霉n)绠楄垏绠楀緥 
    涓昏璎涙巿浠ｆ暩(sh霉)閬�(y霉n)绠楃殑瀹氱京鍙婁緥瀛�锛岀祼(ji茅)鍚堝緥鍙婂叾鎬ц唱(zh矛)锛屼氦鎻涘緥鍙婂叾鎬ц唱(zh矛)锛屽垎閰嶅緥鍙婂叾鎬ц唱(zh矛)绛�銆�
    绗簩绡€(ji茅)  鍚屾厠(t脿i)鑸囧悓妲�(g貌u)
    涓昏浠嬬垂鍏╁€�(g猫)甯舵湁浠ｆ暩(sh霉)閬�(y霉n)绠楃殑闆嗗悎涔嬮枔鐨勪繚鎸佷唬鏁�(sh霉)閬�(y霉n)绠楃殑鏄犲皠銆佹豢灏勫強闆欏皠浠ュ強瀹冨€戝悇鑷殑鎬ц唱(zh矛)銆�
    绗笁绡€(ji茅)  绛夊児(ji脿)闂�(gu膩n)绯昏垏闆嗗悎鍒嗛
    涓昏浠嬬垂绛夊児(ji脿)闂�(gu膩n)绯昏垏闆嗗悎鍒嗛閫欏叐鍊�(g猫)姒傚康浠ュ強绛夊児(ji脿)闂�(gu膩n)绯昏垏闆嗗悎鍒嗛閫欎簩鑰呬箣闁撶殑闂�(gu膩n)绯�銆�   
    鑰冩牳瑕佹眰锛�
    瑕佽畵瀛�(xu茅)鐢熻瓨(sh铆)瑷樹唬鏁�(sh霉)閬�(y霉n)绠�銆佺祼(ji茅)鍚堝緥銆佷氦鎻涘緥銆佸垎閰嶅緥銆佸悓鎱�(t脿i)鑸囧悓妲�(g貌u)銆佺瓑鍍�(ji脿)闂�(gu膩n)绯昏垏闆嗗悎鍒嗛鐨勫畾缇�锛涢牁(l菒ng)鏈�(hu矛)绲�(ji茅)鍚堝緥銆佷氦鎻涘緥銆佸垎閰嶅緥鐨勪綔鐢�锛涢牁(l菒ng)鏈�(hu矛)鍚屾厠(t脿i)婊垮皠淇濇寔绲�(ji茅)鍚堝緥銆佷氦鎻涘緥銆佸垎閰嶅緥锛岀瓑鍍�(ji脿)闂�(gu膩n)绯昏垏闆嗗悎鍒嗛鍙互鐩镐簰姹哄畾閫欎簺鏁�(sh霉)瀛�(xu茅)浜嬪(sh铆)銆�
绗簩绔�  缇よ珫
    鑰冭│瑕侀粸(di菐n)锛�
    瑕佽畵瀛�(xu茅)鐢熸帉鎻℃湁闂�(gu膩n)缇ょ殑涓€浜涘熀鏈蹇碉細缇�銆佽畩鎻涚兢銆佺疆鎻涚兢銆佸惊鐠�(hu谩n)缇ゃ€佸瓙缇�銆侀櫔闆嗐€佷笉璁婂瓙缇�銆佸晢缇�锛涘垽鏂风兢銆佸瓙缇�銆佷笉璁婂瓙缇�銆佸晢缇ょ殑鏂规硶锛涚悊瑙ｇ兢璜栫殑涓€浜涢噸瑕佺祼(ji茅)璜栵細Cayley 瀹氱悊銆丩agrange瀹氱悊銆佺兢鐨勫悓鎱�(t脿i)鍩烘湰瀹氱悊銆�
    鑰冭│鍏�(n猫i)瀹癸細
    绗竴绡€(ji茅)  缇ょ殑瀹氱京鑸囧熀鏈€ц唱(zh矛) 
    浠嬬垂缇ょ殑鍏╃ó瀹氱京鐨勭瓑鍍�(ji脿)鎬�銆傚皪(du矛)鏈夐檺缇ょ郸鍑虹涓夌ó瀹氱京銆備粙绱圭兢鐨勬秷鍘诲緥銆佷互鍙婄兢涓殑鍏冪殑闅庣殑鎬ц唱(zh矛)銆備粙绱圭兢鐨勫悓鎱�(t脿i)銆�
    绗簩绡€(ji茅)  璁婃彌缇�
    浠嬬垂璁婃彌鐨勬蹇�锛涚郸鍑鸿畩鎻涚兢鐨勫畾缇╋紱浠嬬垂涓€鍊�(g猫)闆嗗悎鐨勬渶澶ц畩鎻涚兢銆佹渶灏忚畩鎻涚兢锛涗粙绱笴ayley瀹氱悊銆�
    绗笁绡€(ji茅)  缃彌缇� 
浠嬬垂n娆″皪(du矛)绋辩兢Sn鐨勬蹇�锛涗粙绱筍n涓殑姣忓€�(g猫)缃彌閮藉彲浠ヨ〃鎴愪簰鐩告矑鏈夊叡鍚屾暩(sh霉)瀛楃殑寰挵(hu谩n)缃彌鐨勪箻绌嶉€欎竴閲嶈绲�(ji茅)璜�銆�
绗洓绡€(ji茅)  寰挵(hu谩n)缇�
浠嬬垂寰挵(hu谩n)缇ゅ強鍏剁敓鎴愬厓鐨勬蹇�锛涗粙绱硅垏寰挵(hu谩n)缇ょ殑瀛樺湪鍟忛銆佹暩(sh霉)閲忓晱椤�銆佺祼(ji茅)妲�(g貌u)鍟忛鏈夐棞(gu膩n)鐨勭祼(ji茅)璜�銆�
绗簲绡€(ji茅)  瀛愮兢
浠嬬垂瀛愮兢鐨勫畾缇╀互鍙婂垽鏂锋柟娉�銆佺兢鐨勫瓙闆嗙敓鎴愮殑瀛愮兢鐨勭壒榛�(di菐n)銆�
绗叚绡€(ji茅)  瀛愮兢鐨勯櫔闆�
瀹氱京宸﹀悓浣欓棞(gu膩n)绯讳互鍙婂彸鍚屼綑闂�(gu膩n)绯�锛涚⒑瀹氶€欏叐鍊�(g猫)鍚屼綑闂�(gu膩n)绯荤殑绛夊児(ji脿)椤�锛屽緱鍑轰竴鍊�(g猫)缇鐨勫瓙缇鍦℅涓殑宸︺€佸彸闄泦鐨勬暩(sh霉)鐩浉绛夐€欎竴閲嶈绲�(ji茅)璜�銆備粙绱筁agrange瀹氱悊銆�
绗竷绡€(ji茅)  涓嶈畩瀛愮兢銆佸晢缇� 
浠嬬垂涓嶈畩瀛愮兢鐨勫畾缇�锛岀郸鍑哄垽鏂蜂竴鍊�(g猫)瀛愮兢鏄笉璁婂瓙缇ょ殑鏂规硶銆備粙绱瑰晢缇ゃ€�
绗叓绡€(ji茅)  鍚屾厠(t脿i)鑸囦笉璁婂瓙缇�
浠嬬垂瀛愮兢銆佷笉璁婂瓙缇よ垏缇ょ殑鍚屾厠(t脿i)涔嬮枔鐨勯棞(gu膩n)绯�銆�
    鑰冩牳瑕佹眰锛�
    瀛�(xu茅)鐢熷繀闋堣瓨(sh铆)瑷樺苟闋�(l菒ng)鏈�(hu矛)鏈夐棞(gu膩n)缇ょ殑涓€浜涘熀鏈蹇碉紱鏈�(hu矛)鍒╃敤鎵€瀛�(xu茅)鐭ヨ瓨(sh铆)鍒ゆ柗缇�銆佸瓙缇�銆佷笉璁婂瓙缇ゃ€佸晢缇�锛涘(xu茅)鐢熷繀闋堟湁鍤�(y谩n)鏍肩殑鎬濈董鑳藉姏浠ュ強閭忚集鎺ㄧ悊鑳藉姏锛涘彲浠ョ稖鍚堟噳(y墨ng)鐢ㄦ墍瀛�(xu茅)鐨勭煡璀�(sh铆)鍘昏В姹虹啊(ji菐n)鍠兢璜栧晱椤�,渚嬪杓冨皬闅庣兢鐨勫垎椤炲晱椤岀瓑銆�
绗笁绔�  鐠�(hu谩n)鑸囧煙
    鑰冭│瑕侀粸(di菐n)锛�
    瑕佽畵瀛�(xu茅)鐢熸帉鎻℃湁闂�(gu膩n)鐠�(hu谩n)鑸囧煙鐨勪竴浜涘熀鏈蹇碉細鐠�(hu谩n)銆佷氦鎻涚挵(hu谩n)銆佹湁鍠綅鍏冪挵(hu谩n)銆佺劇闆跺洜瀛愮挵(hu谩n)銆佹暣鐠�(hu谩n)銆侀櫎鐠�(hu谩n)銆佸煙銆佸瓙鐠�(hu谩n)銆佸瓙闄ょ挵(hu谩n)銆佸瓙鏁寸挵(hu谩n)銆佸瓙鍩�銆佺挵(hu谩n)鐨勫悓鎱�(t脿i)銆佺悊鎯�銆侀浂鐞嗘兂銆佸柈浣嶇悊鎯�銆佷富鐞嗘兂銆佺挵(hu谩n)涓鍊�(g猫)鍏冪敓鎴愮殑鐞嗘兂銆佸墿浣欓鐠�(hu谩n)銆佹サ澶х悊鎯�锛涚悊瑙ｇ挵(hu谩n)璜栫殑涓€浜涢噸瑕佺祼(ji茅)璜栵細涓嶅畾鍏冨瓨鍦ㄥ畾鐞�銆佺挵(hu谩n)鐨勫悓鎱�(t脿i)鍩烘湰瀹氱悊銆佸墿浣欓鐠�(hu谩n)鏄煙鐨勫厖瑕佹浠剁瓑銆�
    鑰冭│鍏�(n猫i)瀹癸細
    绗竴绡€(ji茅)  瀹氱京鑸囧熀鏈€ц唱(zh矛) 
    浠嬬垂鍔犵兢銆佺挵(hu谩n)銆佷氦鎻涚挵(hu谩n)銆佹湁鍠綅鍏冪挵(hu谩n)銆佺劇闆跺洜瀛愮挵(hu谩n)銆佹暣鐠�(hu谩n)銆侀櫎鐠�(hu谩n)銆佸煙绛夊熀鏈蹇�锛涚劇闆跺洜瀛愮挵(hu谩n)涓挵(hu谩n)鐨勬秷鍘诲緥鎵嶆垚绔�锛涗粙绱圭劇闆跺洜瀛愮挵(hu谩n)鐨勭壒寰佺殑姒傚康锛涗粙绱圭劇闆跺洜瀛愮挵(hu谩n)鐨勭壒寰佹槸鏈夐檺鏁�(sh霉)鏅�(sh铆)锛岀壒寰佹槸绱�?c谩i)?sh霉)閫欎竴绲�(ji茅)璜栥€�
    绗簩绡€(ji茅)  瀛愮挵(hu谩n)銆佺挵(hu谩n)鐨勫悓鎱�(t脿i)
    浠嬬垂瀛愮挵(hu谩n)銆佸瓙闄ょ挵(hu谩n)銆佸瓙鏁寸挵(hu谩n)銆佸瓙鍩熴€佺挵(hu谩n)鐨勫悓鎱�(t脿i)绛夋蹇�锛涙帰瑷庤垏鐠�(hu谩n)鐨勫悓鎱�(t脿i)鏈夐棞(gu膩n)鐨勭挵(hu谩n)鐨勬€ц唱(zh矛)锛涗粙绱规寲瑁�(b菙)瀹氱悊銆�
    绗笁绡€(ji茅)  澶氶爡(xi脿ng)寮忕挵(hu谩n)
浠嬬垂鍚柈浣嶅厓鐨勪氦鎻涚挵(hu谩n)R涓婄殑澶氶爡(xi脿ng)寮�銆丷涓婄殑澶氶爡(xi脿ng)寮忕挵(hu谩n)浠ュ強R涓婄殑鏈畾鍏冪瓑姒傚康锛涚郸鍑篟涓婄殑鏈畾鍏冩槸瀛樺湪鐨勯€欎竴閲嶈绲�(ji茅)璜�銆�
绗洓绡€(ji茅)  鐞嗘兂
浠嬬垂鐠�(hu谩n)鐨勭悊鎯�銆侀浂鐞嗘兂銆佸柈浣嶇悊鎯炽€佷富鐞嗘兂銆佺挵(hu谩n)涓鍊�(g猫)鍏冪敓鎴愮殑鐞嗘兂绛夋蹇碉紱浠嬬垂鐠�(hu谩n)鐨勪富鐞嗘兂涓殑鍏冪礌鐨勭壒榛�(di菐n)锛涚郸鍑洪櫎鐠�(hu谩n)鍙湁闆剁悊鎯冲拰鍠綅鐞嗘兂閫欎竴閲嶈绲�(ji茅)璜�銆�
绗簲绡€(ji茅)  鍓╀綑椤炵挵(hu谩n)銆佸悓鎱�(t脿i)鑸囩悊鎯�
椤炴瘮浜庣兢璜栦腑鐨勫晢缇�锛屽湪鐠�(hu谩n)璜栦腑鏈夊晢鐠�(hu谩n)锛堜篃鍙墿浣欓鐠�(hu谩n)锛�銆傜郸鍑哄晢鐠�(hu谩n)鐨勬蹇典箣鍚庯紝浠嬬垂鐠�(hu谩n)鐨勫悓鎱�(t脿i)鍩烘湰瀹氱悊锛涗粙绱瑰瓙鐠�(hu谩n)銆佺悊鎯宠垏鐠�(hu谩n)鐨勫悓鎱�(t脿i)涔嬮枔鐨勯棞(gu膩n)绯汇€�
绗叚绡€(ji茅)  妤靛ぇ鐞嗘兂
绲﹀嚭妤靛ぇ鐞嗘兂鐨勫畾缇�锛涗粙绱瑰垽鏂蜂竴鍊�(g猫)鐞嗘兂鏄サ澶х悊鎯崇殑鏂规硶锛屾帰瑷庡浣曞埄鐢ㄦサ澶х悊鎯冲幓妲�(g貌u)閫犲煙銆�
绗竷绡€(ji茅)  鍟嗗煙 
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    绗簩绡€(ji茅)  鍞竴鍒嗚В鐠�(hu谩n)
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    绗笁绡€(ji茅)  涓荤悊鎯崇挵(hu谩n)
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绗洓绡€(ji茅) 榻婃鏂圭▼ 
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渚濇摎(j霉)绶氭€у井鍒嗘柟绋嬬殑瑙ｇ殑琛ㄧず瑙ｉ噵鎸嫊(d貌ng)鐝�(xi脿n)璞�銆�
鑰冩牳瑕佹眰
婧�(zh菙n)纰虹悊瑙ｇ窔鎬у井鍒嗘柟绋嬬殑涓€鑸悊璜栵紱鐔熺反鎺屾彙Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉�銆佺壒寰佹牴娉曘€佹瘮杓冪郴鏁�(sh霉)娉曞拰Laplace璁婃彌锛涜兘澶犱緷鎿�(j霉)瑙ｇ殑涓€鑸〃绀鸿◣璜栬В鐨勪竴浜涘爆鎬с€傜鍥涚珷 绶氭€у井鍒嗘柟绋嬬祫
鑰冭│瑕侀粸(di菐n)
婧�(zh菙n)纰虹悊瑙ｇ窔鎬у井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�锛涜兘澶犵啛绶存帉鎻iouville鍏紡銆佸父鏁�(sh霉)璁婃槗娉�銆佸父绯绘暩(sh霉)绶氭€у井鍒嗘柟绋嬬殑鐗瑰緛鏍规硶鍜岀啊(ji菐n)鍠殑闈為綂娆℃柟绋嬬殑瑙ｆ硶銆�
鑰冭│鍏�(n猫i)瀹�
绗竴绡€(ji茅)    涓€闅庡井鍒嗘柟绋嬬祫 
    涓€闅庡井鍒嗘柟绋嬬祫鍒濆€煎晱椤岃В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞�銆�
绗簩绡€(ji茅)    绶氭€у井鍒嗘柟绋嬬祫鐨勪竴鑸蹇� 
涓€闅庣窔鎬у井鍒嗘柟绋嬬祫鍒濆€煎晱椤岃В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞�銆�
娉細绗竴绡€(ji茅)鑸囩浜岀瘈(ji茅)鍏�2瀛�(xu茅)鏅�(sh铆)
绗笁绡€(ji茅)    绶氭€ч綂娆″井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�
    寤虹珛绶氭€ч綂娆″井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�锛屽緱鍒伴€氳В绲�(ji茅)妲�(g貌u)瀹氱悊锛岃瓑鏄嶭iouville 鍏紡銆�
绗洓绡€(ji茅)    绶氭€ч潪榻婃寰垎鏂圭▼绲勭殑涓€鑸悊璜� 
    绶氭€ч潪榻婃寰垎鏂圭▼绲勭殑涓€鑸悊璜栧拰甯告暩(sh霉)璁婃槗娉曘€�
绗簲绡€(ji茅)    甯哥郴鏁�(sh霉)绶氭€у井鍒嗘柟绋嬬祫鐨勮В娉� 
    鐗瑰緛鏍规硶鈥旂悊璜栬瓑鏄庤垏鏂规硶鐨勭啛绶存噳(y墨ng)鐢�锛涚啊(ji菐n)鍠殑闈為綂娆℃柟绋嬬殑瑙ｆ硶銆�
鑰冩牳瑕佹眰
婧�(zh菙n)纰虹悊瑙ｇ窔鎬у井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�锛涚啛绶存帉鎻iouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉曞拰鐗瑰緛鏍规硶锛涜兘澶犱緷鎿�(j霉)瑙ｇ殑涓€鑸〃绀鸿◣璜栬В鐨勪竴浜涘爆鎬�銆傜浜旂珷 瀹氭€ц垏绌�(w臎n)瀹氭€ф蹇�
鑰冭│瑕侀粸(di菐n)
浜岀董鑷不绯荤当(t菕ng)鍒濈瓑濂囬粸(di菐n)鐨勫垎椤炲強鍏堕檮杩戠殑杌岀窔鍒嗗竷锛涙サ闄愮挵(hu谩n)鐨勫畾缇╄垏绀轰緥锛涚┅(w臎n)瀹氭€ф蹇靛強鍏跺垽瀹氬畾鐞�锛屽垎鍒ユ噳(y墨ng)鐢ㄧ┅(w臎n)瀹氭€ф蹇�銆佺窔鎬у寲绯荤当(t菕ng)鐨勭壒寰佸€�銆丩iapunov绗簩鏂规硶瑷庤珫鑷不绯荤当(t菕ng)鐨勮В鐨勭┅(w臎n)瀹氭€�銆�
鑰冭│鍏�(n猫i)瀹�
绗竴绡€(ji茅) 鐩稿钩闈綔鍦�   鍠摵 
    鑷不绯荤当(t菕ng)鍙婂叾杌岀窔鐨勫垎椤炶垏鎬ц唱(zh矛)銆�
绗簩绡€(ji茅) 鍒濈瓑濂囬粸(di菐n)闄勮繎鐨勮粚绶氬垎甯� 
    浜岀董鑷不绯荤当(t菕ng)鍒濈瓑濂囬粸(di菐n)鐨勫垎椤炩€旂祼(ji茅)榛�(di菐n)銆侀瀺榛�(di菐n)銆佺劍榛�(di菐n)銆佷腑蹇冨強鍏堕檮杩戠殑杌岀窔鍒嗗竷銆�
绗笁绡€(ji茅) 妤甸檺鐠�(hu谩n)鑸変緥 
    妤甸檺鐠�(hu谩n)鐨勫畾缇╄垏绀轰緥銆�
绗洓绡€(ji茅) 绌�(w臎n)瀹氭€ф蹇� 
    绌�(w臎n)瀹氭€ф蹇�銆佸垽瀹氬畾鐞嗗拰鍒ゅ畾鏂规硶锛岃憲閲峀iapunov绗簩鏂规硶銆�
鑰冩牳瑕佹眰
閲嶉粸(di菐n)鎺屾彙浜岀董鑷不绯荤当(t菕ng)鍒濈瓑濂囬粸(di菐n)鐨勫垎椤炲強鍏堕檮杩戠殑杌岀窔鍒嗗竷锛涚悊瑙ｇ┅(w臎n)瀹氭€ф蹇靛強鍏跺垽瀹氬畾鐞�锛屾渻(hu矛)鎳�(y墨ng)鐢ㄧ┅(w臎n)瀹氭€ф蹇�銆佺窔鎬у寲绯荤当(t菕ng)鐨勭壒寰佸€笺€丩iapunov绗簩鏂规硶瑷庤珫鑷不绯荤当(t菕ng)鐨勮В鐨勭┅(w臎n)瀹氭€�銆�
浜�銆� 鍙冭€冩浉鐩�
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2銆� 钁夊毚(y谩n)璎�锛屻€婂父寰垎鏂圭▼銆�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�1982骞达紙绗簩鐗堬級銆�
3銆� 涓北澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯伙紝銆婂父寰垎鏂圭▼銆�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�1983骞达紙绗簩鐗堬級銆�
4銆� 鍦�(gu贸)瀹舵暀鑲插鍝℃渻(hu矛)甯寖鏁欒偛鍙�锛屻€婃櫘閫氶珮搴﹀斧鑼冨(xu茅)鏍℃暩(sh霉)瀛�(xu茅)鏁欒偛灏堟キ(y猫)锛堟湰绉戯級鏁欒偛鏁欏(xu茅)鍩烘湰瑕佹眰锛堣│琛岋級銆�锛岄閮藉斧鑼冨ぇ瀛�(xu茅)鍑虹増绀撅紝1994銆�
娉涘嚱鍒嗘瀽
绗竴绔�  搴﹂噺绌洪枔鑸囩窔鎬ц肠鑼冪┖闁�
    鑰冭│瑕侀粸(di菐n)锛�
    搴﹂噺绌洪枔鐨勬蹇�锛屼緥瀛�锛涘害閲忕┖闁撲腑鐨勬敹鏂傛€ц垏閫ｇ簩(x霉)鎬э紱绋犲瘑鎬�锛涘彲鍒嗘€�锛汣auchy鍒楄垏搴﹂噺绌洪枔鐨勫畬鍌欐€�锛涘绺槧鍍忓師鐞嗗強鍏舵噳(y墨ng)鐢紱绶氭€ц肠鑼冪┖闁撶殑姒傚康锛屼緥瀛�锛汢anach绌洪枔鐨勬蹇�銆�
    鑰冭│鍏�(n猫i)瀹癸細
    绗竴绡€(ji茅)  搴﹂噺绌洪枔鐨勬蹇佃垏渚嬪瓙 
    璺濋洟鍙婂害閲忕┖闁撶殑瀹氱京锛涗緥瀛愶紙姝愭皬绌洪枔 锛涢€ｇ簩(x霉)鍑芥暩(sh霉)绌洪枔 锛涙暩(sh霉)鍒楃┖闁� 绛夛級銆�
    绗簩绡€(ji茅)  搴﹂噺绌洪枔涓殑妤甸檺 绋犲瘑鎬� 鍙垎绌洪枔 
    闋�(l菒ng)鍩熺殑姒傚康锛涙敹鏂傞粸(di菐n)鍒�锛涙湁鐣岄泦锛涘叿楂旂┖闁撲腑鏀舵杺鎬х殑鎰忕京锛涚瀵嗘€ц垏鍙垎绌洪枔鐨勬蹇�锛涗笉鍙垎绌洪枔鐨勪緥瀛愩€�
绗笁绡€(ji茅) 閫ｇ簩(x霉)鏄犲皠 
鏄犲皠閫ｇ簩(x霉)鎬х殑鍚勭ó瀹氱京鍙婂叾绛夊児(ji脿)鎬�銆�
绗洓绡€(ji茅) Cauchy榛�(di菐n)鍒楄垏瀹屽倷搴﹂噺绌洪枔  
    搴﹂噺绌洪枔涓瑿auchy榛�(di菐n)鍒楃殑姒傚康锛涘畬鍌欏害閲忕┖闁撶殑瀹氱京锛涘畬鍌欏害閲忕┖闁撹垏涓嶅畬鍌欏害閲忕┖闁撶殑鍚勯渚嬪瓙锛涘害閲忕┖闁撻枆瀛愮┖闁撶殑瀹屽倷鎬�銆�
绗簲绡€(ji茅) 搴﹂噺绌洪枔鐨勫畬鍌欏寲  
     绛夎窛鍚屾(g貌u)锛涘害閲忕┖闁撶殑瀹屽倷鍖栧畾鐞�锛�
绗叚绡€(ji茅) 澹撶府鏄犲儚鍘熺悊鍙婂叾鎳�(y墨ng)鐢� 
澹撶府鏄犲儚鐨勫畾缇�锛涘绺槧鍍忓師鐞�锛涘湪闅卞嚱鏁�(sh霉)瀹氱悊鍙婂父寰垎鏂圭▼涓殑鎳�(y墨ng)鐢�銆�
绗竷绡€(ji茅) 绶氭€х┖闁�  
     鏈瘈(ji茅)鍏�(n猫i)瀹圭偤绶氭€х┖闁撶殑鍩烘湰姒傚康銆傚洜?q奴)W鐢熷凡鍦ㄩ珮绛変唬鏁�(sh霉)瑾茬▼涓(xu茅)閬庢湁闄愮董绌洪枔鐨勬湁闂�(gu膩n)鍏�(n猫i)瀹�锛屾晠鍙渶绨�(ji菐n)瑕佸洖椤у苟寮�(qi谩ng)瑾�(di脿o)鐒￠檺缍窔鎬х┖闁撶殑鐗瑰緛鍗冲彲銆�
绗叓绡€(ji茅) 绶氭€ц肠鑼冪┖闁撳拰Banach绌洪枔  
     鑼冩暩(sh霉)锛岀窔鎬ц肠鑼冪┖闁撳拰Banach绌洪枔鐨勬蹇�锛涗緷鑼冩暩(sh霉)鏀舵杺锛� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛涙湁闄愮董璩﹁寖绌洪枔鐨勬嫇?f霉)娓懐?g貌u)鎬�銆�
    鑰冩牳瑕佹眰锛�
    鎺屾彙搴﹂噺绌洪枔锛岀窔鎬ц肠鑼冪┖闁撳拰Banach绌洪枔鐨勬蹇靛拰鎬ц唱(zh矛)锛涙帉鎻℃槧灏勯€ｇ簩(x霉)鎬�锛屽害閲忕┖闁撶殑瀹屽倷鎬х瓑姒傚康锛涚啛鎮� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛� 绌洪枔锛涢€忓竟鐞嗚В澹撶府鏄犲儚鍘熺悊鍙婂叾绨�(ji菐n)鍠噳(y墨ng)鐢�銆傝兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤�銆�
绗簩绔�  绶氭€ф湁鐣岀畻瀛愬拰绶氭€ч€ｇ簩(x霉)娉涘嚱
    鑰冭│瑕侀粸(di菐n)锛�
    绶氭€ф湁鐣岀畻瀛愶紝绶氭€ч€ｇ簩(x霉)娉涘嚱锛岀窔鎬х畻瀛愮┖闁�锛屽叡杌涚┖闁�銆�
    鑰冭│鍏�(n猫i)瀹癸細
    绗竴绡€(ji茅)  绶氭€ф湁鐣岀畻瀛愯垏绶氭€ч€ｇ簩(x霉)娉涘嚱 
    绶氭€ф湁鐣岀畻瀛愯垏绶氭€ч€ｇ簩(x霉)娉涘嚱鐨勬蹇�锛屼緥瀛�锛屾湁鐣岃垏閫ｇ簩(x霉)鐨勭瓑鍍�(ji脿)鎬э紝绶氭€ф湁鐣岀畻瀛愰浂绌洪枔鐨勬€ц唱(zh矛)锛岀畻瀛愯寖鏁�(sh霉)銆�
    绗簩绡€(ji茅)  绶氭€х畻瀛愮┖闁撳拰鍏辫粵绌洪枔 
    绶氭€х畻瀛愮┖闁撶殑绲�(ji茅)妲�(g貌u)鍙婂叾瀹屽倷鎬�锛屽叡杌涚┖闁�锛屼繚璺濈畻瀛�锛屽悓妲�(g貌u)鏄犵収锛屽悓妲�(g貌u)锛屼竴浜涘叿楂旂┖闁撶殑鍏辫粵绌洪枔銆�
     鑰冩牳瑕佹眰锛�
    鎺屾彙绶氭€ф湁鐣岀畻瀛�锛岀窔鎬ч€ｇ簩(x霉)娉涘嚱锛屾湁鐣屾€�锛岄€ｇ簩(x霉)鎬э紝绠楀瓙鑼冩暩(sh霉)锛屽叡杌涚┖闁�锛屼繚璺濈畻瀛�锛屽悓妲�(g貌u)鏄犵収锛屽悓妲�(g貌u)绛夊熀鏈蹇碉紱鎺屾彙鏈夌晫鑸囬€ｇ簩(x霉)鐨勭瓑鍍�(ji脿)鎬у畾鐞�锛屽熀鏈畾鐞�锛涜兘澶犺▓(j矛)绠楃啊(ji菐n)鍠殑绠楀瓙鑼冩暩(sh霉)鍜屼竴浜涘叿楂旂┖闁撶殑鍏辫粵绌洪枔銆傝兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤�銆傜涓夌珷  鍏�(n猫i)绌嶇┖闁撳拰Hilbert绌洪枔
    鑰冭│瑕侀粸(di菐n)锛�
    鍏�(n猫i)绌嶇┖闁擄紝鎶曞奖瀹氱悊锛孒ilbert绌洪枔锛屽氨鑼冪洿浜ょ郴锛孒ilbert绌洪枔涓婄窔鎬ч€ｇ簩(x霉)娉涘嚱鐨勮〃绀�銆�
    鑰冭│鍏�(n猫i)瀹癸細
    绗竴绡€(ji茅)  鍏�(n猫i)绌嶇┖闁撶殑鍩烘湰姒傚康 
    鍏�(n猫i)绌嶇┖闁撹垏Hilbert绌洪枔鐨勫畾缇╋紝骞宠鍥涢倞褰㈠叕寮�锛屽収(n猫i)绌嶇┖闁撶殑鍒ゅ畾銆�
    绗簩绡€(ji茅)  鎶曞奖瀹氱悊 
    榛�(di菐n)鍒伴泦鍚堢殑璺濋洟锛屽嚫闆�锛屾サ灏忓寲鍚戦噺瀹氱悊锛岄泦鍚堢殑姝ｄ氦锛孒ilbert绌洪枔鐨勬浜ゅ垎瑙�锛屾姇褰辩畻瀛愬強鍏舵€ц唱(zh矛)銆�
绗笁绡€(ji茅) Hilbert绌洪枔涓殑灏辫寖鐩翠氦绯�
    灏辫寖鐩翠氦绯�锛孎(xi脿n)ourier绯绘暩(sh霉)闆�锛孊essel涓嶇瓑寮�锛孭arseval鎭掔瓑寮�锛屽畬鍏ㄥ氨鑼冪洿浜ょ郴鐨勫畾缇╄垏鍒ゅ畾,  Fourier灞曞紡锛孏ram-Schmidt姝ｄ氦鍖栭亷绋�锛孒ilbert绌洪枔鐨勫悓妲�(g貌u)銆�
绗洓绡€(ji茅) Hilbert绌洪枔涓婄殑绶氭€ч€ｇ簩(x霉)娉涘嚱 
Riesz琛ㄧず瀹氱悊锛屽叡杌涚畻瀛愬強鍏舵€ц唱(zh矛)銆�
绗簲绡€(ji茅) 鑷即绠楀瓙銆� 閰夌畻瀛愬拰姝ｅ父绠楀瓙
鑷即绠楀瓙銆� 閰夌畻瀛愬拰姝ｅ父绠楀瓙鐨勫熀鏈蹇佃垏绨�(ji菐n)鍠€ц唱(zh矛)銆�
    鑰冩牳瑕佹眰锛�
    鎺屾彙鍏�(n猫i)绌嶇┖闁�锛孒ilbert绌洪枔锛屽钩琛屽洓閭婂舰鍏紡锛屽氨鑼冪洿浜ょ郴锛孊essel涓嶇瓑寮�锛孭arseval鎭掔瓑寮�锛孎(xi脿n)ourier灞曞紡锛屾姇褰辩畻瀛�锛屽叡杌涚畻瀛愶紝鑷即绠楀瓙锛岄厜绠楀瓙鍜屾甯哥畻瀛愮瓑鍩烘湰姒傚康锛涙帉鎻℃サ灏忓寲鍚戦噺瀹氱悊锛屾姇褰卞畾鐞�锛屽畬鍏ㄥ氨鑼冪洿浜ょ郴鐨勫垽瀹氬畾鐞�,  Riesz琛ㄧず瀹氱悊绛夊熀鏈畾鐞嗙殑鍏�(n猫i)瀹硅垏璀夋槑锛涜兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤�銆�
 绗洓绔�  Banach绌洪枔涓殑鍩烘湰瀹氱悊
    鑰冭│瑕侀粸(di菐n)锛�
    Hahn-Banach寤舵嫇瀹氱悊锛孯iesz琛ㄧず瀹氱悊锛岀窔鎬ц肠鑼冪┖闁撲腑鐨勫叡杌涚畻瀛愶紝   
绗竴绡€(ji茅) 娉涘嚱寤舵嫇瀹氱悊 
娆＄窔鎬ф硾鍑�锛孒ahn-Banach娉涘嚱寤舵嫇瀹氱悊鐨勫(sh铆)褰㈠紡銆佸京(f霉)褰㈠紡鍙婂叾鎺ㄨ珫銆�
绗簩绡€(ji茅)  鐨勫叡杌涚┖闁�銆丷iesz琛ㄧず瀹氱悊
绗笁绡€(ji茅) 鍏辫粵绠楀瓙 
绗洓绡€(ji茅) 绶氭€ц肠鑼冪┖闁撲腑鍏辫粵绠楀瓙鐨勫畾缇╁強鎬ц唱(zh矛)銆�
绗簲绡€(ji茅) 缍卞畾鐞嗗拰涓€鑷存湁鐣屾€у畾鐞� 
绗竴缍遍泦锛岀浜岀侗闆�锛孊aire缍卞畾鐞�,  涓€鑷存湁鐣屾€у畾鐞嗗挤(qi谩ng)鏀舵杺銆佸急鏀舵杺鍜屼竴鑷存敹鏂� 
    寮�(qi谩ng)鏀舵杺銆佸急鏀舵杺銆佸急*鏀舵杺鍜屼竴鑷存敹鏂傜殑瀹氱京锛屼緥瀛�锛岀浉浜掗棞(gu膩n)绯�锛屽挤(qi谩ng)鏀舵杺鐨勫厖瑕佹浠躲€�
绗叚绡€(ji茅) 閫嗙畻瀛愬畾鐞� 
    閫嗙畻瀛愬畾鐞嗗強鍏惰瓑鏄�銆�
绗竷绡€(ji茅) 闁夊湒璞″畾鐞�  
    绶氭€х畻瀛愮殑鍦栬薄锛岄枆绠楀瓙锛岄枆鍦栬薄瀹氱悊銆�
    鑰冩牳瑕佹眰锛�
    鎺屾彙鏈珷娑夊強鍒扮殑鎵€鏈夊熀鏈蹇�锛屽熀鏈畾鐞�锛涚敱浜嶩ahn-Banach寤舵嫇瀹氱悊锛孯iesz琛ㄧず瀹氱悊锛孊aire缍卞畾鐞�锛岄€嗙畻瀛愬畾鐞嗭紝闁夊湒璞″畾鐞嗘槸娉涘嚱鍒嗘瀽鍩虹(ch菙)鐞嗚珫鐨勪富瑕佹(g貌u)鎴愰儴鍒�锛岃姹傜啛绶存帉鎻￠€欎簺鍏�(n猫i)瀹癸紱鑳界崹(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤�銆�                           绗簲绔�  绶氭€х畻瀛愮殑璀�
    鑰冭│瑕侀粸(di菐n)锛�
    绨�(ji菐n)瑕佷粙绱圭窔鎬х畻瀛愮殑璀滅殑姒傚康锛屽熀鏈€ц唱(zh矛)銆�
    璀滅殑姒傚康 
姝ｅ墖绠楀瓙锛屾鍓囬粸(di菐n)锛屾鍓囬泦锛岃瓬榛�(di菐n)锛岀壒寰佸€�锛岀壒寰佸悜閲�锛岄粸(di菐n)璀�锛岄€ｇ簩(x霉)璀�锛屼緥瀛�銆�
绗竴绡€(ji茅) 绶氭€ф湁鐣岀畻瀛愯瓬鐨勫熀鏈€ц唱(zh矛) 
璀滈泦鐨勯枆鎬�銆�
    鑰冩牳瑕佹眰锛�
    浜嗚В绶氭€х畻瀛愮殑璀滅殑姒傚康锛屽熀鏈€ц唱(zh矛)銆�
    涓�銆佸弮鑰冩浉鐩�
    1銆� 绋嬪叾瑗勭瓑锛屻€婂(sh铆)璁婂嚱鏁�(sh霉)鑸囨硾鍑藉垎鏋愬熀绀�(ch菙)銆�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛� 1983锛� 绗竴鐗�銆�
2銆� 鐜嬭伈鏈�锛� 閯董琛�锛屻€婂(sh铆)璁婂嚱鏁�(sh霉)鑸囨硾鍑藉垎鏋愭瑕併€�锛岀浜屽唺(c猫)锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�1992锛岀浜岀増銆�
3銆� 澶忛亾琛岀瓑锛屻€婂(sh铆)璁婂嚱鏁�(sh霉)璜栬垏娉涘嚱鍒嗘瀽銆�锛屼笅鍐�(c猫)锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛� 1985锛岀浜岀増銆�    瑙ｆ瀽骞句綍
涓€銆佽€冩牳姒傝
锛堜竴锛�銆佽绋嬫€ц唱(zh矛)
銆婄┖闁撹В鏋愬咕浣曘€嬫槸淇℃伅鑸囪▓(j矛)绠楃瀛�(xu茅)灏堟キ(y猫)锛堟湰绉戯級鐨勬牳蹇冭绋嬩箣涓€銆傝В鏋愬咕浣曞氨鏄敤浠ｆ暩(sh霉)鏂规硶鐮旂┒骞句綍銆傚畠鎶婂眬闄愪簬褰�銆佺浉鐨勫畾鎬х爺绌舵帹閫�(j矛n)鍒板彲浠ヨ▓(j矛)绠楃殑瀹氶噺鐮旂┒鐨勫堡闈�銆傜偤鍒濈瓑骞句綍鎻愪緵浜嗘柊鐨勭爺绌舵柟娉�锛涚偤瀛�(xu茅)缈�(x铆)楂樼瓑浠ｆ暩(sh霉)鎻愪緵浜嗗叿楂旂殑妯″瀷锛涚偤瀛�(xu茅)缈�(x铆)缍�(j墨ng)鍏稿垎鏋愭簴(zh菙n)鍌欏繀瑕佺殑鐭ヨ瓨(sh铆)銆傚悓鏅�(sh铆)涔熺偤鍔涘(xu茅)銆佺墿鐞嗗(xu茅)浠ュ強涓€鍒囧伐绋嬫妧琛�(sh霉)鎻愪緵蹇呰鐨勬暩(sh霉)瀛�(xu茅)宸ュ叿銆�
锛堜簩锛�銆佸(xu茅)缈�(x铆)瑭茶绋嬬殑鐩殑
鐝�(xi脿n)瀵�(sh铆)鐨勪笁缍┖闁撴槸浜哄€戝彲鐩存帴鎺ヨЦ鍜岀洿鎺ヨ瀵熺殑姝愭皬绌洪枔銆傛繁鍏ヤ簡瑙ｄ笁缍瓙姘忕┖闁撶殑绲�(ji茅)妲�(g貌u)鍙婂叾搴﹂噺鎬ц唱(zh矛)鏈夊姪浜庡(xu茅)鐢熷缓绔嬭捣鏇村唬娉涚殑鈥滅┖闁撯€濇蹇典互鍙婂悜n缍┖闁撶殑鎺ㄥ唬銆傞€氶亷銆婄┖闁撹В鏋愬咕浣曘€嬭绋嬬殑瀛�(xu茅)缈�(x铆)锛屾帉鎻¤В鏋愬咕浣曠殑鎬濇兂锛屽熀鏈悊璜栧拰鐮旂┒鏂规硶锛涚⿳绱繀瑕佺殑鏁�(sh霉)瀛�(xu茅)鐭ヨ瓨(sh铆)锛涘煿椁�(y菐ng)瀛�(xu茅)鐢熸娊璞℃€濈董鑳藉姏銆佸缓绔嬫暩(sh霉)瀛�(xu茅)妯″瀷鐨勮兘鍔�銆佹帹鐞嗚垏婕旂畻鐨勮兘鍔涖€�
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銆婄┖闁撹В鏋愬咕浣曘€嬭绋嬬殑涓昏鍏�(n猫i)瀹规湁鍚戦噺浠ｆ暩(sh霉)銆佽粚璺¤垏鏂圭▼銆佸钩闈㈠強绌洪枔涓殑鐩寸窔鍜屾洸绶�銆佸咕椤炵壒娈婃洸闈�銆佷簩娆℃洸闈㈢殑涓€鑸悊璜栫瓑浜斿€�(g猫)閮ㄥ垎銆�
鍦ㄧ┖闁撲腑寮曢€�(j矛n)鍚戦噺锛屽(sh铆)璩�(zh矛)鏄娇绌洪枔鐨勫咕浣曠祼(ji茅)妲�(g貌u)浠ｆ暩(sh霉)鐨勯亷绋嬨€傚悜閲忕殑閬�(y霉n)绠楄兘澶犺В姹哄咕浣曚腑鐨勫叿鏈変豢灏勬€ц唱(zh矛)鐨勫咕椤炲熀鏈晱椤屽拰鏈夐棞(gu膩n)璁婇噺鐨勫咕椤炲熀鏈晱椤�銆傚啀閫氶亷鍧愭(bi膩o)娉�銆佸缓绔嬭粚璺★紙鏇查潰銆佹洸绶氾級鐨勬柟绋�锛屽緸鑰屽皣鐮旂┒鏇茬窔鍜屾洸闈㈢殑骞句綍鍟忛姝哥祼(ji茅)鐐虹爺绌跺叾鏂圭▼鐨勪唬鏁�(sh霉)鍟忛銆傚寘鎷爺绌跺湒褰㈢殑鎬ц唱(zh矛)銆佺浉浜掍綅缃棞(gu膩n)绯�銆佹柟绋嬬殑褰㈠紡鍙婄浉浜掕綁(zhu菐n)鍖栦互鍙婂缓绔嬪悇绋舰寮忕殑鏂圭▼鐨勬柟娉曠瓑鏂归潰銆傚皪(du矛)浜屾鏇查潰鐨勪竴鑸悊璜栫殑瑷庤珫锛岃嚜鐒惰€岀劧鍦板紩閫�(j矛n)浜嗗潗妯�(bi膩o)璁婃彌鐨勬柟娉曪紝鍐嶉€�(j矛n)涓€姝ュ氨鍙互杞�(zhu菐n)鍒伴棞(gu膩n)浜庣窔鎬ц畩鎻涚殑浠ｆ暩(sh霉)鐞嗚珫鐨勭爺绌�銆傜敱浜屾鏇查潰鏂圭▼鐨勭郴鏁�(sh霉)妲�(g貌u)鎴愮殑鑻ュ共鍊�(g猫)涓嶈畩閲忓拰鍗婁笉璁婇噺锛屽畬鍏ㄥ彲浠ュ埢鍔冧簩娆℃洸闈㈢殑鍚勭ó鎬ц唱(zh矛)锛屼絾涓嶈兘纰哄畾浜屾鏇查潰鍦ㄧ┖闁撲腑鐨勪綅缃€傞€欎篃鏄竴鍊�(g猫)鍗佸垎閲嶈鐨勬蹇靛拰鎬濇兂銆備簩銆佸叿楂旂殑鑰冩牳鍏�(n猫i)瀹瑰拰瑕佹眰
绗竴绔�  鍚戦噺鑸囧潗妯�(bi膩o)
鑰冩牳瑕侀粸(di菐n)锛�
鍚戦噺鐨勬蹇佃垏閬�(y霉n)绠�銆佸潗妯�(bi膩o)鑸囧潗妯�(bi膩o)绯�銆佺敤鍧愭(bi膩o)閫�(j矛n)琛屽悜閲忕殑閬�(y霉n)绠�銆佸悜閲忓叡绶氭垨鍏遍潰鐨勫繀瑕佹浠�銆�
鑰冩牳鍏�(n猫i)瀹癸細
1•1鍚戦噺鐨勬蹇�銆佸悜閲忕殑绶氭€ч亱(y霉n)绠椼€佸悜閲忕殑绶氭€ч棞(gu膩n)绯诲拰鍚戦噺鍒嗚В 
鍚戦噺鐨勫畾缇�銆佸悜閲忕殑妯�銆佸柈浣嶅悜閲�銆侀浂鍚戦噺銆佺浉绛夌殑鍚戦噺銆佺浉鍙嶇殑鍚戦噺銆佸悜閲忕殑鍏辩窔鑸囧叡闈�銆佸悜閲忕殑鑷敱骞崇Щ鎬с€佸悜閲忕殑鍔犳硶鍙婇亱(y霉n)绠楀緥銆佸悜閲忕殑娓涙硶銆佸悜閲忕殑鏁�(sh霉)涔樺強閬�(y霉n)绠楀緥銆佸悜閲忕殑绶氭€х祫鍚�銆佸悜閲忕敱鍏跺畠鍚戦噺鐨勭窔鎬ц〃鍑�銆佸悜閲忕殑绶氭€х浉闂�(gu膩n)鍜岀窔鎬х劇闂�(gu膩n)鐨勫畾缇╁拰鏈夐棞(gu膩n)瀹氱悊銆�
1•2鍧愭(bi膩o)绯昏垏鍚戦噺鐨勫潗妯�(bi膩o)                          
浠垮皠鍧愭(bi膩o)绯昏垏鐩磋鍧愭(bi膩o)绯�銆佸彸鎵嬬郴銆佸悜閲忓湪鍧愭(bi膩o)绯讳笅鐨勫潗妯�(bi膩o)銆佸潗妯�(bi膩o)绯荤殑鍩哄簳銆佺敤鍧愭(bi膩o)閫�(j矛n)琛屽悜閲忕殑绶氭€ч亱(y霉n)绠�銆佸叡绶氳垏鍏遍潰鐨勫厖瑕佹浠躲€佸畾姣斿垎榛�(di菐n)銆�
1•3鍚戦噺鍦ㄧ郸瀹氭柟鍚戜笂鐨勫皠褰�                      
灏勫奖鐨勫畾缇╁拰鏈夐棞(gu膩n)瀹氱悊
1•4鍚戦噺鐨勫収(n猫i)绌�                                  
鍚戦噺?j墨)?n猫i)绌嶇殑瀹氱京鍜岄亱(y霉n)绠楀緥銆佷簩鍚戦噺鍨傜洿鐨勫厖瑕佹浠�銆佺敤鍧愭(bi膩o)閫�(j矛n)琛屽悜閲�?j墨)?n猫i)绌嶉亱(y霉n)绠�銆佸叐榛�(di菐n)璺濋洟鍏紡銆佸悜閲忕殑鏂瑰悜浣欏鸡銆佷簩鍚戦噺涔嬪ぞ瑙掋€�
1•5鍚戦噺鐨勫绌�                                  
鍚戦噺澶栫⿳鐨勫畾缇╁強閬�(y霉n)绠楀緥銆佸咕浣曟剰缇�銆佺敤鍧愭(bi膩o)閫�(j矛n)琛屽绌嶉亱(y霉n)绠�銆佷簩鍚戦噺鍏辩窔鐨勫厖瑕佹浠�銆�
*1•6涓夊悜閲忕殑娣峰悎绌�
娣峰悎绌嶇殑瀹氱京鍙婇亱(y霉n)绠楀緥銆佸咕浣曟剰缇�銆佷笁鐭㈠叡闈㈢殑鍏呰姊濅欢銆佺敤鍧愭(bi膩o)閫�(j矛n)琛屾贩鍚堢⿳閬�(y霉n)绠�銆�
閲嶉粸(di菐n)锛�
鏈珷鏄缓绔嬭В鏋愬咕浣曠悊璜栫殑鍩虹(ch菙)鍜屽伐鍏�銆傚(xu茅)鐢熸噳(y墨ng)娣卞埢鐞嗚В绌洪枔鐨勫咕浣曠祼(ji茅)妲�(g貌u)鏄浣曞(sh铆)鐝�(xi脿n)浠ｆ暩(sh霉)鍖栫殑銆傚苟鑳界啛绶存帉鎻″拰閬�(y霉n)鐢ㄥ悜閲忕殑鍩烘湰鐭ヨ瓨(sh铆)锛岃В姹洪棞(gu膩n)浜庡叡绶�銆佸叡闈€€佸畾姣斿垎榛�(di菐n)绛変豢灏勬€ц唱(zh矛)鐨勫晱椤�锛涜В姹洪棞(gu膩n)浜庨暦(zh菐ng)搴︺€佸ぞ瑙�銆侀潰绌�銆侀珨绌嶇瓑搴﹂噺鍟忛銆傜浜岀珷 杌岃贰鑸囨柟绋�
鑰冩牳瑕侀粸(di菐n)锛�
杌岃贰鑸囨柟绋嬬殑闂�(gu膩n)绯�銆佹櫘閫氭柟绋嬭垏鍙冩暩(sh霉)鏂圭▼銆佸缓绔嬫柟绋嬬殑鏂规硶銆�
鑰冩牳鍏�(n猫i)瀹癸細
2•1骞抽潰鏇茬窔鐨勬柟绋�                               
骞抽潰鏇茬窔鑸囧叾鏂圭▼鐨勯棞(gu膩n)绯�銆佸钩闈㈡洸绶氱殑鏅€氭柟绋嬪拰鍙冩暩(sh霉)鏂圭▼銆佸悇绋舰寮忕殑鏂圭▼鐩镐簰杞�(zhu菐n)鍖�銆�
2•2鏇查潰鐨勬柟绋�                                   
鏇查潰鐨勭洿瑙掑潗妯�(bi膩o)鏂圭▼鍜屽弮鏁�(sh霉)鏂圭▼銆佸缓绔嬫洸闈㈡柟绋嬬殑鏂规硶銆佺悆闈㈠拰鍦撴煴闈㈢殑鏂圭▼銆�
2•3姣嶇窔骞宠浜庡潗妯�(bi膩o)杌哥殑鏌遍潰鏂圭▼                   
鏌遍潰鐨勬簴(zh菙n)绶氬拰姣嶇窔銆佹瘝绶氬钩琛屼簬鍧愭(bi膩o)杌哥殑姗㈠湏鏌遍潰銆侀洐鏇叉煴闈€€佹媼鐗╂煴闈㈢殑鏂圭▼銆�
2•4绌洪枔鏇茬窔鐨勬柟绋�                               
绌洪枔涓殑浜屾洸闈㈢殑浜ょ窔銆佺┖闁撴洸绶氱殑鍙冩暩(sh霉)鏂圭▼銆佺┖闁撴洸绶氱殑鎶曞奖鏌遍潰銆�
閲嶉粸(di菐n)锛�
寤虹珛鍕�(d貌ng)榛�(di菐n)杌岃贰鐨勬柟绋嬫槸瑙ｆ瀽骞句綍鐨勫熀鏈€濇兂銆傚(xu茅)鐢熸噳(y墨ng)鐣�(d膩ng)娣卞埢鐞嗚В杌岃贰鑸囧叾鏂圭▼涔嬮枔鐨勯棞(gu膩n)绯伙紝鑳界啛绶村湴鎺屾彙寤虹珛鏇查潰鎴栨洸绶氱殑鏂圭▼鐨勬柟娉曚互鍙婄洿瑙掑潗妯�(bi膩o)鏂圭▼鍜屽弮鏁�(sh霉)鏂圭▼鐨勭浉浜掕綁(zhu菐n)鍖�銆傜涓夌珷 骞抽潰鑸囩┖闁撶洿绶�
鑰冩牳瑕侀粸(di菐n)锛�
骞抽潰鑸囩┖闁撶洿绶氱殑鍚勭ó褰㈠紡鐨勬柟绋�锛屽钩闈㈣垏骞抽潰銆佸钩闈㈣垏榛�(di菐n)銆佸钩闈㈣垏鐩寸窔銆佺洿绶氳垏榛�(di菐n)銆佺洿绶氳垏鐩寸窔涔嬮枔鐨勭浉闂�(gu膩n)浣嶇疆銆�
鑰冩牳鍏�(n猫i)瀹癸細
3•1骞抽潰鐨勬柟绋�                                   
骞抽潰鐨勬柟浣嶅悜閲忋€佸悜閲忓紡鍙冩暩(sh霉)鏂圭▼銆佸钩闈㈢殑涓€鑸柟绋嬪強瑷庤珫銆佸钩闈㈢殑鍠綅姝ｆ硶鍚戦噺銆佹硶寮忔柟绋嬨€�
3•2骞抽潰鑸囬粸(di菐n)鐨勭浉闂�(gu膩n)浣嶇疆                           
榛�(di菐n)鍒板钩闈㈢殑闆㈠樊銆佽窛闆�銆佸钩闈㈠妰鍒嗙┖闁撳晱椤屽強涓夊厓涓€娆′笉绛夊紡鐨勫咕浣曟剰缇�
3•3鍏╁钩闈㈢殑鐩搁棞(gu膩n)浣嶇疆                             
浜屽钩闈㈠钩琛�銆侀噸鍚�銆佺浉浜ゃ€佷簩骞抽潰鎵€鎴愮殑浜岄潰瑙�銆佷簩骞抽潰鍨傜洿鐨勫厖瑕佹浠躲€�
3•4绌洪枔鐩寸窔鐨勬柟绋�                               
鐩寸窔鐨勬柟鍚戝悜閲�銆佺洿绶氱殑鍚戦噺鎴栧弮鏁�(sh霉)鏂圭▼銆佺洿绶氱殑妯�(bi膩o)婧�(zh菙n)鏂圭▼銆佺洿绶氱殑涓€鑸柟绋嬨€佺洿绶氬皠褰卞紡鏂圭▼
3•5鐩寸窔鑸囧钩闈㈢殑鐩搁棞(gu膩n)浣嶇疆                         
鐩寸窔骞宠浜庡钩闈�銆佺洿绶氬湪骞抽潰涓�銆佺洿绶氳垏骞抽潰鐩镐氦銆佺洿绶氳垏骞抽潰鐨勫ぞ瑙掋€�
3•6绌洪枔鍏╃洿绶氱殑鐩搁棞(gu膩n)浣嶇疆銆�                         
鐩寸窔鐨勫叡闈㈣垏鐣伴潰銆佺┖闁撳叐鐩寸窔鐣伴潰銆佺浉浜�銆佸钩琛�銆侀噸鍚堢殑鍏呰姊濅欢銆佺┖闁撳叐鐩寸窔鐨勫ぞ瑙�銆佺暟闈㈢洿绶氶枔鐨勮窛闆㈣垏鍏瀭绶氭柟绋�銆�
3•7绌洪枔鐩寸窔鑸囬粸(di菐n)鐨勭浉闂�(gu膩n)浣嶇疆                       
榛�(di菐n)鍒扮洿绶氱殑璺濋洟
3•8骞抽潰鏉�
鏈夎桓骞抽潰鏉熺殑鏂圭▼銆佸钩琛屽钩闈㈡潫鐨勬柟绋�銆�
閲嶉粸(di菐n)锛�
鏈珷鏄┖闁撹В鏋愬咕浣曠殑鍩烘湰鍏�(n猫i)瀹�銆佸(xu茅)鐢熸噳(y墨ng)鐣�(d膩ng)鐔熺反鎺屾彙骞抽潰鍜岀┖闁撶洿绶氱殑鍚勭ó褰㈠紡鐨勬柟绋嬪拰寤虹珛閫欎簺鏂圭▼鐨勬柟娉曘€佺啛绶存帉鎻″悇绋浉闂�(gu膩n)浣嶇疆鐨勮В鏋愯〃閬�(d谩)寮忓拰瑷�(j矛)绠楀叕寮�銆傜鍥涚珷  鏌遍潰銆侀寪闈�銆佹棆杞�(zhu菐n)闈㈣垏浜屾鏇查潰
鑰冩牳瑕侀粸(di菐n)锛�
鏌遍潰鏂圭▼銆侀寪闈㈡柟绋�銆佹棆杞�(zhu菐n)闈㈡柟绋嬬殑寤虹珛鏂规硶銆侀綂娆℃柟绋�銆佺篂鍧愭(bi膩o)杌告棆杞�(zhu菐n)鐨勬棆杞�(zhu菐n)闈㈡柟绋�銆佹鐞冮潰銆侀洐鏇查潰銆佹媼鐗╅潰鐨勬柟绋嬨€佸柈钁夐洐鏇查潰鑸囬洐鏇叉媼鐗╅潰鐨勭洿姣嶇窔鏃忔柟绋�銆�
鑰冩牳鍏�(n猫i)瀹癸細
4•1鏌遍潰                                          
鏌遍潰鐨勬瘝绶氭柟鍚戙€佹簴(zh菙n)绶�銆佹煴闈㈢殑鐩磋鍧愭(bi膩o)鏂圭▼鍜屽弮鏁�(sh霉)鏂圭▼銆�
4•2閷愰潰                                          
閷愰潰鐨勯爞榛�(di菐n)銆佹簴(zh菙n)绶氬拰姣嶇窔銆侀寪闈㈢殑鐩磋鍧愭(bi膩o)鏂圭▼鍜屽弮鏁�(sh霉)鏂圭▼銆侀綂娆℃柟绋�銆�
4•3鏃嬭綁(zhu菐n)鏇查潰                                      
鏃嬭綁(zhu菐n)杌搞€佹瘝绶�銆佺稉(j墨ng)绶氳垏绶窔銆佷竴鑸棆杞�(zhu菐n)鏇查潰鐨勭洿瑙掑潗妯�(bi膩o)鏂圭▼鐨勫缓绔嬫柟娉�銆佺篂鍧愭(bi膩o)杌告棆杞�(zhu菐n)鐨勬棆杞�(zhu菐n)闈㈡柟绋嬨€�
4•4姗㈢悆闈�                                        
姗㈢悆闈㈢殑鐩磋鍧愭(bi膩o)鏂圭▼鑸囧弮鏁�(sh霉)鏂圭▼
4•5闆欐洸闈�                                        
鍠憠闆欐洸闈㈣垏闆欒憠鏇查潰鐨勬柟绋嬪強瑷庤珫
4•6鎷嬬墿闈�                                        
姗㈠湏鎷嬬墿闈㈣垏闆欐洸鎷嬬墿闈㈢殑鏂圭▼鍙婅◣璜�
4•7鍠憠闆欐洸闈㈣垏闆欐洸鎷嬬墿闈㈢殑鐩存瘝绶氥€�              
鍠憠闆欐洸闈㈢殑鐩存瘝绶氭棌鏂圭▼銆侀洐鏇叉媼鐗╅潰鐨勭洿姣嶇窔鏃忔柟绋�銆佸柈钁夐洐鏇查潰鑸囬洐鏇叉媼鐗╅潰鐨勭洿姣嶇窔鐨勬€ц唱(zh矛)銆�
    閲嶉粸(di菐n)锛�
鏈珷浠嬬垂绌洪枔涓殑骞鹃鏈夌獊鍑哄咕浣曠壒寰佸拰鎳�(y墨ng)鐢ㄥ唬娉涚殑鏇查潰銆傚(xu茅)鐢熸噳(y墨ng)鐣�(d膩ng)鐔熸倝閫欏咕椤炴洸闈㈢殑鏂圭▼鍜屽湒褰€€傛洸闈㈡槸绌洪枔涓嫊(d貌ng)榛�(di菐n)鐨勮粚璺�锛屾湁鏅�(sh铆)涔熷彲浠ョ敱涓€姊濇洸绶氭寜鏌愮ó瑕�(gu墨)寰嬮亱(y霉n)鍕�(d貌ng)鐢熸垚锛屾湁鐨勬洸闈㈠彲浠ョ敱涓€鏃忔洸绶氾紙鍖呮嫭鐩寸窔锛夌敓鎴愶紝瀛�(xu茅)鐢熸噳(y墨ng)浜嗚В鍜岄牁(l菒ng)鏈�(hu矛)閫欑ó鏂规硶銆傜浜旂珷 浜屾鏇查潰鐨勪竴鑸悊璜�
鑰冩牳瑕侀粸(di菐n)锛�
浜屾鏇查潰鐨勬几杩戞柟鍚戣垏闈炴几杩戞柟鍚戙€佷腑蹇�銆佸垏绶氥€佸垏骞抽潰銆佸榛�(di菐n)銆佸緫闈�銆佸鍚�銆佷富寰戦潰鑸囦富鏂瑰悜銆佺壒寰佹柟绋嬭垏鐗瑰緛鏍广€佷簩娆℃洸闈㈡柟绋嬬殑鍖栫啊(ji菐n)鑸囧垎椤�銆佺洿瑙掑潗妯�(bi膩o)璁婃彌銆佹噳(y墨ng)鐢ㄤ笉璁婇噺鍖栫啊(ji菐n)浜屾鏇查潰鐨勬柟绋�銆�
鑰冩牳鍏�(n猫i)瀹癸細
5•1浜屾鏇查潰鑸囩洿绶氱殑鐩搁棞(gu膩n)浣嶇疆                     
浜屾鏇查潰鑸囩洿绶氱浉闂�(gu膩n)浣嶇疆鐨�6绋儏娉佺殑瑷庤珫
5•2浜屾鏇查潰鐨勬几杩戞柟鍚戣垏涓績                     
婕歌繎鏂瑰悜鑸囬潪婕歌繎鏂瑰悜銆佷腑蹇冭垏涓績鍧愭(bi膩o)銆佷腑蹇冧簩娆℃洸闈�銆佺窔蹇冧簩娆℃洸闈�銆侀潰蹇冧簩娆℃洸闈�銆佺劇蹇冧簩娆℃洸闈€€�
5•3浜屾鏇查潰鐨勫垏绶氳垏鍒囧钩闈�                       
鍒囩窔鐨勫畾缇�銆佸厖瑕佹浠躲€佸垏骞抽潰鏂圭▼銆佸榛�(di菐n)銆�
5•4浜屾鏇查潰鐨勫緫闈㈣垏濂囧悜                         
寰戦潰鐨勫畾缇�銆佸緫闈㈢殑鏂圭▼銆佸叡杌涘鸡鍜屽叡杌涙柟鍚�銆佸緫闈㈢殑鎬ц唱(zh矛)銆佸鍚戙€�
5•5浜屾鏇查潰鐨勪富寰戦潰鑸囦富鏂瑰悜銆佺壒寰佹柟绋嬭垏鐗瑰緛鏍�   
涓诲緫闈€€佷富鏂瑰悜銆佺壒寰佹柟绋�銆佺壒寰佹牴銆佺壒寰佹牴鐨勬€ц唱(zh矛)銆�
5•6浜屾鏇查潰鏂圭▼鐨勫寲绨�(ji菐n)鑸囧垎椤�                     
绌洪枔鐩磋鍧愭(bi膩o)璁婃彌鍙婅畩鎻涘叕寮忋€佺敱鏂板潗妯�(bi膩o)绯荤殑涓夊€�(g猫)鍧愭(bi膩o)骞抽潰纰哄畾鐨勫潗妯�(bi膩o)璁婃彌鍙婅畩鎻涘叕寮�銆佷簩娆℃洸闈㈡柟绋嬬殑鍖栫啊(ji菐n)鑸囧垎椤�銆�
5•7鎳�(y墨ng)鐢ㄤ笉璁婇噺鍖栫啊(ji菐n)浜屾鏇查潰鐨勬柟绋�                 
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