鍗椾含淇℃伅宸ョ▼澶у纰╁＋鐮旂┒鐢熸嫑鐢熷叆瀛歌€冭│

鑰冭│澶х侗

绉戠洰浠ｇ⒓锛欶02

绉戠洰鍚嶇ū锛氭暩(sh霉)瀛稿皥妤�(y猫)鍩虹缍滃悎

绗竴閮ㄥ垎  鐩鑸囧熀鏈姹�

涓€銆佺洰妯�

鈥滄暩(sh霉)瀛稿皥妤�(y猫)鍩虹缍滃悎鈥濊绋嬪寘鎷父寰垎鏂圭▼鍜屾暩(sh霉)鍊煎垎鏋愬叐閮ㄥ垎锛岄€欏叐閮ㄥ垎鏄熀绀庢暩(sh霉)瀛搞€佽▓绠楁暩(sh霉)瀛�銆佹噳鐢ㄦ暩(sh霉)瀛稿拰绲�(t菕ng)瑷堝鐨勯噸瑕佸熀绀庤绋嬨€傞€氶亷閫欏叐闁€瑾茬▼鐨勫缈�锛屽鐢熻兘绯荤当(t菕ng)鍦版帉鎻℃湁闂滃父寰垎鏂圭▼鐨勫熀鏈悊璜栧拰姹傝В甯稿井鍒嗘柟绋嬬殑鍚勭ó鏂规硶锛屾暩(sh霉)鍊煎垎鏋愮殑鍩烘湰鐞嗚珫銆佹柟娉�锛屽悇绋稉(j墨ng)鍏哥畻娉曞強鍏舵噳鐢�锛屽苟鐐哄悗绻肩殑鍚勬暩(sh霉)瀛稿垎鏀殑娣卞叆鐮旂┒鎵撲笅鍫呭鐨勫熀绀�銆�

浜�銆佸熀鏈姹�

鈥滄暩(sh霉)瀛稿皥妤�(y猫)鍩虹缍滃悎鈥濊绋嬭€冭│鐨勪富瑕佸収瀹圭偤甯稿井鍒嗘柟绋嬬殑鍩烘湰鐞嗚珫鍙婂悇椤炲父寰垎鏂圭▼鐨勬眰瑙ｆ柟娉�銆佹暩(sh霉)鍊煎垎鏋愮殑鐨勫熀鏈悊璜�銆佹柟娉曪紝(闈�)绶氭€ф柟绋嬬祫鐨勬暩(sh霉)鍊兼柟娉�銆佹暩(sh霉)鍊煎井鍒嗚垏鏁�(sh霉)鍊肩⿳鍒嗗強鐗瑰緛鍊肩殑鏁�(sh霉)鍊兼柟娉曠瓑銆傚悓鏅傝姹傝€冪敓浜嗚В甯稿井鍒嗘柟绋嬬殑绌�(w臎n)瀹氭€х悊璜�銆佹帉鎻＄煩闄ｅ垎鏋愬熀绀�锛岀啛鎮夊悇绋畻娉曠殑鍎�(y艒u)鍔ｏ紝鐔熸倝鍚勭ó绠楁硶鍙婂叾鎳夌敤銆�

绗簩閮ㄥ垎 鍏у鑸囪€冩牳鐩

涓€銆佸父寰垎鏂圭▼閮ㄥ垎锛�

1銆佸垵绛夌⿳鍒嗘硶

(1) 浜嗚В甯稿井鍒嗘柟绋嬬敘(ch菐n)鐢熺殑鑳屾櫙锛屽畠鑸囨暩(sh霉)瀛稿垎鏋愬拰楂樼瓑浠ｆ暩(sh霉)瑾茬▼涔嬮枔鐨勯棞绯�锛屼簡瑙ｇ窔鎬�

鏂圭▼鍜岄潪绶氭€ф柟绋嬬殑鍒ゅ垾锛�

(2) 浜嗚В璁婇噺鍒嗛噺鍒嗛洟鏂圭▼銆侀綂娆℃柟绋嬬浉闂滄蹇碉紱

(3) 浜嗚В涓€闅庣窔鎬ф柟绋嬬殑鐩搁棞瀹氱京,濡傞綂娆℃柟绋�銆侀潪榻婃鏂圭▼銆侀綂娆￠爡鍜岄潪榻婃闋呯瓑锛屼簡

瑙ernoulli鏂圭▼鐨勬蹇碉紱

(4) 浜嗚В鍏ㄥ井鍒嗘柟绋�銆佺⿳鍒嗗洜瀛愮殑姒傚康锛�

(5) 浜嗚В涓€闅庨毐寮忔柟绋嬬殑瀹氱京, 涓€闅庨毐寮忔柟绋嬬殑鍥涚ó椤炲瀷,楂橀殠鏂圭▼鐨勫畾缇�;

(6) 鐞嗚В甯稿井鍒嗘柟绋嬬浉闂滄蹇碉細甯稿井鍒嗘柟绋嬶紝瑙�銆佺壒瑙ｈ垏閫氳В锛屽垵濮嬫浠�锛岀⿳鍒嗘洸绶氱瓑

(7) 鐞嗚В鍒濈瓑绌嶅垎娉曠殑鍏ф兜锛屽嵆鍒╃敤涓嶅畾绌嶅垎姹傚井鍒嗘柟绋嬬殑瑙�锛涚悊瑙ｅ井鍒嗗舰寮忕殑璁婇噺鍒�

闆㈡柟绋�

(8) 鐞嗚ВBernoulli鏂圭▼鐨勮В娉�锛屼竴闅庣窔鎬ф柟绋嬪垵濮嬪晱椤岀殑姹傝В鍏紡锛�

(9) 鐞嗚В鍏ㄥ井鍒嗘柟绋嬫眰瑙ｆ€濇兂锛屽嵆鍒╃敤浜屽厓鍑芥暩(sh霉)寰垎鐞嗚珫锛屾眰浜屽厓鍑芥暩(sh霉)寰垎鐨勫師鍑芥暩(sh霉)锛�

绌嶅垎鍥犲瓙鐨勪笉鍞竴鎬�锛�

(10) 鐞嗚В涓€闅庨毐寮忔柟绋嬭垏椤ず鏂圭▼鐨勪笉鍚屼箣铏�, 涓€闅庨毐寮忔柟绋嬬殑姹傝В闆ｉ粸, 楂橀殠鏂圭▼鐨�

姹傝В闆ｉ粸;

(11) 鎺屾彙璁婇噺鍒嗛洟鏂圭▼鐨勮В娉曪紱

(12) 鎺屾彙涓€闅庣窔鎬ч綂娆℃柟绋嬬殑瑙ｆ硶锛屽父鏁�(sh霉)璁婃槗娉曪紝涓€闅庣窔鎬ч潪榻婃鏂圭▼鐨勮В娉�锛�

(13) 鎺屾彙鍏ㄥ井鍒嗘柟绋嬬殑瑙ｆ硶锛屽叏寰垎鏂圭▼鐨勫垽鏂凤紝鐗规畩绌嶅垎鍥犲瓙鐨勬眰娉�锛�

(14) 鎺屾彙鍥涚ó椤炲瀷鐨勪竴闅庨毐寮忔柟绋嬬殑姹傝В鏂规硶,楂橀殠鏂圭▼鐨勯檷闅庢硶(涓嶉’鍚嚜璁婇噺鐨勯珮闅�

鏂圭▼, 鎭扮暥灏庢暩(sh霉)鏂圭▼)銆�

2銆佸熀鏈畾鐞�

(1) 浜嗚В瑙ｇ殑瀛樺湪鑸囧敮涓€鎬у畾鐞嗙殑姊濅欢鍜岀祼璜�锛岃В鐨勫瓨鍦ㄥ崁(q奴)闁擄紝Picard閫愭閫艰繎娉曠瓑姒�

蹇�锛�

(2) 浜嗚В灞€閮↙ipschitz姊濅欢鐨勬蹇�锛屽嚱鏁�(sh霉)鏄惁婊胯冻灞€閮↙ipschitz姊濅欢鐨勯璀�锛屽眬閮�

Lipschitz姊濅欢鍦ㄨВ鐨勫欢灞曢亷绋嬩腑鐨勪綔鐢�锛岃В灏嶅垵鍊肩殑閫ｇ簩(x霉)渚濊炒鎬у拰鍙井鎬э紱

(3) 鐞嗚ВLipschitz姊濅欢鐨勬蹇�锛屽嚱鏁�(sh霉)鏄惁婊胯冻Lipschitz姊濅欢鐨勯璀�锛汱ipschitz姊濅欢鍦�

瀛樺湪鍞竴鎬у畾鐞嗚瓑鏄庝腑鐨勪綔鐢�锛�

(4) 鐞嗚В椋藉拰瑙�銆佹渶澶у瓨鍦ㄥ崁(q奴)闁撶殑姒傚康锛岃В鐨勫欢灞曢亷绋嬶紝椋藉拰瑙ｇ殑瀛樺湪鍗€(q奴)闁撹垏瑙ｇ殑婕歌繎

鐨勯棞绯�锛�

(5) 鎺屾彙瑙ｇ殑瀛樺湪鑸囧敮涓€鎬у畾鐞嗙殑璀夋槑锛孭icard瑙ｅ簭鍒楃殑妲嬮€犲強鏀舵杺鎬х殑璀夋槑锛屽埄鐢�

Picard閫愭閫艰繎娉曟眰杩戜技瑙�銆�

(6) 鎺屾彙姣旇純鍘熺悊鍜岃В鐨勫欢灞曞畾鐞嗗強鍏惰瓑鏄庯紝鍒濆€煎皪瑙ｇ殑瀛樺湪鍗€(q奴)闁撶殑褰遍熆銆�

3銆佷竴闅庣窔鎬у井鍒嗘柟绋嬬祫

(1) 浜嗚В绶氭€у井鍒嗘柟绋嬬祫鐨勬湁闂滄蹇�(绯绘暩(sh霉)鐭╅櫍銆佸悜閲忓€煎嚱鏁�(sh霉)銆佹柟绋嬬祫鐨勫垵濮嬪晱椤�)銆佹柟

绋嬬祫瑙ｇ殑瀛樺湪鍞竴鎬у畾鐞嗗強璀夋槑鎬濊矾锛�

(2) 浜嗚В甯哥郴鏁�(sh霉)绶氭€у井鍒嗘柟绋嬬祫鐨勭郴鏁�(sh霉)鐭╅櫍鐨勭壒寰佹柟绋嬨€佺壒寰佹牴銆佺壒寰佸悜閲忥紝鐗瑰緛鏍广€�

鐗瑰緛鍚戦噺鑸囪В鐨勯棞绯�锛�

(3) 鐞嗚В鍚戦噺鍊煎嚱鏁�(sh霉)绶氭€х浉闂溿€佺窔鎬х劇闂滅殑姒傚康锛學ronsky琛屽垪寮忕殑姒傚康锛屽熀鏈В绲勭殑

姒傚康锛屽熀鏈В鐨刉ronsky琛屽垪寮忕殑鎬ц唱锛孡iouville鍏紡锛�

(4) 鐞嗚В鍒╃敤绯绘暩(sh霉)鐭╅櫍鐨勭壒寰佹牴銆佺壒寰佸悜閲忔眰甯哥郴鏁�(sh霉)绶氭€у井鍒嗘柟绋嬬祫鐨勫熀鏈В绲勭殑鏂�  

娉�锛�

(5) 鎺屾彙绶氭€э紙榻婃銆侀潪榻婃锛夊井鍒嗘柟绋嬬祫瑙ｇ殑绲愭锛岄€氳В鍩烘湰瀹氱悊锛屽父鏁�(sh霉)璁婃槗娉�锛涘悜

閲忓€煎嚱鏁�(sh霉)绶氭€х浉闂溿€佺窔鎬х劇闂滅殑鍒ゆ柗銆�

(6) 鎺屾彙甯哥郴鏁�(sh霉)绶氭€у井鍒嗘柟绋嬬祫鐨勮В娉�銆�

4銆乶闅庣窔鎬у井鍒嗘柟绋�

(1) 浜嗚Вn闅庣窔鎬у井鍒嗘柟绋嬭В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞嗭紝鍑芥暩(sh霉)绲勭窔鎬х浉闂�銆佺窔鎬х劇闂滐紝鍑芥暩(sh霉)绲�

鐨刉ronsky琛屽垪寮忕瓑姒傚康锛�

(2) 浜嗚Вn闅庡父绯绘暩(sh霉)绶氭€ч綂娆″井鍒嗘柟绋嬬殑鐗瑰緛鏂圭▼銆佺壒寰佹牴锛涚敱鐗瑰緛鏍圭⒑瀹氬井鍒嗘柟绋嬬殑

瑙�锛�

(3) 浜嗚В闈為綂娆￠爡鐨勬蹇�锛屽埄鐢ㄥ父鏁�(sh霉)璁婃槗娉曟眰鐗硅В鐨勬柟娉�锛�

(4) 浜嗚В璩粸閬嬪嫊鏂圭▼鐨勭墿鐞嗘剰缇�锛屾尟鍕�銆佺劇闃诲凹鑷敱鎸嫊銆侀樆灏艰嚜鐢辨尟鍕曘€佺劇闃诲凹寮�

杩尟鍕�銆侀樆灏煎挤杩尟鍕曠瓑姒傚康锛�

(5) 浜嗚ВLaplace璁婃彌鍙婂叾鍦ㄥ井鍒嗘柟绋嬪垵鍊煎晱椤屾眰瑙ｅ晱椤屼腑鐨勬噳鐢�锛�

(6) 鐞嗚Вn闅庣窔鎬у井鍒嗘柟绋嬭垏n缍窔鎬ф柟绋嬬祫涔嬮枔鐨勯棞绯�锛屽嵆灏嶄换鎰忎竴鍊媙闅庣窔鎬у井鍒�

鏂圭▼锛屽彲灏囧叾鍖栫偤涓€鍊媙缍窔鎬ф柟绋嬬祫锛屼笖浠栧€戠殑瑙ｆ槸绛夊児鐨�锛� 鍩烘湰瑙ｇ祫锛� Liouville鍏紡锛�

(7) 鐞嗚В鐢卞京鐗瑰緛鏍瑰浣曠⒑瀹氬井鍒嗘柟绋嬭В鐨勬柟娉�锛�

(8) 鐞嗚В姣旇純绯绘暩(sh霉)娉曡垏甯告暩(sh霉)璁婃槗娉曠殑宸暟锛�

(9) 鐞嗚В寰垎鏂圭▼鐨勮В鑸囨尟鍕曚箣闁撶殑鑱�(li谩n)绯�锛屽叡鎸蹇�锛�

(10) 鐞嗚В鍐礆鏁�(sh霉)瑙ｆ硶澶ф剰锛�

(11) 鎺屾彙鍑芥暩(sh霉)绲勭窔鎬х浉闂溿€佺窔鎬х劇闂滅殑璀夋槑鏂规硶锛宯闅庯紙榻婃銆侀潪榻婃锛夌窔鎬у井鍒嗘柟绋�

鐨勯€氳В绲愭瀹氱悊鐨勮瓑鏄庯紱

(12) 鎺屾彙n闅庡父绯绘暩(sh霉)绶氭€ч綂娆″井鍒嗘柟绋嬬殑瑙ｆ硶锛�

(13) 鎺屾彙绗竴椤炲瀷銆佺浜岄鍨媙闅庡父绯绘暩(sh霉)绶氭€ч潪榻婃寰垎鏂圭▼鐨勮В娉曪紱

(14) 鎺屾彙閫氶亷姹備簩闅庡父绯绘暩(sh霉)绶氭€ф柟绋嬬殑閫氳В鎺㈣◣鍔涘鍟忛涓尟鍕曠従(xi脿n)璞＄殑鏂规硶锛岄樆灏奸爡

鍜屽挤杩爡灏嶆尟鍕曠殑褰遍熆锛�

(15) 鎺屾彙鐨勭浉闂滃畾鐞嗗強鍏跺湪寰垎鏂圭▼鍒濆€煎晱椤屾眰瑙ｅ晱椤屼腑鐨勬噳鐢ㄣ€�

5銆佸畾鎬�銆佺┅(w臎n)瀹氭€х悊璜栫啊浠�

(1) 浜嗚В绌�(w臎n)瀹氭€х浉闂滄蹇�

(2) 鐞嗚В绨″柈鐨勬潕闆呮櫘璜惧か鍑芥暩(sh霉)鐨勬閫犳柟娉�锛� 姝ｅ畾鍑芥暩(sh霉)銆佽矤瀹氬嚱鏁�(sh霉)鐨勫畾缇�锛�

(3) 鎺屾彙鏉庨泤鏅澶嚱鏁�(sh霉)鐨勫畾缇╋紝閫氶亷妲嬮€犵啊鍠殑鏉庨泤鏅澶嚱鏁�(sh霉)锛屽埄鐢ㄧ浉闂滃畾鐞嗭紝鍒�

鏂烽浂瑙ｇ殑绌�(w臎n)瀹氭€�銆�

浜�銆佹暩(sh霉)鍊煎垎鏋愰儴鍒�

1銆佺窉璜�

(1) 浜嗚В瑷堢畻姗熺畻娉曠殑鐗规€�锛�

(2) 鐞嗚В瑾ゅ樊鐨勫畾鎬у垎鏋愯垏閬垮厤瑾ゅ樊鐨勫嵄瀹�銆佹暩(sh霉)鍊奸亱绠楃殑瑾ゅ樊浼拌▓銆佺畻娉曠殑鏁�(sh霉)鍊肩┅(w臎n)瀹氭€�锛�

(3) 鎺屾彙瑾ゅ樊鐨勪締婧愯垏鍒嗛銆佽宸垏鏈夋晥鏁�(sh霉)瀛�锛�

2銆佺煩闄ｅ垎鏋愬熀绀�

(1) 寤虹珛绶氭€х┖闁�銆佽肠鑼冪窔鎬х┖闁�銆佸収绌嶇┖闁撶殑姒傚康锛�

(2) 鎺屾彙鍚戦噺鍜岀煩闄ｇ殑鑼冩暩(sh霉)銆佸悜閲忓拰鐭╅櫍搴忓垪鐨勬サ闄�锛�

(3) 鎺屾彙鍏х⿳绌洪枔涓殑姝ｄ氦绯�銆佺煩闄ｇ殑涓夎鍒嗚В銆佹浜ゅ垎瑙�銆佸鐣板€煎垎瑙�锛�

(4) 鏂藉瘑鐗�(Schmidt) 姝ｄ氦鍖栭亷绋嬨€佹浜ゅ闋呭紡锛�

3銆佹暩(sh霉)鍊奸€艰繎

(1) 浜嗚В涓婅堪骞剧ó甯哥敤鎻掑€兼硶鐨勫劒(y艒u)缂洪粸锛屽苟鑳藉鏍规摎(j霉)瀵﹂殯鍟忛閬告搰閬╃暥?sh霉)鐗熼€崳妞掋劅M琛�

鍑芥暩(sh霉)閫艰繎锛�

(2) 浜嗚В涓夎澶氶爡寮忛€艰繎鍙婂揩閫熷倕绔嬭憠璁婃彌锛�

(3) 鐞嗚В鎻掑€兼硶鐨勫熀鏈師鐞�锛涙帉鎻＄敤鎷夋牸鏈楁棩鎻掑€煎叕寮�銆佺墰闋撴彃鍊煎叕寮忛€茶鎻掑€肩殑鏂规硶锛�

(4) 鐞嗚В鍑芥暩(sh霉)閫艰繎銆佹湁鐞嗛€艰繎鐨勬蹇碉紱

(5) 鎺屾彙鍒嗘浣庢鎻掑€�銆佹ǎ姊濇彃鍊�銆佸焹鐖剧背鐗规彃鍊煎強鍏舵彃鍊间綑闋呭拰瑾ゅ樊浼拌▓鏂规硶锛�

(6) 鎺屾彙鏈€浣冲钩鏂归€艰繎鏂规硶銆佹洸绶氭摤鍚堢殑鏈€灏忎簩涔樻硶锛涘皪浜庣郸瀹氱殑涓€绲勬暩(sh霉)鎿�(j霉)锛岃兘澶犳牴鎿�(j霉)

鏈€灏忎簩涔樺師鐞嗗湪鏌愪竴鍑芥暩(sh霉)椤炰腑閬告搰鍑芥暩(sh霉)锛岃垏鍏舵墍绲︽暩(sh霉)鎿�(j霉)绲勬摤鍚堜締瑙ｆ焙涓€浜涘闅涘晱椤�

4銆佺窔鎬ф柟绋嬬祫鐨勬暩(sh霉)鍊艰В娉�

(1) 浜嗚В鐮旂┒姹傝В绶氭€ф柟绋嬬祫鐨勬暩(sh霉)鍊兼柟娉曞垎椤炲強鐩存帴娉曠殑鎳夌敤鑼冨湇锛�

(2) 浜嗚В妤靛皬鍖栨柟娉曪細鏈€閫熶笅闄嶆硶銆佸叡杌涙搴︽硶锛�

(3) 鎺屾彙绶氭€ф柟绋嬬祫鐨勭洿鎺ヨВ娉曗€斺€旈珮鏂富鍏冩秷鍘绘硶銆� LU涓夎鍒嗚В娉�銆佸钩鏂规牴娉�銆� 杩�

瓒曟硶鑸囦笁灏嶈鏂圭▼绲勭殑瑙ｆ硶锛�

(4) 鐞嗚В鐭╅櫍鐨勮瓬鍗婂緫銆佺煩闄ｇ殑姊濅欢鏁�(sh霉)绛夋蹇�锛屽苟鑳藉埄鐢ㄦ浠舵暩(sh霉)鍒ゅ垾鏂圭▼绲勬槸鍚︾梾鎱�(t脿i)浠�

鍙婂皪鏂圭▼绲勭殑鐩存帴鏂规硶鐨勮宸€茶浼拌▓锛�

(5) 鎺屾彙绶氭€ф柟绋嬬祫鐨勭稉(j墨ng)鍏歌凯浠ｆ柟娉曗€斺€旈泤鍙瘮杩唬娉�銆侀珮鏂� - 濉炲痉鐖捐凯浠ｆ硶鍙� SOR

 鏂规硶鐨勮▓绠楀垎閲忓舰寮忋€佺煩闄ｅ舰寮忎互鍙婅凯浠ｆ硶鐨勬敹鏂傛€у垽瀹氭柟娉�锛�

(6) 鎺屾彙绶氭€ф柟绋嬬祫鐨凨rylov 瀛愮┖闁撴柟娉曘€�

5銆侀潪绶氭€ф柟绋嬬祫姹傛牴

(1) 浜嗚В姹傝В闈炵窔鎬ф柟绋嬪拰闈炵窔鎬ф柟绋嬬祫鐨勫父鐢ㄦ暩(sh霉)鍊兼柟娉�锛�

(2) 鐞嗚В杩唬娉曠殑鍩烘湰鍘熺悊銆佽凯浠ｉ亷绋嬬殑鏀舵杺鎬у強鏀舵杺閫熷害锛涜凯浠ｉ亷绋嬬殑鍔犻€熷師鐞�锛�

(3) 鎺屾彙姹傝В闈炵窔鎬ф柟绋嬬祫鐨勪笉鍕曢粸杩唬娉�銆佺墰闋撴硶鍙婂叾鏀舵杺鎬�锛�

6銆佹暩(sh霉)鍊肩⿳鍒嗚垏鏁�(sh霉)鍊煎井鍒�

(1) 浜嗚В鏁�(sh霉)鍊煎井鍒嗘柟娉曠殑鍩烘湰鎬濇兂锛涢珮鏂�-鍕掕畵寰风瓑姹傜⿳鍏紡銆佸閲嶇⿳鍒�銆佹暩(sh霉)鍊煎井鍒嗗叕

寮�锛�

(2) 鐞嗚В鏁�(sh霉)鍊肩⿳鍒嗗叕寮忕殑涓€鑸舰寮忓強灏庡嚭鏂规硶銆佺悊瑙ｈ嚜閬╂噳绌嶅垎鏂规硶锛涙瘮杓冪墰闋� - 鏌�

鐗规柉姹傜⿳鍏紡鑸囬珮鏂眰绌嶅叕寮忕殑鐣板悓榛�锛涢緧璨濇牸绠楁硶锛�

(3) 鎺屾彙浠ｆ暩(sh霉)绮惧害鐨勬蹇�銆佹彃鍊煎瀷鐨勬眰绌嶅叕寮忋€佸咕绋綆闅庢眰绌嶅叕寮忓強浣欓爡浣跨敤

7銆佺煩闄ｇ壒寰佸€煎晱椤�

(1) 浜嗚В鐗瑰緛鍊肩殑浼拌▓銆佹浜よ畩鎻涚殑Givens鍜孒ouseholder璁婃彌銆佺煩闄ｇ殑QR娉曞垎瑙ｏ紱

(2) 鐞嗚В鍐硶鍜屽弽鍐硶鐨勫師鐞嗗拰瑙ｆ焙鐨勫皪璞″強鍏跺姞閫熸柟娉�, 鐭╅櫍鐨凲R娉曞垎瑙ｇ殑鍘熺悊鍜�

璁婂舰鍜屽悓鏅傞亷绋�锛�

(3) 鎺屾彙鍐硶鍜屽弽鍐硶鍜屽熀鏈殑QR娉曘€�

绗笁閮ㄥ垎  鏈夐棞瑾槑鑸囧鏂借姹�

1銆佸熀鏈姹傦細鎺屾彙绲�(t菕ng)瑷堝鍩烘湰姒傚康锛岀悊瑙ｈ€冭│鑼冨湇鍏х殑鍚勭ó甯稿井鍒嗘柟绋嬭垏鏁�(sh霉)鍊煎垎鏋愮殑鍩烘湰鐞嗚珫銆佹柟娉�锛屾帉鎻″悇绋畻娉曞強鍏舵噳鐢�锛涙帉鎻＄畻娉曠殑鍩烘湰鍘熺悊鍜岀悊璜栧熀绀庛€�

2銆佸懡椤岃鏄庯細

(1) 鍒嗗€兼瘮渚嬶細瑭﹀嵎婊垮垎鐐�150鍒�锛岃€冭│鏅傞枔180鍒嗛悩銆傝│鍗峰収瀹瑰寘鎷細鏁�(sh霉)鍊煎垎鏋� 75鍒�锛涘父寰垎鏂圭▼ 75鍒�銆�

(2) 椤屽瀷鍒嗗竷锛氱啊绛旈锛岀磩40%锛涜▓绠椼€佽瓑鏄庨锛岀磩60%銆�

3銆佸弮鑰冩浉鐩�:

(1) 鏉卞寳甯寖澶у寰垎鏂圭▼鏁欑爺瀹�. 甯稿井鍒嗘柟绋�. 鍖椾含锛氶珮绛夋暀鑲插嚭鐗堢ぞ锛�2005.

(2) 鏉庢叾妤�. 鏁�(sh霉)鍊煎垎鏋�. 鍖椾含锛氭竻鑿ぇ瀛稿嚭鐗堢ぞ锛�2008.

4銆佸叾浠栬(gu墨)瀹氾細鑰冭│鏂瑰紡鐐洪枆鍗风瓎瑭�锛岀附鍒�150鍒�锛岃€冭│鏅傞枔鐐�180 鍒嗛悩銆�