姝¤繋瑷晱鑰冪爺绉樼睄鑰冪爺缍�(w菐ng)!    鐮旂┒鐢熸嫑鐢熶俊鎭恫(w菐ng)    鑰冨崥鐪熼涓嬭級    鑰冪爺鐪熼涓嬭級    鍏ㄧ珯鏂囩珷绱㈠紩
鏂囩珷鎼滅储
   
  楂樼礆鎼滅储   

 鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 鑰冪爺绉樼睄鑰冪爺缍�(w菐ng) >> 鏂囩珷涓績 >> 灏堟キ(y猫)瑾� >> 姝f枃  2019骞磋タ鍖楀斧鑼冨ぇ瀛�(xu茅)945鏁�(sh霉)瀛�(xu茅)缍滃悎鑰冪爺澶х侗

鏂拌仦璩囪▕
鏅€氭枃绔� 涓婃捣甯�50瀹跺柈浣嶇恫(w菐ng)涓婃帴鍙楀挩瑭㈠拰鍫�(b脿o)鍚�
鏅€氭枃绔� 鍖椾含澶у(xu茅)鐢�“灏辨キ(y猫)涔嬪”鐮旂┒鐢熷皥鍫存嫑鑱樺牬闈㈢伀鐖�
鏅€氭枃绔� 寤堝ぇ濂崇爺绌剁敓琚妗堢祩瀵╁垽姹� 鍏囨墜琚垽姝诲垜
鏅€氭枃绔� 寤f澅鍏牎缍�(w菐ng)涓婅│榛�(di菐n)鑰冪爺鍫�(b脿o)鍚嶅皣闁嬪
鏅€氭枃绔� 2004骞寸ⅸ澹寳浜嫑鐢熷柈浣嶅牨(b脿o)鍚嶉粸(di菐n)涓€瑕�
鏅€氭枃绔� 娲涢櫧楂樻柊鍗€(q奴)21鍚嶇ⅸ澹爺绌剁敓琚仒鐐轰腑灞ら牁(l菒ng)灏�(d菐o)
鏅€氭枃绔� 娴欐睙鐪佺ⅸ澹爺绌剁敓鍫�(b脿o)鍚嶅緸涓嬪懆涓€闁嬪
鏅€氭枃绔� 2004骞翠笂?锛熺礀^(q奴)缍�(w菐ng)涓婂牨(b脿o)鍚嶆檪(sh铆)闁撳畨鎺掕〃
鏅€氭枃绔� 寤f澅锛氱爺绌剁敓鍏ュ(xu茅)鑰冭│2003骞磋捣閲嶅ぇ瑾�(di脿o)鏁�
鏅€氭枃绔� 2004骞村叏鍦嬬爺鎷涗笂娴疯€冨崁(q奴)鍫�(b脿o)鍚嶉粸(di菐n)涓€瑕借〃
瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 瀵у澶у(xu茅)04骞寸ⅸ澹爺绌剁敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 澶ч€i惖閬撳(xu茅)闄�04骞寸ⅸ澹帴鏀惰(di脿o)鍔戠敓婧愬熀鏈師鍓�
鏅€氭枃绔� 鍚夋灄澶у(xu茅)寤鸿ō(sh猫)宸ョ▼瀛�(xu茅)闄�04骞寸爺绌剁敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 婧窞甯寖瀛�(xu茅)闄�(婧窞澶у(xu茅)绫�)05鐮旂┒鐢熻(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 浣虫湪鏂ぇ瀛�(xu茅)04骞磋€冪爺瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 娌堥櫧寤虹瓚宸ョ▼瀛�(xu茅)闄�04骞寸爺绌剁敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 澶╂触甯寖澶у(xu茅)鏀挎不鑸囪鏀垮(xu茅)闄�05骞寸ⅸ澹(di脿o)鍔戦渶姹�
鏅€氭枃绔� 绗簩蹇楁効鑰冪爺瑾�(di脿o)鍔戠▼搴忕瓟鐤�
鏅€氭枃绔� 涓婃捣澶у(xu茅)04骞寸爺绌剁敓鎷涙敹绲�(t菕ng)鑰冪敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 寤hタ澶у(xu茅)04骞寸ⅸ澹爺绌剁敓瑾�(di脿o)鍔戜俊鎭�

鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�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骞达紝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�鈥� 涓嬭級 

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�銆佸父寰�
鍒嗘柟绋嬶級绉戠洰澶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 2014 骞� 8 鏈� 30 鏃�
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▼锛夌鐩ぇ缍�
(绉戠洰浠g⒓锛�945)
杩戜笘浠f暩(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�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)鏈冪祼(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)鏈冨悓鎱�(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锛�
绛夊児(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�銆佸瓙缇ゃ€侀櫔闆�銆佷笉
璁婂瓙缇�銆佸晢缇�锛涘垽鏂风兢銆佸瓙缇ゃ€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�锛涗粙绱逛竴鍊�(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�
Cayley 瀹氱悊銆�
绗笁绡€(ji茅) 缃彌缇�
浠嬬垂 n 娆″皪绋辩兢 Sn 鐨勬蹇碉紱浠嬬垂 Sn 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)璜栥€�
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� G 鐨勫瓙
缇� H 鍦� G 涓殑宸�銆佸彸闄泦鐨勬暩(sh霉)鐩浉绛夐€欎竴閲嶈绲�(ji茅)璜栥€備粙绱� Lagrange 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�銆�
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)鐢熷繀闋堣瓨瑷樺苟闋�(l菒ng)鏈冩湁闂�(gu膩n)缇ょ殑涓€浜涘熀鏈蹇碉紱鏈冨埄鐢ㄦ墍瀛�(xu茅)鐭ヨ瓨鍒ゆ柗缇�銆佸瓙缇�銆佷笉璁婂瓙缇�銆�
鍟嗙兢锛涘(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)鐨勭煡璀樺幓瑙f焙绨″柈
缇よ珫鍟忛,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)銆佸瓙鍩熴€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炽€佷富鐞�
鎯�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�
瀹氱悊銆佺挵(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�
鍥犲瓙鐠�(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�銆�
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�銆佺挵(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�
浠嬬垂鎸栬(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� R 涓婄殑鏈畾鍏冩槸瀛樺湪鐨勯€欎竴閲嶈绲�(ji茅)璜栥€�
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�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)锛夈€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�銆�
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�
鍘绘(g貌u)閫犲煙銆�
绗竷绡€(ji茅) 鍟嗗煙
椤炴瘮浜庢暣鏁�(sh霉)鐠�(hu谩n)鑸囨湁鐞嗘暩(sh霉)鍩熶箣闁撶殑闂�(gu膩n)绯伙紝浠嬬垂涓€鍊�(g猫)鐠�(hu谩n)鐨勫晢鍩熺殑姒傚康锛屽苟绲﹀嚭涓€鍊�(g猫)鐒¢浂鍥�
瀛愮殑浜ゆ彌鐠�(hu谩n)鐨勫晢鍩熺殑瀛樺湪鎬ц垏鍞竴鎬у畾鐞�銆�
鑰冩牳瑕佹眰锛�
瀛�(xu茅)鐢熷繀闋堣瓨瑷樺苟闋�(l菒ng)鏈冩湁闂�(gu膩n)鐠�(hu谩n)鐨勮嫢骞插熀鏈蹇�锛涙渻鍒╃敤鎵€瀛�(xu茅)鐭ヨ瓨鍒ゆ柗鐠�(hu谩n)銆佸瓙鐠�(hu谩n)銆佸瓙闄ょ挵(hu谩n)銆�
鐞嗘兂銆佹サ澶х悊鎯�銆佸晢鐠�(hu谩n)绛�锛涘彲浠ョ稖鍚堟噳(y墨ng)鐢ㄦ墍瀛�(xu茅)鐨勭煡璀樺幓瑙f焙绨″柈鐠�(hu谩n)璜栧晱椤�銆�
绗洓绔� 鏁寸挵(hu谩n)閲岀殑鍥犲瓙鍒嗚В
鑰冭│瑕侀粸(di菐n)锛�
瑕佽畵瀛�(xu茅)鐢熸帉鎻′竴浜涘熀鏈蹇碉細涓嶅彲绱勫厓銆佸敮涓€鍒嗚В銆佷富鐞嗘兂鐠�(hu谩n)銆佹瓙姘忕挵(hu谩n)锛涚悊瑙i棞(gu膩n)浜庢暣鐠�(hu谩n)
閲岀殑鍥犲瓙鍒嗚В鐨勪竴浜涢噸瑕佺祼(ji茅)璜栵細涓€鍊�(g猫)鏁寸挵(hu谩n)鏄敮涓€鍒嗚В鐠�(hu谩n)鐨勫厖瑕佹浠�锛涗富鐞嗘兂鐠�(hu谩n)鏄敮涓€鍒嗚В鐠�(hu谩n)銆�
姝愭皬鐠�(hu谩n)鏄敮涓€鍒嗚В鐠�(hu谩n)绛�銆�
鑰冭│鍏�(n猫i)瀹癸細
绗竴绡€(ji茅) 涓嶅彲绱勫厓銆佸敮涓€鍒嗚В
绲﹀嚭鏁寸挵(hu谩n)涓厓绱犳暣闄ょ殑瀹氱京锛涗粙绱瑰钩鍑″洜瀛愩€佷笉鍙磩鍏�銆佸敮涓€鍒嗚В銆佸敮涓€鍒嗚В鐠�(hu谩n)绛夋蹇�锛�
鑸変緥瑾槑锛屽瓨鍦ㄤ笉鏄敮涓€鍒嗚В鐠�(hu谩n)鐨勬暣鐠�(hu谩n)銆�
绗簩绡€(ji茅) 鍞竴鍒嗚В鐠�(hu谩n)
浠嬬垂涓€鍊�(g猫)鏁寸挵(hu谩n)鏄敮涓€鍒嗚В鐠�(hu谩n)鐨勫厖瑕佹浠�锛涗粙绱瑰敮涓€鍒嗚В鐠�(hu谩n)涓垏鏈€澶у叕鍥犲瓙鐨勫瓨鍦ㄥ晱椤�銆�
鏁�(sh霉)閲忓晱椤屾湁闂�(gu膩n)鐨勭祼(ji茅)璜�銆�
绗笁绡€(ji茅) 涓荤悊鎯崇挵(hu谩n)
浠嬬垂涓荤悊鎯崇挵(hu谩n)锛屽苟绲﹀嚭涓荤悊鎯崇挵(hu谩n)鏄敮涓€鍒嗚В鐠�(hu谩n)閫欎竴閲嶈绲�(ji茅)璜�銆�
绗洓绡€(ji茅) 姝愭皬鐠�(hu谩n)
浠嬬垂姝愭皬鐠�(hu谩n)锛屽苟绲﹀嚭姝愭皬鐠�(hu谩n)鏄敮涓€鍒嗚В鐠�(hu谩n)閫欎竴閲嶈绲�(ji茅)璜�銆�
鑰冩牳瑕佹眰锛�
瀛�(xu茅)鐢熷繀闋堣瓨瑷樺苟闋�(l菒ng)鏈冩湁闂�(gu膩n)鏁寸挵(hu谩n)閲岀殑鍥犲瓙鍒嗚В鐨勮嫢骞插熀鏈蹇碉紱鏈冨埄鐢ㄦ墍瀛�(xu茅)鐭ヨ瓨鍒ゆ柗杓冪啊
鍠殑鏁寸挵(hu谩n)鏄惁鐐哄敮涓€鍒嗚В鐠�(hu谩n)锛涘彲浠ョ稖鍚堟噳(y墨ng)鐢ㄦ墍瀛�(xu茅)鐨勭煡璀樺幓瑙f焙涓€浜涚啊鍠殑闂�(gu膩n)浜庢暣鐠�(hu谩n)鐨勫洜瀛愬垎
瑙g殑鍟忛銆�
涓�銆佸弮鑰冩浉鐩�
1銆佸嫉绂剧憺锛屻€婅繎涓栦唬鏁�(sh霉)鍩虹(ch菙)銆嬶紝楂樼瓑鏁欒偛鍑虹増绀�锛�1978 骞� 5 鏈堜慨瑷傜 1 鐗�銆�
2銆佸惓鍝佷笁锛屻€婅繎涓栦唬鏁�(sh霉)銆�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�1979 骞� 12 鏈堢 1 鐗�銆�
3銆佸妷绱瑰(xu茅)锛屻€婅繎涓栦唬鏁�(sh霉)鍩虹(ch菙)銆�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�1999 骞� 10 鏈堢 1 鐗�銆�
4銆佹姘镐繚锛屻€婅繎涓栦唬鏁�(sh霉)銆�锛岃タ鍖楀斧鑼冨ぇ瀛�(xu茅)娌瑰嵃鏈�锛�2000
甯稿井鍒嗘柟绋�
绗竴绔� 鍒濈瓑绌嶅垎娉�
鑰冭│瑕侀粸(di菐n)
婧�(zh菙n)纰虹悊瑙e井鍒嗘柟绋嬬殑涓€浜涙渶鍩烘湰鐨勬蹇碉紱鎸夊涓嬪叐姊濅富绶氭帉鎻′竴闅庢柟绋嬬殑鍒濈瓑绌嶅垎娉曪細
璁婇噺鍒嗛洟鏂圭▼鍜岄€氶亷璁婃彌鍙寲鐐鸿畩閲忓垎闆㈡柟绋嬬殑鏂圭▼锛屽叏寰垎鏂圭▼鍜岄€氶亷绌嶅垎鍥犲瓙娉曟垨鍒嗛爡(xi脿ng)
绲勫悎娉曞彲鍖栫偤鍏ㄥ井鍒嗘柟绋嬬殑鏂圭▼锛涙帉鎻¢毐寮忓井鍒嗘柟绋嬬殑寰垎娑堝弮娉曞拰鍙檷闅庣殑楂橀殠寰垎鏂圭▼
鐨勮В娉�銆�
鑰冭│鍏�(n猫i)瀹�
绗竴绡€(ji茅) 寰垎鏂圭▼鑸囪В
鍩烘湰姒傚康锛氬井鍒嗘柟绋�銆侀殠銆佽В鑸囩⿳鍒嗭紙閫氳В鑸囬€氱⿳鍒嗭紝鐗硅В鑸囩⿳鍒嗭級銆佸畾瑙e晱椤岋紝閫�
閬庡柈鎿烘柟绋嬪拰浜哄彛妯″瀷绛変粙绱瑰井鍒嗘柟绋嬬殑鑳屾櫙鍜屽缓绔嬪井鍒嗘柟绋嬫眰瑙f噳(y墨ng)鐢ㄥ晱椤岀殑鍩烘湰鏂规硶銆�
绗簩绡€(ji茅) 璁婇噺鍙垎闆㈡柟绋�
绗笁绡€(ji茅) 璁婇噺鍒嗛洟娉�銆�
绗洓绡€(ji茅) 榻婃鏂圭▼
榻婃鏂圭▼鍜屼竴浜涢綂娆℃柟绋嬬殑璁婂舰鐨勮В娉�銆�
绗簲绡€(ji茅) 涓€闅庣窔鎬ф柟绋�
涓€闅庣窔鎬ф柟绋嬬殑瑙f硶鈥斿父鏁�(sh霉)璁婃槗娉曡垏 Bernoulli 鏂圭▼鐨勮В娉�锛涢€氶亷瑙g殑涓€鑸〃閬�(d谩)寮忚◣璜�
瑙g殑鎬ц唱(zh矛)銆�
绗叚绡€(ji茅) 鍏ㄥ井鍒嗘柟绋嬪強绌嶅垎鍥犲瓙
鍏ㄥ井鍒嗘柟绋嬬殑瑙f硶鍜岀⿳鍒嗗洜瀛愭硶銆佸垎闋�(xi脿ng)绲勫悎娉曘€�
绗竷绡€(ji茅) 绶氱礌鍫� 姝愭媺鎶樼窔
涓€闅庡井鍒嗘柟绋嬬殑骞句綍瑙i噵鍜屾瓙鎷夋姌绶氭硶銆�
绗叓绡€(ji茅) 涓€闅庨毐寮忓井鍒嗘柟绋�
涓€闅庨毐寮忓井鍒嗘柟绋嬬殑寰垎娑堝弮娉曪紝鐗瑰垾鏄� Clairaut 鏂圭▼鐨勮В娉�銆佸瑙h垏鍖呯怠(lu貌)銆�
绗節绡€(ji茅) 涓€闅庡井鍒嗘柟绋嬫噳(y墨ng)鐢ㄨ垑渚�
绨′粙
绗崄绡€(ji茅) 骞剧ó鍙檷闅庣殑楂橀殠鏂圭▼
骞剧ó鍙檷闅庣殑楂橀殠寰垎鏂圭▼鐨勮В娉�銆�
鑰冩牳瑕佹眰
鎺屾彙寰垎鏂圭▼鐨勫熀鏈蹇�--寰垎鏂圭▼銆侀殠銆佽В鑸囩⿳鍒嗭紙閫氳В鑸囬€氱⿳鍒�锛岀壒瑙h垏绌嶅垎锛�
绛�锛涙帉鎻¤畩閲忓垎闆㈡柟绋嬪拰閫氶亷璁婃彌鍙寲鐐鸿畩閲忓垎闆㈡柟绋嬬殑鏂圭▼銆佸叏寰垎鏂圭▼鍜岄€氶亷绌嶅垎鍥�
瀛愭硶鎴栧垎闋�(xi脿ng)绲勫悎娉曞彲鍖栫偤鍏ㄥ井鍒嗘柟绋嬬殑涓€闅庡井鍒嗘柟绋嬬殑瑙f硶锛涙帉鎻¢毐寮忓井鍒嗘柟绋嬬殑寰垎娑�
鍙冩硶鍜屽彲闄嶉殠鐨勯珮闅庡井鍒嗘柟绋嬬殑瑙f硶锛涜兘澶犻€氶亷瑙g殑涓€鑸〃閬�(d谩)寮忚◣璜栬В鐨勬€ц唱(zh矛)锛岀悊瑙e拰鎳�(y墨ng)
鐢ㄥ瑙f蹇�锛涢€氶亷寤虹珛寰垎鏂圭▼姹傝В涓€浜涙噳(y墨ng)鐢ㄥ晱椤屻€�
绗簩绔� 鍩烘湰瀹氱悊
鏁欏(xu茅)瑕侀粸(di菐n)
瑙g殑瀛樺湪鍞竴鎬у畾鐞�銆佸欢鎷撳畾鐞嗐€佽В灏嶅垵鍊肩殑閫g簩(x霉)渚濊炒鎬у拰鍙井鎬у畾鐞嗕互鍙婃墍娑夊強姒傚康
鐨勬簴(zh菙n)纰虹悊瑙�锛岃В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞嗙殑瑭崇窗(x矛)璀夋槑銆�
鏁欏(xu茅)鍏�(n猫i)瀹�
绗竴绡€(ji茅) 瑙g殑瀛樺湪鎬ц垏鍞竴鎬у畾鐞�
寮曢€�(j矛n)骞惰┏绱�(x矛)璀夋槑瑙g殑瀛樺湪鍞竴鎬у畾鐞�锛涗緷鎿�(j霉)鍏烽珨渚嬪瓙灏嶅畾鐞嗙殑姊濅欢鍋氳┏绱�(x矛)瑾槑銆�
绗簩绡€(ji茅) 瑙g殑寤跺睍
浠嬬垂骞惰瓑鏄庤В鐨勫欢灞曞畾鐞嗭紝绀轰緥瑾槑瑭插畾鐞嗙殑姊濅欢锛涗粙绱圭涓€姣旇純瀹氱悊銆�
绗笁绡€(ji茅) 瑙e皪鍒濆€肩殑閫g簩(x霉)渚濊炒鎬�
浠嬬垂骞惰瓑鏄庤В灏嶅垵鍊肩殑閫g簩(x霉)渚濊炒鎬у畾鐞�銆�
绗洓绡€(ji茅) 瑙e皪鍒濆€肩殑鍙井鎬�
浠嬬垂骞惰瓑鏄庤В灏嶅垵鍊肩殑鍙井鎬у畾鐞嗐€�
鑰冩牳瑕佹眰
閲嶉粸(di菐n)鎺屾彙瑙g殑瀛樺湪鍞竴鎬у畾鐞�銆佸欢鎷撳畾鐞嗙殑鍏�(n猫i)瀹逛互鍙婅В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞嗙殑璀夋槑鎬濇兂锛�
鐔熺反鎺屾彙 Picard 閫艰繎鍒�銆丩ipschits 姊濅欢鍜屽欢鎷撴蹇点€�
绗笁绔� 绶氭€у井鍒嗘柟绋�
鑰冭│瑕侀粸(di菐n)
婧�(zh菙n)纰虹悊瑙g窔鎬у井鍒嗘柟绋嬬殑涓€鑸悊璜�锛涚啛绶存帉鎻� Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉曞拰甯哥郴鏁�(sh霉)绶�
鎬у井鍒嗘柟绋嬬殑鐗瑰緛鏍规硶銆佹瘮杓冪郴鏁�(sh霉)娉曘€丩aplace 璁婃彌锛涚悊瑙f尟鍕曠従(xi脿n)璞�銆�
鑰冭│鍏�(n猫i)瀹�
绗竴绡€(ji茅) 绶氭€ф柟绋嬬殑涓€鑸€ц唱(zh矛)
绶氭€у井鍒嗘柟绋嬬殑瑙g殑瀛樺湪鍞竴鎬у畾鐞嗗強绶氭€у井鍒嗙畻瀛愮殑鎬ц唱(zh矛)銆�
绗簩绡€(ji茅) n 闅庣窔鎬ч綂娆″井鍒嗘柟绋�
寤虹珛榻婃绶氭€у井鍒嗘柟绋嬬殑涓€鑸悊璜栵紝寰楀埌閫氳В绲�(ji茅)妲�(g貌u)瀹氱悊锛岃瓑鏄� Liouville 鍏紡骞舵噳(y墨ng)鐢ㄥ埌
2 闅庡井鍒嗘柟绋嬨€�
绗笁绡€(ji茅) n 闅庣窔鎬ч潪榻婃鏂圭▼
n 闅庣窔鎬ч潪榻婃鏂圭▼鐨勯€氳В绲�(ji茅)妲�(g貌u)瀹氱悊鑸囧父鏁�(sh霉)璁婃槗娉�銆�
绗洓绡€(ji茅) n 闅庡父绯绘暩(sh霉)绶氭€ч綂娆″井鍒嗘柟绋嬭В娉�
鐢ㄧ壒寰佹牴娉曡В甯哥郴鏁�(sh霉)绶氭€ч綂娆″井鍒嗘柟绋嬬殑鍩烘湰姝ラ銆佺悊璜栬瓑鏄�銆佸吀鍨嬬ず渚�銆�
绗簲绡€(ji茅) n 闅庡父绯绘暩(sh霉)绶氭€ч潪榻婃寰垎鏂圭▼瑙f硶
姣旇純绯绘暩(sh霉)娉曠殑寤虹珛銆佺悊璜栬瓑鏄庛€佸吀鍨嬬ず渚�銆�
绗叚绡€(ji茅) Laplace 璁婃彌
浠嬬垂 Laplace 璁婃彌浠ュ強濡備綍鎳�(y墨ng)鐢� Laplace 璁婃彌姹傝В涓€浜涘父绯绘暩(sh霉)绶氭€ч潪榻婃寰垎鏂圭▼鐨�
Cauchy 鍟忛銆�
绗竷绡€(ji茅) 2 闅庡父绯绘暩(sh霉)绶氭€ф柟绋嬭垏鎸嫊鐝�(xi脿n)璞�
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�銆�
姣旇純绯绘暩(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�銆�
绗洓绔� 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悊璜栵紱鑳藉鐔熺反鎺屾彙 Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉曘€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畾鐞嗐€�
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� Liouville 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�銆�
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悊璜栵紱鐔熺反鎺屾彙 Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉曞拰鐗瑰緛鏍�
娉�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€�
绗簲绔� 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�
鍙婂叾鍒ゅ畾瀹氱悊锛屽垎鍒ユ噳(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€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�
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蹇点€佸垽瀹氬畾鐞嗗拰鍒ゅ畾鏂规硶锛岃憲閲� Liapunov 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�
瀹氱悊锛屾渻鎳�(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€�銆丩iapunov 绗簩鏂规硶瑷庤珫鑷不绯荤当(t菕ng)鐨勮В鐨�
绌�(w臎n)瀹氭€�銆�
浜屻€� 鍙冭€冩浉鐩�
1銆� 鏉卞寳甯寖澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯�锛屻€婂父寰垎鏂圭▼銆嬶紝楂樼瓑鏁欒偛鍑虹増绀�锛�1982 骞�銆�
2銆� 钁夊毚(y谩n)璎欙紝銆婂父寰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� 鍦嬪鏁欒偛濮斿摗鏈冨斧鑼冩暀鑲插徃锛屻€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│琛岋級銆嬶紝棣栭兘甯寖澶у(xu茅)鍑虹増绀�锛�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蹇碉紝渚嬪瓙锛涘害閲忕┖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�
鑸囧害閲忕┖闁撶殑瀹屽倷鎬�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 n
R 锛涢€g簩(x霉)鍑芥暩(sh霉)绌洪枔 ],[ baC 锛涙暩(sh霉)鍒楃┖闁�
p
l 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蹇碉紱
涓嶅彲鍒嗙┖闁撶殑渚嬪瓙銆�
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� Cauchy 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嗭紱
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)瀹癸紝鏁呭彧闇€绨¤鍥為¨骞跺挤(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蹇碉紱渚濊寖鏁�(sh霉)鏀舵杺锛� n
R 绌洪枔锛� ],[ baC 绌洪枔锛� ?
l
绌洪枔锛� ?
L 绌洪枔锛� ],[ baL
p
绌洪枔锛� p
l 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э紝搴﹂噺绌�
闁撶殑瀹屽倷鎬х瓑姒傚康锛涚啛鎮� n
R 绌洪枔锛� ],[ baC 绌洪枔锛� ?
l 绌洪枔锛� ?
L 绌洪枔锛� p
l 绌洪枔锛� ],[ baL
p
绌�
闁�锛涢€忓竟鐞嗚В澹撶府鏄犲儚鍘熺悊鍙婂叾绨″柈鎳�(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�锛岀窔鎬ч€g簩(x霉)娉涘嚱锛岀窔鎬х畻瀛愮┖闁�锛屽叡杌涚┖闁撱€�
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�锛屼緥瀛愶紝鏈夌晫鑸囬€g簩(x霉)鐨勭瓑鍍�(ji脿)鎬�锛岀窔鎬ф湁鐣岀畻瀛愰浂绌�
闁撶殑鎬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€э紝閫g簩(x霉)鎬�锛岀畻瀛愯寖鏁�(sh霉)锛屽叡杌涚┖闁擄紝淇濊窛绠楀瓙锛�
鍚屾(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)绠楃啊鍠殑绠�
瀛愯寖鏁�(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�
绗笁绔� 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�锛屾姇褰卞畾鐞�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�锛屽钩琛屽洓閭婂舰鍏紡锛屽収(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 涓嶇瓑寮忥紝Parseval 鎭掔瓑寮�锛屽畬鍏ㄥ氨鑼冪洿浜ょ郴鐨勫畾缇�
鑸囧垽瀹�, 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″柈鎬ц唱(zh矛)銆�
鑰冩牳瑕佹眰锛�
鎺屾彙鍏�(n猫i)绌嶇┖闁擄紝Hilbert 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
鎭掔瓑寮忥紝F(xi脿n)ourier 灞曞紡锛屾姇褰辩畻瀛愶紝鍏辫粵绠楀瓙锛岃嚜浼寸畻瀛愶紝閰夌畻瀛愬拰姝e父绠楀瓙绛夊熀鏈蹇�锛�
鎺屾彙妤靛皬鍖栧悜閲忓畾鐞�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�
鐨勫収(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) ],[ baC 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� Hahn-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�锛岄枆鍦栬薄瀹氱悊鏄硾鍑藉垎鏋愬熀绀�(ch菙)鐞嗚珫鐨勪富瑕佹(g貌u)鎴愰儴鍒嗭紝瑕佹眰
鐔熺反鎺屾彙閫欎簺鍏�(n猫i)瀹�锛涜兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤屻€�
绗簲绔� 绶氭€х畻瀛愮殑璀�
鑰冭│瑕侀粸(di菐n)锛�
绨¤浠嬬垂绶氭€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€�锛岀壒寰佸悜閲忥紝榛�(di菐n)璀�锛岄€g簩(x霉)璀滐紝渚嬪瓙銆�
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)銆嬶紝楂樼瓑鏁欒偛鍑虹増绀�锛� 1983锛� 绗竴鐗堛€�
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浜屽唺锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�1992锛�
绗簩鐗�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�锛屼笅鍐婏紝楂樼瓑鏁欒偛鍑虹増绀�锛� 1985锛岀浜岀増銆�

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)锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹广€佹枃瀛楃殑鐪熷(sh铆)鎬�銆佸畬鏁存€�銆佸強鏅�(sh铆)鎬ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵�(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�

  • 涓婁竴绡囨枃绔狅細

  • 涓嬩竴绡囨枃绔狅細
  • 鑰冨崥鍜ㄨQQ 3455265070 榛�(di菐n)鎿婇€欓噷绲︽垜鐧�(f膩)娑堟伅 鑰冪爺鍜ㄨ QQ 3455265070 榛�(di菐n)鎿婇€欓噷绲︽垜鐧�(f膩)娑堟伅 閮电锛� 3455265070@qq.com
    鍏徃鍚嶇ū:鏄嗗北鍓�(chu脿ng)閰蜂俊鎭鎶€鏈夐檺鍏徃 鐗堟瑠(qu谩n)鎵€鏈�
    鑰冪爺绉樼睄缍�(w菐ng) 鐗堟瑠(qu谩n)鎵€鏈� © kaoyanmiji.com All Rights Reserved
    鑱叉槑锛氭湰缍�(w菐ng)绔欏皧閲嶅苟淇濊(h霉)鐭ヨ瓨鐢�(ch菐n)娆�(qu谩n)锛屾牴鎿�(j霉)銆婁俊鎭恫(w菐ng)绲�(lu貌)鍌虫挱娆�(qu谩n)淇濊(h霉)姊濅緥銆�锛屽鏋滄垜鍊戣綁(zhu菐n)杓夋垨寮曠敤鐨勪綔鍝佷镜鐘簡鎮ㄧ殑娆�(qu谩n)鍒�锛岃珛閫氱煡鎴戝€戯紝鎴戝€戞渻鍙婃檪(sh铆)鍒櫎锛�