|
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�锛岄儴鍒嗗(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
銆婃暩(sh霉)瀛�(xu茅)绯伙紙甯稿井鍒嗘柟绋嬶級銆嬫暀瀛�(xu茅)澶х侗
瀛�(xu茅)鏅�(sh铆)锛�64 瀛�(xu茅)鏅�(sh铆) 瀛�(xu茅)鍒嗭細3 鐞嗚珫瀛�(xu茅)鏅�(sh铆)锛�51 瀛�(xu茅)鏅�(sh铆)
閬╃敤灏堟キ(y猫)锛氭暩(sh霉)瀛�(xu茅)銆佺郴绲�(t菕ng)绉戝(xu茅)鑸囧伐绋嬪強鎺у埗鐞嗚珫鑸囨噳(y墨ng)鐢ㄧ瓑灏堟キ(y猫)銆�
澶х侗鍩�(zh铆)绛嗕汉锛氶涓栧钩 澶х侗瀵╁畾浜猴細鍔夋ü(sh霉)寰�
涓€銆佽(shu艒)鏄�(500 瀛楀乏鍙�)
1銆� 瑾茬▼鐨勬€ц唱(zh矛)銆佸湴浣嶅拰浠诲嫏(w霉)
鏈绋嬫槸楂樼瓑甯寖闄㈡牎鏁�(sh霉)瀛�(xu茅)灏堟キ(y猫)鍜岀稖鍚堟€уぇ瀛�(xu茅)鏁�(sh霉)瀛�(xu茅)灏堟キ(y猫)銆佺郴绲�(t菕ng)绉�
瀛�(xu茅)鑸囧伐绋嬪皥妤�(y猫)銆佹帶鍒剁悊璜栬垏鎳�(y墨ng)鐢ㄧ瓑灏堟キ(y猫)鐨勪竴闁€(m茅n)閲嶈鍩虹(ch菙)瑾茬▼锛屽畠
鐨勪换鍕�(w霉)鏄娇瀛�(xu茅)鐢熺嵅寰楀井鍒嗘柟绋嬬殑鏈夐棞(gu膩n)姒傚康銆佷竴闅庡井鍒嗘柟绋嬬殑鍒濈瓑
瑙ｆ硶銆佸井鍒嗘柟绋嬭В鐨勫瓨鍦�銆佸敮涓€鎬у畾鐞嗐€佺窔鎬у井鍒嗘柟绋嬭В鐨勭悊璜�銆�
绶氭€у井鍒嗘柟绋嬬殑姹傝В鏂规硶鍜岀窔鎬у井鍒嗙郴绲�(t菕ng)鐞嗚珫鍙婂叾瑙ｆ硶绛夋柟闈㈢殑
绯荤当(t菕ng)鐭ヨ瓨(sh铆)銆�
2銆� 瑾茬▼鏁欏(xu茅)鐨勫熀鏈姹�
锛�1锛� 鎺屾彙寰垎鏂圭▼鐨勬蹇典互鍙婁竴闅庡井鍒嗘柟绋嬬殑鍒濈瓑瑙ｆ硶銆� 灏�(du矛)寰�
鍒嗘柟绋嬭В鐨勫瓨鍦ㄦ€у拰鍞竴鎬у畾鐞嗚瓑鏄庣殑鎬濇兂鏈夎純娣卞埢鐨勮獚(r猫n)
璀�(sh铆)銆傜啛绶存帉鎻＄窔鎬у井鍒嗘柟绋嬪拰绶氭€у井鍒嗙郴绲�(t菕ng)鐨勭悊璜栧拰鍚勭ó
瑙ｆ硶锛岀壒鍒ユ槸闈為綂娆＄窔鎬ф柟绋嬬殑瑙ｆ硶锛屾帉鎻″父鏁�(sh霉)璁婃槗娉曡垏
鍏跺畠鏂规硶鐨勫崁(q奴)鍒�銆�
锛�2锛� 绯荤当(t菕ng)鎺屾彙寰垎鏂圭▼鐨勫熀鏈蹇碉細寰垎鏂圭▼鐨勫垵鍊煎晱(w猫n)椤岀殑瑙ｃ€�
鍑芥暩(sh霉)绶氭€х浉闂�(gu膩n)鍜岀窔鎬х劇(w煤)闂�(gu膩n)銆乄ronsky 琛屽垪寮�銆佸父鏁�(sh霉)璁婃槗娉曘€�
鍩鸿В鐭╅櫍绛�銆傛帉鎻″井鍒嗘柟绋嬫湁闂�(gu膩n)瑙ｇ殑瀛樺湪鎬х殑璀夋槑鏂规硶锛�
鐛插緱杓冪啛绶寸殑瑷�(j矛)绠楁妧鑳藉拰鍒濇鐨勬噳(y墨ng)鐢ㄨ兘鍔�銆�
锛�3锛� 鏈绋嬬附鏁欏(xu茅)鏅�(sh铆)鏁�(sh霉)鐐� 70 瑾叉檪(sh铆)锛屽叾涓悊璜栬鏅�(sh铆)鐐� 57锛岃◣璜栬
鏅�(sh铆)鐐� 13銆�
3銆� 瑾茬▼鏁欏(xu茅)鏀归潻
锛�1锛� 娉ㄩ噸鑳藉姏鐨勫煿椁�(y菐ng)
鍦ㄦ暀瀛�(xu茅)鏈绋嬫檪(sh铆)锛岃娉ㄩ噸瀛�(xu茅)鐢熻畩閲忚畩鎻涘拰鍒嗘瀽鎶€宸х殑瑷�(x霉n)绶�锛�
浣垮緱閫欎簺鎶€宸ф垚鐐哄(xu茅)鐢熼€�(j矛n)涓€姝ュ(xu茅)缈�(x铆)鍜岀爺绌剁殑灏堟キ(y猫)鎶€鑳�銆傛澶�锛岃
鍩归(y菐ng)瀛�(xu茅)鐢熷埄鐢ㄦ墍瀛�(xu茅)鐨勭煡璀�(sh铆)瑙ｆ焙瀵�(sh铆)闅涘晱(w猫n)椤岋紝寰炶€岄仈(d谩)鍒板煿椁�(y菐ng)瀛�(xu茅)鐢熸噳(y墨ng)鐢�
鑳藉姏鐨勭洰鐨�銆�
锛�2锛� 娉ㄩ噸鏈绋嬬煡璀�(sh铆)鑸囧叾瀹冪浉闂�(gu膩n)瑾茬▼鐨勮伅(li谩n)绯�
鍦ㄨ瑳鎺堟瑾茬▼鏅�(sh铆)锛岃娉ㄩ噸鏈绋嬭垏鐩搁棞(gu膩n)瑾茬▼銆婄窔鎬т唬鏁�(sh霉)銆�銆併€婃暩(sh霉)
瀛�(xu茅)鍒嗘瀽銆嬪拰銆婂姏瀛�(xu茅)銆嬬瓑涔嬮枔鐨勮伅(li谩n)绯�銆�
浜�銆佸ぇ 缍� 鍏�(n猫i) 瀹�
绗竴绔狅細鍩� 鏈� 姒� 蹇碉紙3 瑾叉檪(sh铆)锛�
[鍏�(n猫i)瀹硅榛�(di菐n)]
甯稿井鍒嗘柟绋嬨€� 寰垎鏂圭▼鐨勮В銆侀€氳В鑸囩壒瑙ｃ€佸垵濮嬫浠惰垏鍒濆€�
鍟�(w猫n)椤�銆佹柟鍚戝牬(ch菐ng)鑸囩⿳鍒嗘洸绶氥€佸井鍒嗘柟绋嬬殑瀵�(sh铆)闅涘晱(w猫n)椤岃垑渚�
[鏁欏(xu茅)瑕佹眰]
1锛庣悊瑙ｅ井鍒嗘柟绋嬪強鍏惰В鐨勫畾缇�銆傛帉鎻″井鍒嗘柟绋嬬殑涓€浜涘熀鏈蹇碉紝
濡傚井鍒嗘柟绋嬬殑闅庢暩(sh霉)銆佺窔鎬ц垏闈炵窔鎬�锛岄€氳В鑸囩壒瑙ｏ紝鍒濆姊濅欢鑸�
鍒濆€煎晱(w猫n)椤岀瓑銆�
2锛庣悊瑙ｅ井鍒嗘柟绋嬪強鍏惰В鐨勫咕浣曡В閲嬨€傚緸鐞嗚珫涓婅(shu艒)锛屽畠鎶婁綔鐐鸿В鏋�
灏�(du矛)璞＄殑寰垎鏂圭▼鍙婂叾瑙ｈ垏浣滅偤骞句綍灏�(du矛)璞＄殑鏂瑰悜鍫�(ch菐ng)鍙婄⿳鍒嗘洸绶�
婧濋€氳捣渚�(l谩i)锛屽緸鑰屽湪寰垎鏂圭▼閫欓杸(m茅n)瀛�(xu茅)绉戜腑寤虹珛浜嗘暩(sh霉)鑸囧舰涔嬮枔鐨勮伅(li谩n)
绯�锛涘緸瀵�(sh铆)鐢ㄤ笂瑾�(shu艒)锛屾垜鍊戝彲浠ラ€氶亷(gu貌)鍋氬嚭鏂瑰悜鍫�(ch菐ng)渚�(l谩i)鐣�(hu脿)鍑虹⿳鍒嗘洸绶氱殑
澶ф鍦栧舰銆�
3锛庨€氶亷(gu貌)鏈珷渚嬮鐨勫(xu茅)缈�(x铆)锛屽垵姝ヤ簡瑙ｆ湰闁€(m茅n)瀛�(xu茅)绉戠殑鏌愪簺瀵�(sh铆)闅涜儗鏅€�
绗簩绔� 涓€闅庡井鍒嗘柟绋嬬殑鍒濈瓑瑙ｆ硶锛�12 瑾叉檪(sh铆)锛�
[鍏�(n猫i)瀹硅榛�(di菐n)]
璁婇噺鍒嗛洟鏂圭▼寮�銆侀綂娆℃柟绋嬨€佷竴闅庣窔鎬ф柟绋�銆佷集鍔埄鏂圭▼
鎭扮暥(d膩ng)鏂圭▼鑸囩⿳鍒嗗洜瀛�銆佷竴闅庨毐鏂圭▼鍙婂叾瑙ｆ硶銆俁iccati 鏂圭▼鍙婂叾瑙ｆ硶銆�
[鏁欏(xu茅)瑕佹眰]
锛堜竴锛� 鎺屾彙鍙垎闆㈣畩閲�
)()( yxf
dx
dy
??
鐨勮В娉�
锛堜簩锛� 鎺屾彙鍙寲鐐鸿畩閲忓垎闆㈡柟绋嬬殑瑙ｆ硶锛�
锛�1锛夐綂娆℃柟绋�
?
?
?
?
?
?
?
x
y
g
dx
dy
鐨勮畩閲忚畩鎻�
x
y
u ? 鍙婂叾瑙ｆ硶銆�
锛�3锛� 褰㈠鏂圭▼
222
111
cybxa
cybxa
dx
dy
??
??
?
鍜� ?
?
?
?
?
?
?
?
??
??
?
222
111
cybxa
cybxa
f
dx
dy
鐨勮畩閲忚畩鎻涘強鍏惰В娉曘€�
锛�4锛� 鎺屾彙绶氭€ф柟绋�
)()( xQyxP
dx
dy
??
鐨勮В娉�锛屽嵆甯告暩(sh霉)璁婃槗娉曪紝鐔熻绶氭€ф柟绋嬬殑閫氳В鍏紡銆�
锛�5锛変簡瑙� Cauchy 鍟�(w猫n)椤�
?
?
?
?
?
?
??
00
)(
)()(
yxy
xQyxP
dx
dy
鐗硅В鐨勬眰娉曞拰鐗硅В琛ㄩ仈(d谩)寮忓強鍏舵噳(y墨ng)鐢�銆�
锛�6锛� 鎺屾彙鍒╃敤璁婇噺璁婃彌灏� Bernoulli 鏂圭▼
1,0,)()( ??? nyxQyxP
dx
dy n
鍖栫偤绶氭€ф柟绋嬬殑鏂规硶锛屽緸鑰屽彲姹傚嚭鍏堕€氳В銆�
锛堜笁锛夋帉鎻℃伆鐣�(d膩ng)鏂圭▼鐨勫垽鍒ユ柟娉曞拰鎭扮暥(d膩ng)鏂圭▼鐨勯€氳В姹傛硶銆傛帉鎻�
鍒嗛爡(xi脿ng)绲勫悎鐨勬柟娉曟眰鎭扮暥(d膩ng)鏂圭▼鐨勯€氳В銆�
锛�1锛夋帉鎻＄⿳鍒嗗洜瀛愮殑姒傚康鍜岄潪鎭扮暥(d膩ng)鏂圭▼鐨勭⿳鍒嗗洜瀛愯В娉�銆�
锛�2锛夋帉鎻″瓨鍦ㄥ儏鑸� x 鍜� y 鏈夐棞(gu膩n)鐨勭⿳鍒嗗洜瀛愮殑姊濅欢鍙婃眰娉�銆�
锛�3锛変簡瑙ｅ叾瀹冪⿳鍒嗗洜瀛愮殑姹傛硶銆�
锛堝洓锛夋帉鎻′竴闅庨毐鏂圭▼鐨勫弮鏁�(sh霉)琛ㄧず鍙婇€氳В鐨勬眰娉曘€�
锛堜簲锛変簡瑙ｆ眰瑙� Riccati 鏂圭▼閫氳В鐨勬鍙�锛屽緸鑰岀煡閬撳井鍒嗘柟绋嬪垵绛�
瑙ｆ硶鐨勫眬闄愭€�銆�
绗笁绔� 涓€闅庡井鍒嗘柟绋嬬殑瑙ｇ殑瀛樺湪瀹氱悊锛�9 瑾叉檪(sh铆)锛�
[鍏�(n猫i)瀹硅榛�(di菐n)]
Lipschitz 姊濅欢銆佷竴闅庡井鍒嗘柟绋嬭В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞�銆佷竴闅庡井鍒�
鏂圭▼瑙ｇ殑寤舵嫇瀹氱悊銆佷竴闅庡井鍒嗘柟绋嬭В闂�(gu膩n)浜庡垵鍊奸€ｇ簩(x霉)鍜屽彲寰€у畾鐞嗐€�
[鏁欏(xu茅)瑕佹眰]
锛堜竴锛夌啛瑷樹竴闅庡井鍒嗘柟绋�
? ? ? ?
? ??
?
?
?
??
00
,
yxy
yxfxy
瑙ｇ殑瀛樺湪鍞竴鎬у畾鐞嗙殑姊濅欢鍜岀祼(ji茅)璜�銆�
锛堜簩锛変簡瑙ｇ毊鍗￠€愭閫艰繎娉曞拰涓€闅庡井鍒嗘柟绋嬭В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞�
鐨勮瓑鏄�銆�
锛堜笁锛夋帉鎻� Lipschitz 姊濅欢涓诲眬閮� Lipschitz 姊濅欢鐨勬蹇�銆�
锛堝洓锛夋帉鎻′竴闅庡井鍒嗘柟绋嬭В鐨勫欢鎷撳畾鐞嗙殑璀夋槑鏂规硶锛岀啛瑷橀＝鍜岃В
鐨勬蹇�锛屽皪(du矛)鐗瑰畾鐨勫崁(q奴)鍩� G 浜嗚В鍦ㄥ叾涓婂畾缇╃殑涓€闅庡井鍒嗘柟绋�
椋藉拰瑙ｅ瓨鍦ㄥ崁(q奴)闁撶殑鍙兘鎯呮硜銆�
锛堜簲锛変簡瑙ｄ竴闅庡井鍒嗘柟绋嬭В灏�(du矛)鍒濆€肩殑閫ｇ簩(x霉)鎬у拰鍙井鎬�銆�
锛堝叚锛夌啛瑷樹竴闅庡井鍒嗘柟绋嬭В ? ?00
,, yxxy ?? 灏�(du矛)鍒濆€肩殑鍙井鍏紡锛�
? ?
? ?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
x
x
dx
y
xf
yxf
x
0
,
exp, 00
0
??
? ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
x
x
dx
y
xf
x
0
,
exp
0
??
? ?? ?00
,,, yxxxf
x
?
?
?
?
?
绗洓绔� 楂樺井鍒嗘柟绋嬶紙14 瑾叉檪(sh铆)锛�
[鍏�(n猫i)瀹硅榛�(di菐n)]
鍑芥暩(sh霉)绶氭€х浉闂�(gu膩n)銆佺窔鎬х劇(w煤)闂�(gu膩n)锛沇ronsky 琛屽垪寮�锛涢綂娆＄窔鎬у井鍒嗘柟绋嬮€�
瑙ｇ祼(ji茅)妲�(g貌u)瀹氱悊锛涢潪榻婃绶氭€у井鍒嗘柟绋嬮€氳В绲�(ji茅)妲�(g貌u)瀹氱悊锛涘父鏁�(sh霉)璁婃槗娉曪紱
甯哥郴鏁�(sh霉)榻婃绶氭€у井鍒嗘柟绋嬭В娉�锛涘埄鐢ㄦ瘮杓冪郴鏁�(sh霉)娉曞拰 Laplace 璁婃彌娉�
姹傞潪榻婃甯哥郴鏁�(sh霉)绶氭€у井鍒嗘柟绋嬬殑閫氳В锛涙瓙鎷夋柟绋嬪強鍏堕€氳В鐨勬眰娉曪紱
浜岄殠绶氭€ф柟绋嬬殑鍐礆(j铆)鏁�(sh霉)瑙ｆ硶銆�
[鏁欏(xu茅)瑕佹眰]
锛堜竴锛夋帉鎻″嚱鏁�(sh霉)绶氭€х浉闂�(gu膩n)銆佺窔鎬х劇(w煤)闂�(gu膩n)锛沇ronsky 琛屽垪寮忓拰鍩烘湰瑙ｇ祫
绛夋蹇�銆�
锛堜簩锛夋帉鎻￠綂娆＄窔鎬у井鍒嗘柟绋�
? ? ? ? ? ? 011
1
1
????? ??
?
xta
dt
dx
ta
dt
xd
ta
dt
xd
nnn
n
n
n
?
閫氳В绲�(ji茅)妲�(g貌u)瀹氱悊銆�
锛堜笁锛夋帉鎻￠潪榻婃绶氭€у井鍒嗘柟绋嬮€氳В绲�(ji茅)妲�(g貌u)瀹氱悊
? ? ? ? ? ? ? ?tfxta
dt
dx
ta
dt
xd
ta
dt
xd
nnn
n
n
n
????? ??
?
11
1
1
?
鍒╃敤甯告暩(sh霉)璁婃槗娉曟眰鍏堕€氳В銆�
锛堝洓锛夋帉鎻″父绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋嬪拰姝愭媺鏂圭▼鐨勮В娉�銆�
锛堜簲锛夊埄鐢ㄦ瘮杓冪郴鏁�(sh霉)娉曞拰 Laplce 璁婃彌娉曟眰甯哥郴鏁�(sh霉)闈為綂娆＄窔鎬ф柟绋�
鐨勯€氳В銆�
锛堝叚锛夊埄鐢ㄦ湭鐭ュ嚱鏁�(sh霉)璁婃彌鐨勬柟娉曟眰瑙ｅ彲闄嶉殠鐨勪竴浜涙柟绋�銆�
锛堜竷锛夋帉鎻′簩闅庤畩绯绘暩(sh霉)绶氭€у井鍒嗘柟绋嬬殑鍐礆(j铆)鏁�(sh霉)瑙ｆ硶銆�
锛堝叓锛変簡瑙ｇ浜屽畤瀹欓€熷害鐨勮▓(j矛)绠楀拰璩�(zh矛)榛�(di菐n)鎸嫊(d貌ng)鐞嗚珫鍙婂叾鎳�(y墨ng)鐢�銆�
绗簲绔� 绶氭€у井鍒嗘柟绋嬬祫锛�13 瑾叉檪(sh铆)锛�
[鍏�(n猫i)瀹硅榛�(di菐n)]
鐭╅櫍鍑芥暩(sh霉)閫ｇ簩(x霉)銆佸皫(d菐o)鏁�(sh霉)鍜岀⿳鍒嗙瓑姒傚康锛涚窔鎬у井鍒嗘柟绋嬬祫鐨勫垵鍊煎晱(w猫n)椤�
瑙ｇ殑瀛樺湪鍞竴鎬у畾鐞�锛涚窔鎬у井鍒嗘柟绋嬬祫閫氳В绲�(ji茅)妲�(g貌u)瀹氱悊锛涘熀瑙ｇ煩闄�锛�
姹傝В绶氭€у井鍒嗘柟绋嬬祫銆�
[鏁欏(xu茅)瑕佹眰]
锛堜竴锛夋帉鎻＄煩闄ｅ嚱鏁�(sh霉)閫ｇ簩(x霉)銆佸皫(d菐o)鏁�(sh霉)鍜岀⿳鍒嗙瓑姒傚康銆�
锛堜簩锛変簡瑙ｇ窔鎬у井鍒嗘柟绋嬬祫鍒濆€煎晱(w猫n)椤岃В瀛樺湪鍞竴鎬у畾鐞嗗強鍏惰瓑
鏄庛€�
锛堜笁锛夋帉鎻″埄鐢ㄥ父鏁�(sh霉)璁婃槗娉曟眰瑙ｉ潪榻婃绶氭€у井鍒嗘柟绋�銆�
锛堝洓锛夋帉鎻″父绯绘暩(sh霉)绶氭€у井鍒嗘柟绋嬬祫鐨勮В娉�銆�
锛堜簲锛夋帉鎻″熀瑙ｇ煩闄ｇ殑瑷�(j矛)绠椼€�
锛堝叚锛変簡瑙ｅ埄鐢� Laplace 璁婃彌娉曟眰瑙ｉ潪榻婃甯哥郴鏁�(sh霉)绶氭€у井鍒嗘柟绋�
绲�銆�
鍙冭€冩暀鏉愶細鐜嬮珮闆� 銆佸懆涔嬮姌绛� 涓北澶у(xu茅) 2003 骞寸鍥涚増鍜屽寳浜�
澶у(xu茅) 2002 骞寸涓夌増銆�
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)锛屽鏈変镜鐘紝璜�(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(w煤)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€�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(q菒ng)璁€鑰呭儏浣滃弮鑰�锛屽苟璜�(q菒ng)鑷鏍稿(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
|
鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
